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Artificial intelligence for Sustainability in Energy Industry: A Contextual Topic Modeling and Content Analys
Tahereh Saheb t.saheb@modares.ac.ir
Mohammad Dehghani mohamad.dehqani@modares.ac.ir
Management Studies Center
Industrial and Systems Engineering
Tarbiat Modares University
TehranIran
Tarbiat Modares University Tehran
Iran
Artificial intelligence for Sustainability in Energy Industry: A Contextual Topic Modeling and Content Analys
Research Assistant Professor, Science & Technology Studies Group, 1 Corresponding Author 2Artificial intelligencesustainabilityenergytopic modelingcontent analysissustainable energy
Parallel to the rising debates over sustainable energy and artificial intelligence solutions, the world is currently discussing the ethics of artificial intelligence and its possible negative effects on society and the environment. In these arguments, sustainable AI is proposed, which aims at advancing the pathway toward sustainability, such as sustainable energy. In this paper, we offered a novel contextual topic modeling combining LDA, BERT and Clustering. We then combined these computational analyses with content analysis of related scientific publications to identify the main scholarly topics, sub-themes and cross-topic themes within scientific research on sustainable AI in energy. Our research identified eight dominant topics including sustainable buildings, AI-based DSSs for urban water management, climate artificial intelligence, Agriculture 4, convergence of AI with IoT, AI-based evaluation of renewable technologies, smart campus and engineering education and AI-based optimization. We then recommended 14 potential future research strands based on the observed theoretical gaps. Theoretically, this analysis contributes to the existing literature on sustainable AI and sustainable energy, and practically, it intends to act as a general guide for energy engineers and scientists, AI scientists, and social scientists to widen their knowledge of sustainability in AI and energy convergence research.On May 29th 2021, we searched the following keywords inside the title, keyword, and abstract: "artificial intelligence" OR "AI" AND "sustainable" OR "sustainability" AND "energy". This search resulted in the retrieval of 981 documents. Following that, we restricted the document type to Articles and the language toEnglish. This exclusion resulted in 296 articles. Following that, we manually evaluated the titles and abstracts of the articles to identify the most pertinent ones that examined the role of artificial intelligence in ensuring the energy sector's sustainability. This screening yielded 182 publications spanning the years 2004 to 2022.Given that abstracts of research articles are the most succinct summary of key ideas [22], we included abstracts of the final publications in the study's corpus.Preprocessing and Post-Processing StagesPython 3.7.9 was utilized for pre-and post-processing, as well as for topic modeling analysis. We preprocessed our corpus using the NLTK and Scikit-learn packages, as well as Regular Expressions or RegEX. We import the word tokenize from the NLTK to begin the tokenization process. After removing punctuation, we lowercased our characters and deleted all numeric characters, punctuation, and whitespace.Additionally, we eliminated no-word repetitions and anything enclosed in parenthesis. Additionally, we eliminated the NLTK library's stopwords.We reviewed the first findings and created a manual exclusion list for more relevant topic identification during the postprocessing step. We added the core keywords (i.e. artificial intelligence, AI, energy, sustainable, sustainability) in the exclusion list to enhance the coherence of the findings. We used stemming throughout the preprocessing step; however, after observing the first results, we decided to remove the stemming to make the words displayed in the word clouds more understandable. We next used the lemmatization procedure, which we abandoned following the findings of the word clouds in order to make our topic labeling approach more comprehensible. Additionally, we estimated the TF-IDF score for each word in the corpus. We eliminated words with scores that were lower than the median of all TF-IDF values. We calculated the TF-IDF scores using the Scikit-learn package. The maximum TF-IDF score was set to 0.8 and the minimum value at 0.11. Additionally, we incorporated unigrams and bigrams.Topic ModelingWe applied the following libraries to conduct the topic modeling: Pandas to read the dataset, Gensim to perform LDA, Transformers to perform BERT, Keras to perform auto-encoding, and Seaborn and Matplotlib to visualize the results. We imported the TFID vectorizer from the Scikit-learn feature extraction and KMeans from the Scikit-learn cluster. The probabilistic topic assignment vector was constructed using LDA, while the sentence embedding vector was constructed using BERT. To begin, we used the TF-IDF,
Introduction
The rise of unsustainable practices and procedures co-occurred with the rising urbanization and civilization have driven the emergence of AI-based solutions to assist the path toward sustainability [1][2][3]. Excessive consumption and unsustainable energy sources, which have increased at an unprecedented rate due to factors such as urbanization, improper building construction, transportation, environmental changes, and population growth, have pressured the energy industry to pursue clean energy sources and smart solutions [4]. The deployment of alternative energy sources and access to sustainable energy are pillars of global economic growth [5] and fight against environmental hazards, in particular climate change [6]. Thus, the energy sector has focused its efforts not only on developing new sources of energy, but also on inventing novel technical solutions that increase the efficiency of existing mitigation measures [7]. AI-based interventions, which are available in the form of both hard and soft solutions, such as robots and algorithms and models, are one of these solutions that have come to assist humanity [8]. Artificial intelligence can provide a wide range of intelligent solutions, from predictive and prescriptive energy consumption insights to intelligent energy generation and distribution.
Parallel to the escalating discussions over sustainable energy and artificial intelligence solutions, the world is now debating the ethics of artificial intelligence and its potentially negative effects on society and the environment. Ethical AI considers not just AI's moral dimensions, but also its epistemic perspectives [9].
While prior studies have urged scholars to focus on the epistemological aspects of sustainable AI and to open the black box of algorithms to develop sustainable models and algorithms [10], other researches have concentrated on AI for social good and its favorable societal and environmental circumstances [11,12]; such as the development of sustainable AI.
In this article, we define sustainable AI as AI that is designed to achieve sustainability and is called AI for sustainability, as differed from AI that is designed to be sustainable and is called sustainability of AI [10]. In this paper, the term "sustainable AI" refers to the extent to which artificial intelligence can help society accomplish their sustainability goals [13,14]. The energy industry is one of the core industries that will benefit from sustainable AI, which will aid in the development of energy sustainability [15]. Sustainable energy strives to fulfill today's energy demand without depleting energy supplies or harming the environment. Sustainable energy systems are regarded as a requirement for achieving all the Sustainable Development Goals (SDGs) [16]. Sustainable artificial intelligence can help to expedite the development of sustainable energy [14]. To advance sustainable energy, the industry has supplied a wide variety of choices, including wind energy, fossil fuels, solar energy, and bioenergy. It's also vital to recognize how academics have dealt with the confluence of sustainability, artificial intelligence, and energy. This research is novel from various perspectives. First, this study intends to foster discussions on sustainable AI by identifying the most important research issues in the area, highlighting intellectual gaps, and proposing potential research streams. It is obvious that the energy sector and scientific research and innovation are inextricably linked. Scientific research is seen to be the cornerstone of technological advancements [17].
Identifying the intellectual frameworks of scientific research across time and the historical progression of its themes can have a huge influence on the effectiveness or failure of new technological solutions. To our knowledge, scientific research on sustainable energy is lacking a coherent understanding of how artificial intelligence has been integrated into this domain and how it should be conducted in the future. It is therefore imperative to perform a mixed-method literature review to have a deeper understanding of the deployment of AI to achieve sustainable energy in order to identify existing research gaps and potential future research streams. The second aspect of this research that distinguishes it from prior research is its novel methodology.
Extensive literature reviews are conducted by scholars using bibliometric methodologies [18][19][20] or topic modeling techniques such as Latent Dirichlet Allocation (LDA) [21,22] or qualitative content analysis [23]. As a result, we incorporated all the aforementioned review methodologies to ensure that their findings were complementary. Furthermore, because both bibliometric and LDA topic modeling are based on keyword cooccurrence analysis, we included a contextual embedding-based topic modeling analysis that incorporates use of sentences as fundamental units of analysis. This method which is the latest development in natural language processing (NLP) is offered by Google under the name of Bidirectional Encoder Representations for Transformers (BERT) [24] . BERT makes use of the Transformer library, which uses machine learning to discover contextual relationships between words in a text. Our integrated adoption of computational and advanced topic modeling tools, as well as qualitative analysis, enables us to gain highly objective, coherent, superior, and meta-analytical insight into present research on sustainable artificial intelligence in energy and to forecast its future. The final contribution of this research is that we offer a thorough list of research gaps and potential research agendas that may be used to increase the depth of research on sustainable artificial intelligence in the energy industry In sum, the theoretical contribution of this research is to extent the literatures on sustainable AI and sustainable energy by determining the key academic themes, sub-themes and cross-topic common themes addressed by scientists working on sustainable AI in energy, as well as how these subjects have evolved over time. Practically, this research attempts to enlighten policymakers, the energy sector, and engineers and developers of artificial intelligence about the productivity of science while emphasizing the challenges that require more AI-based responses. Additionally, it encourages policymakers to design artificial intelligence regulations that promote the development of sustainable AI in the energy sector while mitigating the unintended consequences of unsustainable energy sources and AI solutions.
4
The study is structured as follows: we begin with an explanation of our methodology and then go on to the findings, which include our topic modeling and content analysis of topics. We conclude the study by discussing our findings, theoretical research gaps, and potential future research directions. We also discussed the theoretical and practical contribution of the study. We conclude the paper with a conclusion.
Methodology
It is a widely held belief among researchers that each quantitative and qualitative research technique has inherent strengths and weaknesses; hence, combining both methods is advised to ensure that their results complement one another. We drew on and included four complimentary sets of research methodologies in our study. Three of these, BERT, LDA topic modeling and clustering are connected with text mining techniques. Additionally, we supplemented these quantitative findings with a qualitative topic-based content analysis. Our mixed-methods approach is new in three ways. First, we employed computational approaches such as BERT, LDA, and clustering to discover the thematic content of research on sustainable AI in energy.
Second, we conducted a comprehensive analysis of the retrieved topics using content analysis as a qualitative approach. Third, we integrated LDA and BERT topic modeling approaches in this study to achieve the highest level of topic identification accuracy. Our suggested mixed-method methodology may be used by researchers from a variety of disciplines to improve our understanding of quantitative and computational analyses through the use of topic-based content analysis.
LDA is predicated on the premise that documents are made of topics and that some words are more likely to occur in certain topics than others (Xie et al., 2020). While LDA has been regularly used by academics to identify topics, it does have some limitations due to the fact that it is a word co-occurrence analysis and so cannot incorporate the entire content of the sentence. Additionally, it does not do well on short texts [26].
Additionally, the outcomes of LDA may be challenging for humans to comprehend and consume [27]. By contrast, BERT topic modeling is focused on detecting semantic similarity and integrating topics with pretrained contextual representations [28] It substantially enhances the coherence of neural topic models by including contextual information into the topic modeling process [29]. BERT makes use of the Transformer library, which has an Autoencoder technique: an encoder that scans the text input. We combined the LDA and BERT vectors in this study to improve topic recognition and clustering. Moreover, because one of the most difficult aspects of word-sentence embedding is dealing with high dimensions, we applied the Uniform Manifold Approximation and Projection (UMAP) approach. In comparison to other approaches, UMAP is one of the most efficient implementations of manifold learning [30]. order to balance the information content of each vectors. We incorporated the Keras package to process the auto-encoder in order to learn a lower-dimensional latent space representation for the concatenated vector.
To ensure the clusters were of good quality, we calculated the Silhouette Score, which was 0.566 and near to one for LDA+BERT+ Clustering. TFIDF+clustering received a score of 0.048, while BERT+clustering received a score of 0.095 ( Figure 2). The Silhouette Score is used for cluster quality [31]. The score ranges from -1 to 1. If the score is near to one, the cluster is dense and well isolated from neighboring clusters. In comparison to other topic modeling techniques, LDA BERT Clustering is closer to 1, indicating that the clusters are of excellent quality. The final topic identification obtained by LDA+BERT+Clustering Algorithms is depicted in Figure 3. We utilized the UMAP package to do dimension reductions and set the topic count to eight. We also evaluated several topic clustering, including 10, 4, and 6. The authors determined that eight topics were better separated from one another and had a greater density within each topic; this demonstrates the excellent quality of clustering. As indicated by the percentage of documents contained inside each topic, approximately 11% of documents belong to topic 0 and approximately 16% to topic 1. Clustering resulted in a balanced distribution of documents within each topic, confirming the clustering's excellent quality.
TF-IDF Clustering BERT LDA Figure 3 The global view of the topic model on sustainable AI in energy research area. We integrated LDA, BERT and clusetering for topic modeling detection. uncovered eight different topics. These topics will be described, and then a content analysis of the papers that are associated with each one will be carried out throughout this part of the article.
Results
Descriptive Analysis
These articles were organized according to their relative likelihood of belonging to each topic. As seen in The word cloud visualization ( Figure 6.0) shows the identified topics after labeling based on the topic three keywords. The Figure 6 shows that the first three most-used terms in each subject are as follows: Topic 1(building, consumption, environment); topic 2 (design, water, decision); topic 3 (building, climate, fuel); topic 4 (decision, agriculture, improve); topic 5 (IoT, devices, consumption); topic 6 (urban, technology, industrial); topic 7 (engineering, efficiency, students); topic 8 (optimization, efficient, building).
Figure 4 The distribution of documents across topics
The evolution of topics over time
Once we scoured the corpus for hidden topics, we determined how often they appear throughout time. however, topic reached its apex in 2019 and 2020. The topic of AI for energy efficiency has shown a reasonably steady increase from 2013, with its greatest growth occurring between 2020 and 2021. In 2020, significant academic focus was given to AI-based DSSs for urban water management.
Content analysis to detect topics, sub-themes and cross-topic common themes
In this part of the paper, we conducted content analysis of detected topics for three purposes: First, to detect the general topics from articles; second, to identify the sub-themes from each topic, and third to find the cross-topic common themes.
Topic 1: Sustainable Buildings and Energy Consumption
The primary concerns of topic 1 are related to the design of automated and intelligent systems and the incorporation of cutting-edge technologies, particularly IoT and AI-based DSSs, in order to construct sustainable buildings. These buildings will be part of the sustainable cities initiative, which aims to promote sustainable energy consumption and smart grids.
One of the primary scholarly interests is the creation of sustainable buildings and smart grids for the purpose of reducing energy consumption. One way to accomplish this aim is to redefine the design and architecture of buildings, whether residential, public, commercial, industrial, or manufacturing. According to studies, the application of automation and intelligent systems in the construction of sustainable buildings will result in sustainable energy usage [32,33]. Several AI-based approaches are proposed to achieve a more sustainable building, including building management systems, knowledge-based engineering (KBE), fuzzy logic, neural [34]. From a broad standpoint, sustainable building development falls under the umbrella of sustainable smart cities and reducing building energy consumption [35]. Additionally, scholars have drawn inspiration from nature and advocated regenerative design influenced by nature for pattern detection, prediction, optimization, and planning of buildings [36]. Additionally, scholars discuss the potential of AI in reducing CO2 emissions in buildings, suggesting that AI may be used to construct smart multi-energy systems, such as those found in industrial districts, resulting in significant energy savings and CO2 emission reductions (Simeoni, Nardin and Ciotti, 2018 ). As a result, sustainable building design would be a way to combat climate change.
Several additional studies integrate AI solutions with other cutting-edge technologies, most notably the Internet of Things and big data, to improve not only the design and optimization of sustainable buildings, but also the efficiency of their power usage (Chui, Lytras and Visvizi, 2018). For instance, one project focused on the application of IoT in public buildings in order to discover and anticipate energy usage trends [39]. A preceding study, for illustration, outlines the obstacles involved in understanding the semantics of IoT devices using machine learning models. Image Encoded Time Series has been identified as an alternate method to other statistical feature-based inference [35]. Sustainability analysts from [40] and [41] studies have also advocated for continual monitoring of sustainability metrics by integrating AI with DSSs or ambient intelligence.
Both residential buildings and plants and commercial buildings and offices have the same issue in regard to energy usage. Previous studies incorporated multi-objective and multi-attribute decision making modeling as well as impact evaluation of the emission outputs to help designers and manufacturers to make environmentally sustainable decisions about the designs and production of facilities [42]. Researchers also believe that in order to provide bulk energy consumption forecast, control, and management, simulation techniques could be utilized [15], for instance in public buildings, offices and factories. Due to new modes of consumption and distributed intelligence, the electrical power grids have been also influenced, and as a result, smart energy grids have been generated to achieve sustainability [43].
Topic 2: AI-based DSSs for Sustainable Urban Water Management
The second topic is sustainable water management, which includes utilizing AI to create DSSs for consumption and water usage. Forecasting, real-time monitoring, and customized and adjustable pricing and tariffs are the primary strategies. AI is used with other sophisticated technologies to assist in the development of a smart city.
The previous studies have postulated several approaches, such as optimization and AI-based decision support systems, for water infrastructure management [44], better delivery of public services of smart cities such as water treatment and supply [45], AI-based water pricing and tariff options [46] and sustainable water consumption [47]. For this goal, AI is integrated with recent technological advances in urban life. This includes using open source data, employing deep learning algorithms, and developing smart street lighting systems. Such decisions about social impacts of smartphone applications or smart travel behavior are also examined [48].
AI techniques are utilized to anticipate water resource management [49], such as water quality by adopting algorithms such as neuro-fuzzy inference system [50]. Real-time optimization of water resources and cloud technologies are integrated with visual recognition techniques and created to improve efficiency with irrigation systems [51]. A study conducted on ecological water governance implementation using AI found that including algorithms into the system yields higher-quality information and better prediction models for accurate evaluation of water quality [52]. AI may be used for tracking water use and demand as well as forecasting water quality, but it can also be used for estimating water infrastructure maintenance, monitoring dam conditions, water-related diseases and disasters [53] and water reuse [54].
By critiquing conventional decision support systems, research offer alternatives based on artificial intelligence, such as a systematic decision process [55], sustainability ranking framework based on Mamdani Fuzzy Logic Inference Systems to develop a sustainable desalination plant [56] or an comprehensive and flexible decision-making process fueled by social learning and engagement aimed at ensuring the urban water system's environmental and energy sustainability [57]. One research offers a unique DSS for analyzing the energy effect of each of the urban water cycle's macro-sectors, including assessing the system's energy balance and proposing potential energy-efficient solutions ( Puleo et al., 2016).
Topic 3: Climate Artificial Intelligence (Climate Informatics)
Climate informatics, specially climate artificial intelligence as a new field of study is concerned with issues such as AI-based DSSs to reduce greenhouse gas emissions, optimizing grid assets, enhancing climate resiliency and reliability, increasing energy efficiency, forecasting energy consumption and modeling earth systems. Moreover, within this topic, scholars have addressed the issue of explainable and trustworthy AL models due to the controversial nature of climate change.
Climate change has compelled societies to seek alternate energy sources and fuels [59]. Climate informatics [60], such as several AI-based solutions, including novel algorithms and DSSs, have been hugely beneficial in lowering greenhouse gas emissions in the energy sector. By improving grid assets, and strengthening climate adaptability these innovations have greatly contributed to this ultimate goal [15]. Reliable and explainable artificial intelligence models, as advocated in prior studies, might help stakeholders and decision-makers achieve climate-resilient and sustainable development goals [61]. By integrating advanced machine learing techniques, AI can propose fresh insights in complex climate simulations in the field of climate modeling [62].
Energy consumption patterns might undergo considerable changes due to climatic change, which means AI forecasts can aid in estimating future energy use for various climate scenarios [63]. It's not only businesses and other organizations that are using AI algorithms these days-AI algorithms are also being utilized to foster sustainable urban growth and mitigate climate change by examining how future urban expansion will affect material and energy flows [64]. Fossil fuel, used as the primary energy source, is the primary contributor to human greenhouse gases that influence the climate. AI is extensively utilized for decreasing carbon footprints and for avoiding fossil fuel combustion [65] as prior studies show that AI can act as an automated carbon tracker [66]. Artificial intelligence-powered technologies may help investors in analyzing a company's climate effect while making investment choices [67]. By drawing attention to climate change through visualization techniques, they help to educate the public on the effects of climate change [68] Ultimately, AI algorithms may provide great resources for climate change conflicts, including in the field of modeling earth systems [69], teleconnections [70], weather forecasting ( McGovern and Elmore, 2017), future climate scenarios [72], climate impacts [73] and climate extremes [74].
Topic 4: Agriculture 4.0 and Sustainable Sources of Energy
The fourth area that academics in the field of sustainable AI for energy extensively address is the development of smart agriculture and sustainable energy sources. The primary issue in this subject is how to combine advanced technologies like IoT, drones, and renewable energy with AI in order to create automated and real-time systems.
According to some researchers, the agriculture industry is suffering from an insufficient application of responsible innovation [75]. As a result, the researchers are calling for a system referred to as Responsible Agriculture 4.0, which incorporates drones, IoT, robotics, vertical farms, AI, and solar and wind power linked to microgrids [76][77][78]. When it comes to the productivity of agriculture, factors such as the cost of energy for cultivation are equally significant [79]. Based on the premise that most agricultural machinery operates on fossil fuels, it may potentially contribute to climate change. Thus, new energy solutions, and AI-based approaches are provided. One way in which bioproduction and renewable energy may positively influence sustainable agriculture and farming is via the development of bioproduction and renewable energy [80].
Proposing new AI methods to forecast agricultural energy use has also been researched [79]. biomass may also be used to provide sustainable energy in agriculture, and care should be taken to avoid any injuries [81].
Real-time alerting systems, AI-based DSSs, real-time DSS forecasting models, and alternative energy sources such as solar and wind play a vital role in sustainable agriculture [82]. Maximizing agricultural production and economic stabilization while minimizing the use of natural resources and their harmful environmental consequences may be accomplished using renewable energy and AI [82]. Artificial intelligence enables academics to provide accurate forecasts of agricultural energy use [83]. Especially, a drastic shift toward sustainability in agricultural practices has occurred because of its confluence with other cutting-edge 14 technology, including sensors, DSSs, greenhouse monitoring, intelligent farm equipment, and drone-based crop imaging. [84].
15 AI is used in tandem with a number of cutting-edge technologies for sustainable energy development, such as improved energy conservation [85] and building intelligent energy management [86] such as building management systems [35]. Internet of Things (IoT) is one of the most promising and pervasive technologies [85]; whose integration with AI has generated a revolution in the energy sector. There are many functions in creating sustainable energy in the IoT-enabled smart city dubbed City 4.0 [87] such as simulation and optimization of power plant energy sustainability [86]. City systems such as water and electricity, as well as other infrastructures, such as data analytics, will be driven by sensor and data collection in the smart city [87].
A significant use of IoT is in the design of intelligent buildings, which with AI included may support a goal of energy or water conservation [39,88], for instance, by educating the citizens on how to use energy more effectively and giving them warnings if they are using excessive amounts of energy. [89]. IoT is integral to modern grid development as well. In particular, it seeks to transform the traditional, fossil-fuel-based power grids with distributed energy resources and integrate it with cutting-edge technology such as artificial intelligence for improved grid management [90]. In the same manner, Blockchain has also been considered to be a viable alternative for smart cities. Fusing blockchain with AI may be leveraged for smart services, including energy load forecasting, categorizing customers, and evaluating energy load [91]. Smart connected devices such as IoT devices have successfully employed blockchain in time to retain these devices safe and secure in a blockchain network [92].
The effect of IoT and AI on agriculture and food sectors is also substantial [93,94]. Manufacturing facilities such as food factories and plants may be transformed more intelligent and more environmentally friendly via the use of IoT and AI, which merge with nonthermal and advanced thermal technologies [94]. Sustainable and green IoT are other topics covered in this subject. The two main objectives of the literature on green IoT are to increase the recyclability and usefulness of IoT devices, as well as to minimize the carbon footprints of such devices. The second objective is to incorporate more effective life cycle assessment (LCA) methods integrating artificial intelligence (AI) in order to cut costs and time [95]. Another of the many topics that apply to IoT is with developing smart campuses, which are carbon neutral, energy efficient, use less water, and are laced with various high-quality green energy tools [96] and smart teaching and learning platforms [97].
Researchers have identified the positive traits of IoT devices, but they've also forewarned about the possible risks of the devices and proposed various techniques for detecting weaknesses [93] or challenges regarding the heterogeneity of smart devices and their associated meta-data [35].
Topic 6: AI-based Evaluation of Renewable Energy Technologies
Scholarly interest has been generated by the discussion of leveraging AI for DSSs to enhance the efficiency of conventional system evaluations for renewable energy technologies. To a great extent, a sustainable future will depend on maximizing the use of energy sources that cannot be depleted [98]. Artificial intelligence is important for the survival of the future by leveraging a wide range of renewable energy technologies such as biomass energy, wind energy, solar energy, geothermal energy, hydro energy, marine energy, bioenergy, hydrogen energy, and hybrid energy [99]. AI is used to evaluate renewable energy solutions based on their cost of energy production, carbon footprint, affordability of renewable resources, and energy conversion efficiency [100]. Artificial intelligence will ensure the most effective use of these resources while also pushing for improved management and distribution systems [14]. Distributed energy management, generating, forecasting, grid health monitoring, and fault detection are also made more efficient by using automated AI systems [101]. AI can help disperse the supply and demand of energy in real-time and improve energy consumption and storage allocation (Sun, Dong and Liang, 2016).
To mitigate against the barrier of utilizing renewable energy technology, the following measures are taken:
Renewable energy sustainability is evaluated [103]; in addition, the turbulent and sporadic character of renewable energy data is addressed [104]. One research group claims that standard techniques such as LCA and EIA (Environmental Impact Assessment) may be improved by developing more advanced digital intelligent decision-making systems, or DSSs. It is feasible that improved assessments of renewable energy sources may be achieved via intelligent and automated technologies [105]. With the smart mechanisms in place, long-term detrimental consequences can be calculated, as well as visible and invisible factors [106].
Artificial intelligence (AI) increases the adaptability of power systems, providing DSSs for energy storage applications [107]. For instance, to ensure more use of battery-electric buses, and minimize the effect on the power grids, the researchers developed an AI-powered DSS [108]. Another research leveraged AI to create a DSS for forecasting future energy consumption patterns, and to provide a solution for utilizing renewable energy alternatives [109].
Topic 7: Smart Campus & Engineering Education
It is possible to break down the discussions inside this topic into two distinct types: those about engineering education and those which deal with using AI and IoT to construct intelligent campuses to help maintain sustainability objectives. The two themes represent two elements of education: one dealing with the learning contents, and the other with behavioral outcomes of developing smart campuses.To build a model of smart campuses, we should focus on incorporating IoT into the infrastructure, with subsequent implementations of smart apps and services, with smart educational tools and pedagogies and smart analysis as well [97]. A smart campus is in charge of energy consumption scheduling, while its telecommunications infrastructure serves as the place where data transfers are conducted [110]. Integrating cutting-edge technology, a smart campus captures real-time data on energy usage, renewable energy power generation , air quality, and more [111].
Another point of view is that higher education should equip itself with relevant skills and competences to help in realizing long-term sustainable objectives [112]. The energy sustainability in this respect may be addressed via engineering education and engineering assistance for high-level strategic decision-making [113].
This objective can be achieved by using innovative instructional programs, alongside cutting-edge technology such as artificial intelligence and the Internet of Things. A living lab campus equipped with technology, as well as a deep well of talent and competency, may serve as a digital platform for education and sustainable growth [114]. For illustration, to support ongoing research, teaching, and learning on sustainable development, the University of British Columbia (UBC) implemented the Campus as a Living Laboratory project, which included AI and IoT and other cutting-edge technologies [115]. Furthermore, there have been several research done to help AI seamlessly integrate with current educational institutions in order to aid in sustainable development learning [116].
Topic 8: AI for Energy Optimization
Conventional optimization methods may be a roadblock for making progress toward sustainability, and AIbased solutions can help eliminate such roadblocks. Whilst renewable energy sources, like solar and wind, have many merits, there are some downsides to consider. They are usually not always available and often rely on the climate, which renders employing them complicated [117]. A proper optimization of energy may be utilized to minimize greenhouse gas emissions and cut energy usage. Efforts to reduce costs and side effects of energy consumption are facilitated using optimization models [118]. Computational and intelligent resources have enabled academics to progress with optimization problems by employing advanced AI methods. Manufacturers have developed numerous energy-efficient appliances for this reason. Even if the deployment of digital technologies in buildings will likely lead to improved energy efficiency, that is not the sole solution. Studies recommend implementing energy-saving measures that don't just target environmental variables, but also include building inhabitants' comfort and preferences, which is achievable via the integration of AI-augmented algorithms [119]. For illustration, AI algorithms that not only monitor current actions but also give real-time alerts and warnings to users and providers allow optimization to be significantly accelerated. Some approaches, such as algorithms that use energy consumption data to lower energy costs in buildings that use advanced AI, are only one example of how AI and advanced technology may be used to benefit society [120].
Weather has a direct effect on energy consumption, which is indisputable. To ensure the winter heating demand of non-residential buildings was calculated correctly, researchers used an optimized artificial neural network method to determine and forecast this need [121]. By utilizing AI along with the use of smart metering and non-intrusive load monitoring, one may improve energy efficiency by evaluating the electricity use of appliances [38]. Using a new approach, researchers found that the GP model was capable of making accurate predictions and a multi-objective genetic algorithm, NSGA-II, was also capable of optimizing sustainable building design [32]. The use of a fuzzy-enhanced energy system model to represent a route to a sustainable energy system has also been presented in another research [122]. The views of other researchers in the field include techniques based on artificial neural networks, evolutionary algorithms, swarm intelligence, and their hybrids, all of which rely on biological inspiration. These findings imply that sustainable energy development is computationally challenging conventional optimization, demanding advanced techniques [123].
Discussion, Theoretical Gaps, and Future Strands of Research
To For topic 1, the key problems are the importance of sustainable buildings for smart city development and smart grid services. The issue of AI and its application in decision-making, pricing, forecasting, and sustainable consumption are all addressed in this topic. To reach sustainability, various cutting-edge technologies are tied to AI. One problem which may be especially neglected is the use of AI technology to make buildings eco-friendlier and enhance their inhabitants' feeling of accountability toward sustainability.
One approach might be to design real-time warning systems to ensure people are prohibited from excessive energy use, while also ensuring that they benefit from the AI-based solutions. Convergence research may also explore how green architecture is uniquely enabled to deal with complex issues, including environmental efficiency, such as using eco-lighting, natural ventilation, shading, green roofs, and artificial intelligence. Most of prior research focuses on eco-design and overlooks other factors of green architecture. However, there is a dearth of distributed energy resource optimization models, particularly due to the emergence of blockchain.
Figure 6 Identified cross-topic common themes
As shown in Figure 8, we discovered six core problems that were prevalent throughout the majority of the topics. For example, tariff and price models based on artificial intelligence are prevalent in topics 1 and 2;
while economic issues in general are a concern in topics 4, 6, and 8. The dilemma of sustainable consumption is prevalent in all of these topics, demonstrating the critical role of AI in attaining sustainable energy use.
Forecasting is inextricably connected to sustainable consumption, since more than half of the topics cover both; demonstrating the progress of AI forecasting algorithms for sustainable consumption. Forecasting, on the other hand, is not restricted to anticipating consumption patterns.
The topic's second significant recurring theme is the development of AI-based DSSs. The majority of research have contested traditional DSSs and devised decision-making systems based on artificial intelligence.
Sustainable building, urban water management, climate change, and renewable energy evaluation have all been substantially influenced by AI-based DSSs. Automated and real-time systems enabled by artificial intelligence are also discussed in relation to buildings, agriculture, the Internet of Things, and renewable energy technologies. Scholars have combined various digital technologies to promote sustainability in the energy sector via the management of buildings, water, agriculture, IoT, and smart campuses.
Theoretical and Practical Contribution
Theoretical Contribution
Our results supplement existing work on sustainable AI and sustainable energy by delivering the following results. Results from this study provide and highlight a thematic map of the sustainable AI research topics existing in several fields, such as energy, ethics, and management. We developed a novel mixed-method approach, the contextual topic modeling and content analysis, to visualize the latent knowledge structures pertaining to AI and sustainability and energy. This yielded in a conceptual framework representing the main topics, subtopics and common terms in each topic pertaining to sustainable AI in energy. Using LDA and BERT, eight themes related to AI in the sustainability and energy sectors were discovered. We provided the most likely terms for each topic, as well as the distribution of articles and topics throughout time. Finally, by using a thematic analysis method, we identified and qualitatively analyzed the hidden themes.
Second, we examined and analyzed hidden sub-themes within each topic, as well as common themes between topics, using a content analysis method. Figure 8 illustrates the sub-domain themes within each topic, whereas Figure 9 depicts the common cross-topic themes. Our content analysis of each topic reveals six recurring themes: sustainable consumption, AI-based DSSs, forecasting models, economic and pricing problems, automated and real-time systems, and convergence with digital technology. To further our knowledge, we highlighted how these themes intersect across topics in order to articulate the commonalities across topics. These six separate but related topics demonstrate that sustainable AI solutions can be observed at a range of behavioral, decision-making, economic, operational, and technical dimensions. At the behavioral level, shifts in consumption patterns are illustrated; at the decision-making level, decision automation is outlined; at the economic level, personalized tariffing is demonstrated; at the operational level, automation and real-time operations are addressed; and at the technological level, convergence with other technologies is studied.
Practical Implications
This research provides energy engineers, social scientists, scientists, and policymakers with a variety of insights. Engineers may develop sustainable energy products and services. Energy scientists can also integrate sustainability considerations into their research and development of new energy sources such as renewable energy. In their discussions on AI and energy, social scientists may also emphasize ethical problems, including sustainability. Additionally, policymakers may create and construct new laws and policy initiatives aimed at mitigating the harmful effects of unsustainable energy on society and the environment.
Conclusion
To discover heavily discussed scholarly topics, our study utilized a new topic modeling technique. While this illustration depicts the trajectory of previous efforts, it also prompted us to propose a number of possible future research strands targeted at increasing energy sector sustainability via the application of artificial intelligence technology. The aim of this study is to further the conversation on sustainable AI and energy, as well as their intersection, in order to get a deeper understanding of how AI may be incorporated to achieve sustainability in the energy sector.
Figure 1 Figure 2
12The concatenating and encoding LDA and BERT vectors to extract contextual topics The separate and independent results of topic modeling of research on sustainable AI in energy by using TF-IDF, BERT and LDA algorithms
Figure 3 .
30 shows a representation of the topic model on sustainable AI in energy research field with respect to the overall global view. This visualization represents the topic modeling results, where topics are illustrated as clusters on a two-dimensional plane. Also shown in Figure 4 is the word cloud visualization of the topics with the most frequently used terms in each topic. Topics 1, 2, and 3 represent the greatest research interest in the model based on 8 topics and including 21.67%, 17.22%, and 15.0% of the corpus. Our research
Figure 4 .
40, the three most-covered topics by academia are topic 1: Sustainable buildings (22.5%), Topic 2: AIbased DSSs for urban water management (16.5%) and Topic 3: Climate Artificial Intelligence (14.8%). About 54% of the articles in the corpus are concerned with these three themes.
Figure 5
5depicts the ratios of all the eight topics (beginning in 2004 and extending into 2021). Since 2018 forward, topics have garnered a substantial amount of academic interest. Specifically, the first topic, which is about the design of sustainable buildings and minimizing energy usage via the application of artificial intelligence. This subject gained considerable attention between 2012 and 2014, but then slipped off the spotlight between 2015 and 2018. The discussions about AI-based evaluation of renewable energy solutions peaked around 2008 but then became less prominent until 2019. Climate artificial intelligence experienced two distinct phases, with the second one peaking in 2015 and 2016 and the first between 2009 and 2012;
Figure 5
5The evolution of topics over time
Figure 6
6Topics detected by the combination of LDA+BERT+Clustering algorithms on sustainable AI in energy sector
identify the relevant research topics in the literature on artificial intelligence for sustainability in the energy industry, we performed a contextual topic modeling combined with qualitative cluster analysis. We went beyond previous approaches in developing this novel analysis by combining three algorithms of topic modeling (LDA, BERT, and clustering) with content analysis. In this research, eight academic topics were discovered including sustainable buildings and energy consumption, AI based DSSs for sustainable urban water management, climate artificial intelligence, agriculture 4.0 and sustainable sources of energy, convergence of IoT and AI for sustainable smart cities, AI-based evaluation of renewable energy technologies, smart campus and engineering education and AI for energy optimization. Concerns and problems addressed in each topic are summarized in Figure 7. The Figure illustrates that each topic addresses a number of specific issues, which some of them overlap.
Figure 7
7Possible future streams of research pertaining to each topic
networks, genetic algorithms, and Monte-Carlo simulationTopic 1: Sustainable Buildings and
Energy Consumption
Topic 2: AI-based DSSs for Sustainable
Urban Water Management
Topic 3: Climate Artificial Intelligence
Topic 4: Agriculture 4.0 and
Sustainable Sources of Energy
Topic 5: Convergence of IoT & AI for
Sustainable Smart Cities
Topic 6: AI-based Evaluation of
Renewable Energy Technologies
topic 7: Smart Campus & Engineering
Education
Topic 8: AI for Energy Optimization
Convergence of IoT & AI for Sustainable Smart CitiesA significant step in the implementation of sustainable energy solutions is to implement smart cities and services using internet of things technology. This topic exhibits how AI and IoT operate together to drive environmental progress. Much of this topic focuses on measure such as smart buildings, smart grid systems, green IoT, and smart campuses.Topic 1: Sustainable
Buildings and Energy
Consumption
Topic 2: AI-based DSSs for
Sustainable Urban Water
Management
Topic 3: Climate Artificial
Intelligence (Climate
Informatics)
Topic 4: Agriculture 4.0 and
Sustainable Sources of
Energy
Topic 5: Convergence of IoT
& AI for Sustainable Smart
Cities
Topic 6: AI-based Evaluation
of Renewable Energy
Technologies
Topic 7: Engineering
Education & Smart Campus
Topic 8: AI for Energy
Optimization
16
Topic 5:
future study area is the confluence of smart grids, renewable energy, and 5G technology, since these technologies have the potential to generate enormous volumes of big data. Furthermore, the use of AI in transportation seems worthy of analysis, for example, with regard to traffic predictions, public transit planning, and so on.The agricultural 4.0 and sustainable energy sources are examined in Topic 4. Many problems relevant to the subject of "prosperity, sustainable consumption, forecasting, and convergence with other automated and realtime technologies" are covered in this topic. There is only a limited body of studies dedicated to precision farming and digital mapping, but both developments promise to lead to better knowledge of the environment and to improved energy management. Precision farming by assessing soil nutrients, detecting humidity in the air, and monitoring crops allows farmers to leverage digital maps for better energy management and fight against climate change. Other related areas of study include developing automated working environments. It is worthwhile to investigate the effect that artificial intelligence and other green technologies will have onthe working conditions of farmers and farm operators, since AI may help with deeper speculations of working conditions in farms.In Topic 5, convergent IoT and AI technologies for smart city development were addressed. The primary goal of this topic was to discuss issues around sustainable consumption, LCA analysis, and the development of intelligent energy grids. Pervasive Wi-Fi connection, due to its ability to save energy, is critical in this subject. Additionally, a significant problem is open data sharing in energy management. AI-based assessment of renewable energy technologies, such as DSSs, financial problems, sustainable consumption, and automated and real-time systems are all issues in this topic that focus on renewable energy. One potential study path in this topic involves the challenges that AI algorithms and models face when attempting to evaluate renewable energy solutions. Other sophisticated AI systems, such as deep learning, make use of supervised learning using human-annotated data, and thus they are limited when it comes to complicated situations.The subject of smart campus and engineering education is examined in the seventh topic. Labs that facilitate continuous innovation are discussed in this article, as well as the idea of sustainable consumption, AI skills, and convergence with other technologies. There is an imperative requirement for further research to clarify how AI might be leveraged for practical learning and training for a range of stakeholders across businesses, farmers, residents, and employees in relation to energy management. AI is discussed in relation to energy optimization in Topic 8 of the study. This subject covers many elements of sustainable optimization, including forecasting, consumption, affordable pricing, and societal and financial impacts.Topic 2 addresses sustainable urban water management via the use of AI-based DSSs. Conventional DSSs
were under criticism from academics who suggested alternatives, and innovative approaches to DSSs were
revealed, particularly with regard to water utilities in a smart city. The second discussion point, focused on
sustainable consumption and real-time and predictive modeling, is also addressed in topic 2. Mitigating
urban problems, notably air pollution, waste management, and wastewater management, are applicable here
to exemplify how smart energy management leveraging AI improves environmental sustainability. Topic 3
deals with the connection between climate change and artificial intelligence, and the emergence of the climate
informatics field. This topic highlights the role of trustworthy of explainable AI algorithms, an issue which is
marginalized in other topics. As a result, a future potential study direction may be the development of ethical
artificial intelligence in other topics to help with the sustainable management of energy. One prospective
Figure 5 Sub-themes extracted from each topic
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| sample_15 | 0.5348 | arxiv | |
EFFET DU CHLORURE DE SODIUM (NaCl) SUR LA CROISSANCE DE SIX ESPECES d'Acacia EFFECT OF SODIUM CHLORIDE (NaCl) ON THE GROWTH OF SIX Corresponding and Author
|Received | 01 March 2017| |Accepted | 29 March 2017| |Published 10 April 2017 |
|khalil Chérifi
Laboratory of Biotechnology and Valorization of Natural Resources | Faculty of sciences | Ibn Zohr University |
P.O. Box 8106 | 8000Agadir| Morocco |
|abdelmjid Anagri
Laboratory of Biotechnology and Valorization of Natural Resources | Faculty of sciences | Ibn Zohr University |
P.O. Box 8106 | 8000Agadir| Morocco |
| El
Houssine Boufous
American Journal of Innovative Research and Applied Sciences. ISSN
Department of Biochemistry and Microbiology | Laval University | Quebec City (Quebec)
2429-5396 I www.american-jirasCanada |
|
| Abelhamid
El Mousadik
Laboratory of Biotechnology and Valorization of Natural Resources | Faculty of sciences | Ibn Zohr University |
P.O. Box 8106 | 8000Agadir| Morocco |
Acacia Species
American Journal of Innovative Research and Applied Sciences. ISSN
2429-5396I www.american-jiras
EFFET DU CHLORURE DE SODIUM (NaCl) SUR LA CROISSANCE DE SIX ESPECES d'Acacia EFFECT OF SODIUM CHLORIDE (NaCl) ON THE GROWTH OF SIX Corresponding and Author
|Received | 01 March 2017| |Accepted | 29 March 2017| |Published 10 April 2017 |105 ORIGINAL ARTICLE See: http://creativecommons.org/licenses/by-nc/4.0/Mots-clés: Tolérance à la salinitéVariabilitéAcaciaAmélioration des plantesRéhabilitation Keywords: Salt toleranceVariabilityAcaciaPlant breedingRehabilitation
RESUMEIntroduction : Au cours de ces dernières décennies on assiste à une diminution progressive des superficies cultivables dans les régions arides et semi-arides à cause de l'accumulation des sels liée à la rareté des précipitations, au mauvais drainage, à la sècheresse prolongées et à l'absorption de l'eau par les plantes. Contexte : Devant l'ampleur de ce problème, il s'avère donc nécessaire de proposer des programmes d'évaluation et de conservation des espèces menacées d'extinction. Le repérage d'espèces plus adaptées et la sélection des variétés tolérantes à la salinité resteraient la voie économique la plus efficace pour l'exploitation des terrains affectés. Objectifs : L'objectif de cette étude est de déterminer la capacité de tolérance à la salinité au cours du développement végétatif chez six espèces appartenant au genre Acacia. Ceci dans le but d'élaborer une classification des seuils de tolérance au stress salin, critère important dans le choix des espèces à retenir dans un programme de mise en valeur des zones affectées par la salinité. Méthodes : L'effet du stress salin a été abordé sur un certain nombre de caractères agro-morphologiques en conditions contrôlées. Les concentrations de NaCl appliquées, en plus du témoin, sont : 100 mM, 200 mM, 300 mM et 400 mM. Résultats : Les résultats ont montré une variabilité non négligeable dans le comportement des plantes des différentes espèces en fonction du stress salin. Chez les six espèces d'Acacia, le sel a exercé un effet dépressif sur tous les paramètres de croissance étudiés. Toutefois, le taux de réduction diffère selon l'intensité de stress salin et le degré de sensibilité ou de tolérance de l'espèce. La croissance en hauteur, le nombre de feuilles et la biomasse sèche totale sont vraisemblablement les paramètres les plus affectés. Cependant, il est important de signaler que toutes les espèces d'Acacia considérées dans ce travail ont survécu, même à 400 mM de NaCl, et ont présenté différents degrés de tolérance à la salinité. Dans cette situation, les espèces A. horrida et A. raddiana s'avèrent globalement les plus performantes au stade végétatif. Conclusions : La variabilité génétique, dévoilée par ces espèces dans les différentes conditions de stress salin, permettrait un choix d'écotypes pouvant entrer dans des schémas de sélection et d'amélioration variétale pour la réhabilitation des parcours dégradés surtout en zones affectées par la salinité.ABSTRACTBackground: Salinity is one of the major abiotic stresses affecting plant production in arid and semi-arid regions. It causes reduction of cultivable area and combined with other factors, presents a serious threat to food stability in these areas. Context: In front of this problem, the selection of salt tolerant species and varieties remains the best economic approach for exploitation and rehabilitation of salt-affected regions. Objective: The purpose of this study was to assess and compare the seed germination response of six Acacia species under different NaCl concentrations in order to explore opportunities for selection and breeding salt tolerant genotypes. Methods: The salinity effect was examined by measuring some agro-morphological parameters in controlled growth environment using five treatment levels: 0, 100, 200, 300 and 400 mM of NaCl. Results: The analyzed data revealed significant variability in salt response within and between species. All growth parameters were progressively reduced by increased NaCl concentrations. Growth in height, leaf number and total plant dry weight were considered as the most sensitive parameters. However, the growth reduction varied among species in accordance with their tolerance level. It is important to note that all species survived at the highest salinity (400 mM). Whereas A. horrida and A. raddiana were proved to be often the best tolerant, they recorded the lowest reduction percentage at this stage. Conclusion: The genetic variability found in the studied species at seedling stage may be used to select genotypes particularly suitable for rehabilitation and exploitation of lands affected by salinity.
INTRODUCTION
La salinisation est un processus important de dégradation des sols. Elle constitue un facteur limitant à la croissance et au développement des plantes. Les conséquences de ce phénomène qui ne cesse de prendre de l'ampleur, se manifestent par la toxicité directe due à l'accumulation excessive des ions (Na + et Cl -) dans les tissus des organes, et à un déséquilibre nutritionnel imputable essentiellement à des compétitions entre les éléments minéraux, tel que le sodium avec le potassium et le calcium, le chlorure avec le nitrate, le phosphate et le sulfate [1,2]. En conséquence, les glycophytes les plus tolérantes seront celles qui, tout en utilisant le Na + comme osmoticum, conserveront une forte sélectivité vis à vis du K + [3]. La stratégie utilisée par les végétaux pour éviter les problèmes d'excès d'ions tout en réalisant leur équilibre osmotique est la compartimentation cellulaire, qui se traduit par une accumulation préférentielle du Na + dans la vacuole [4]. Cependant, chez les glycophytes tolérantes, on discerne également une compartimentation à l'échelle de la plante, surtout dans les organes jeunes où la teneur en Na+ reste faible [5,6].
La variabilité pour la tolérance à la salinité a été étudiée chez beaucoup d'espèces [5,[7][8][9][10][11]. Pour des raisons pratiques, de nombreuses explorations de cette variabilité ont été abordées au stade végétatif sur des plantes très jeunes. Cette approche est justifiée par le fait que la réponse des plantules est parfois fortement prédictive de celle des plantes adultes [12][13][14]. Dans certains cas, l'écart entre la tolérance au stade plantule et celle au stade adulte peut justifier les différences entre les mécanismes impliqués d'un stade de développement à un autre [15][16][17][18][19]. Plusieurs recherches ont montré que la croissance en hauteur [20,21], la production de biomasse des tiges et des racines [22,23] est négativement affectée par l'augmentation de la salinité.
Face à la salinisation des sols qui constitue l'un des facteurs abiotiques majeurs réduisant le rendement agricole, l'introduction d'espèces végétales tolérantes à la salinité est une stratégie alternative recommandée pour valoriser les sols touchés par ce phénomène. Cette approche, permettraient d'améliorer le couvert végétal et résoudre les problèmes de régénération de certaines espèces forestières en zones arides et semi-arides, particulièrement celles appartenant au genre Acacia qui représentent certainement une richesse écologique menacée en Afrique du Nord [24]. Acacia, appartenant à la famille des Fabacées, est identifié comme étant un genre cosmopolite, varié et riche. Ces espèces à usage multiple peuvent coloniser des sols pauvres grâce à leur capacité de fixer l'azote atmosphérique par leur association symbiotique avec le Rhizobium des nodosités racinaires. Au Maroc les écosystèmes à base d'Acacia représentent un enjeu stratégique pour les régions semi-arides, arides et sahariennes du pays aussi bien sur le plan écologique que socio-économique. Ces écosystèmes rares et originaux, peuvent constituer une protection naturel contre la désertification.et fournir un intérêt multifonctionnel et multi-usager, tels que leurs utilisations dans la production de bois d'énergie et de service, de gomme arabique, de substances pharmaceutiques, de fourrage, de produits mellifères, ainsi que leur utilisation en reboisement et en foresterie urbaine [25]. La maîtrise des exigences de croissance des plantules est une étape importante dans le succès des opérations de reboisement de ces espèces. Ce stade, très important pour le développement des plantes, est surtout contrôlé par des facteurs génétiques et environnementales, en particulier la salinité [26]. Malheureusement, au Maroc, peu de travaux de recherche sur le degré de tolérance à la salinité chez les Acacia ont été effectués. Notre présente étude s'inscrit dans le cadre d'une évaluation de la variabilité des réponses au stade plantule de six espèces d'Acacia soumises à des doses croissantes de NaCl. L'effet du stress salin a été abordé sur un certain nombre de caractères agro-morphologiques en conditions contrôlées. Ceci dans le but d'identifier le matériel végétal le plus performant pour des programmes de restauration et de valorisation de la productivité végétale, particulièrement pour la réhabilitation des parcours dégradés, c'est le cas d'Acacia gummifera et Acacia raddiana, ainsi que pour des projets de reboisements en milieux affectés par la salinité, dans le cas des espèces exotiques, comprenant Acacia eburnea, Acacia cyanophylla, Acacia cyclops et Acacia horrida.
MATERIELS ET METHODES
Matériel végétal
L'analyse de la diversité de la tolérance à la salinité a porté sur deux espèces autochtones, représentées par Acacia gummifera et Acacia raddiana et quatre espèces exotiques, représentées par Acacia eburnea, Acacia cyanophylla, Acacia cyclops et Acacia horrida. La majeure partie des graines des différentes espèces testées ont été collectées sous forme de gousses dans différentes régions du sud-ouest marocain (Tableau 1). Elles nous ont été aimablement fournies par la station régionale des semences forestières de Marrakech et ont été conservées au froid (4°C) jusqu'à l'analyse.
Caractères mesurés
Après huit semaines de culture, quatre paramètres ont été mesurés dans différentes conditions de stress salin (Tableau 2). Les caractères retenus se rapportent au développement végétatif des plantes ainsi qu'à l'estimation de la valeur fourragère : Nombre totale de feuilles (Nbr.Fll). Ces mêmes critères ont été aussi utilisés par d'autres auteurs dans l'estimation de la croissance de la biomasse chez certaines espèces d'Acacia cultivées sous stress salin [29,30].
Tableau 2:
Le tableau montre les paramètres mesurés dans l'évaluation de l'effet de la salinité au stade végétatif.
Code des caractères Signification
Analyses statistiques
Les six espèces ont été traitées selon un dispositif complètement randomisé, à raison de 10 plantes par population et par traitement. Les données relatives aux pourcentages de réduction des différents paramètres de croissance ont été transformées en arcsin racine carrée avant d'être soumises à l'analyse de variance à deux critères de classification (espèce et [NaCl]). La comparaison des moyennes entre les différentes espèces, pour chaque traitement, a été réalisée par le test de Newman et Keuls. Pour chaque concentration, les espèces dont les moyennes ne sont pas significativement différentes ont été regroupées dans une même ellipse sur les graphiques. Les traitements des données ont été réalisés par le logiciel Statistica (Version 6) [31].
RESULTATS
Le tableau 3 résume l'analyse de variance de l'effet espèce et de l'effet NaCl ainsi que leur interaction. Pour l'ensemble des caractères, le teste ANOVA montre un effet très hautement significatif entres les espèces et entre les différents traitements de sel. Ces différences sont plus marquées dans le cas des caractères se rapportant à la croissance en longueur des plantules. De la même manière, l'interaction (NaCl * Espèce) révèle aussi un effet très hautement significatif pour les caractères longueur de la tige et le nombre de feuilles et un effet significatif si on considère le poids total de la matière sèche tandis que pour le diamètre du collet l'interaction n'est pas significative. En conséquence, pour ce dernier critère, la salinité agit sur les différentes espèces de la même manière, quel que soit la concentration. Pour le reste des paramètres étudiés, l'effet de NaCl diffère d'une espèce à l'autre.
Tableau 3: Le tableau montre l'analyse de la variance à deux critères de classification abordée sur les différents caractères végétatifs mesurés chez les espèces d'Acacia étudiées.
Caractères
Diamètre du collet (D.Coll)
L'augmentation de la concentration en sel dans la solution d'eau d'irrigation, diminue de façon significative le taux de croissance relative du diamètre du collet chez toutes les espèces considérées (figure 4). Pour ce critère on note une réduction plus faible par rapport aux autres caractères étudiés. À des concentrations allant de 200 à 400 mM, la réduction du diamètre du collet chez A. gummifera est significativement plus importante que celles des autres espèces. En effet, à 400 mM on note une régression qui peut atteindre 52% chez cette espèce comparativement à A. horrida chez laquelle la régression n'a été que de 14%. Les espèces A. horrida, A. raddiana et A. cyanophylla forment un groupe homogène et réagissent de la même manière au stress salin avec les réductions les plus faibles.
Nombre de feuilles (Nbr.Fll)
Pour ce caractère, on note une classification moins nette des différentes espèces surtout au niveau des concentrations modérées en sel (figure 5). L'espèce A. cyanophylla semble encore une fois la plus affectée par le sel et montre une réduction de sa production foliaire atteignant les 86% à la concentration 400 mM de NaCl. En générale cette espèce exhibe la plus grande sensibilité à la salinité à ce stade de développement. D'un autre côté, A. raddiana a présenté une faible réduction du nombre de feuilles par plante à la concentration 300 mM de NaCl. On note, dans ce cas, une réduction de 33% chez l'espèce la plus tolérante contre 63% chez A. cyanophylla pour atteindre à la concentration de 400 mM une réduction de 48% chez A. raddiana et 86% chez l'espèce la plus sensible.
Biomasse totale (PS)
L'augmentation de la concentration de NaCl a un effet significatif sur la biomasse sèche de toutes les parties de la plante (feuilles, tiges et racines) des espèces testées (figure 6). La plus grande variabilité a été observée pour les deux concentrations 300 et 400 mM de NaCl. Comme pour les caractères nombre de feuilles et longueur de la tige, A. cyanophylla se distingue, encore une fois, des autres espèces en affichant pour ce critère, toutes concentrations confondues, les réductions les plus élevées. Par ailleurs, A. horrida et A. raddiana semblent être, en générale, moins affectées pour ce caractère, elles ont montrée de ce fait les plus faibles régressions de la matière sèche totale élaborée, variant en moyenne entre 13 et 34% contre 40 et 77% pour A cyanophylla, la plus sensible. Les autres espèces occupent une situation intermédiaire et montrent une grande variabilité au niveau des doses élevées en NaCl (400 mM) par rapport aux concentrations faibles.
DISCUSSIONS
Les résultats présentés dans cette partie, montrent que la salinité réduit en générale la croissance des plantules chez l'ensemble des espèces étudiées. Néanmoins, une grande variabilité entre les espèces a été révélée à ce stade. Les interactions très hautement significatives entre les deux effets (espèce*salinité), observées dans notre cas, montre la possibilité d'une sélection essentiellement sur la base des caractères : Longueur de la tige, nombre de feuille et la biomasse totale. Toutefois, on a constaté qu'une espèce performante pour un caractère donné n'est pas forcément la meilleure pour un autre critère. C'est le cas d'A. cyanophylla dont le nombre de feuilles, la biomasse totale et la longueur de la tige paraissaient relativement affectée par le sel, mais dans le cas du caractère relatif au diamètre du collet elle était classée parmi les espèces les plus tolérantes.
Nos résultats sont en concordance avec les travaux de Nguyen et al. [32] dans lesquels ils ont révélés que les deux espèces Acacia auriculiformis et Acacia mangium ont réagi également par une réduction de la croissance de la partie aérienne en réponse au stress salin. Cet effet est fréquent chez les glycophytes [33], où la diminution de la croissance de l'appareil végétatif observée peut être expliquée par une augmentation de la pression osmotique provoquée par NaCl, ce qui bloque l'absorption de l'eau par les racines. Les plantes s'adaptent ainsi au stress salin par la réduction de leur croissance afin d'éviter les dommages causés par le sel [34,35]. Les effets de la salinité sur la croissance des plantules cultivés en conditions semi contrôlées, dépendent de plusieurs facteurs. Ils varient selon la teneur de NaCl appliquée, l'espèce, la provenance, le stade végétatif et la partie de la plante [2]. Les effets de la salinité se manifestent principalement par un ralentissement de la croissance de l'appareil végétatif. D'autre part, il est important de signaler que toutes les espèces d'Acacia considérées dans ce travail ont survécu, même à 400 mM de NaCl, alors que selon Ghulam et al. [36], ce niveau de salinité a été nuisible pour A. nilotica tandis que A. ampliceps tolère cette concentration. La comparaison de la tolérance à la salinité chez cinq espèces d'Acacia : A. ampliceps, A. salicina, A. ligulata, A. holosericea et A. mangium a révélé que A. ampliceps était la plus tolérante et a survécu même à 428 mM en NaCl, concentration à laquelle toutes les autres espèces ont été sévèrement affectées [37].
Pour le paramètre matière sèche, les réductions les plus faibles sont enregistrées chez A. horrida et A. raddiana. Le pourcentage de réduction de la matière sèche, généralement considéré comme indice de sensibilité des plantes vis-à-vis du stress salin, montre que la concentration 400 mM NaCl est insuffisante pour engendrer une réduction relative de 50 % par rapport aux témoins, seuil très utilisé pour le classement de la tolérance des plantes [21]. En outre, même à une concentration plus faible (300 mM) les autres espèces manifestent des réductions plus marquées.
Les feuilles sont les parties les plus sensibles de la plante au stress salin. Cependant, chez l'ensemble des espèces on assiste à une réduction significative du nombre de feuilles par rapport au témoin surtout à partir de 300 mM de NaCl. Des résultats similaires ont été rapportés sur d'autres espèces par [38][39][40][41]. D'autre part, au cours de l'expérimentation on a constaté que la croissance foliaire est également très affectée par l'augmentation du stress salin quelle que soit l'espèce. L'expansion des feuilles est considérablement inhibée par le sel, les nouvelles feuilles se développent lentement et le vieillissement des feuilles âgées s'accélère. D'ailleurs, quand la surface foliaire est réduite par la salinité, la production de carbohydrates devient insuffisante pour supporter la croissance et le rendement [42].
La réduction de la croissance, dans les conditions d'un stress salin est attribuée à plusieurs facteurs, parmi lesquelles l'accumulation des ions, aussi bien en Na + qu'en Clà des teneurs élevées dans les tissus foliaires qui est la cause principale des contraintes ioniques au niveau des tissus de la plante [43]. Selon ces auteurs, le stress salin cause un déséquilibre nutritionnel qui en résulte l'inhibition de l'absorption des éléments nutritifs essentiels comme le Ca 2+ , K + , Mg 2+ , NO3par les phénomènes de compétition minérale de fixation apoplasmique [44]. En outre, il est établi qu'un supplément de Ca 2+ dans le milieu de culture améliore les conditions de croissance sous stress salin [45]. Le dérèglement de l'absorption du calcium inhibe également l'établissement de la nodulation et la fixation d'azote chez les légumineuses [46]. Il parait que cet ion est impliqué dans le processus de la reconnaissance Rhizobium-poil absorbant [47].
Par ailleurs, la diminution de la croissance des parties aérienne peut aussi être expliquer par des perturbations des taux des régulateurs de croissance dans les tissus, particulièrement l'acide abscissique et les cytokinines induites par le sel [48], mais aussi à une diminution de la capacité photosynthétique provoqué par la diminution de la conductance stomatique de CO 2 sous la contrainte saline. Dans tous les cas, cette réduction de la croissance des différentes parties aériennes est considérée comme une stratégie adaptative nécessaire à la survie des plantes exposées à la salinité [49]. Ceci permet à la plante d'emmagasiner de l'énergie nécessaire pour faire face au stress afin de réduire les dommages irréversibles occasionnés, quand le seuil de la concentration létale est atteint [39].
De plus, il a été constaté que la tolérance au stade germination, dans les conditions de nos expériences, ne reflète pas dans tous les cas celle au stade végétatif. En effet, l'espèce A. horrida, classée parmi les plus sensibles au sel durant la germination, manifeste une tolérance importante vis-à-vis de NaCl au stade plantule. Par contre l'espèce A. raddiana, reconnue par sa tolérance à la salinité, très marquée, au stade germination, conserve globalement sa performance aux stades avancés. Cependant, la germination sous contrainte saline n'est pas suffisante pour identifier des espèces tolérantes au sel [26,50]. Dans ce contexte, de nombreux auteurs ont montré que la réponse à la salinité variait selon le stade de développement de la plante [51][52][53]. Toutefois, la germination et les premiers stades de la croissance seraient les phases les plus sensibles [54].
CONCLUSION
Le stress salin exerce chez les Six espèces d'Acacia un effet dépressif sur tous les paramètres de croissance étudiés. Toutefois, le taux de réduction diffère selon l'intensité de stress salin et le degré de sensibilité ou de tolérance de l'espèce. La croissance en hauteur, le nombre de feuilles et la biomasse sèche totale sont vraisemblablement les plus affectés. Cependant, toutes les espèces d'Acacia considérées dans ce travail ont survécu, même à 400 mM de NaCl et présentent différents degrés de tolérance à la salinité. Les espèces A. horrida et A. raddiana s'avèrent globalement les plus performantes. Cette variabilité génétique dévoilée par ces espèces dans les différentes conditions de stress salin, surtout sous des seuils élevés en NaCl allant jusqu'à 400 mM, constitue un atout intéressant qui peut être utilisé aussi bien dans le choix des espèces à retenir pour améliorer la tolérance à la salinité que dans les programmes de valorisation et de réhabilitation des sols salés.
Par ailleurs, ces recherches doivent être poursuivies par des expériences à des stades végétatifs plus avancés afin de confirmer les résultats constatés aux stades germination et juvénile. Toutefois, le dosage et l'identification des osmorégulateurs tels que la proline, pourrait mieux éclaircir les mécanismes d'ajustement osmotique nécessaires à ces plantes pour s'adapter au stress salin. Cela pourrait expliquer, par la même, leur tendance à l'halophilie, observée au cours des deux stades étudiés.
Reconnaissance : Nous exprimons toute notre reconnaissance et nos remerciements aux responsables de la Station Régionale des Semences Forestières de Marrakech (Maroc) pour leurs informations et orientations au cours des prospections pour la récolte des gousses.
Diamètre au collet (D.Coll) : Le diamètre au collet en (mm), mesuré à l'aide d'un pied à coulisse (figure 1). Longueur finale de la tige (Lg.Tige) : Mesurée en utilisant une règle graduée du collet à l'insertion du méristème apicale (figure 2). Poids de la matière sèche (PS) : Ce paramètre est nettement plus fiable et plus simple. La biomasse totale (en mg de matière sèche) est séchée dans l'étuve à 87°C puis pesée 48 heures plus tard.
Figure 1 :
1Mesure du diamètre au collet à l'aide d'un pied à coulisse.
Figure 2 :
2Mesure de la longueur de la tige à l'aide d'une règle graduée.
3. 1 .
1Etude des caractères pris séparément pour l'ensemble des espèces étudiées 3.1.1. Longueur de la tige (Lg.Tige) L'analyse de variance pour la longueur de la tige révèle un effet très hautement significatif des deux facteurs, salinité et espèce ainsi que leur interaction. Le classement des différentes espèces par le test de Newman et Kheuls selon leur tolérance à la salinité, montre une régression de la croissance en hauteur de la tige des plantules chez les différentes espèces étudiées (figure 3). Cependant, les réductions les plus importantes ont été notées pour A. cyanophylla, surtout dans le cas des fortes concentrations. Elle enregistre jusqu'à 92% pour une concentration de 400 mM. Par ailleurs, A. horrida semble la moins perturbée par le sel, du moins pour ce caractères, et affiche les valeurs les plus faibles. Les pourcentages de réduction varient dans ce cas entre 10 % et 47 %, respectivement pour les concentrations 100 et 400 mM. Le reste des espèces réagissent avec modération et occupent une situation relativement intermédiaire entre ces deux dernières espèces.
Figure 3 :
3Représentation des moyennes calculées pour chaque espèce étudiées par traitement de NaCl pour la longueur de la tige. (Les moyennes des espèces groupées dans la même ellipse ne sont pas significativement différentes selon le test de Newman et Keuls à 5%).
Figure 4 :
4Représentation des moyennes calculées pour chaque espèce étudiées par traitement de NaCl pour le diamètre du collet. (Les moyennes des espèces groupées dans la même ellipse ne sont pas significativement différentes selon le test de Newman et Keuls à 5%).
Figure 5 :
5Représentation des moyennes calculées pour l'ensemble des espèces étudiées par traitement en NaCl pour le nombre de feuilles. (Les moyennes des espèces groupées dans la même ellipse ne sont pas significativement différentes selon le test de Newman et Keuls à 5%).
Figure 6 :
6Représentation des moyennes calculées pour l'ensemble des espèces étudiées par traitement en NaCl pour la biomasse totale (PS). (Les moyennes des espèces groupées dans la même ellipse ne sont pas significativement différentes selon le test de Newman et Keuls à 5%).
Tableau 1 :
1Le tableau montre la localisation géographique des différents échantillons d'espèces étudiées.Espèces
Provenance
Région de provenance
A. gummifera
Reserve de faune de Rmila (Marrakech)
Haut Atlas occidental
A. raddiana
Reserve de faune de Rmila (Marrakech)
Haut Atlas occidental
A. cyclops
Région d'Essaouira
Souss Nord
A. cyanophylla
Canal de Rocade (Marrakech)
Haut Atlas occidental
A. horrida
Commune rurale de Saada (Marrakech)
Haut Atlas occidental
A. eburnea
Commune rurale de Saada (Marrakech)
Haut Atlas occidental
Lg.Tige D.Coll Nbr.Fll PS Longueur de la tige Diamètre au collet Nombre totale de feuilles Biomasse totale (en mg de matière sèche)
CM : Carré moyen ; NS : test non significatif ; * : test significatif ; *** : test très hautement significatifCM Espèce
CM Sel
CM Interaction
F Espèce
F Sel
F Interaction
Lg.Tige
11439,2
20596,0
555,2
121,697***
219,111***
5,907***
D.Coll
6051,7
2732,7
114,2
19,932***
9,000***
0,376 NS
Nbr.Fll
3425,2
11918,6
317,0
32,291***
112,363***
2,988***
PS
6379,6
10101,6
279,3
42,478***
67,261***
1,860*
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| sample_17 | 0.8825 | arxiv | |
Scenario-based Optimization Models for Power Grid Resilience to Extreme Flooding Events
Ashutosh Shukla
Erhan Kutanoglu
John J Hasenbein
Scenario-based Optimization Models for Power Grid Resilience to Extreme Flooding Events
Graduate Program in Operations Research and Industrial Engineering The University of Texas at Austin, Austin, United Stateshurricanesstorm-surgestochastic programmingrobust optimization
We propose two scenario-based optimization models for power grid resilience decision making that integrate output from a hydrology model with a power flow model. The models are used to identify an optimal substation hardening strategy against potential flooding from storms for a given investment budget, which if implemented enhances the resilience of the power grid, minimizing the power demand that is shed. The same models can alternatively be used to determine the optimal budget that should be allocated for substation hardening when longterm forecasts of storm frequency and impact (specifically restoration times) are available. The two optimization models differ in terms of capturing risk attitude: one minimizes the average load shed for given scenario probabilities and the other minimizes the worst-case load shed without needing scenario probabilities. To demonstrate the efficacy of the proposed models, we further develop a case study for the Texas Gulf Coast using storm surge maps developed by the National Oceanic and Atmospheric Administration and a synthetic power grid for the state of Texas developed as part of an ARPA-E project. For a reasonable choice of parameters, we show that a scenario-based representation of uncertainty can offer a significant improvement in minimizing load shed as compared to using point estimates or average flood values. We further show that when the available investment budget is relatively high, solutions that minimize the worst-case load shed can offer several advantages as compared to solutions obtained from minimizing the average load shed. Lastly, we show that even for relatively low values of load loss and short post-hurricane power restoration times, it is optimal to make significant investments in substation hardening to deal with the storm surge considered in the NOAA flood scenarios.
Introduction
In the past few years, hurricanes and tropical storms have caused significant damage to critical infrastructures such as transportation systems, healthcare services, and the power grid. Hurricanes Maria, Irma, and Harvey together cost nearly $265B which was more than 85% of total weatherrelated disaster costs in the U.S. in 2017 [1]. Harvey became not only the longest-lasting hurricane with a record level of rainfall but also the costliest at $130B, part of which was due to power outages.
Harvey damaged 90+ substations, downed 800+ transmission assets, 6000+ distribution poles, and 800+ miles of power lines, with a peak power generation loss of 11GW, affecting over 2 million people. It took 2 weeks and 12,000 crew members to restore power [2].
The power grid is impacted by hurricanes and tropical storms primarily due to strong winds and flooding. To address this, a vast body of research that examines the effect of wind fields on transmission lines and towers has been developed. However, to the best of our knowledge, the literature is quite scant on the models that assess the impact of flooding. At the same time, the cost of such disasters has increased in states like Texas which is exposed to the Atlantic basin through the Gulf of Mexico. Moreover, recent studies suggest that we are likely to see more frequent and intense hurricanes in the near future [3]. In response to this, some utilities have employed on-site meteorologists which they have reported to be beneficial [2]. These meteorologists localize the predictions to obtain flood estimates for the region of interest. The estimates are then used to determine the resources needed for forecasted damage and post-storm recovery. To further improve this decision-making process, we present an end-to-end scenario-based optimization approach that integrates the output from a predictive geoscience-based flood model with a power flow model to recommend a plan for substation hardening to relieve the flood impacts of the potential storms.
While doing so, the scenario-based approach accounts for the uncertainty associated with storms and their flood forecasts.
Specifically, we propose two scenario-based optimization models (stochastic and robust) for grid resilience decision making under uncertainty. The choice of the model to be used for decisionmaking depends on the available information about the uncertain parameters which in our case are the flood levels at substations in a flood scenario. We show how the proposed models can be used to identify the substations that should be protected and to what extent. We further explain how the same models can be used for deciding the optimal budget that should be allocated for substation hardening to minimize the expected total disaster management cost. The aforementioned features of the models can help power utilities and grid operators address their concerns like the unpredictable nature of the load loss, the potential for substation flooding, and the potential reduction in generator output due to loss of load as outlined in [2].
The rest of the article is organized as follows. Section 2 presents a review of the literature on power grid resilience, particularly from a modeling and decision making viewpoint. Section 3 presents the overview of the proposed models followed by the notation, assumptions, mathematical formulation, and a brief discussion on the characteristics of the models. Section 4 is dedicated to the development of a case study for the Texas Gulf Coast and Section 5 is to the discussion of the results. We conclude with directions for future research in Section 6.
Literature Review
Power grid resilience to extreme events like cyber-attacks and natural disasters has been a topic of intense research in the past few years [4]. This includes studies focused on developing resilience metrics, methodological frameworks to enhance power grid resilience, and approaches to risk analysis [5,6,7]. In addition, several mathematical models have been developed to aid decision-making in different stages of the power grid resilience management cycle. These models can be categorized based on the planning phase they are developed for: mitigation, preparedness, response, and recovery. Using the flood as an extreme event that the resilience models are designed to respond to, the mitigation decisions are about the permanent hardening of the grid components, re-design of the grid through the introduction of new substations/transmission lines, installation of backup generation, etc. These decisions are made well before the start of the hurricane season when limited information about upcoming hurricanes is available. Similarly, before an imminent hurricane, during the preparedness phase, one has to make decisions about where to install temporary flood barriers like Tiger Dams™ , where to deploy mobile substations to quickly recover damaged substations, and what part of the grid to disconnect to avoid fatal accidents due to the collapse of power lines.
In both the mitigation and preparation phases, decision-makers face significant uncertainty about storm characteristics like path, intensity, forward speed, and precipitation. The decision-making in the response and recovery phase, on the other hand, is not plagued by weather uncertainty. Since this paper focuses on decision-making under weather uncertainty, we limit the review's focus to models that aid decision-making during the mitigation and preparedness phases.
Models for both the mitigation and preparedness phases can be broadly categorized into two groups: (1) machine learning-based and (2) optimization-based. In the case of machine learningbased models, the focus is on prediction, not decision making. For example, a machine learningbased model may predict metrics of interest such as the number of outages, outage duration, etc., for an upcoming hurricane [8,9,10]. However, decision making based on these predictions, like which substations to protect and how to reconfigure the power grid network to minimize load shed, are not typically considered within the model. Optimization-based models leverage predictions for decision making. To do so, the predictions with associated uncertainty are represented using scenarios. The decision-making model is then coupled with these scenarios. The models that we propose in this study belong to the class of optimization-based models. In the subsequent paragraphs, we survey the key characteristics of some of these models and highlight their differences from what we propose.
The optimization models generally consist of two components: uncertainty quantification and decision modeling. To quantify uncertainty about the weather, we first generate a set of scenarios using various kinds of models, such as machine learning-based models, physics-based models, and expert opinions. Then, irrespective of how the scenarios are generated, the decision-making model considers the impacts on the grid under each scenario to recommend decisions that minimize a certain risk measure. The models we review in this subsection are based on different ways the aforementioned components of the optimization model can be developed. In particular, we review various methods of generating representative scenarios and incorporating them into alternative decision making models.
Scenario generation
Scenario generation is one of the most common uncertainty quantification methods for extreme weather. We divide scenario generation techniques into four categories. The first is based on fragility curves. The curve represents the failure probability of a component as a function of some loading parameter. For example, fragility curves for transmission towers have been developed with respect to wind speeds. Such curves have been used in various power grid resilience decision making studies [11,12]. The second is based on statistical methods. For example, in [13], the authors use historical hurricane and tropical storm data for developing a baseline scenario. The alternative scenarios are then developed by altering parameters from the historical data to simulate plausible climate-induced changes to storm behavior. In [14], the path and the wind field of typhoons are simulated using Monte Carlo sampling to quantify the spatio-temporal impacts of wind speed on the transmission line status. In addition to wind and flooding, winter storms in Texas, such as Uri of 2021, have propelled research in power grid resilience to extreme cold events. For example, in [15], the authors have developed a statistical model where they incorporate historical outage data to generate scenarios of generator outages due to extreme cold events. The third set of methods is based on physics-based hydrological models. Two such models, called WRF-Hydro and SLOSH, are used in [16,17] to generate flooding scenarios. In [18], the authors use physics-based climate models to evaluate the resilience of levee-protected electric power networks with the primary focus on performance degradation. The fourth category is based on combinatorial criteria like N − k. In this case, each scenario represents a way in which k out of N components can fail. A model based on this criterion is used in [19].
Decision modeling
Several optimization models have been developed for power grid resilience decision-making against extreme weather events. These include models that can aid in decision-making about the upgrade of the power grid network through a combination of hardening existing components, adding redundant lines, switches, generators, and transformers [14,19,20]. However, hardening large parts of the power grid can be financially infeasible. In such a scenario, stockpiling power grid components in strategic locations enhances resilience by expediting network restoration after the disaster. To decide how stockpiling of components should be done, Coffrin et al. [21] developed a two-stage stochastic mixed-integer program where the first-stage discrete decisions are about stockpiling power grid components and the second-stage decisions are about how to operate the power grid to minimize load-shed. Additionally, network reconfiguration before an imminent hurricane can also enhance resilience. The models proposed in [12] make such decisions using grid islanding techniques. However, none of these models have explicitly focused on assessing the impact of flooding on the power grid. On the other hand, there are several studies that assess the impact of flooding on other critical infrastructures. For example, Kim et al. [16] present a framework and a case study using hurricane Harvey to generate physics-based (hydrological) flood scenarios. These scenarios are then used for resilience decision-making for healthcare infrastructure in [22]. Scenarios generated from physicsbased models have also been used in [23] that developed a model to estimate the overall disaster cost due to physical damage loss, income losses, and inventory losses. In comparison, our proposed models are explicitly geared towards resilience decision-making for the power grid and have a power flow model nested within a larger substation hardening model.
The models closest to ours are [17] and [24]. [17] uses a set of scenarios all based on Hurricane Harvey run on a hydrology model focusing on inland flooding. We instead consider a wider range of storms and storm characteristics and scenarios that are based on NOAA's storm surge simulations. Mohadese et al. [24] propose a stochastic optimization model for identifying and protecting substations a day before the anticipated flooding event, meaning a focus on preparedness. Here, our proposed models differ in several ways. First, we generate scenarios using outputs from physicsbased hydrological models to create flood maps for the region of interest. Our choice is based on the rationale that physics-based models represent flood levels across the region of interest such that they are correlated in space and time. Mohadese et al. [24] have not considered the impact of correlated flooding. They also assume that a substation will transmit power if it is not flooded. In reality, this may not be true due to the network effects and we embed a power flow model within our larger resilience optimization model to address such effects. Finally, our models focus on long-term decision making, highlighting mitigation-phase budgeting and decision making.
Modeling
In this section, we first present an overview of the stochastic and robust optimization models developed to assist in grid resilience decision-making against extreme flooding events. Next, we state the key assumptions, introduce the notation and provide detailed mathematical formulations. Finally, we highlight some of the key characteristics of the proposed models and explain how they can be used to address a wide variety of questions in grid resilience decision-making. We highlight that the models proposed in subsection 3.4 and 3.5 are developed to minimize a risk measure over the load shed for a single flood event. In subsection 3.6, we explain how the same models can be leveraged for multi-year planning. we represent the uncertainty in the meteorological forecasts using a set of hurricane parameters (Hurricane 1, . . . , n). In the next step, using the aforementioned parameters as input, we run a hydrological model to get the corresponding flood maps. The flood maps are then used as input to the two-stage decision-making models. The final output from the decision-making models is a plan for substation hardening. Decision making in both models occurs in two stages. Here we specify first-stage decisions that determine which substations to harden and to what extent. We assume that the substation hardening measures are taken during the mitigation phase of the power grid resilience management cycle. Consequently, the decisions made using the model are not a response to any particular imminent hurricane. Instead, they are intended to harden the grid against multiple hurricanes potentially occurring over multiple years and minimize the long-term disaster costs incurred due to flooding. One such mitigation measure for substation hardening is to build permanent protective structures like walls around the substation periphery as shown in Figure 2.
Overview of the proposed models
After we make the first-stage decisions, we assess their performance in dealing with the flood levels in the second stage. The second-stage assessment involves minimization of the load shed in multiple flood scenarios that may impact the power grid during the multi-year planning horizon.
Assumptions
In the proposed models, we make the following assumptions. The first assumption is that a DCbased power flow approximation is acceptable. For a detailed explanation and derivation of the DC power flow equations from the AC equations, we refer to [25]. This approximation has been widely used and is embedded within larger strategic decision-making problems such as long-term capacity planning and operation of wholesale electricity grids. For the kind of models proposed in this paper, a detailed discussion on the difference in the quality of solutions obtained from different power flow approximation models is given in [26]. The second assumption is that we can model the substation hardening cost with fixed and variable components. The fixed cost is incurred when a substation is chosen for hardening. It can represent the cost of building the foundation on which the protective structure is built. Furthermore, it can also include the costs associated with transporting construction resources to the substation site. The variable cost, on the other hand, is a function of the height of flooding to which the substation is made resilient. In our case, we assume that the variable cost linearly depends on height. This is reasonable when we build wall-like structures to protect substations, as shown in Figure 2. Third, we assume that each substation's hardening and flood levels are discrete and finite. In the proposed formulations, they are assumed to be nonnegative integers. Fourth, we assume that all the flooded substations within the network experience the same downtime and are recovered simultaneously. Lastly, we assume that the value of load loss can be quantified in dollars per hour.
Notation
The proposed models use the following notation. Note that all the cost parameters used in the models are in dollars and all power grid parameters are in the per-unit system. Notation not defined in this section and appearing later in the text is defined as introduced.
Stochastic Optimization Model
The two-stage stochastic optimization model (SO) is expressed as:
L * SO = min x∈X L SO (x),(1a)
where
L SO (x) = k∈K p k L(x, k). (1b)
The objective function in (1a) minimizes the expected unsatisfied power demand (load shed) over the scenarios in set K. Here, X represents the set of feasible first-stage decisions. The following constraints define the set:
i∈I f f i y i + v i x i ≤ I,(2a)x i ≤ H i y i , ∀i ∈ I f .(2b)
Note that the variables x i and y i are defined only for substations that are flooded in at least one scenario. Constraint (2a) enforces that the sum of the fixed and variable costs incurred due to substation hardening does not exceed the investment budget. Constraints (2b) place an upper bound on the extent of flooding to which the substation can be made resilient while linking variables
x i and y i for each substation i. Such constraints represent engineering and practical challenges that may arise while building protective structures that are too tall.
In (1b), L SO (x) represents the expected load shed when the first-stage decision is x. Here, p k represents the probability of scenario k and L(x, k) is the recourse function representing the minimum load shed when the first-stage decision is x and scenario k is realized. The recourse function is defined as follows:
L(x, k) = minimize j∈J D j − s j ,(3a)
subject to
(1 − z j )M ≥ ∆ θ(j)k − x θ(j) , ∀j : θ(j) ∈ I f , (3b) 2z j M ≥ 1 − 2(∆ θ(j)k − x θ(j) ), ∀j : θ(j) ∈ I f ,(3c)z j = 1, ∀j : θ(j) ∈ I \ I f , (3d) u j ≤ z j , ∀j ∈ J ,(3e)s j ≤ z j D j , ∀j ∈ J , (3f) u j G j ≤ g j ≤ u j G j , ∀j ∈ J , (3g) − z λ(r) F r ≤ e r ≤ z λ(r) F r , ∀r ∈ R, (3h) − z µ(r) F r ≤ e r ≤ z µ(r) F r , ∀r ∈ R, (3i) B r (α λ(r) − α µ(r) ) ≥ M (z λ(r) + z µ(r) ) − 2M + e r , ∀r ∈ R, (3j) B r (α λ(r) − α µ(r) ) ≤ −M (z λ(r) + z µ(r) ) + 2M + e r , ∀r ∈ R, (3k) r∈N out j e r − r∈N in j e r = g j − s j , ∀j ∈ J, (3l) − π ≤ α j ≤ π, ∀j ∈ J ,(3m)α β = 0. (3n)
The objective function in (3a) minimizes the unsatisfied power demand when the first-stage decision is x and the flood scenario realized is k. Constraints (3b) and (3c) link the first-stage substation hardening decisions to the second-stage scenario-dependent power flow decisions. For a given hardening decision at a substation, the provided protection level is compared against the flood height at that substation in a given scenario. Depending on whether the hardening level can withstand the flooding, we set the status of the corresponding bus as operational or not. This is indicated by variable z j . For the substations that are not flooded in any of the scenarios, the status of the corresponding buses is set to operational in constraints (3d).
Constraints (3e) capture generator dispatch decisions for operational generators. When z j = 0, we cannot inject power to the network through bus j and therefore set u j = 0. If z j = 1, we let the recourse problem decide if power generated at bus j should be used or not. Constraints (3f) place an upper bound on the amount of power that can be supplied at bus j (which is the demand at that bus). If bus j is flooded, then z j = 0 and no power can be supplied to the loads that are connected to the bus. Constraints (3g) place upper and lower bounds on the amount of power that can be generated at bus j. If bus j is flooded, then u j = 0 and thus g j = 0. If on the other hand bus j is not flooded, the model solves the recourse problem which is a binary linear program to determine the amount of power that should be generated at bus j. Constraints
Robust optimization model
In the two-stage robust optimization model (RO), we minimize the maximum unsatisfied power demand value across all scenarios. Mathematically, the problem can be stated as follows:
L * RO = min x∈X L RO (x),(4a)
where
L RO (x) = max k∈K L(x, k).(4b)
The expression in (4b) finds the maximum scenario-based load shed via a max(·) function. RO in (4a) can be reformulated as
min x∈X {τ : τ ≥ L(x, k) ∀ k ∈ K} ,(5)
where τ is an epigraphical variable.
Model Discussion
In this section, we highlight some of the key characteristics of the models proposed above. This leads us to a feasible solution with no power generation and maximum load shed.
Second, the proposed models can be further tightened based on some simple observations. To do so, we first compute the maximum flood level across all the scenarios for the flooded substations.
Let us represent this value using parameter W i , ∀ i ∈ I f . Next, we observe that the model need not harden any substation to flood height that is higher than W i . Therefore, in constraints (2b), we
can replace H i with min(H i , W i ), ∀i ∈ I f . Constraints (3b) and (3c) use the big-M method. Here, we need to determine the smallest value for M for each constraint. The smallest big-M value for constraints (3b) and (3c) is given by W θ(j) and min(H θ(j) , W θ(j) ) + 0.5, respectively. To verify this, recall the assumption that both the flood height and hardening level can only take non-negative integer values. Also, observe that
− min(H θ(j) , W θ(j) ) ≤ ∆ θ(j)k − x θ(j) ≤ W θ(j) .
Now, in constraints (3b), we need
∆ θ(j)k −x θ(j) M ≤ 1. The smallest value of M that ensures this is W θ(j) .
Similarly, in constraints (3c), we need
1−2(∆ θ(j)k −x θ(j) ) 2M ≤ 1.
The smallest value of M to achieve this is min(H i , W i ) + 0.5. Finally, we can also tighten constraints (3j) and (3k). For both sets of constraints, the smallest value of M is F r + 2πB r .
Third, both SO and RO can be used for hardening decisions that will provide flood mitigation over a planning horizon. To see how, notice that the objective function in the SO computes the expected load shed for a single flood event. However, substation hardening in practice is done over the planning horizon that lasts multiple hurricane seasons and provides permanent protection for multiple flood events. Therefore, to help make hardening decisions that impact performance over multiple events, we first need to compute the disaster management costs due to load shedding over the multi-year planning horizon. To do so, let us assume that the expected number of hurricanes that the study region experiences during the planning horizon is γ. We further assume that during the planning horizon, the total recovery, economic and social costs are represented by the value of load loss of $δ/megawatt-hour. Finally, we assume that it takes h hours to repair all the substations (and restore power to normal operation) starting immediately after a flood event. We believe this assumption is reasonable at the mitigation phase of the decision making process and avoids explicit and detailed modeling of the recovery process. Then, for a given investment budget, the substation hardening decisions that achieve the minimum expected total disaster management cost due to load shedding during the planning horizon is found by solving
DM SO = γhδ L * SO .(6)
In (6), the optimal substation hardening plan to minimize DM SO is the same as the plan obtained by solving SO. This is because the DM SO always equals the objective function of the SO multiplied by a positive constant. Therefore, irrespective of how the frequency of hurricanes, the restoration time, and the value of load loss change over time, the optimal substation hardening plan remains the same as the one obtained from SO. In this case, we assume that the probability distribution over the flood scenarios, and thus, the hurricanes causing them, does not significantly change over time. In practice, this is reasonable for planning horizons for which substation hardening is considered (5-10 years). Similarly, the optimal substation hardening decision that minimizes the maximum total disaster management cost due to load shedding during the planning horizon is found by solving
DM RO = γhδ L * RO .(7)
A key observation is that DM RO provides an upper-bound for DM SO . To understand why, note that the set of feasible first-stage solutions is same for both SO and RO. Further, observe that both the models are bounded below with a minimum objective value of zero and have relatively complete recourse. Now, let x R be a feasible solution to RO. Then,
L * SO = min x∈X L SO (x) (8a) ≤ L SO (x R ) (8b) = k∈K p k L(x R , k) (8c) ≤ k∈K p k max k∈K L(x R , k) (8d) = max k∈K L(x R , k) k∈K p k (8e) = max k∈K L(x R , k) (8f) = L RO (x R ).(8g)
with Equation (8b) holding at equality if and only if x R is optimal for SO and Equation (8d) Finally, in the models proposed so far, we assume that we have a predetermined budget for substation hardening. One may however be interested in determining the optimal budget allocation for minimizing a risk measure over the disaster cost incurred due to both load shedding and substation hardening. The proposed models can easily be modified to find the optimal budget for substation hardening and corresponding hardening decisions. In the case of SO, this can be done by solving
T DM SO = min ω k∈K p k L(x, k) + i∈I f f i y i + v i x i : x i ≤ H i y i , ∀i ∈ I f ,(9)
where ω = γhδ. The value of i∈I f f i y i + v i x i in the optimal solution represents the value of the optimal investment budget. Similarly, for RO, we compute the optimal investment budget by
solving T DM RO = min ωτ + i∈I f f i y i + v i x i : τ ≥ L(x, k) ∀ k ∈ K .(10)
Case Study
In this section, using a case study for the Texas coastal region, we show how the proposed models can be used for power grid resilience decision making. The two main inputs to the proposed models are a set of scenarios that represent flood profiles for different hurricane types and the network parameters for the DC power flow model. To represent flood profiles, we use storm-surge maps developed by the National Oceanic and Atmospheric Administration (NOAA) [27]. For the electric grid, we use the ACTIVSg2000 dataset developed as part of an ARPA-E project [28]. The details of each component are described in the following subsections. We further highlight that although we use the proposed models for storm surge-induced damages, they can be adopted for flooding of any kind as long as the corresponding flood scenarios are available. This could include scenarios for inland flooding as developed in [16] and used for infrastructure resilience problems in [17] and [22].
Lastly, to solve the various parameterizations of the proposed models discussed in this case study, we use the Gurobi solver with the barrier algorithm [29]. Within the solver, we set the MIP-gap threshold to 0.5 percent and limit the solve time to 6 hours. The model is solved on an Apple M1 pro machine with 16 GB of unified memory.
Flood Scenarios
We use the storm-surge maps developed by NOAA using the Sea, Lake, and Overland Surges from Hurricanes (SLOSH) model as flood scenarios. To generate these flood maps, SLOSH uses a simplified parametric wind field model that takes as input the following parameters: storm track, the radius of the maximum wind speeds, and the pressure differential between the storm's central pressure and the ambient pressure. The simulated wind fields are then used to compute surface stresses on the water beneath the hurricane. Finally, the induced stress on the surface of the water is used to determine the storm surge. For a detailed discussion on SLOSH, we refer to [30].
Simulation studies developed using SLOSH have been extensively used to assist agencies like the In addition to real-time storm-surge guidance for imminent hurricanes, NOAA has developed two composite products, Maximum Envelopes of Water (MEOW) and Maximum of the MEOWs (MOM), to provide manageable datasets for medium to long-term hurricane evacuation planning.
To develop these datasets, hurricane simulations with different combinations of intensity, forward speed, direction, and tide levels are run in parallel using SLOSH for the region of interest. Each run may yield different storm surge values for the same grid cell. A maximum overall such value is taken to represent the MEOW value of that grid cell. The same process is repeated for each grid cell within the study region to construct a MEOW map. The resolution of the grid cell is varied to balance accuracy with computation cost. It is finer in regions close to the coast and gets coarser as we move farther away in the ocean. MEOW maps are used to incorporate the uncertainties associated with a given forecast and eliminate the possibility that a critical storm track will be missed in which extreme storm surge values are generated. These maps are generated from several thousand SLOSH runs. In this study, we use the MEOW maps to represent flooding due to storm
surge. An example MEOW map is shown in Figure 3.
Within a MEOW map, it is possible that the water level for adjacent cells may come from different SLOSH runs of specific simulated storms. Nevertheless, since these are the maximum water levels over multiple tracks, we can be assured that if we have hardened a substation for a particular MEOW map, it will provide resilience towards flooding for any of the parallel runs that constitute the MEOW map. Arguably, MEOW maps are still better at representing flood uncertainty than other scenario generation methods where flooding at different nodes within a network is considered independent of each other. Moreover, these MEOW maps have been considered as scenarios in different stochastic optimization models for patient evacuation [16] and grid hardening [31]. before, we assume that in the mitigation phase, the decision-maker does not have information on any specific storm. Therefore, to model the uncertainty in the mitigation phase, we assume that all the remaining MEOW maps are representative of the flooding scenarios. In our case, they are considered equally likely for the stochastic model. This is based on the premise that the larger set of simulations that produced the MEOW maps were sampled according to some underlying distribution and therefore already reflects the underlying characteristics of the distribution implicitly used by NOAA in their development of the MEOW product. Furthermore, these MEOW maps provide us with the storm-surge flood height above ground at each of the substations (and thus for buses within) in the power grid network. In the proposed models, this is represented by ∆ ik ; the level of flooding at substation i in scenario k.
Power Grid
To model the power grid for the state of Texas, we use the synthetic grid called ACTIVSg2000 which contains 2000 buses (within 1250 substations) and 3206 branches. The grid, though synthetic, is designed such that it maintains statistical similarities with the actual Texas grid. We make two further modifications to the grid instance to make it computationally tractable while also considering the coastal part of the grid which is affected due to to storm-surge and thus is the focus of the study.
First, we perform a network reduction on the original grid instance using the electrical equivalent (EEQV) feature in PSS®E to focus on the grid components subject to storm surge flooding. The reduction is such that the buses in the inland region that are not exposed to storm-surge induced flooding are aggregated within a much smaller set of nodes. The part of the grid that is in close proximity to the Texas Gulf Coast, and therefore is prone to flooding due to storm-surge, is retained almost as is. The effect of the network reduction is detailed in Table 1. The topological changes are visualized in Figure 4. Second, we alter the locations of some of the substations. This is because, in
Results and Discussion
In this section, we first determine the expected value of perfect information from a model that can produce perfect forecasts. In the same subsection, we compute the value of the stochastic solution for the different budget levels. Next, in subsection 5.2 we show how the proposed model can be used to determine the optimal investment budget for substation hardening.
Due to dynamically changing climate conditions and ocean temperature, the probabilities of different types of hurricanes can change over time. In subsection 5.3, we show when a decisionmaker can take advantage of using solutions from RO to hedge against this uncertainty by paying a relatively insignificant premium. Finally, the last subsection is dedicated to the analysis of the distribution of load shed across scenarios for the solutions obtained from SO and RO.
The Values of Stochastic Solution and Perfect Information
In the proposed two-stage decision-making models, both the number of variables and constraints grow linearly with the number of scenarios; thus making it computationally challenging. In that case, instead of solving SO for large grid instances with many scenarios, one may be interested in solving simpler versions of the problem. One approach could be to reduce the size of the problem by constructing a single scenario problem where the flood height at each substation is the average of the flood height across all the scenarios. Another way could be to solve the problem for each scenario individually. The first-stage solutions thus obtained can then be analyzed and potentially combined using some heuristic rule. In this section, we analyze the quality of the solutions we get using such approaches. To do so, we use two widely known concepts in the stochastic programming literature: the value of the stochastic solution and the expected value of perfect information.
In Figure 5, we plot the value of L * SO as a function of the investment budget. To determine the budget levels on which the parametric study should be performed, we first compute the minimum budget such that L * SO = 0. This is computed by solving a slightly modified version of SO. Specifically, we first remove constraint (2a) from the formulation and replace the objective function with the minimization of the substation hardening expenditure (i.e., the left-hand-side of (2a)). We also force full satisfaction of demand by replacing constraint (3f) with s j = D j , ∀ j ∈ J . The optimal value to this modified version of SO is in turn the minimum hardening budget required for zero load shed. For the parameters assumed in this case study, the corresponding minimum budget turns out to be $71.35M. Any additional budget beyond this will not improve the objective function value (load shed) and therefore the corresponding optimal solution. Using $71.35M as the reference, in Figure 5, we increase the budget from $0M, in increments of $10M, until the value exceeds $71.35M.
(We note that the same budget values can be used for the RO parametric study. This is because the minimum budget required to achieve the expected load shed of zero is the same as what is required to achieve zero load shed in all the scenarios.)
In addition to computing L * SO for different budget levels, we also compute lower and upper bounds on this value as shown in Figure 5. To compute the upper bound, let us first consider a single-scenario problem called the expected value problem which is defined as
L * EV = min x∈X L(x,k).(11)
Here,k represents a scenario where the flood level at each substation is the mean of the flood heights at that particular substation across all the scenarios. The optimal solution to this problem is called Next, to evaluate the quality of the first-stage substation hardening decisions obtained by solving (11), we compute the expected load shed across all the scenarios by fixing the first-stage decisions tox, denoted by L SO (x). This value serves as an upper bound on L * SO . For a detailed explanation on this, we refer to [33]. We also observe in Figure 5 that the difference between L SO (x) and L * SO increases with an increase in the budget. We refer to this difference as the value of the stochastic solution (VSS) as it represents the value of using a scenario-based representation of the uncertainty as opposed to the average flood values, all calculated within the SO framework. We further highlight that whenx is implemented, the load shed does not strictly decrease with an increase in the budget beyond $50M. This is expected because, for the mean scenario, the model obtains zero load shed with $50.15M. As discussed before, we know that it takes a minimum of $71.35M to achieve zero load shed across all the scenarios. However, once the model achieves zero load shed in the mean scenario, there is no incentive to use additional resources. This also shows that the value of using SO over the expected value problem increases with increases in the investment budget.
To compute a lower bound on L * SO for a given budget level, we assume that the decision-maker has access to perfect information about the flood levels, and therefore can better prepare for each scenario (i.e., in a way, fine-tuning the mitigation plan according to each scenario). That is, perfect information allows the decision maker to make possibly different substation hardening decisions in each scenario to minimize the load shed in that particular scenario. These solutions are referred to as wait-and-see solutions. In this case, we compute
L * WS = k∈K p k min x∈X L(x, k) ,(12)
where the first-stage decisions are scenario-dependent and the value L * WS is referred to as the waitand-see bound. Due to the scenario-specific mitigation decisions, L * WS provides a lower bound on L * SO . The difference in the values L * SO and L * WS is referred to as the expected value of perfect information. It represents the maximum value a decision-maker would be willing to pay in exchange for complete and accurate information about the uncertainty.
The key point that we want to emphasize is that unless the flood model can make perfect predictions, which is usually not the case with the weather models, then not accounting for uncertainty and using just point estimates or mean values of the flood forecasts can lead to significantly inferior decisions. This is evident from the VSS. In fact, as it turns out in this case, the first-stage decisions obtained from SO, even with not-so-perfect forecasts, lead to a load shed performance that is close to what we would get from using a flood model that offers perfect prediction. To put it another way, accounting for flood uncertainty, even with a small number of scenarios, can help reduce the burden of getting perfect information on the decision-maker without making a significant compromise on the performance.
We also note that all bounds converge to the same expected value at the zero budget. This is because, no matter how well we represent the uncertainty or how good the predictions are, if we do not have any resources to use towards mitigation in the first stage, we cannot prevent load shed in the second stage with no protection towards flooding. Then, the expected value of the load shed is only a function of the second-stage decisions (i.e., the best power flow the grid can deliver with flooded substations). Moreover, at a sufficiently high budget value, both L * SO and L * WS converge to zero. This is expected because, despite the fact that we have poor predictions or poor uncertainty representation, we can still prevent any load shed in all the scenarios if we have enough resources to harden all substations to any desirable extent. Performing analysis with the budget level as a parameter, as described in this subsection, requires repeatedly solving SO with different parameters and can be time-consuming. To address this, the property that SO has relatively complete recourse is exploited to warm start the optimization solver and improve the solution time. As was stated in subsection 3.6, we can heuristically generate an initial feasible solution with a hundred percent load shedding for an investment budget value of zero. Once we get an optimal solution corresponding to budget level zero, we use it to warm start the solver for the next higher budget level. The process is repeated to generate high-quality feasible solutions for the next budget level. We further note that the aforementioned approach for warm-starting the solver is also applicable in the case of RO.
Determining optimal budget for substation hardening
Subsection 5.1 focuses on demonstrating how SO is used for resilience decision making for a given investment budget for substation hardening. The models can alternatively be used to decide the optimal value of the investment budget that minimizes the expected total disaster management cost over a multi-year planning horizon. To demonstrate this, we solve T DM SO as described in Section 3.6 assuming that, on average, 10 hurricanes hit the Texas Gulf Coast during the planning horizon. The values of the expected total disaster management cost for different combinations of restoration times and the value of load loss are plotted in Figure 7. As we see in the figure, when the value of load loss is low and the restoration time is short ($250 and 6 hours, respectively), the total disaster management cost is relatively low. Furthermore, the model recommends investing only a quarter of the budget required to achieve zero load shed for substation hardening. This is because the cost associated with losing power is quite low and the outage is restored relatively quickly. On the other hand, when both the load loss value and restoration time are high ($5000 and 48 hours, respectively), the model recommends investing $71.35M (equal to the investment required to achieve zero load shed) for substation hardening, avoiding any costs due to load loss. This is because, for the chosen values, the costs associated with power loss are quite high and it is better to make Texas, the value of load loss was determined to be around $6000 per MWh for Texas [34]. If we take that as given, the results in Figure 7 suggest that we must make investments to achieve close to zero load shed even if restoration time is as short as 6 hours.
We further observe in Figure 7 that the solution corresponding to the value of load loss of $1000 per MWh and restoration time of 6 hours is the same as the solution with the value of load loss of $250 per MWh and a restoration time of 24 hours. This is expected because in T DM SO , both sets of parameters lead to the same optimization problem (ω is the same). It is further apparent that the optimal investment budget for substation hardening increases monotonically from 0 to $71.35M with the increase in the value of ω. Therefore, for any investment budget value between 0 and $71.35M, there exists a unique ω for which the corresponding budget is optimal. We can use this insight to quickly approximate the optimal investment budget for any combination of the value of load loss, restoration time, and the average number of hurricanes that may hit the region of study during the planning horizon. To do so, we use only the values of L * SO for I ∈ {0, 10, 20...80} as computed in Section 5.1. For any given value of γ, h, and δ for which the optimal investment budget needs to be approximated, we compute the value of DM SO + I for each I ∈ {0, 10, 20...80}. The value of I for which DM SO + I is the smallest is the best approximation for the optimal investment budget for a chosen value ω (calculated from γ, h, and δ). In Figure 8, we show the value of DM SO + I for I ∈ {0, 10, 20...80} for different values of ω. The depicted values of ω are reasonable in the sense that they can be derived from the γ, h, and δ used in Figure 7. For example, we notice in Figure 7 that when γ = 10, h = 6, and δ = 250 (ω = 15000), the optimal investment budget is $17.05M. An approximate of this value can be quickly inferred by looking at Figure 8 for the value of ω = 15000.
Optimization in the face of uncertain probabilities
While framing the power-grid resilience decision-making problem as a two-stage stochastic program, we assume that the probability distribution over the scenarios is known. However, the probabilities that we assign to each scenario need not be constant with time. Changing climate oscillations and ocean temperatures routinely affect these probabilities. This is reflected in NOAA's annual hurricane season prediction categories: normal, above normal, and below normal. In this case, if probabilities over scenarios change as compared to what we planned for, the expected performance may deteriorate. To hedge against this, we recommend solving RO and comparing the expected performance of the corresponding decisions. If the difference in the expected performance of decisions recommended by RO and SO is not significant, we advise adopting decisions as recommended by RO. In this way, irrespective of how the probabilities evolve with time, we know that the expected total cost due to the load loss will be less than or equal to the bound obtained in Section 3.6 if the optimal first-stage decisions as recommended by RO are adopted. This can be confirmed for the parameters assumed in the case study through Figure 6. The robust solution refers to the value of the expected load shed when the first-stage hardening decisions as recommended by RO are adopted. Since these decisions are not necessarily optimal for the assumed probability distribution, they lead to a higher expected load shed as compared to the stochastic solution. However, for the RO first-stage decisions, the maximum load shed in any scenario is capped by τ as represented by the red curve. In this case, we observe that the difference in the expected value of performance is almost trivial for investment budget values of $40M and above. Therefore, in those cases, it makes sense to adopt decisions recommended by RO as opposed to what we get from SO to hedge against the change in probabilities due to factors like ocean temperature and climate oscillations. In cases when the difference between the expected performance of SO and RO is significant, the decisions depend on the risk preference of the decision-maker.
SO vs RO: Analysis of the load shed distribution
We conclude the discussion with an analysis of the distribution of the load shed across scenarios for both SO and RO. The load shed in each scenario for both models is represented by the value of the recourse function corresponding to the optimal solution. These values are used to construct the corresponding histogram for both SO and RO at different budget levels as shown in Figure 9.
As expected, the histograms shift to the left with the increase in the budget for both SO and RO.
We observe that the histograms for both SO and RO coincide when the investment budget is $0M. This is expected because there is no hardening done in either model. Consequently, the load shed in each scenario is identical. Moreover, using Figure 6 and Figure 9, we observe that the robust solutions provide an inferior performance in expectation but the RO load shed remains relatively stable across scenarios as compared to SO. We also conclude that for investment budget values of more than $40M, the robust solutions offer much better performance against extreme scenarios while also offering good expected value performance. Therefore, in this case, it is reasonable to implement RO decisions for budget values beyond $40M. In this way, Figures 6 and 9 can be used together to understand the behavior of both SO and RO in expectation and across all the individual scenarios. Figure 9: The histograms of load shed across scenarios for the SO and RO solutions at different budget levels. Notice that the x-axis for each sub-plot has a different scale for better depiction.
Conclusions
In this study, we propose an integrated framework supported by two scenario-based optimization models for power grid resilience decision making against extreme flooding events. The models recommend an optimal substation hardening plan by integrating the predictions generated from a state-of-the-art hydrological model with a DC optimal power flow model. While doing so, we account for uncertainty in hurricane predictions using a scenario-based representation. Furthermore, using a case study for the state of Texas, specifically the coastal region prone to storm surge flooding, we demonstrate how the proposed models can together be used to address a wide variety of insightseeking questions related to power grid resilience decision making. Specifically, we show that using a scenario-based representation of flood uncertainty can offer significant value over mean flood forecasts. We also explain the advantages of using flood maps generated from physics-based models as opposed to other scenario generation methods popular in the literature. Furthermore, we show how can we estimate the expected value of perfect information from near-perfect flood forecasts.
For the case study developed in the paper, we observe that by using a scenario-based representation of uncertainty, the decision-makers can reduce their burden of having access to perfect forecasts.
In addition to quantifying the value of using flood scenarios, we further show how we can use the proposed two-stage framework to determine the optimal investment budget for substation hardening.
Lastly, we explain how we can use the two-stage robust optimization model for power-grid resilience decision making when information about the probability distribution over the flood scenarios is unavailable.
For future research, we suggest four directions. First is the development of scenarios that can consider precipitation-induced inland flooding in addition to storm-surge. Second is the development of methods to account for equity while making substation-hardening decisions. Third is developing models that take into account preparedness measures while making longer-term mitigation decisions, leading to three-stage optimization models. Fourth is the development of decomposition techniques to solve such models in a reasonable time. These challenges form the basis of our ongoing research.
A two-stage stochastic optimization model is developed to address situations where the uncertainty about hurricane-induced flooding is modeled using a probability distribution. In this case, the model minimizes the expected unsatisfied power demand (also referred to as the expected load shed) due to the components' failures (i.e., flooded substations) over a set of scenarios. The two-stage robust model on the other hand requires no information about the probability distribution. The model instead minimizes the maximum load shed in any scenario within the uncertainty set. A general framework representative of the proposed models is shown inFigure 1. As shown in the figure,
A scenario in the proposed models represents the water levels at different substations obtained from the flood map of a specific hurricane type. Hurricanes with different characteristics such as direction, intensity, forward speed, etc. lead to different levels of flooding, generating different scenarios. These scenarios are representative of the flooding that the region of study can experience
Figure 1 Figure 2 :
12An example permanent hardening structure at a substation over a specific time period (typically multiple years). A distinguishing feature of the proposed models is the way we generate the scenarios. Instead of using popular techniques like fragility curves, we use flood maps for scenario representation because they capture the effects of correlated flooding. This is important because the failure of a substation within a power grid can have network effects on the other parts of the grid. To account for such details, we need not only know which substations fail more frequently but also the combination of substations that fail together. Our proposed model accounts for these details and uses them to evaluate the effects of such damages (in the form of load shed) during decision-making by solving a power flow model.The power grid network considered in the proposed models is represented by a graph where the buses are represented by the nodes and the branches interconnecting the buses are represented by the edges of the graph. The branches of the network are held using the transmission towers. We assume that these towers are well above the ground and therefore immune to flooding. It is the substations and components within them that are susceptible to flooding. In this study, we assume that the substations are outdoor open-air facilities. Therefore, when a substation is flooded, we assume that all the components within the substation and the branches connected to all the buses within the substation are out of order.
For
each of these scenarios, we overlay the power grid network on the flood map to identify parts of the network that are flooded. Given the flood height and the level of hardening at a substation, the model infers if a substation is flooded in a particular scenario. If a substation is flooded, all the buses within the substation and the branches connected to those buses are considered to be out of order. Once the damaged state of the power grid network is determined, we solve the second-stage assessment (the so-called recourse problem) which is a DC power flow model to estimate the load shed given the state of the grid. The second-stage decisions in the recourse problem determine the routing of power to minimize unsatisfied power demand. It should be noted that although both the stochastic and robust models involve the same sets of decision variables, the specific solutions suggested by them can be vastly different. The robust model gives us the flexibility to make decisions in the absence of any information about the probability distribution. These decisions can however be far more conservative than the decisions recommended by the stochastic model.
Set of substations indexed by i I f : Set of substations that are flooded in at least one scenario J : Set of buses indexed by j K: Set of scenarios indexed by k R: Set of branches indexed by r B i : Set of buses at substation i N in j : Set of branches incident on bus j with power flowing into bus j N out j : Set of branches incident on bus j with power flowing out of bus j Parameters M : An arbitrarily large constant f i : Fixed cost of hardening at substation i v i : Variable cost of hardening at substation i H i : Maximum flood height to which substation i can be hardened θ(j): Substation that contains bus j ∆ ik : Flood height at substation i in scenario k (a non-negative integer value) B r : Susceptance of branch r F r : Maximum power that can flow in branch r λ(r), µ(r): Head bus and tail bus of branch r D j : Load at bus j G j , G j : Minimum and maximum generation at bus j β: Index of the reference bus p k : Probability of scenario k I: Total investment budget for substation hardening Variables y i : Binary variable indicating whether substation i is chosen for permanent hardening x i : Non-negative integer variable indicating discrete height of hardening at substation i z j : Binary variable indicating if bus j is operational s j : Non-negative real variable indicating load satisfied at bus j g j : Non-negative real variable indicating power generated at bus j u j : Binary variable indicating if generator at bus j is used α j : Real variable indicating voltage phase angle of bus j e r : Real variable indicating power flowing in branch r
(3h) and (3i) place restrictions on the amount of power that can flow through branch r. If the bus at either end of a branch is flooded, then no power can flow through it. On the other hand, if buses at both ends of the branch are operational, then a maximum of F r power can flow through it in either direction. Constraints (3j) and (3k) enforce an approximation to Ohm's Law. If both ends of a branch are operational, then the amount of power flowing in the branch is governed by equations B r (α λ(r) − α µ(r) ) = e r , ∀r ∈ R.If the bus at either end of the branch is flooded, then the above equation need not hold. This is achieved by introducing big-M values. The formulation can be further tightened by appropriately determining the values of big-M . A discussion on this is presented in Section 3.6. Constraints (3l) represent the flow balance which states that the net power injected into the network at bus j is the difference between the power generated and consumed at the same bus. Constraints (3m) impose limits on the phase angle values at buses. Finally, constraints (3n) set the phase angle of the reference/slack bus to 0.
First, both SO and RO have relatively complete recourse. That is, no matter what first-stage decisions we make, the second-stage problem always has a feasible solution. To verify this, consider a case where irrespective of the value of z j 's, we set the value of u j = 0 for all j in the recourse function.
holding at equality if and only if load shed values are equal across all the scenarios. The above inequalities establish that the objective function value corresponding to any feasible solution to RO provides an upper bound on the optimal objective function value of SO. Since any optimal solution to RO is also feasible, it acts as a valid upper bound. In fact, it is the tightest upper bound that can be obtained in this manner.
Figure 3 :
3A sample MEOW generated using category 5 storms approaching the Texas Gulf Coast in the north-west direction with a forward speed of 5 mph
Figure 4 :
4the original dataset, some of the substations are placed in the middle of a water body and are thus flooded by default. To address this, we remap the coordinates of the 1250 substations in the dataset with the coordinates of substations obtained from the Homeland Infrastructure Foundation-Level Data (HIFLD) Electric Substations dataset [32]. The HFILD dataset contains information about real-world substations across the U.S. The remapping is done by solving an optimization problem The figure shows (a) ACTIVSg2000 Synthetic Grid for Texas, and (b) the reduced grid obtained after performing the network reduction. The red elements represent the new nodes andbranches that were introduced as the artifacts of the reduction procedure to maintain equivalence in the grid characteristics that minimizes the total displacement due to remapping. Note that this process does not change the power grid's electrical structure and makes it more realistic using the real-world substation locations (closer to the actual Texas grid) and capturing their real-world flood risks via MEOW-based flood scenarios. Lastly, the fixed cost and the variable cost for substation hardening are assumed to be $25,000 and $100,000 per foot, respectively. These values are derived from various utility reports.
Figure 5 :Figure 6 :
56The graph of the expected load shed values for the expected value solution (green), the stochastic solution (blue), and the wait-and-see solution (orange), as a function of the budget for substation hardening The objective function value for RO (i.e., the optimal maximum load shed) and the expected load shed values for the robust and the stochastic solutions as a function of budget for substation hardening the expected value solution or the mean value solution, henceforth represented byx. We note that the problem in (11) is a single scenario problem and therefore much smaller in size. However, the reduction of scenarios leads to the loss of information about the substations that flood together.
Furthermore
, for sensitivity analysis, we consider three different values of restoration time: 6, 24, and 48 hours. Similarly, for the value of load loss, we consider 5 different values: $250, $500, $1000, $3000, and $5000 per MWh.
Figure 7 :
7significant investments (in fact, everything possible) in substation hardening such that there is no loss of power. For all other combinations in between, both the total expected disaster management cost and its composition vary. Based on a study undertaken by the Electric Reliability Council Total disaster management cost as a function of the value of load loss for different restoration times
For that value, the top-left curve achieves its minimum at $20M which is closest to $17.05M in the set {0, 10, 20...80}.
Figure 8 :
8Total disaster management cost as a function of budget for different values of ω
Table 1 :
1Grid characteristics before and af-ter the electrically equivalent reduction was
performed.
Grid Characteristic
Before After
Substations (#)
1250
362
Buses (#)
2000
663
Transformers (#)
860
358
Transmission Lines (#)
2346 1151
Generators (#)
544
254
Generation Capacity (GW)
96.29 50.98
Load (GW)
67.11 39.69
The original MEOW map dataset for the Texas coastal region comprises 192 flood maps whichare constructed using eight different storm directions (west-south-west, west, west-north-west, north-
west, north-north-west, north, north-north-east, and north-east), six different intensity categories
(0-5), and four different, forward speeds (5,10,15, and 25 mph). To demonstrate the usefulness of
the proposed approach with a computationally tractable use case, we reduce the size of the problem
by eliminating a subset of less severe scenarios. We first drop all the MEOW maps corresponding to
four directions (west-south-west, north, north-north-east, and northeast) as hurricanes belonging to
these categories do not cause significant flooding in the Texas Gulf Coast. We also drop the MEOW
maps corresponding to category 0-4 hurricanes. The storms belonging to category 5 are more intense
versions of these storms. Hence, the model ends up recommending decisions to prepare for worst-case
situations (and thus implicitly prepares for category 0-4 hurricanes as well). Moreover, as discussed
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| sample_23 | 0.8983 | arxiv | |
Mémoire de Mastère
2016-2017 5 Oct 2018
Mémoire de Mastère
2016-2017 5 Oct 2018Soutenu le 19/02/2018 devant le jury composé de : Mme Hajer Baazaoui Professeur à l'ISAMM Présidente M. Sami Zghal Maître-Assistant à la FSEGJ Rapporteur M. Sadok Ben Yahia Professeur à la FST Directeur de mémoire Au sein du laboratoire : LIPAH
Présenté en vue de l'obtention du diplôme de Mastère de recherche en Informatique Par Inès Osman Proposition d'une nouvelle méthode pour l'intégration sémantique des ontologies OWL en utilisant des alignements
Introduction générale
L'intégration des données est un vaste domaine qui permet d'unifier les données provenant des sources hétérogènes partageant des informations en commun, ou qui permet de les transférer d'une représentation à une autre, pour but de faire l'échange entre différents systèmes. Elle concerne des sources de données telles que les bases de données, les fichiers textes, et les ontologies, etc.
Pour ce faire, un sous-domaine a fait son apparition. Il s'agit de l'intégration des schémas tels que les schémas relationnels, orientés objet, XML (DTD, XML Schema), etc.). Rappelons que le schéma ou le modèle des données permet de décrire avec précision la structure d'un document, les conventions de structuration, de typage, et de nommage de ses données.
Par ailleurs, les ontologies ont été reconnues comme une composante essentielle pour la concrétisation de la vision du Web Sémantique. En définissant et décrivant les termes associés à des domaines particuliers, elles permettent d'annoter ou d'attacher les termes de multiples documents avec les mêmes termes propres à elles, ainsi elles arrivent à intégrer le contenu de différentes sources des données telles que les pages Web, les documents XML, les bases de données relationnelles, etc. L'utilisation de ces terminologies partagées permet un certain degré d'interopérabilité entre ces sources de données.
Cependant, cela ne résout pas complètement le problème d'intégration des données, car nous ne pouvons pas s'attendre à ce que tous les individus et toutes les organisations dans le Web sémantique s'accordent sur l'utilisation d'une terminologie ou d'une ontologie commune. Par conséquent, il est peu probable qu'une ontologie globale couvrant l'ensemble des systèmes distribués puisse être développée ; au contraire, un domaine donné pourrait avoir plusieurs ontologies concurrentes, chacune incomplète ou couvrant le domaine d'une certaine perspective. En effet, dans la pratique, les ontologies de différents systèmes sont développées indépendamment les unes des autres, par des communautés différentes, et pour des buts différents.
Suite à ce problème d'hétérogénéité, le domaine de l'intégration des ontologies, qui est aussi un sous-domaine de l'intégration des données, a fait son apparition. D'ailleurs, il ressemble énormément au domaine de l'intégration des schémas des bases de données, car les approches récentes de ces deux domaines se composent toutes les deux de deux étapes principales : l'étape de matching qui va réconcilier les différences en déterminant des correspondances (les similarités et les différences), puis l'étape de fusion (ou d'union) qui va exploiter le résultat du matching. L'intégration des ontologies de différents domaines vise à la construction d'une nouvelle ontologie pour un nouveau domaine plus large composé des domaines des ontologies intégrées. Elle est aussi appelée "composition" d'ontologies. L'intégration des ontologies de mêmes domaines vise à les unifier pour obtenir une ontologie plus complète qui couvre mieux ce même domaine. Elle est appelée "fusion" d'ontologies.
En général, les ontologies peuvent couvrir des domaines différents, ou bien des domaines identiques, proches (liés), complémentaires, ou interdisciplinaires dans lesquels les termes se chevauchent et les niveaux de détail (de leur conceptualisation) diffèrent. Ainsi, si les connaissances et les données doivent être partagées (e.g. dans le Web, ou par des entreprises en collaboration), il faudrait au moins établir des correspondances sémantiques ou des liens entre les ontologies qui les décrivent (matching des ontologies).
La tâche d'intégration des ontologies (composée d'une étape de matching, puis d'une étape d'union) est particulièrement importante dans les systèmes d'intégration puisqu'elle autorise la prise en compte conjointe des ressources décrites par des ontologies différentes. Ce thème de recherche a donné lieu à de très nombreux travaux.
Dans un contexte plus large, les ontologies produites sur le Web peuvent être graduellement d'une très grande taille. Ainsi, le processus d'intégration des ontologies nécessitera l'utilisation de mécanismes de prise en charge pour le passage à l'échelle des techniques d'intégration.
Pour conclure, l'idée de base est de réconcilier et d'intégrer des ontologies ou des fragments d'ontologies pour en fédérer d'autres qui encapsulent les données des ontologies initiales. Ainsi, l'objectif de ce mastère est de proposer une nouvelle méthode d'intégration des ontologies qui cherche à mettre en place une solution capable de raisonner sur des ontologies déjà existantes pour en produire une nouvelle en utilisant des techniques d'intégration.
Motivations et contributions :
Les techniques actuelles d'intégration des ontologies sont encore non efficaces en termes de temps d'exécution, semi-automatiques (qui reposent beaucoup sur l'intervention humaine), non extensibles (non scalables), générant une ontologie de mauvaise qualité (ayant énormément de contradictions sémantiques / logiques), et non complètes (avec perte d'informations précieuses, car ils n'arrivent pas à préserver toutes les connaissances des ontologies sources surtout les disjonctions).
Dans ce mémoire, nous proposons de développer une méthode automatique d'intégration des ontologies (OIA2R) ayant pour but d'intégrer deux ou plusieurs ontologies (de toute taille) en utilisant les mappings (ou les alignements) entre elles, pour former à la fin une nouvelle ontologie qui conserve toutes les informations des ontologies sources et des mappings, tout en les personnalisant (refactoring). Autrement dit, il s'agit d'une ontologie de pont qui englobe les ontologies d'entrée et les "bridging" axiomes qui les réconcilient. Notre algorithme produit une ontologie de sortie de bonne qualité en des temps d'exécution compétitifs. Nous proposons aussi une nouvelle classification des terminologies ambiguës utilisées dans le domaine de l'intégration des ontologies, car il y a une très grande confusion dans les appellations de l'état de l'art.
Introduction
Dans ce chapitre, nous rappelons les grandes étapes de l'évolution du Web, citons la définition du terme Web sémantique et Ontologie, présentons le langage OWL, rappelons les types d'hétérogénéité entre les ontologies, et présentons tous les domaines de l'ingénierie des ontologies et leurs applications dans le monde réel. Enfin, nous terminons ce chapitre par une conclusion qui introduit les causes du recours aux domaines de l'intégration et la fusion des ontologies dans lesquels nous allons entrer en détail dans le chapitre 2.
Notion du Web sémantique
Introduction au Web sémantique
Le Web actuel est un ensemble de documents (données et pages) dédiés aux humains, stockés et manipulés d'une façon purement syntaxique. Voici les deux principaux problèmes du Web actuel.
D'une part, il y a énormément de sources de données, du fait que n'importe qui peut facilement publier un contenu (sachant qu'il n'a pas la moindre idée sur la probabilité que ce contenu soit trouvé par autrui) ; il n'a qu'à l'annoter, ainsi les moteurs de recherche à base de mot-clé auront la tâche de l'indexer pour pouvoir l'afficher aux utilisateurs lorsqu'ils font une recherche. Par conséquent, l'information sur Internet est tellement énorme que l'utilisateur a du mal à la retrouver.
D'une autre part, les résultats de recherche sont imprécis, très sensibles au vocabulaire, et assez longs à trouver. En effet, les moteurs de recherche ne sont capables de répondre qu'à deux questions principales :
-Quelles sont les pages contenant ce terme ? et ; -Quelles sont les pages les plus populaires à ce sujet ?
Le Web est essentiellement syntaxique, et l'Homme est le seul à pouvoir interpréter son contenu (des documents et des ressources) inaccessible et non interprétable par la machine ; lui seul doté 1.1. NOTION DU WEB SÉMANTIQUE de la capacité de comprendre ce qu'il a trouvé et décider en quoi cela se rapporte à ce qu'il veut vraiment chercher. Finalement, nous ne pourrons pas se passer de l'intervention humaine pour naviguer, chercher, faire le tri des documents manuellement, interpréter, et combiner les résultats.
Pour conclure, le Web actuel ne peut pas être manipulé de façon intelligente par les programmes informatiques car il y a un vrai manque de sémantique.
Voici un exemple qui illustre ces problèmes : Supposons que nous voulons rechercher un fabricant de portes et de fenêtres pour construire une maison, nous tapons les mots "gates" et "windows" dans Google, nous aurons des résultats non satisfaisants concernent en grande partie Bill Gates et Microsoft Windows. Idéalement, les résultats devraient contenir les deux sens équitablement, ou selon le contexte de l'utilisateur.
Objectifs du Web sémantique
L'intérêt croissant porté à la recherche d'information sur le Web a donné lieu à l'initiative du Web sémantique. De nos jours, le souci du Web n'est plus vraiment l'augmentation continuelle de sa taille d'informations, mais plutôt l'amélioration de la recherche dans cette énorme masse d'informations, et la réalisation de systèmes permettant de filtrer et délivrer les informations de façon "intelligente".
Le but ultime du Web de troisième génération est de permettre aux utilisateurs d'exploiter tout le potentiel du Web en s'aidant par les machines qui pourront accomplir les tâches encore réalisées par l'Homme comme la recherche ou l'association d'informations, et ainsi atteindre un Web intelligent qui regroupera l'information de manière utile et qui apportera à l'utilisateur ce qui cherche vraiment.
Définition du Web sémantique
En 1993, Tim Berners-Lee a fournit une solution au problème du partage de connaissances entre les applications Web à l'aide d'un mécanisme à base d'ontologies qui structure les données d'une manière compréhensible par la machine. En 2001, il a envisagé un WWW accessible pour les machines et les humains, de telle sorte qu'ils soient mis dans une position égale.
Le Web sémantique (nommé aussi Web intelligent ou Web des données) est un ensemble de connaissances, où toutes les machines peuvent lier sémantiquement les données du Web, ainsi comprendre leurs significations, y accéder plus intelligemment, pour améliorer le dialogue entre les applications et l'interaction avec l'utilisateur en lui offrant une meilleure qualité des tâches de recherche (d'association des informations, et d'apprentissage, etc.).
Il peut être vu aussi comme une couche supplémentaire de connaissances (au-dessus du Web actuel) ou une extension du Web actuel.
De la même manière que le Web actuel, le Web sémantique est construit principalement autour des identifiants (URIs) et du protocole HTTP, mais il est par contre basé sur le langage RDF et non plus sur le HTML, pour but de séparer l'information qui décrit le sens et le contexte 1.2. ONTOLOGIE des données, de l'information qui décrit la présentation des données. Il est basé principalement sur les bases de connaissances et non seulement sur les bases de données. La recherche aussi va s'affecter et devenir une recherche par concept, non plus par mot clé.
Dans le Web sémantique, toutes les données du Web, textuelles ou multimédia, doivent être annotées sémantiquement par des métadonnées pertinentes, car les machines (les agents logiciels) ne pourront comprendre les données et prendre des décisions qu'à travers une explication plus spécifique du contenu, et cela en utilisant un mark-up sémantique nommé "méta-données". L'annotation de ces ressources d'information repose sur l'accès à des représentations de connaissances (des ontologies) partagées sur le Web.
Pour résumer, le Web sémantique donnera naissance à un nouvel aspect intelligent basé sur la recherche, le raisonnement, et la prise de décision automatique, faisant ainsi croître la productivité et les capacités des moteurs de recherche.
Ontologie
Ontologies et Web
Le domaine des ontologies est né d'une volonté de pallier les limites du Web (déjà évoquées). Les ontologies font partie intégrante des normes du W3C pour le Web sémantique, car elles sont indispensables pour représenter la sémantique des documents (les connaissances) qui coexistent dans le Web, en structurant et en définissant la signification des termes actuellement collectées et normalisées. En effet, les ressources du Web telles que les pages Web, les bases de données, ou les documents XML, etc. sont annotées par (attachées à) la signification des termes (concepts) de sorte que nous aurons besoin du même concept de la même ontologie pour représenter la même chose dans l'indexation de ces différentes ressources. C'est ici que se manifeste le rôle et l'utilité des ontologies.
Elles sont utilisées pour publier des bases de connaissances réutilisables et faciliter l'interopérabilité entre plusieurs systèmes hétérogènes et bases de données. Ainsi, nous pouvons considérer les ontologies comme une représentation pivot qui a pour but d'intégrer les sources de données hétérogènes.
Elles sont utilisées dans beaucoup de filières telles que : la gestion des connaissances, l'intelligence artificielle, ou le Web sémantique. Et elles aident à réaliser de nombreuses applications comme la recherche d'informations, la réponse aux requêtes, la recherche documentaire, et la synthèse de texte, etc.
Nous pouvons conclure que l'ontologie est un outil essentiel permettant l'exploitation automatique (le traitement machine) des connaissances, et la concrétisation des principes de réutilisabilité et du partage de l'information entre différentes sources de données, et cela grâce au vocabulaire commun fourni pour un domaine de connaissances réel ou imaginaire. Caldarola and Rinaldi (2016) constatent que les ontologies disponibles dans la littérature sont en train de devenir de plus en plus volumineuses en termes de nombre d'entités, à un tel point qu'elles peuvent être considérées comme de la Big Data.
Revue des définitions d'une ontologie
L'ontologie est un terme qui est apparu dans la Métaphysique avec Aristote qui considérait que l'ontologie est une "Science qui étudie l'être en tant qu'être et les attributs qui lui appartiennent essentiellement". Dans ce contexte, élaborer une ontologie, revient à faire l'étude philosophique de la nature de l'être et de l'existence, i.e. l'étude des propriétés générales de ce qui existe, en définissant l'ensemble des connaissances sur le monde.
Pendant la dernière décennie, les informaticiens ont repris le terme "Ontologie" qui est devenu très utilisé dans le domaine de l'informatique. C'est au début des années 90 qu'il est apparu pour la première fois dans le cadre des recherches sur les Systèmes à Base de Connaissances (SBC).
Une des premières définitions a été donnée par Neches et al. (1991) : "Une ontologie définit les termes et les relations de base comportant le vocabulaire d'un domaine, aussi bien que les règles pour combiner ces termes et ces relations afin de définir des extensions du vocabulaire". Studer et al. (1998) ont conclu qu'"une ontologie est une spécification formelle et explicite d'une conceptualisation partagée d'un domaine de connaissances".
Le terme "conceptualisation" ou conceptualiser un domaine veut dire faire une abstraction décrivant un phénomène quelconque du monde réel de ce domaine ; faire les choix quant à la manière de décrire ce domaine particulier (par des entités).
Une "spécification" est une conceptualisation représentée dans une forme concrète. Une spécification de la conceptualisation est par conséquent une définition formelle des termes qui décrivent un domaine, des relations entre eux, et des axiomes qui les contraignent (Nous en parlerons en détail juste après).
Le terme "formelle" signifie qu'une ontologie doit être interprétable et lisible par la machine.
Le terme "explicite" veut dire que les entités et les axiomes doivent être explicitement définis.
Le terme "partagée" indique qu'une ontologie doit annoter multiples sources de données, être consensuelle et accessible par tous les utilisateurs d'une communauté particulière. Gruber et al. (2009) définissent une ontologie comme suit : "Dans le contexte des sciences de l'informatique et de l'information, une ontologie définit un jeu de primitives représentatives avec lequel un domaine de connaissance ou un univers de discours peut être modélisé".
Le terme "jeu de primitives" est la traduction la plus fidèle possible du monde réel à représenter.
Constituants d'une ontologie
Une ontologie est une collection structurée de termes, de relations entre les termes, et d'un ensemble de règles d'inférence sur ces termes. Elle est nommée avec un IRI. Et puisqu'elle est un document Web, elle est ainsi référencée par un URI (IRI physique) qui doit pointer sur (coïncider avec) la localisation de l'URL choisi pour la publier.
ONTOLOGIE
Dans la syntaxe abstraite, une ontologie OWL est une séquence d'axiomes (de règles ou de contraintes) logiques et non logiques (y compris les faits), et éventuellement de références à d'autres ontologies (des importations) qui sont considérées incluses dans l'ontologie.
La particularité des ontologies réside dans l'existence d'une sémantique (de théorie) de logique mathématique. En effet, les relations entre les entités peuvent être formellement modélisées par la logique de description formelle de premier ordre.
L'ontologie est formalisée par des entités pouvant avoir chacune un IRI qui est une référence d'URI. Il existe cinq types d'entités : les concepts (ou classes), les propriétés (relations, attributs, slots, rôles, ou actions), les individus (objets, instances, ou extensions des classes), les types de données, et les valeurs de données. La déclaration de ces entités dans l'ontologie est faite par des axiomes non logiques :
• Les concepts sémantiques de l'ontologie correspondent aux abstractions d'une partie de la réalité (du domaine). Ce sont les concepts auxquels nous nous référons, choisis en fonction des objectifs que nous nous donnons et de l'application envisagée pour l'ontologie. Ils sont les entités principales d'une ontologie. Ils peuvent représenter des concepts abstraits (une notion, une intention, une idée, une croyance, un sentiment, etc.), ou bien des concepts spécifiques (un objet matériel, un ensemble ou un groupe d'individus de caractéristiques similaires, etc.). § Les concepts sont organisés hiérarchiquement à travers la relation conceptuelle "Sous classes de" ou "is a" d'héritage ou de spécialisation, utilisée pour construire une taxonomie / hiérarchie de concepts ; Cette relation peut aussi signifier une relation d'agrégation ou de composition "Partie de" ou "has a". D'autres relations prédéfinies telle que l'équivalence et la disjonction peuvent également lier les concepts pour véhiculer plus de sémantique.
• Les propriétés permettent de définir des liens pour les individus présents dans le domaine. Les propriétés sont des relations non prédéfinies et non taxonomiques utilisées pour exprimer la sémantique qui relie deux concepts, et c'est justement l'apport des ontologies qui peuvent définir d'autres relations spécifiques non prédéfinies.
• Le premier type de propriétés, nommé propriété d'objet, est défini tel que le premier argument de la relation corresponde au domaine (un concept pour lequel est définie la propriété) et que le deuxième argument corresponde au co-domaine / à l'image (un concept relié au domaine par la propriété). Ainsi, il définit une relation entre deux individus.
• Le deuxième type de propriétés, nommé propriété de type de données, est utilisé pour exprimer les attributs des concepts. Les attributs sont des relations dans lesquelles le domaine est un concept, et le co-domaine / l'image est un type de donnée (un littéral) tel que "String", "Integer", "Double", "Date", etc. Ainsi, il définit une relation entre un individu d'une classe et une valeur de donnée. § Ces deux types de propriétés peuvent être organisés hiérarchiquement, et liés par des relations conceptuelles prédéfinies telles que l'équivalence, la disjonction, et beaucoup d'autres. Ces propriétés sont instanciées à l'aide de la relation d'affectation qui leur associe une valeur de domaine (un individu) et une valeur de co-domaine (un individu ou une valeur de donnée).
• Le troisième type de propriétés, nommé propriété d'annotation, ne se conforme pas à la définition des propriétés décrite ci-dessus. Le rôle de cette propriété est d'annoter les entités ou les ontologies. Son domaine peut être une entité (classe, propriété, ou individu) ou une ontologie, et son co-domaine peut être une entité, un littéral généralement de type "String", ou une ontologie. § Les propriétés d'annotation peuvent également être organisées hiérarchiquement.
• Les individus constituent la définition extensionnelle / l'extension des concepts, et ainsi l'extension (les données) de l'ontologie. Les IRIs des individus sont utilisés pour faire référence aux ressources. Ce sont des objets particuliers instanciés par les concepts à l'aide de la relation d'instanciation prédéfinie "Instance de" ou "is kind of" ou "type". Ils peuplent les classes et véhiculent les connaissances à propos du domaine. (Il existe aussi des individus anonymes qui sont des individus non utilisés en dehors de l'ontologie. Ils sont identifiés par un ID local plutôt qu'un IRI global). § Les instances peuvent être liées par des relations conceptuelles d'identité et de différence.
• Les types de données sont des parties particulières du domaine qui spécifient des valeurs. Les ontologies référencent des types de données intégrés de XML Schema (des littéraux) au moyen d'une référence URI à ce type de données.
• Les valeurs de données sont, contrairement aux autres entités, des valeurs simples qui n'ont pas d'IRI. Ce sont les valeurs des types de données.
• Les axiomes logiques constituent des assertions liées aux entités. Au lieu de compter sur les labels et les termes des entités (qui sont destinés aux humains) pour transmettre la sémantique, le concepteur d'ontologies doit contraindre l'interprétation possible des entités à travers une utilisation judicieuse d'axiomes logiques pour rende leurs sens beaucoup plus précis. § Ils sont aussi utilisés pour vérifier la consistance de l'ontologie, car ils permettent à un "raisonneur" d'inférer des connaissances additionnelles qui ne sont pas déclarées directement. Plus les axiomes exprimés dans les ontologies sont complexes, plus ils transportent des connaissances implicites qui peuvent être inférées par le raisonneur.
• Les faits sont des axiomes qui énoncent des informations sur les individus, telles que les classes auxquelles les individus appartiennent, et les propriétés et les valeurs des propriétés de ces individus.
Définitions formelles d'une ontologie
Selon Kalfoglou and Schorlemmer (2003), une approche algébrique plus formelle identifie une ontologie comme étant une paire <S, A>, où S est la signature des entités de l'ontologie (modélisée par une structure mathématique comme un treillis ou un ensemble non structuré) et A est l'ensemble des axiomes ontologiques qui spécifient l'interprétation voulue de la signature dans un domaine donné. Udrea et al. (2007), les ontologies modélisent la structure des données (i.e., les ensembles de classes et de propriétés), la sémantique des données (sous la forme d'axiomes tels que les relations d'héritage ou les contraintes sur les propriétés), et les instances des données (les individus). Ainsi, les entités d'une ontologie se composent d'une partie "structure", et d'une partie "donnée".
ONTOLOGIE
Selon Cheatham and Pesquita (2017), les informations des classes, des propriétés, et des axiomes qui restreignent leur interprétation, sont appelées la "structure", le "schéma", ou "Tbox" (comme Terminologie) de l'ontologie, et les informations des instances et leurs axiomes sont appelées "données", "données d'instances" ou "A-box" (comme Assertions) et contiennent des assertions sur des instances utilisant des données du T-box. D'après Zhang et al. (2017), une ontologie est un modèle en arbre, à cause du principe de l'hyponymie (la subsomption -is-a -) qui fait que chaque entité (classe ou propriété) soit héritée d'une seule super-entité directe, formant ainsi une structure de graphe acyclique enracinée Raunich and Rahm (2012). Mais dans le cas d'un héritage multiple, l'ontologie devient un modèle en réseau qui peut contenir des cycles et dans lequel plusieurs chemins peuvent mener à une entité.
Langage d'ontologie OWL
Il existe une grande variété de langages pour exprimer les ontologies. Quelques exemples de langages incluent RDF, RDFS, OWL, KIF, F-Logic, UML, SQL DDL, ou XML Schema, etc.
Le défi du Web sémantique est de fournir un langage qui exprime à la fois des règles, des structures, et des données sur lesquelles il va raisonner (à l'aide de ces règles). Par la suite, les règles de n'importe quel système de représentation de connaissances pourront être exportées dans le Web sémantique. Un individu peut ne pas avoir de classe(s) qui l'instancie(nt) ; dans ce cas, il sera implicitement une instance de la classe « owl:Thing ».
OWL (Web
Il y a une variété de syntaxes (formats) pour persister, partager, et éditer des ontologies OWL, telles que Functional OWL, RDF/XML, Turtle, OWL/XML, Manchester OWL, OBO, KRSS, etc. La spécification OWL décrit ce qui constitue une ontologie d'un point de vue structurel de haut niveau, qui est ensuite mappée en diverses syntaxes concrètes. RDF/XML est la syntaxe d'échange officiellement recommandée par W3C, que tout outil OWL doit pouvoir prendre en charge.
La diversité du monde réel est une source de richesse et d'hétérogénéité. En effet, dans les systèmes ouverts et distribués, tels que le Web sémantique, l'hétérogénéité ne peut pas être évitée. Plusieurs ontologies de mêmes domaines ou de domaines proches peuvent exister, à cause du développement déconnecté qui se focalise sur des applications particulières de différents buts et intérêts. Par ailleurs, les concepteurs ont des habitudes et des pré-requis différents, et modélisent les connaissances avec des niveaux de détails différents et des outils différents. Tout cela va influencer de différentes manières leurs décisions de conception. Par conséquent, la conception des ontologies ne peut jamais être un processus déterministe ; même deux ontologies de même domaine ne vont pas être identiques. Toutes ces raisons mènent à diverses formes d'hétérogénéité.
Prenons l'exemple du domaine biomédical. Il y a neuf ontologies qui décrivent une maladie neurologique, allant des ontologies très spécifiques couvrant une seule maladie (e.g. l'épilepsie, l'Alzheimer) à des ontologies couvrant toutes sortes de maladies telles que la "Disease Ontology". Il en résulte plusieurs ontologies qui décrivent les mêmes concepts sous des modèles légèrement différents. Klein (2001) distingue deux niveaux d'hétérogénéité qui peuvent exister entre les ontologies :
Hétérogénéité des langages
Ce sont les différences au niveau du langage, du méta-modèle, ou des primitives du langage utilisées pour spécifier une ontologie. Ce sont des différences entre les mécanismes (à partir desquels les entités vont être définies). Nous pouvons classifier ces différences en quatre catégories de difficulté croissante :
Syntaxe
Les différents langages d'ontologie utilisent souvent des syntaxes différentes, e.g., pour définir la classe de chaises dans RDF Schema (RDFS), nous utilisons <rdfs:Class ID="Chair">. Dans LOOM, l'expression (defconcept Chair) est utilisée pour définir la même classe. L'exemple typique d'incompatibilité de "syntaxe seulement" est quand un langage d'ontologie a plusieurs représentations syntaxiques, comme les différentes syntaxes de OWL.
Représentation logique
La différence de représentation des notions logiques, e.g. dans certains langages, il est possible d'indiquer explicitement que deux classes sont disjointes (A disjoint B), alors que dans d'autres langages, il est nécessaire d'utiliser la négation dans des instructions de sous-classes (A subclass-of (NOT B), (B subclass-of (NOT A)) pour indiquer la disjonction.
Sémantique des primitifs
Une différence plus subtile au niveau du méta modèle est la sémantique des constructions du langage. Malgré le fait que parfois le même nom est utilisé comme un constructeur dans deux langages, la sémantique peut différer, e.g. il existe plusieurs interprétations de A equalTo B.
Même lorsque deux langages d'ontologie semblent utiliser la même syntaxe, la sémantique des constructeurs peut différer.
Expressivité des langages C'est la différence fondamentale qui a le plus d'impact. Cette différence implique que certains langages sont capables d'exprimer des choses qui ne sont pas exprimables dans d'autres langages, e.g. certains langages ont des constructions pour exprimer la négation, d'autres non ; également pour le support des listes, des ensembles, et des valeurs par défaut, etc.
Hétérogénéité des modèles du domaine
Ce sont des différences dans la façon dont le domaine est modélisé. Elles sont décrites par Visser et al. (1998) :
Différence de conceptualisation (de sémantique) C'est une différence dans la façon dont un domaine est interprété (conceptualisé / modélisé), ce qui entraîne différents concepts, différentes relations entre les concepts, ou différentes instances des concepts. Elle est classée en deux catégories :
Portée Quand il s'agit de deux classes qui semblent représenter le même concept mais qui n'ont pas exactement les mêmes instances (extensions) bien que l'ensemble de leurs instances se croise (se chevauche), e.g. les concepts "Student" et "TaxPayer".
Couverture et granularité du modèle C'est une différence dans la partie du domaine couverte par les deux ontologies (e.g., les ontologies des employés universitaires et des étudiants), ou une différence dans le niveau de détail avec lequel le modèle est modélisé / couvert (e.g., une ontologie peut avoir un concept "Person" alors qu'une autre peut distinguer "YoungPerson", "MiddleAgedPerson" et "OldPerson").
Tenons l'exemple d'une ontologie sur les voitures : -Une ontologie peut modéliser des voitures mais pas des camions.
-Une autre pourrait représenter les camions mais les classer seulement dans quelques catégories. -Alors qu'une troisième pourrait faire des distractions très fines entre les types de camions en se basant sur leur structure physique générale, poids, but, etc.
Différence d'explications
C'est une différence dans la façon dont la conceptualisation est spécifiée. Elle se base sur la manière d'exprimer les entités. Elle est classée en trois catégories :
Style de modélisation Une différence dans le style de modélisation qui résulte des choix explicites du modélisateur :
Paradigme De différents paradigmes peuvent être utilisés pour représenter certains concepts tels que le concept du temps (e.g., représentation basée sur les "intervalles" vs représentation basée sur les "points"), l'action, les plans, la causalité, les attitudes propositionnelles, etc.
Description des concepts ou convention de modélisation Les différences dans la description des concepts ou les conventions de modélisation peuvent se manifester par l'utilisation de différentes structures pour représenter des informations identiques ou similaires, e.g. une distinction entre deux classes peut être modélisée en utilisant un attribut qualificatif (une propriété), ou en introduisant une autre (sous-) classe. Un autre choix dans les descriptions des concepts est la manière dont la hiérarchie is-a "<" est construite, en effet, les entités peuvent être augmentées ou réduites dans la hiérarchie, e.g. la classe "thèse" ou "dissertation" peut être modélisée comme dissertation < livre < publication scientifique < publication, ou comme dissertation < livre scientifique < livre < publication, ou même comme sous-classe de "livre" et de "publication scientifique".
Terminologie Une différence terminologique peut voir deux cas :
Termes synonymes Lorsque deux concepts sont équivalents, mais représentés en utilisant des noms différents. Un exemple trivial est l'utilisation du terme "Car" dans une ontologie et du terme "Automobile" dans une autre. Un type particulier de ce problème est le cas où le langage naturel avec lequel les ontologies sont décrites diffère.
Termes homonymes Lorsque le même nom est utilisé pour des concepts différents, e.g. dans le domaine musical, le terme "Conductor" (le chef d'orchestre) a une signification différente que celle dans le domaine de l'ingénierie électrique (le conducteur électrique).
Différence de codage Une différence de codage se produit lorsque les valeurs dans les différentes ontologies sont codées dans différents formats, e.g. une date peut être représentée par "jj/mm/aaaa" ou "mm-jj-aa", la distance peut être décrite en "mile" ou en "kilomètre", le poids peut être décrit en "gramme" ou en "pound", le prix peut être décrit en différentes monnaies, etc.
Ingénierie ontologique
L'ingénierie des ontologies est un contexte dans lequel les utilisateurs sont confrontés à des ontologies hétérogènes. Et plus généralement, c'est la tâche de concevoir, mettre en oeuvre, et maintenir des applications basées sur les ontologies Euzenat and Shvaiko (2013). Elle doit traiter plusieurs ontologies distribuées et évolutives.
Dans le but d'atténuer l'hétérogénéité croissante et la complexité des ontologies modernes, plusieurs domaines de recherche connexes ont vu le jour au cours des dernières années, tels que le "matching", le "mapping", l'"alignement", l'"intégration", la "fusion", le "versionning", et l'"évolution" des ontologies qui sont les domaines les plus répandus. Caldarola and Rinaldi (2016) Nous n'allons expliciter que les domaines liés à notre thème.
Médiation
La médiation des ontologies est un vaste domaine de recherche qui vise à déterminer et réconcilier les différences entre les ontologies afin de permettre leur réutilisation dans différentes applications hétérogènes dans le Web sémantique. De Bruijn et al. (2006) distinguent deux types principaux de médiation ontologique : le mapping et la fusion. Leung et al. (2014) distinguent trois types de médiation : le matching, la fusion, et l'intégration (qui sont basées sur le matching).
Réconciliation
La réconciliation des ontologies est un processus qui harmonise le contenu de deux ou de plusieurs ontologies. Il exige typiquement de faire un matching entre deux ontologies, et des changements dans un des deux côtés, ou dans les deux côtés Euzenat and Shvaiko (2013). Dans ce cas, il ne s'agit pas d'une fusion ou d'une intégration d'ontologies, mais plutôt d'une coévolution. Sachant que la réconciliation des ontologies peut être effectuée pour le but de fusionner ou d'intégrer deux ontologies.
Matching (Appariement)
Le matching des ontologies peut être une solution au problème de l'hétérogénéité sémantique des systèmes car il permet que la connaissance et les données exprimées dans les ontologies correspondues soient interopérables. C'est le processus de découverte des relations sémantiques ou des correspondances entre des entités provenant de deux différentes ontologies (ou de plusieurs ontologies dans le cas du matching multiple). Ces entités sont généralement des entités nommées (des classes, des propriétés, ou des individus), mais elles peuvent aussi être des entités anonymes i.e. des expressions plus complexes (des formules).
Le matching des ontologies peut concerner des ontologies entières (i.e. tout type d'entités : T-box et A-box), ou bien uniquement la partie "schéma" (la structure) des ontologies (i.e. T-box : seulement les classes et les propriétés) Cheatham and Pesquita (2017). La correspondance est la relation sémantique détenue ou supposée être détenue entre deux entités des différentes ontologies. La relation entre les deux entités n'est pas limitée à la relation d'équivalence, elle peut être plus sophistiquée, e.g. la subsomption, la disjonction, l'instanciation, et même des relations floues. Certains auteurs, utilisent le terme mapping, au lieu de correspondance.
Le résultat du matching, l'"alignement" (éventuellement le "mapping"), exprime, avec de différents degrés de précision, les relations sémantiques entre les ontologies mises en correspondance. Plusieurs auteurs utilisent le terme "alignement" (qui est le résultat du matching), au lieu de "matching", et utilisent le terme "mapping" au lieu d'"alignement" (que nous expliquerons juste après) Euzenat and Shvaiko (2013). Le type le plus simple de relations à trouver est l'équivalence ou la disjonction (l'exclusion) un à un (1-à-1) entre deux entités appartenant chacune à une ontologie. Le niveau de complexité suivant est la relation de subsomption (d'inclusion) 1-à-1. Pour trouver des relations 1-à-1, une recherche exhaustive doit comparer chaque entité de la première ontologie avec chaque entité de la deuxième ontologie, ce qui peut être réalisable pour de petites ontologies, mais infaisable pour des ontologies contenant des millions d'entités. C'est pour cela que les systèmes de matching peuvent employer une étape de filtrage ou de hachage pour déterminer les entités qui valent la peine d'être comparées Cheatham and Pesquita (2017).
Les relations un-à-plusieurs (1-à-m) sont encore plus difficiles à trouver. Tenons comme exemple une relation d'équivalence entre une classe de la première ontologie et l'union de trois classes de la deuxième ontologie. Ce type de relation cause un problème de complexité. Pour trouver des relations 1-à-m, une approche exhaustive aurait besoin de comparer chaque entité de la première ontologie avec toutes les combinaisons possibles des m entités de la deuxième ontologie, ce qui n'est pas possible Cheatham and Pesquita (2017).
Trouver des relations plusieurs-à-plusieurs (n-à-m) arbitraires est la tâche d'alignement la plus complexe. Une relation arbitraire signifie tout type de relation, non seulement l'équivalence, la disjonction, et la subsomption Cheatham and Pesquita (2017). § Les systèmes de matching actuels traitent l'identification des relations 1-à-1. Ils sont devenus très compétents dans la découverte des relations d'équivalence 1-à-1 entre les classes et les instances, mais moins performants dans la découverte des relations entre les propriétés. Leur compétence et leur exactitude est due principalement aux mesures de similarité syntaxiques (de chaînes de caractères). § Les travaux qui traitent un matching multiple sont très spécifiques pour le moment, et seul un petit nombre d'algorithmes le considère.
Voici les travaux qui ont été menés au sein de notre laboratoire LIPAH concernant le matching des ontologies : Zghal et al. (2007aZghal et al. ( ,b,c,d, 2011Zghal (2010); Kachroudi et al. (2011Kachroudi et al. ( , 2012Kachroudi et al. ( , 2013bKachroudi et al. ( ,c,a, 2014Kachroudi et al. ( , 2015Kachroudi et al. ( , 2016Kachroudi et al. ( , 2017b; Djeddi et al. (2015); El Abdi et al. (2015).
Méthodes de matching
Pour évaluer la similarité des entités, les systèmes de matching utilisent différentes approches. Ils peuvent utiliser zéro ou plusieurs approches de mesure de similarité, soit en combinant 1.5. INGÉNIERIE ONTOLOGIQUE leurs valeurs pour former une seule mesure, soit en les appliquant en série pour filtrer les correspondances et ne mesurer que les correspondances candidates Cheatham and Pesquita (2017).
La similarité reflète à quel point deux entités ont des choses en commun, c'est une mesure du degré qu'une entité puisse être utilisée à la place d'une autre. En général, la mesure ou le degré de confiance nous renseigne à quel point la correspondance est correcte et fiable. Plus elle est élevée, plus la relation qui la détient est solide. Généralement, c'est un nombre réel appartenant à un ensemble ordonné qui varie dans l'intervalle [0 1], mais il existe des systèmes qui utilisent simplement les booléens "vrai" et "faux" où le plus grand élément (1) est interprété en tant que "vrai", et le plus faible élément (0) est interprété en tant que "faux" Euzenat and Shvaiko (2013). Un seuil peut être mis pour ne pas afficher les correspondances de mesure de similarité inférieure à ce seuil.
Parmi les méthodes utilisées par les approches de matching des ontologies, nous citons Abels et al. (2005) :
Méthode basée sur les chaînes Elle compare deux entités en se basant sur les chaînes de caractères associées à elles. Les chaînes de caractères sont généralement les labels de l'entité, mais ils peuvent aussi inclure les commentaires et d'autres annotations de l'entité. Plus les chaînes sont similaires, plus elles sont susceptibles de désigner les mêmes concepts. § Cette approche souffre lorsque les concepts sémantiquement identiques sont modélisés avec des noms différents, i.e. lorsqu'il s'agit de synonymes Fahad et al. (2010).
Méthode linguistique Telle que la suppression de mots inutiles (stop-words), la tokenisation, la stemmatisation du texte, la considération des préfixes ou des suffixes, etc. pour gérer les noms des entités, e.g. cette méthode détecte que les classes "house" et "houses" sont identiques.
Méthode sémantique Elle tente d'utiliser les sens des labels de l'entité, plutôt que leurs orthographes. Des ressources linguistiques externes comme les lexiques, les thésaurus, les dictionnaires, les encyclopédies, et les moteurs de recherche du Web sont souvent utilisées afin d'identifier les synonymes, les hyperonymes (is-a), ou les hyponymes (is-a). Il est courant d'utiliser la base de données lexicale WordNet, l'ontologie de référence (UMLS), ou les règles d'articulation (les mappings), pour identifier les relations entre les entités Cheatham and Pesquita (2017). § L'inconvénient de cette méthode c'est qu'elle est spécifique au domaine particulier de la ressource externe utilisée, et ne produit des résultats efficaces que lorsqu'elle est utilisée pour des ontologies dans ce même domaine. Elle manquerait de précision si elle aurait été appliquée à des ontologies de domaine plus général ou totalement différent Fahad et al. (2010).
Méthode taxonomique / structurelle Elle ne considère que la relation de spécialisation (héritage). Son intuition est que la spécialisation (is-a) relie des termes qui sont déjà similaires (étant interprétés comme un sous-ensemble ou un sur-ensemble de l'autre), par conséquent, leurs voisins peuvent aussi être en quelque sorte similaires. Elle examine le voisinage de deux entités pour déterminer leur similarité Euzenat and Shvaiko (2013).
INGÉNIERIE ONTOLOGIQUE
Méthode basée sur les attributs / propriétés Elle examine les attributs de deux concepts pour déterminer leur similarité Fahad et al. (2010). § Son inconvénient est qu'elle produit des correspondances inexactes lorsque de différents concepts ont les mêmes attributs, e.g. le concept "Person" et "Company" sont supposés être les mêmes sur la base des labels de leurs attributs qui sont identiques, tels que les attributs "name", "adress", et "phone", etc.
Méthode extensionnelle Elle se base sur l'intuition qui dit : si deux classes ont les mêmes instances, alors ce sont des classes similaires. § L'inconvénient majeur de cette méthode se manifeste lorsque des concepts sémantiquement distincts ayant des instances en commun sont considérés comme identiques Fahad et al. (2010).
Méthode basée sur les graphes Cette méthode interprète la représentation graphique de la structure de deux ontologies et regarde les chemins, les enfants et les feuilles pour identifier leurs structures similaires en recherchant leurs parties identiques. Elle se base sur l'intuition qui dit : si deux noeuds de deux ontologies sont similaires, alors leurs voisins doivent aussi être plus ou moins similaires Euzenat and Shvaiko (2013), e.g. deux entités qui ont la même superclasse et qui partagent quelques instances en commun, sont considérées plus similaires que deux entités n'ayant pas ces choses en commun ; deux classes de deux ontologies sont similaires ou identiques si elles ont les mêmes attributs et les mêmes classes voisines.
Nous pouvons trouver une première classification qui groupe ces méthodes de matching en des approches syntaxiques, structurelles, et sémantiques ; et une autre classification qui les groupent en des approches élémentaires (qui calculent les correspondances en analysant les entités isolément, en ignorant leurs relations avec les autres entités), et des approches structurelles (qui calculent les correspondances en analysant l'apparition des entités ensemble dans une structure).
En pratique, il n'existe aucun système de matching automatisé qui peut générer des alignements complètement corrects. En effet, les alignements manqueront toujours quelques correspondances correctes, contiendront quelques correspondances incorrectes, ou bien les deux en même temps Cheatham and Pesquita (2017).
Concernant notre sujet
Ces quinze dernières années, la grande majorité des recherches sur l'intégration des ontologies s'est concentrée surtout sur l'étape de matching des ontologies et a négligé la partie de fusion des ontologies qui vient après Raunich and Rahm (2014). En effet, la résolution de l'hétérogénéité par les stratégies de matching des ontologies est considérée comme une phase interne nécessaire et très importante pour l'intégration (ou la fusion) des ontologies en une nouvelle ontologie les regroupant. L'amélioration du processus de matching va améliorer considérablement les résultats de l'intégration (et de la fusion) des ontologies Umer and Mundy (2012).
Les systèmes de matching peuvent faire à la fin une vérification d'incohérence et une réparation à l'alignement (ou le mapping) produit, en supprimant les correspondances incorrectes ou incohérentes i.e. celles qui sont correctes mais qui causent une incohérence logique dans l'ontologie produite suite à l'intégration ou la fusion des ontologies sources à l'aide de cet alignement-là (Nous détaillerons ce volet dans le chapitre 3).
Résolution de coréférence
Les systèmes de matching des ontologies se concentrent généralement sur la recherche des relations entre les entités de schéma / T-box (les classes et les propriétés), alors que les systèmes de résolution de coréférence se concentrent sur l'identification des mêmes individus qui sont référencés par différents URIs Cheatham and Pesquita (2017).
Les relations cherchées par les algorithmes de résolution de coréférence sont uniquement des identités 1-à-1, car deux individus ne peuvent être qu'identiques ou distincts, tandis que 1.5. INGÉNIERIE ONTOLOGIQUE les matchings (de schéma / T-box) impliquent (aussi) des classes et des propriétés, et ainsi peuvent avoir toute relation traditionnelle qui existe entre deux ensembles comme la subsomption, l'exclusion (la disjonction), etc.
Le nombre d'instances (A-box) d'un data set (dans les linked data du Web) est souvent beaucoup plus grand que le nombre de ses entités de schéma (T-box), ainsi ce n'est pas faisable de comparer chaque individu d'un data set avec chaque individu d'un autre data set pour déterminer s'ils sont identiques ou pas. Par conséquent, une méthode de filtrage est utilisée pour décider si deux individus sont suffisamment proches pour valoir la peine d'être comparés ; s'ils le sont, un algorithme de comparaison va se produire en mesurant la similarité entre les individus, ou bien entre les individus et les noms des propriétés auxquelles elles sont liées. La mesure de similarité la plus utilisée est la similarité syntaxique (de chaînes de caractères). Enfin, le système doit prendre le résultat de la comparaison de deux individus et décider s'ils sont identiques ou pas en spécifiant souvent un seuil (une valeur empirique malheureusement) Cheatham and Pesquita (2017).
Le matching (des schémas) a un plus grand historique de recherche que celui de la résolution de coréférence qui vise l'intégration des linked data Cheatham and Pesquita (2017). Etant donné deux ou plusieurs ontologies (dans le cas d'un matching multiple), l'alignement est un ensemble de correspondances (relations) sémantiques entre des paires d'entités appartenant à différentes ontologies. Rappelons que l'alignement est la sortie du processus de matching des ontologies Euzenat and Shvaiko (2013).
Alignement
Plusieurs auteurs, utilisent le terme "mapping" au lieu d'"alignement". Dans le reste de ce mémoire, nous utiliserons le mot "alignement" dans ce sens.
Puisque la relation est une relation binaire valable dans les deux sens et pouvant être décomposée en une paire de fonctions totales, Kalfoglou and Schorlemmer (2003) supposent que l'alignement des ontologies peut être décrit au moyen d'une paire de mappings (chacun contenant des correspondances dans un seul sens). Ils introduisent la notion de l'ontologie intermédiaire commune O 0 (ou l'articulation) qui peut être créée à travers cet alignement. Euzenat and Shvaiko (2013). L'alignement peut avoir des correspondances ayant la même entité source, i.e. une entité source peut avoir plus qu'une relation avec des entités cibles.
Les alignements peuvent être utilisés dans des tâches variées, telles que la réponse aux requêtes, la liaison des données, la navigation dans le Web sémantique, la transformation des ontologies, l'intégration et la fusion des ontologies, et le raisonnement sur les ontologies.
Concernant notre sujet
Il est possible d'utiliser des relations à partir d'un langage ontologique pour exprimer un alignement. Tenons l'exemple du langage OWL qui peut être considéré comme un langage d'expression de correspondances entre les ontologies. En effet, dans OWL, les primitifs "equi-valentClass", "equivalentProperty" et "sameAs" ont été introduits initialement pour lier les éléments des ontologies de même domaine ; d'ailleurs, dès qu'une ontologie OWL implique des entités provenant d'autres ontologies, elle exprime implicitement des alignements. Par conséquent, il est possible d'utiliser ces constructeurs pour relier les entités de deux ontologies mises en correspondance ou pour créer une ontologie OWL intermédiaire. (2012), le "mapping" des ontologies est une approche pour l'intégration des ontologies où l'ontologie intégrée O contient les règles de correspondance entre les entités des ontologies A et B. Klein (2001) considère également le mapping comme une intégration virtuelle. (C'est la même notion d'ontologie intermédiaire O 0 ou d'articulation rencontrée dans la partie "alignement").
Mapping
Définition 1
Selon Umer and Mundy
Selon Ziemba et al. (2015), le mapping permet d'obtenir un résultat similaire à l'ontologie de pont (c'est l'ontologie que nous allons réaliser dans ce mémoire). Cependant, dans l'ontologie de pont, par opposition au mapping, les ontologies sources et les connexions entre elles sont stockées ensemble, or que dans le mapping, les connexions sont à part. Le mapping entre les ontologies forme des "ponts sémantiques" De Bruijn et al. (2006).
Définition 2 (consensuelle)
Le mapping est la version orientée d'un alignement où une entité d'une première ontologie est correspondue à une entité d'une deuxième ontologie, et pas l'inverse. Il assigne chaque entité d'une ontologie à au plus une (exactement une ou aucune) entité de l'autre ontologie. Il se conforme à la définition mathématique d'une fonction totale (une relation unidirectionnelle (injective)), et non pas à la définition d'une relation générale bidirectionnelle (bijective). Selon Euzenat and Shvaiko (2013), cette définition mathématique exige que l'entité mise en correspondance soit égale à son image, i.e. que la relation soit une relation sémantique d'équivalence ou d'identité.
Selon Flouris et al. (2006), un mapping peut être perçu comme une collection de règles (ou d'axiomes) toutes orientées dans la même direction, de telle sorte que les entités de l'ontologie source et cible apparaissent au maximum une fois. Ils ajoutent que les deux ontologies mappées doivent partager le même domaine de discours (ou des domaines proches). Ceci est implicite sinon nous n'aurons pas de mapping. Dans le reste de ce mémoire, nous utiliserons le terme "mapping" dans ce sens.
D 'après De Bruijn et al. (2006), le mapping, comme l'alignement, est stocké séparément des deux ontologies, ainsi il n'est pas incorporé dans les définitions de ces ontologies. Processus d'intégration des ontologies Il s'agit du mapping entre une ontologie globale et des ontologies locales dans le processus de l'intégration des ontologies : Il décrit les relations (les correspondances) entre l'ontologie globale (cible) et les ontologies locales (sources) la composant. Il peut être aussi utilisé pour exprimer une entité de l'ontologie globale dans une vue ou une requête sur les autres ontologies (approche global-centric), ou l'inverse (approche local-centric).
Processus de fusion ou d'alignement Il s'agit du mapping entre des ontologies sources dans le processus de fusion ou d'alignement (définition 1) des ontologies. Il identifie les similitudes (synonymies) entre les différentes ontologies pour pouvoir les fusionner ou les aligner.
Processus de transformation des ontologies Il s'agit du mapping entre deux ou plusieurs ontologies sources dans le processus de transformation des ontologies : Il peut être utilisé pour transformer les entités sources en des entités cibles en se basant sur leurs correspondances, i.e. leurs relations d'équivalence sémantique dans le mapping. Il fournit une interopérabilité entre les différentes ontologies qui ne peuvent pas être intégrées ou fusionnées à cause d'une inconsistance mutuelle de leurs informations. § Les utilisations du mapping dans une ontologie intermédiaire, une ontologie de pont, une transformation des ontologies, une interconnexion des données, ou une requête, s'avèrent très utiles pour les environnements dynamiques, ouverts et distribués, et évitent également la complexité et les coûts de l'intégration ou de la fusion des ontologies sources. En effet, le mapping forme une sorte de couche ou d'interface commune entre les ontologies.
Mophisme
Selon Flouris et al. (2006), le morphisme des ontologie est une collection de correspondances sous forme de fonctions qui relient non seulement les signatures (les vocabulaires, les entités) de deux ontologies, mais aussi leurs axiomes (les syntaxes, les formalismes, les constructeurs des langages).
Selon Euzenat and Shvaiko (2013), le terme "morphisme" est utilisé pour représenter un mapping entre différents types de modèles*. Il contient des relations binaires sur deux ensembles d'identificateurs d'objets (OIDs) et il peut être inversé et composé.
* Les modèles, tels que les schémas relationnels ou les schémas XML, sont représentés implicitement (intérieurement) sous la forme de graphes étiquetés et orientés, dans lesquels les noeuds désignent les éléments du modèle (les relations et les attributs). Chacun de ces éléments est identifié par un identifiant d'objet (OID) Euzenat and Shvaiko (2013).
Transformation
La transformation des ontologies est le processus de changement / de traduction des entités (vocabulaire, signature) d'une ontologie par les entités d'une autre ontologie. Elle est utile quand nous voulons exprimer une ontologie par rapport à une autre. En général, les deux ontologies initiales sont inchangées et une troisième ontologie (le résultat de la transformation de la première ontologie par rapport à la deuxième) est créée. Les conséquences de la première ontologie sont aussi les conséquences du résultat de la transformation Euzenat and Shvaiko (2013).
Ce terme est très confondu à la notion de traduction (que nous allons expliquer juste après). La transformation des ontologies n'est pas bien supportée par les outils. Elle peut être particulièrement utile dans la connexion d'une ontologie à une autre ontologie (réconciliation des ontologies), ou dans la connexion d'une ontologie locale à une ontologie globale dans le cadre de l'intégration ou la fusion des ontologies. Elle est utilisée aussi pour importer des données sous une autre ontologie sans importer l'ontologie elle-même.
Traduction
La traduction des ontologies est le processus qui transforme la représentation formelle de l'ontologie d'un langage (d'un formalisme de représentation) à un autre, tout en préservant la sémantique, e.g. de "Ontolingua" à "Prolog". Elle change la forme syntaxique des axiomes, mais pas le vocabulaire (pas la signature) de l'ontologie Klein (2001); Kalfoglou and Schorlemmer (2003); Flouris et al. (2006); Euzenat and Shvaiko (2013).
Interconnexion des données
L'interconnexion des données est le processus qui consiste à établir des liens explicites, principalement des déclarations de la relation d'identité "owl :sameAs" entre les instances de deux ensembles de données RDF différents dans le Web de données (Linked Data). Il est possible de traiter les alignements en tant que spécifications de liaison, ainsi l'interconnexion des données pourrait être exprimée par l'opérateur Interlink(d, d , A) = L dans lequel un alignement A résultant de chaque couple d'ontologies (O et O ) sous lesquels deux ensembles de données (d et d ) sont exprimés, est utilisé pour les lier, et générer un ensemble de liens L entre les ressources (les URIs des instances) de ces deux data sets Euzenat and Shvaiko (2013). Bien qu'il y a une quantité très énorme de liens de type "owl:sameAs" entre les instances des data sets du LOD, il n'existe que quelques liens rares de type "owl:equivalentClass" ou "owl:equivalentPropery" entre leurs classes et leurs propriétés Zhao and Ichise (2014).
Dans le Web des données, le "matching" et la "résolution de coréférence" sont utiles dans l'aide à la génération de ces liens qui fournissent le contexte nécessaire pour rendre les données plus utiles Cheatham and Pesquita (2017). Ils sont effectués hors ligne et sans contraintes de temps de telle sorte que les correspondances résultantes soient correctes, mais pouvant être non exhaustives (non complètes).
Dans ce contexte, citons le travail de Hamdi et al. (2015), membre de notre laboratoire LIPAH, qui a exploité l'ontologie du Web de données FOAF pour les réseaux sociaux.
Intégration / Fusion
Nous allons l'expliquer en détail dans le chapitre 2
Raisonnement
Le raisonnement consiste en l'utilisation des alignements comme des règles pour raisonner sur les ontologies mises en correspondance. Les "bridging" axiomes utilisés dans l'intégration (l'ontologie de pont) sont des règles. Cet ensemble de règles est vu comme une ontologie O qui doit être écrite dans un langage ontologique supportant les règles ou les expressions des axiomes de pont. C'est la même notion de l'ontologie intermédiaire ou l'articulation des ontologies (définition 1 d'un mapping). Le raisonnement peut être décrit par la fonction T ransf ormAsRules(A) = O où A est un alignement entre deux ontologies O et O Euzenat and Shvaiko (2013).
Toute transformation des alignements sous une forme adaptée au raisonnement, telle que SWRL ou OWL, peut être utilisée par les moteurs d'inférence (les raisonneurs) de ces langages, tels que Pellet ou HermiT.
Enrichissement
L'enrichissement est le processus qui cherche de nouvelles entités (généralement à partir de ressources textuelles externes) et les place correctement au sein de l'ontologie à enrichir.
Voici quelques travaux d'enrichissement d'ontologies réalisés au sein de notre laboratoire LIPAH : Kamoun et al. (2010); Hamdi et al. (2012); Ben Yahia (2012c,a,b, 2014).
Conclusion
A présent, les entreprises ont migré vers l'adoption des stratégies de mondialisation et d'internationalisation. En effet, traditionnellement, les entreprises partageaient seulement les biens physiques en collaboration, mais maintenant elles ont aussi besoin de partager et intégrer leurs connaissances. C'est pourquoi la notion de l'interopérabilité s'impose car elle permet aux systèmes informatiques hétérogènes de communiquer, interpréter et traiter l'information échangée.
Pour ce faire, les ontologies se présentent comme le meilleur outil pour communiquer et partager des connaissances en fournissant une compréhension commune d'un domaine donnée. Malheureusement, les concepteurs des ontologies eux-mêmes appliquent des visions différentes du même domaine lors du développement des ontologies, et ceci engendre le problème de l'hétérogénéité sémantique qui est l'un des principaux obstacles de l'interopérabilité sémantique ; Il se produit lors de l'utilisation des ontologies de même domaine, i.e. quand des ontologies hétérogènes réutilisent les mêmes connaissances. L'intégration sémantique est indispensable pour remédier à ce problème. Elle se base sur la sémantique des systèmes inter-opérants pour comparer leurs différents concepts et déduire leurs correspondances, et éventuellement les associer et créer des bases de connaissances intégrées. Par conséquent, l'intégration sémantique mènera inévitablement à un matching inter ontologique qui est une étape essentielle dans l'intégration des ontologies.
Introduction
A présent, il existe une très grande confusion dans l'utilisation des termes "intégration" et "fusion" dans la littérature. En effet, il arrive que nous trouvons des travaux sur la fusion que les auteurs nomment "intégration", et des travaux sur l'intégration que les auteurs nomment "fusion" ; il y a des cas où les auteurs utilisent les deux termes comme synonymes et choisissent l'un d'entre eux comme titre de l'article (ils choisissent généralement le terme "intégration" car il parait plus général, ainsi vrai dans les deux cas). Par ailleurs, plusieurs auteurs utilisent le terme "intégration" dans le titre de leurs travaux, sans pour autant faire une intégration ; ils se contentent d'un matching ; et même s'ils font une intégration, ils ne l'explicitent et ne l'évaluent pas, ils se concentrent seulement sur l'évaluation du matching.
Toutes les définitions et les approches qui vont suivre vont être ordonnées chronologiquement dans chaque section.
Dans ce chapitre, nous citons les différentes définitions et approches du terme fusion des ontologies dans la littérature. Puis, nous citons les différents types d'intégration des ontologies, les définitions du terme intégration des ontologies dans la littérature, et ses principales approches existantes. Par la suite, nous évoquons les avantages de l'intégration et la fusion, leurs différences et leurs points communs, et nous expliquons les causes des erreurs qui peuvent se produire suite à ces deux processus. Ensuite, nous consacrons une petite section pour parler de ce qui nous intéresse parmi toutes ces définitions et approches évoquées. Enfin, nous clôturons ce chapitre par une conclusion qui résume le tout.
Fusion des ontologies
Puisque de nombreuses ontologies se réfèrent au même domaine et aux mêmes objets, il existe un besoin croissant de les fusionner et les organiser. En effet, le but ultime de la fusion est de représenter une meilleure perspective des connaissances d'un domaine.
En général, la fusion des ontologies est utilisée dans le domaine de l'intégration des données, mais elle peut être aussi perçue comme une technique utilisée dans le domaine de l'enrichissement des ontologies (de domaine) qui consiste à insérer dans l'ontologie des connaissances connexes en moins de temps et de coût.
La façon dont le processus de fusion est effectué est encore très peu claire. En effet, il n'y a pas de consensus sur la méthodologie à suivre pour fusionner les ontologies. La seule phase commune est la phase initiale qui prend en entrée un ensemble d'ontologies (deux ou plus). Certains commencent directement par toutes les ontologies à fusionner (méthode non incrémentale), d'autres commencent par un groupe initial sélectionné d'ontologies (généralement par une seule ontologie) qui est élargi ensuite de manière incrémentielle par les autres ontologies (méthode incrémentale) Pinto and Martins (2004).
Définitions de la fusion
Fusion de Noy D'après Noy and Musen (2000), dans la fusion, une ontologie unique qui est une version fusionnée des ontologies d'entrée est créée. Souvent, les ontologies sources couvrent des domaines similaires ou liés. C'est une définition très vague (et qui peut convenir aussi au terme "intégration des ontologies").
Fusion de Pinto (consensuelle)
Selon Pinto (1999), dans la fusion, nous avons, d'une part, un ensemble d'ontologies (au moins deux) qui vont être fusionnées (O 1 , O 2 , . . . , O N ) et, d'autre part, l'ontologie résultante du processus de fusion (O). Ainsi, cette méthode est non incrémentale. Le sujet des ontologies sources et de l'ontologie résultante est le même (S), bien que certaines ontologies sources soient plus générales que d'autres (leur niveau de généralité peut ne pas être le même). Le but est de remplacer les ontologies existantes, portant sur un sujet particulier, par une ontologie plus riche et plus large qui couvre mieux ce même sujet en fusionnant leurs connaissances (les terminologies, les définitions, et les axiomes des ontologies sources).
Selon eux, dans la fusion (l'unification qui est le troisième cas d'intégration de Sowa (1997)), les ontologies sources sont unifiées en une seule. Dans certains cas, les connaissances des ontologies sources sont homogénéisées et modifiées par l'influence d'une ontologie source sur une autre (à l'aide des opérations d'abstraction, de généralisation, de transformation (mapping)). Dans d'autres cas, les connaissances provenant d'une ontologie source particulière sont dispersées et mêlées avec les connaissances des autres sources. Malik et al. (2010) donnent une autre définition proche qui considère que la fusion est le fait de former des ontologies mieux modélisées à partir d'ontologies mal définies ou plus petites (i.e. qui ne couvrent pas tout le domaine). (2014), la fusion peut être symétrique ou asymétrique par rapport aux ontologies d'entrée. Ils exigent, dans ces deux types d'union, que la propriété de "préservation de l'égalité" soit assurée, ce qui signifie que les entités correspondues (comme prescrit dans le mapping entre les deux ontologies d'entrée) doivent être fusionnées dans la même entité afin qu'elles ne soient représentées qu'une seule fois dans l'ontologie résultante. Selon eux, en fusionnant les entités équivalentes ainsi, ils réduisent le chevauchement sémantique (même si que l'héritage multiple est aussi une source de conflits), ainsi le résultat de la fusion sera plus compact et moins redondant qu'une simple union directe des ontologies d'entrée (i.e. une ontologie de pont avec des "bridging" axiomes).
Approche symétrique L'approche symétrique est la plus courante et vise à fusionner les ontologies d'entrée avec la même priorité (en préservant toutes les entités de toutes les ontologies). C'est une approche "Full Merge" qui prend l'union des ontologies d'entrée et qui combine leurs entités équivalentes (en une seule entité). Mais elle engendre une quantité importante de conflits sémantiques due à l'organisation hétérogène des mêmes concepts dans les ontologies d'entrée et à l'introduction de l'héritage multiple dans les entités fusionnées, ce qui génère des chemins redondants (plusieurs chemins conduisant à une même entité), réduisant ainsi la compréhensibilité de l'ontologie résultante.
Approche asymétrique L'approche asymétrique, prend l'une des ontologies d'entrée comme cible, dans laquelle les autres ontologies sources seront fusionnées (d'une façon incrémentale) pour l'étendre, donnant la préférence uniquement à l'ontologie cible dont toutes les entités à elle seule doivent être préservées. Les entités des ontologies sources ne doivent pas obligatoirement faire partie de l'ontologie résultante (cible). Ici, nous n'aurons plus affaire à l'héritage multiple, ainsi nous n'aurons pas (ou presque pas) de conflits sémantiques dans l'ontologie résultante qui aura bien une structure d'arbre (où un seul chemin conduit à une entité). § Mais d'après nous, cette approche asymétrique est un enrichissement de l'ontologie cible, plutôt qu'une fusion des ontologies sources.
Fusion comme étant synonyme à l'intégration
Raunich and Rahm (2012)
Fusion comme étant une intégration
Chatterjee et al. (2017) considèrent la création d'une ontologie à l'aide de la fusion comme étant un processus incrémental où des ontologies de petites tailles, de différents domaines, et de développement indépendant, devraient être fusionnées en une seule ontologie pour former un domaine (interdisciplinaire) plus vaste. (C'est la définition de la composition / l'intégration).
Ils donnent l'exemple du domaine de l'agriculture qui peut se composer de plusieurs sous domaines tels que les pesticides et les engrais, la récolte, la terre (le sol), les prévisions météo, l'infrastructure d'irrigation, la gestion de la sécheresse, la gestion du bétail, l'infrastructure de marketing, le suivi des régimes et des programmes, etc.
Fusion comme étant une ontologie de pont
Selon De Bruijn et al. (2006), dans la seconde approche de fusion (l'ontologie de pont), les ontologies originales ne sont pas remplacées, elles sont conservées après l'opération de fusion, c'est plutôt une "vue", appelée "Bridge Ontology", qui est créée. Elle importe les ontologies originales et spécifie des correspondances entre elles pour relier les entités de ces ontologies par des axiomes de pont. Ces "Bridging" axiomes sont des règles de transformation utilisées pour connecter la partie de chevauchement des ontologies sources. D'après Euzenat and Shvaiko (2013), la fusion des ontologies est la création d'une nouvelle ontologie O qui lie les différentes entités de deux ontologies O et O (qui se chevauchent) par des axiomes de pont ou des axiomes d'articulation, comme prescrit dans l'alignement entre O et O . Ils expriment la fusion par l'opérateur suivant : f usion(O, O , A) = O . Selon eux, les ontologies sources sont inchangées et l'ontologie résultante est supposée contenir les connaissances des ontologies initiales de sorte que les conséquences de chaque ontologie source soient les conséquences de la fusion.
Dans la fusion de Abbas and Berio (2013), une nouvelle ontologie peut être créée à partir d'ontologies sources, en établissant des correspondances entre les ontologies sources (un matching), puis en les combinant avec ces correspondances trouvées. Ils ne spécifient pas également les domaines des ontologies sources. § C'est l'approche que nous allons suivre. En général, leurs algorithmes consistent en une itération de trois étapes principales : 1. Trouver un endroit où il y a un chevauchement dans les deux ontologies (trouver des entités candidates identiques ou apparentées) ; 2. Relier ces entités (qui sont sémantiquement proches) via des relations d'équivalence ou de subsomption ; ou les fusionner (après avoir transformé et uni les ontologies). 3. Vérifier la consistance, la cohérence et la non-redondance de la nouvelle structure de l'ontologie résultante, et les résoudre (trouver des solutions possibles à ces conflits). Si deux ou plusieurs entités (concepts ou relations) des ontologies sources sont équivalentes à une certaine entité cible, elles seront automatiquement fusionnées pour former une seule entité dans l'ontologie cible ; Si une entité source est subsumée par une entité cible, elle sera importée dans l'ontologie cible avec le consensus des experts du domaine ; La même approche sera appliquée si une entité source subsume une autre entité cible ; Si une entité source est disjointe à toutes les entités cibles, elle peut être non pertinente et ainsi rejetée, ou peut être considérée comme une nouvelle entité qui enrichit éventuellement l'ontologie cible.
Mais ce processus nécessite beaucoup de travail manuel. Bien qu'ils déclarent que leur outil assure que chaque aspect des ontologies sources soit présent dans l'ontologie de sortie, ils n'expliquent pas la manière avec laquelle ils ont fait les mises à jour de tous les axiomes sources qui appellent les entités nouvellement modifiées suite à la fusion (en effet, deux ou plusieurs entités similaires formeront une nouvelle entité).
Ils n'ont pas évoqué non plus le traitement des conflits sémantiques (les incohérences) générés certainement suite à la fusion. ¶ La sortie de ces deux étapes est un modèle en réseau où toutes les paires de concepts équivalents sont fusionnées générant ainsi un héritage multiple. Selon eux, il ne s'agit plus d'une ontologie (qui doit être un modèle en arbre), mais plutôt d'un réseau. C'est pourquoi ils ont ajouté deux autres étapes pour transformer le modèle initial de fusion en une structure d'arbre 3. La décomposition du modèle (de réseau) en plusieurs blocs dont les concepts fusionnés sont les frontières.
4. La reconstitution de ce modèle, de sorte que les concepts contenus dans les blocs (à part les concepts fusionnés) soient réorganisés pour former un seul chemin acyclique entre les deux concepts fusionnés. Cette réorganisation va être réalisée à l'aide d'un matching de subsomption / d'inclusion (is-a) entre les concepts de chaque bloc.
Dans la figure 2.5, ils donnent un exemple de correspondances entre deux fragments d'ontologies à fusionner. Dans l'image 2.6, ils donnent un modèle qui illustre le résultat des deux premières étapes, où les concepts fusionnés ont plus qu'un super-concept direct (héritage multiple), ce qui forme une structure de réseau. Dans la figure 2.7, ils donnent le modèle qui illustre le résultat des deux dernières étapes, où la sortie finale est une ontologie ayant les concepts réorganisés sous forme d'arbre. Il s'agit bien de très petites ontologies fusionnées en un temps relativement long.
FUSION DES ONTOLOGIES
INTÉGRATION DES ONTOLOGIES
Intégration des ontologies
En général, les techniques d'intégration des ontologies sont utilisées dans le développement des ontologies ou dans le domaine de l'intégration des données.
L'intégration des ontologies joue un rôle important dans le développement des ontologies en réutilisant des ontologies publiques existantes pour construire une ontologie en cours de développement ; ce qui réduit le coût de l'ingénierie des ontologies et favorise la réutilisation des modules d'ontologies standards. Tenons l'exemple de la construction d'une ontologie de catalogage des bibliothèques qui peut nécessiter l'assemblage d'ontologies dans les domaines des personnes, des livres, des sujets, des coordonnées géographiques, des numéros d'identification des livres, etc.
Types d'intégration
Voici les trois types d'intégration d'ontologies selon Keet (2004) :
Intégration sémantique
Elle se focalise sur le sens voulu des entités, e.g. découvrir si le concept C1 dans l'ontologie I est synonyme (ou hyponyme ou hyperonyme) au concept C2 dans l'ontologie II. C'est le type auquel nous nous intéressons.
Intégration structurelle
Quand la sémantique est (convenue d'être) identique mais l'organisation des entités (la catégorisation, le schéma) ne l'est pas et doit ainsi être alignée et intégrée. Il faut noter que la distinction entre la sémantique et la structure n'est pas aussi claire que cela puisse paraître, car la structure transporte une interprétation sémantique de la conceptualisation.
Intégration syntaxique
Elle se concentre sur la réalisation d'un formalisme uniforme à partir des formalismes avec lesquels les ontologies sources sont exprimées, tels que la description logique, KIF, OWL, F-logic etc. Dans la méthodologie, ce type d'intégration vient logiquement en troisième position (après l'intégration sémantique et structurelle), car c'est inutile de faire correspondre les formalismes si le sens de ce qui est intégré n'est pas compatible. Cependant, ces traductions, telles que la représentation syntaxique d'un concept dans deux langages formels, peuvent être recherchées indépendamment du domaine de l'intégration (le domaine de traduction des ontologies).
Définitions de l'intégration
Intégration comme étant une fusion Comme le montre la figure 2.8, pour Mena et al. (1996), l'intégration relie les entités des ontologies à intégrer, en traversant les hyponymes, les hyperonymes, et les synonymes entre eux. C'est en effet une fusion des ontologies. Selon la quantité de changement nécessaire pour dériver C de A et B, Sowa (1997) distingue trois niveaux d'intégration qui ressemblent un peu à la classification de Heflin and Hendler (2000) :
Alignement C'est la définition 1 de l'alignement (expliquée dans le chapitre 1). Il s'agit du plus bas niveau d'intégration qui ne nécessite aucun changement dans A et B. Il supporte l'interopérabilité la plus limitée (le mapping de Heflin and Hendler (2000)).
Compatibilité partielle Elle nécessite plus de changements dans A et B, et permet une interopérabilité moyenne. Toute inférence exprimée dans une ontologie en utilisant seulement les entités alignées, peut être traduite en une inférence équivalente dans l'autre ontologie (les révisions de mappings et l'intersection des ontologies de Heflin and Hendler (2000)).
Unification (Compatibilité totale) Elle nécessite des changements ou des réorganisations majeures dans A et B, pour entraîner l'interopérabilité la plus complète (le plus haut niveau d'intégration). En effet, tout ce qui peut être fait avec une ontologie peut être fait d'une manière exactement la même avec l'autre. Autrement dit, toute inférence exprimée dans une ontologie, peut être traduite en une inférence équivalente dans l'autre (C'est la fusion de Pinto and Martins (2004)).
Intégration de Heflin et Hendler
Selon Heflin and Hendler (2000), l'intégration des ontologies implique généralement l'identification des correspondances entre deux ontologies, la détermination des différences dans les définitions des entités, et la création d'une nouvelle ontologie qui résout ces différences. Selon eux, la simple création d'une nouvelle ontologie intégrée ne résout pas le problème d'intégration de l'information sur le Web. En effet, puisque d'autres ontologies et pages Web dépendent des ontologies intégrées, tous les objets dépendants devraient être révisés pour refléter la nouvelle ontologie. Vu que cette tâche est impossible, ils ont suggéré trois façons d'incorporer les résultats de l'intégration dans le Web comme le montre la figure 2.9 :
Mapping des ontologies C'est la définition 1 du mapping (expliquée dans le chapitre 1 ) les règles qui mettent en correspondance les entités de O 2 par rapport à O 1 (A ne pas confondre avec la notion de révision de mapping qui veut dire le débogage ou la réparation de mapping ! ! !). § Ils pensent que l'inconvénient de ces deux premières approches est que les concepts partagés entre deux domaines pourraient être également utilisés dans plusieurs autres domaines connexes, ainsi chaque nouveau domaine aurait besoin d'un ensemble de règles pour le mapper à tous les autres domaines en chevauchement. Et cela peut devenir très lourd. . § Ils considèrent cette troisième approche comme l'approche la plus naturelle d'intégration des ontologies car elle a l'avantage que l'équivalence des termes soit déterminée dans la phase de pré-traitement plutôt que lors de l'exécution de la requête.
INTÉGRATION DES ONTOLOGIES
Intégration de Pinto (consensuelle)
Dans l'intégration ou la composition des ontologies, Pinto (1999) considère que nous avons, d'une part, une (ou plusieurs) ontologies (O 1 , O 2 , ..., O N ) qui vont être intégrées dans l'ontologie cible, et d'une autre part, l'ontologie cible en cours de construction (O) qui sera issue du processus de l'intégration. Ainsi, cette méthode est incrémentale. Les domaines des ontologies sources (à intégrer dans l'ontologie cible) sont généralement différents entre eux, et différents du domaine de l'ontologie cible, mais il peut y avoir une relation entre eux (D 1 , D 2 , ..., D k ).
Il s'agit de deux ou plusieurs ontologies sources de sujets différents (ou de sujets liés) qui vont tout simplement être assemblées, composées, agrégées, ou combinées pour former une ontologie résultante, peut-être après que les ontologies sources aient subi quelques changements, comme l'extension, la spécialisation, la transformation, ou l'adaptation.
L'intégration vise à créer une ontologie d'un nouveau domaine plus large composé de tous les domaines des ontologies d'entrée. C'est un processus de réutilisation qui vise à construire des ontologies à partir d'autres ontologies existantes.
Les ontologies à intégrer doivent répondre à certaines exigences avant de leur appliquer le processus d'intégration, e.g., le domaine, l'abstraction, le type, la généralité, la modularité, l'évaluation, etc.
L'ontologie résultante doit avoir toutes les propriétés d'une bonne ontologie : consistante, cohérente, complète, ayant un niveau adéquat de détail, et décrivant seulement le vocabulaire nécessaire pour le domaine, etc. Il ne devrait pas avoir une ontologie existante similaire à la résultante, sinon il faudrait tout simplement réutiliser l'ontologie existante.
Avant leur inclusion dans l'ontologie résultante, les entités de l'ontologie à intégrer peuvent être :
• incluses (utilisées telles quelles) ;
• spécialisées (conduisant à une ontologie plus spécifique dans le même domaine) ;
• augmentées (étendues) par de nouvelles entités manquantes (soit par des entités plus générales, soit par des entités de même niveau) ; • adaptées (modifiées) pour les corriger ou les améliorer en changeant :
-leurs terminologies (pour se conformer aux règles de normalisation des noms, ou introduire une terminologie standard ou plus usuelle), -leurs documentations (pour les mettre à jour ou améliorer leur clarté), -leurs définitions (pour les mieux représenter dans le domaine concerné) ; • retirées (à cause de leur non pertinence). Ces adaptations transforment l'ontologie source choisie en l'ontologie voulue.
Ils précisent que des problèmes tels que la cohérence, la consistance, et le niveau de détail de l'ontologie résultante doivent être traités (i.e. elle ne doit pas avoir des parties de niveau de détail exagéré et d'autres de niveau adéquat).
La figure 2.10 illustre leur définition. Pinto (1999) interprétée par Keet (2004) Intégration comme étant synonyme à la fusion Klein (2001) considère l'intégration et la fusion comme égales. Il les définit par la création d'une nouvelle ontologie à partir de deux ou plusieurs ontologies existantes qui se chevauchent. C'est une définition très vague qui ressemble à la définition de la fusion des ontologies de Noy and Musen (2000). (2012) Autres définitions D'après Kokla (2006), une intégration d'ontologies génère une nouvelle ontologie intégrée sans modifier les originales. (2012), l'intégration des ontologies est un processus de construction d'une nouvelle ontologie en utilisant des ontologies disponibles. Elle peut être divisée en trois différents scénarios : -Le mapping (définition 1 de l'alignement dans le chapitre 1) ; -L'intégration (la réutilisation) ; -La fusion.
Raunich and Rahm
Selon Umer and Mundy
Selon Wróblewska et al. (2012), il existe différents types d'intégration des ontologies : -L'alignement, le mapping (définition 1 de l'alignement dans le chapitre 1) -La transformation -La fusion -L'intégration, etc.
Principaux outils d'intégration et leurs limites
Les approches récentes d'intégration des ontologies suivent un schéma modulaire qui décompose ce problème en sous-problèmes indépendants tels que le matching et puis la composition. De cette façon, elles profitent des grands progrès déjà réalisés dans le domaine du matching automatique des ontologies qui identifie les entités à intégrer dans le deuxième sous-problème (la composition).
La plupart des outils actuels d'intégration des ontologies sont semi-automatiques, car les experts de domaine et les ingénieurs de connaissances sont souvent nécessaires pour aider à la prise de décisions.
L'outil ILIADS
L'algorithme ILIADS de Udrea et al. (2007) prend en entrée deux ontologies consistantes O1 et O2, et retourne en sortie un alignement A entre O1 et O2, de telle sorte que l'intégration future de O1 et O2 à travers A soit consistante et cohérente. Les auteurs combinent un algorithme de matching de similarité (lexicale, structurelle, extensionnelle, et de clusters) avec un algorithme d'inférence logique qui raisonne sur les conséquences des relations (des correspondances) de l'alignement. Les relations de l'alignement sont exprimées comme des axiomes OWL (owl:equivalentClass, owl:equivalentProperty, owl:sameAs) ajoutés à l'ontologie résultante (qui compose O1 et O2).
Ils ont utilisé le raisonneur Pellet pour vérifier, à la fin de chaque expérience, si l'ontologie résultante est consistante ou pas. ILIADS a produit des inconsistances dans moins de 0,5% de leurs essais.
Mais ils n'ont pas évoqué les incohérences (e.g. le nombre de classes insatisfiables), car une ontologie peut être consistante tout en ayant une multitude de classes insatisfiables. Leur approche qui consiste en un processus interactif semi-automatique composé de quatre étapes principales (le calcul des correspondances, le calcul des nouvelles inférences, la détection des erreurs, et la réparation des erreurs identifiées à l'aide de l'utilisateur) a été appliquée pour réaliser l'outil "ContentMap", un plugin téléchargeable destiné à être utilisé dans Protégé 4.
ContentMap permet à l'utilisateur de choisir un ou plusieurs outils d'alignement à sélectionner (comme OLA, AROMA, CIDER, etc.) en leur attribuant différents poids. Il lui permet aussi de filtrer automatiquement les correspondances en choisissant un seuil de confiance minimal.
Le calcul des nouvelles inférences a été fait à l'aide de la notion de "différence déductive" qui compare les axiomes de l'ontologie résultante U (la composition de O1, O2, et M (Mapping)) avec les axiomes de chacune des ontologies initiales (O1, O2, et M ) pour détecter ceux qui existent dans l'ontologie de sortie mais qui n'existent pas dans les ontologies initiales, i.e. le système calcule la différence logique entre les inférences avant et après l'application des correspondances. Pour aider l'utilisateur à comprendre les conséquences sémantiques de U , ils lui montrent les justifications et les explications derrière la manifestation de ces nouveaux axiomes.
Les inférences imprévues de l'ontologie de sortie U (i.e. les inférences qui se trouvent dans l'ontologie résultante U mais qui ne se trouvent pas dans les ontologies individuelles O1, O2, et M ) seront présentées à l'utilisateur qui aidera à réparer U en choisissant la ou les source(s) d'axiomes à modifier (O1, O2, et/ou M ) et en supprimant les axiomes non désirés (qui sont, selon lui, générateurs d'incohérences) :
• Il peut choisir de supprimer uniquement des axiomes provenant de l'ontologie M et laisser les axiomes des ontologies initiales O1 et O2 intacts, puisque M est généralement considérée la plus grande source d'erreurs.
• Mais si deux entités correspondues sont originairement contradictoires dans O1 et O2, et leur relation dans M est correcte, l'utilisateur sera en face d'un dilemme ; soit supprimer l'axiome de la correspondance correcte, soit supprimer les axiomes originaux dans l'une ou les deux ontologies O1 et O2.
Par suite, le système exécute un algorithme de réparation qui essaie de supprimer le minimum d'axiomes tout en préservant les inférences jugées valides par l'utilisateur. (b) Sélectionner la première ontologie source à intégrer ; ouvrir l'ontologie cible "Intégrée" dans l'éditeur Protégé et importer l'ontologie source sélectionnée ;
(c) Utiliser l'option "Merge ontologies" de Protégé pour intégrer l'ontologie source dans la destination ("Intégrée"). De cette façon, l'ontologie source sera incluse dans le même fichier de l'ontologie cible ;
(d) Puis, en utilisant les outils de refactoring, changer l'IRI de tous les éléments de l'ontologie source en "Intégrée" qui est l'IRI de l'ontologie cible. 3. La vérification de la consistance et la cohérence de l'ontologie cible (en utilisant un raisonneur dans Protégé) et la vérification de l'absence de redondances, puis leur résolution en éliminant les relations "is-a" redondantes entre les entités (causées par les relations d'équivalence).
Les étapes 2 et 3 sont itératives (elles se répètent pour chaque ontologie source à intégrer).
Cette approche est simple et claire, et bien que nous n'ayons pas la moindre idée sur la qualité du matching réalisé, son inconvénient majeur est qu'elle est toute manuelle (elle est difficile à appliquer pour les grandes ontologies).
Dans les expérimentations, ils ont créé une ontologie cible vide dans laquelle ils ont intégré l'ontologie source eQual. Puis ils ont intégré l'ontologie source Ahn dans l'ontologie cible (contenant déjà eQual) en reliant les paires d'entités mises en correspondance par des relations d'équivalence. De la même manière, ils ont intégré trois autres ontologies sources (SiteQual, Website Evaluation Questionnaire, et Web Portal Site Quality) dans l'ontologie cible. Toutes ces ontologies sources appartiennent au domaine de l'évaluation de la qualité des sites Web. Dans chacune de ces itérations, le raisonneur a détecté des incohérences et des relations de subsomption redondantes dans l'ontologie résultante qu'il fallait corriger. Il s'agit d'une fusion, non pas d'une intégration. Dans ce travail, il n'y a pas une partie d'évaluation à l'aide d'une référence ou des résultats d'un travail concurrent pour se comparer avec.
L'outil FITON pour l'intégration des data sets
Zhao and Ichise (2014) ont proposé un système semi-automatique, nommé FITON, qui prend en entrée des data sets (deux ou plusieurs ontologies) du LOD (Linked Open Data) et qui retourne en sortie une ontologie intégrée (et enrichie).
Dans ce cas, la problématique c'est qu'il existe très peu (ou pas) de liens d'équivalence préétablis entres les différentes classes et propriétés des data sets (contrairement aux liens "sameAs" disponibles avec abondance entre leurs instances -des centaines de millions -) ; ce qui rend difficile l'extraction directe des classes et des propriétés équivalentes pour faire l'intégration de ces data sets.
Pour ce faire, ils ont intégré tout d'abord les instances identiques (informations déjà fournies sous forme de propriétés "owl:sameAs" dans les data sets) et ont extrait les classes et les propriétés qui décrivent ces instances pour former un graphe nommé graphe "sameAs" à partir duquel ils vont découvrir les similarités entre les différentes classes et propriétés contenues dans le graphe en combinant des méthodes de matching (terminologiques et sémantiques) pour parvenir enfin à intégrer tous les types d'entités des data sets.
Puisqu'il n'existe pas de benchmark pour les ensembles de données du LOD, un expert a créé manuellement un alignement de référence entre les deux data sets DBpedia et Geonames. DBpedia, la version "linked data" de Wikipédia de domaine transversal, contient (au moment Au final, leur ontologie de sortie contenait seulement 135 classes et 453 propriétés. Nous concluons qu'ils ont fait une sorte d'intersection entre les deux ontologies plutôt qu'une intégration, car la conservation des informations initiales des ontologies d'entrée n'est pas respectée.
Puisqu'ils comptent sur l'analyse des instances inter-liées (sameAs) pour découvrir les alignements entre les data sets, leur outil ne pourra pas fonctionner s'il n'existe pas (ou s'il n'existe que peu) de liens "sameAs" entre les instances. Ainsi, l'inconvénient de FITON est qu'il ne peut fonctionner efficacement que lorsqu'au moins 4% des instances d'un data set soient liées (identiques) aux instances de l'autre data set.
Différences entre la fusion et l'intégration
L'intégration et la fusion des ontologies sont tous les deux des processus de construction d'une nouvelle ontologie en se basant sur les informations de deux ou plusieurs ontologies sources. Cependant, dans la fusion, il y a beaucoup de connaissances en chevauchement entre les entités des ontologies sources, alors que dans l'intégration (la composition), il y a peu ou pas de chevauchement Pinto (1999).
Par conséquent, la différence principale entre ces deux processus est que, après le processus d'intégration (composition), nous pouvons identifier dans l'ontologie résultante les régions issues des ontologies sources, car les connaissances ont été laissées plus ou moins inchangées. En effet, l'ontologie résultante est composée de modules (sous-ontologies). Tandis qu'après le processus de fusion, il est généralement difficile d'identifier dans l'ontologie résultante les régions issues des ontologies sources car les connaissances ont été mêlées ou unifiées et homogénéisées ainsi modifiées.
Avantages de ces deux processus
Dans le contexte de l'ingénierie des ontologies, la réutilisation des modèles de connaissances existants est recommandée comme étant un facteur clé pour le développement d'ontologies rentables et de haute qualité. Ziemba et al. (2015) ont conclu que la construction d'une ontologie à l'aide de l'intégration ou de la fusion des ontologies sources, est beaucoup moins complexe que son processus de construction à partir de zéro.
L'intégration des ontologies réduit le coût et le temps requis pour la conceptualisation des domaines à partir de zéro, et améliore la qualité des ontologies nouvellement développées pour une application particulière en réutilisant des composants déjà validés.
La fusion des ontologies évite la confusion qui peut être générée à partir de plusieurs représentations du même domaine et renforce l'orchestration et l'harmonisation des connaissances.
CONSÉQUENCES SÉMANTIQUES DE CES DEUX PROCESSUS
Ces deux processus sont aussi particulièrement utilisés lorsqu'il est nécessaire d'effectuer un raisonnement impliquant plusieurs ontologies. Jiménez-Ruiz et al. (2009) affirment que quand nous raisonnons sur les ontologies à intégrer et leurs correspondances, sur l'ontologie produite suite à l'intégration (contenant les axiomes des correspondances), ou sur l'ontologie produite suite à la fusion, il est souvent nécessaire de détecter des conflits ; ainsi des erreurs vont probablement se manifester. Ces erreurs sont dues à deux causes principales :
Conséquences sémantiques de ces deux processus
• Les correspondances (générées généralement par un outil de matching automatique) peuvent comporter quelques fautes ou être erronées (incorrectes).
• Même si les correspondances trouvées étaient toutes correctes, les ontologies à intégrer peuvent contenir des descriptions contradictoires des entités correspondues, et ceci est à cause de la représentation variable des ontologies sources. En effet, selon Cheatham and Pesquita (2017), les correspondances qui forment l'alignement ne sont pas indépendantes les unes des autres :
• Il y a des cas dans lesquels seulement une parmi plusieurs correspondances peut être vraie (parmi les correspondances ayant la même entité source). • Dans d'autres cas, plusieurs correspondances, réunies ensemble, peuvent conduire à une inférence involontaire et indésirable ou une classe insatisfiable.
• Ou la combinaison de ces deux causes.
Ces erreurs sont des conséquences logiques imprévues (e.g. des classes insatisfiables, de nouvelles subsomptions (suite aux axiomes d'équivalence), etc.) difficiles à détecter, à comprendre, et à réparer. Par conséquent, l'ontologie globale créée, associée aux règles de correspondances, est très prédisposée aux erreurs et nécessite une supervision d'un expert de domaine ou une supervision automatique supportée par les applications.
Récemment, la recherche a été conduite au debugage et à la révision des alignements, ainsi que le debugage et la réparation des insatisfiabilités dans les ontologies OWL. Cependant, la suppression de certaines insatisfiabilités peut entraîner une perte d'informations précieuses provenant des ontologies sources. D'ailleurs, c'est le plus grand inconvénient de l'intégration ou de la fusion des ontologies dans les travaux actuels.
Exemples
Les mêmes données peuvent être décrites par des ontologies de différentes perspectives. Cependant, même en se concentrant sur une même perspective, la multitude d'ontologies actuellement utilisées pour les décrire, empêche leur intégration transparente. En effet, l'intégration de deux ontologies de différents modèles peut causer des incohérences logiques.
Supposons que A est une classe satisfiable dans O1, et B et C sont des classes disjointes dans O2, et supposons que deux correspondances (d'un alignement entre O1 et O2) disent que A est une sous classe de B, et que A une est sous classe de C. Si ces correspondances, exprimées sous forme d'axiomes, sont ajoutées à la composition des deux ontologies O1 et O2, ils vont créer un problème car une classe ne peut pas être une sous classe de deux classes mères disjointes. Par conséquent, A sera insatisfiable et l'ontologie résultante sera incohérente. Et si jamais A avait une instance, l'ontologie résultante serait inconsistante Abbas and Berio (2013).
Voici un autre exemple : Fahad et al. (2010), les outils de fusion ou d'intégration existants ne préservent pas la connaissance disjointe des ontologies sources (pour but de produire à la fin une ontologie cohérente) et sont en général semi-automatiques nécessitant beaucoup d'intervention humaine pour la validation des correspondances suggérées et également la résolution des conflits générés durant ou après la construction de l'ontologie résultante. Par conséquent, le résultat est incomplet (il viole la description des disjonctions) et très dépendant de l'observation et de l'intelligence de l'utilisateur.
Conséquences dans les outils existants
D'après
La raison de l'inexactitude de ces outils c'est qu'ils n'exploitent pas la sémantique cachée (et précisément les disjonctions) des ontologies sources pendant la phase de matching, et détectent ainsi des correspondances non fiables qui créent des situations erronées dans l'ontologie de sortie.
CONSÉQUENCES SÉMANTIQUES DE CES DEUX PROCESSUS
Remarque
Les alignements peuvent être réalisés pour aider l'interrogation distribuée ou bien le raisonnement logique Cheatham and Pesquita (2017) :
• Pour l'interrogation, le rappel (i.e. les résultats pertinents) des correspondances est un aspect important. Cela signifie que, pour les applications centrées sur les requêtes, ce n'est pas grave si les correspondances provoquent d'inconsistance logique, l'essentiel c'est que les relations soient correctes. Ce cas s'applique dans le contexte des linked data, et l'intégration des ontologies tout en les maintenant séparées.
• Pour le raisonnement logique, le rappel n'est pas suffisant car les correspondances peuvent être correctes, mais générant de conflits. En effet, les applications qui ont l'intention d'employer un raisonneur sur les données intégrées ne peuvent pas utiliser un alignement qui génère une inconsistance logique. Ce cas s'applique dans le contexte de l'intégration des ontologies tout en les regroupant en une seule ontologie (la fusion et l'ontologie de pont entre autres).
Discussion et synthèse
Dans notre mémoire, nous allons nous intéresser aux ontologies de pont, qui, suivant les définitions ci-dessus, peuvent entrer dans le cadre de la fusion et de l'intégration, les deux à la fois, mais vu que le terme "intégration" peut être également un terme générique qui inclut la fusion, nous avons choisi d'utiliser le terme intégration, d'où le titre de notre mémoire. L'ontologie de pont peut être considérée comme le plus faible niveau de "fusion" des ontologies car dans nos expérimentations, nous avons uni des ontologies ayant un domaine identique ou proche ; cependant, elle peut être considérée aussi comme une "intégration", car il s'agit bien d'une composition des ontologies sources de telle manière que les éléments de chacune des ontologies sources soient facilement reconnus dans l'ontologie résultante.
Ce type d'intégration est utilisé par exemple dans le cas où des entreprises en coopération veulent unir leurs connaissances sans tout de même changer leurs ontologies de base, ainsi changer toutes les données qui s'y conforment. En d'autres termes, elles veulent coopérer tout en restant indépendantes. Dans l'ontologie résultante, les noms et les descriptions des entités issues des ontologies sources restent comme ils le sont originairement, sans changer tout un système qui en est dépendant.
Conclusion
L'intégration des ontologies est encore plus difficile avec les ontologies de domaines identiques, similaires, complémentaires, et surtout interdisciplinaires. Les difficultés apparaissent aussi avec les ontologies de différents niveaux formels (les ontologies légères et lourdes). Or, les ontologies qui ont beaucoup de points communs dans la structuration et l'organisation de leurs entités ont plus de chance de ne pas avoir des conflits et des difficultés d'intégration.
Il y a de multiples possibilités pour intégrer les ontologies. Les approches peuvent être distinguées par trois facteurs principaux : le niveau d'intégration (d'interopérabilité sémantique), le(s) domaine(s) des ontologies d'entrée, et la méthode d'intégration (incrémentale ou non).
Introduction
Dans ce chapitre, nous décrivons les étapes de notre méthode et celle de la référence, citons les conditions favorables pour avoir les meilleurs résultats, et proposons une nouvelle terminologie à utiliser au lieu des notions floues et mal appropriées de la littérature.
Description de la nouvelle méthode
En général, le processus d'intégration des ontologies passe par deux étapes majeures : le matching des ontologies d'entrée, puis la composition / l'union / l'agrégation de ces ontologies avec les mappings (ou les alignements) générés suite à l'étape de matching. La figure 3.1 illustre ce processus.
Mais dans notre travail, nous avons utilisé des alignements de référence comme entrée, sans avoir fait l'étape de matching par nous-mêmes, ainsi nous allégeons notre charge de travail et nous nous concentrons sur l'intégration concrète. Les temps d'exécution de nos expérimentations ne comprennent pas le temps de matching. En effet, le vrai temps d'exécution sera la somme de notre temps global et celui du matching (supposé fait). Ainsi, le temps d'exécution réel de notre méthode dépendra du temps d'exécution de l'algorithme du matching utilisé, et la qualité de l'ontologie résultante dépendra de la qualité des alignements d'entrée utilisés. La
Approche générale de OIA2R
Notre implémentation et également celle de la référence sont divisées en deux parties majeures :
1. La première consiste à composer (assembler) les ontologies d'entrée. Avec ce code seul, nous obtiendrons une ontologie composée des sous-ontologies sources, ainsi contenant les axiomes de description des entités des ontologies sources, sans "bridging" axiomes entre elles. § Pour l'instant, il s'agit d'une intégration (composition) simple sans interopérabilité sémantique.
2. La deuxième consiste à ajouter (aux axiomes créés dans la première étape) des axiomes de pont qui sont en fait des axiomes d'équivalence entre les différentes entités. Ce sont des axiomes qui traduisent fidèlement les correspondances provenant des alignements entre les ontologies sources. § Ces deux étapes font une intégration qui produit une ontologie dite "ontologie de pont" qui permet l'interopérabilité sémantique.
Ontologie de sortie = axiomes des entités sources + "bridging" axiomes 3.
Démarche détaillée de OIA2R
Introduction au refactoring
Un IRI d'une ontologie (Internationalised Resource Identifier) identifie l'ontologie d'une façon unique. Il est considéré comme son nom. Il peut être un IRI physique, i.e. un fichier .owl local, ou bien un URI à publier dans le Web, i.e. une adresse Web contenant ce fichier .owl. L'IRI d'une entité (classe, propriété, ou instance) est composé d'un "IRI de préfixe" (un préfixe) suivi du "nom" court de l'entité (un suffixe). En général, la partie "préfixe" de l'entité est exactement l'IRI de l'ontologie actuelle (ou d'une autre ontologie existante), mais elle peut aussi contenir en plus un "ID" (identifiant), juste après l'IRI de l'ontologie :
Dans une ontologie, nous ne pouvons pas avoir deux IRIs identiques, i.e. si deux entités (deux objets créés dans OWL API) ont le même IRI, alors après leur création, il s'agira de la même entité. Ainsi, dans une ontologie, une entité (un IRI complet d'une entité) doit être unique. Mais quand nous allons intégrer des ontologies de même domaine en une seule ontologie, il y aura un grand risque de rencontrer des entités, même si originaires d'ontologies différentes (donc d'IRIs de préfixe différents), mais ayant exactement le même "nom local" (suffixe). Ceci nous causera un problème, car nous voulons, conformément aux standards, que les entités de notre future ontologie aient comme "IRI de préfixe" l'IRI de cette dernière. Dans ce cas, pendant la création de ces entités ayant le même "nom", seulement une sera créée, et elle aura dans sa description toutes les informations de ces entités. Elle sera bien évidemment sémantiquement erronée.
Voici un exemple pour concrétiser ce que nous étions en train de dire. Les entités de nom "Paper", "Person", et "Conference" existent dans au moins trois ontologies de la base "Conference" : cmt (Ont1), conference (Ont2), et confOf (Ont3) :
• Voici les IRIs complets originaux des entités ayant le nom "Paper" :
- Pour pallier cette redondance et ne pas mettre les informations (les définitions) de toutes ces entités dans l'ontologie de sortie dans une seule entité ayant ce nom, nous avons choisi d'ajouter un ID aux IRIs de préfixe des entités de notre ontologie, pour pouvoir les différencier.
Nous allons attribuer à chaque ontologie un numéro ; celle qui sera parsée la première aura le numéro 1, la suivante aura le numéro 2, et ainsi de suite. L'ID sera le numéro de l'ontologie originale d'où venait l'entité en question. Par conséquent, nous pourrons garder intacte la partie "nom" des entités redondantes, sans être obligés de la modifier. C'est seulement la partie "IRI de préfixe" qui va changer. Nous avons défini l'ID sur quatre caractères, ainsi les quatre derniers caractères du préfixe de chaque entité seront réservés à l'ID.
• Voici comment vont paraître les IRIs complets des entités de nom "Paper" dans notre ontologie de sortie : -http ://intégration/001#Paper -http ://intégration/002#Paper -http ://intégration/003#Paper
• Voici comment vont paraître les IRIs complets des entités de nom "Person" dans notre ontologie de sortie : -http ://intégration/001#Person -http ://intégration/002#Person -http ://intégration/003#Person
• Voici comment vont paraître les IRIs complets des entités de nom "Conference" dans notre ontologie de sortie : -http ://intégration/001#Conference -http ://intégration/002#Conference -http ://intégration/003#Conference
DÉMARCHE DÉTAILLÉE DE OIA2R
De cette manière, le "nom" redondant d'une entité quelconque sera préservé, aura un IRI unique dans la nouvelle ontologie, et toutes ses informations liées (sa définition dans son ontologie originale) seront conservées correctement.
Première étape
En détail
Pendant le parsing des classes des ontologies d'entrée, nous extrayons pour chaque classe sa définition qui consiste en ses annotations utilisées (ses labels, ses commentaires, ses propriétés d'annotation), ses superclasses, ses classes équivalentes, et disjointes (informations avec lesquelles nous créons les classes de notre future ontologie). Et nous remplissons au fur et à mesure le HMap des classes qui contiendra comme "clé" l'URI original de la classe, et comme "valeur" le numéro de l'ontologie dont il est issu.
Pendant le parsing des propriétés d'objet/data des ontologies d'entrée, nous extrayons pour chaque propriété sa définition qui consiste en ses annotations utilisées (ses labels, ses commentaires, et ses propriétés d'annotation), ses super-propriétés, ses domaines, ses images, ses propriétés inverses (pour les propriétés d'objet seulement), équivalentes, disjointes, et son type (informations avec lesquelles nous créons les propriétés de notre future ontologie). Et nous remplissons au fur et à mesure les deux HMaps (des propriétés d'objet, et des propriétés data) qui contiendront comme "clé" l'URI original de la propriété, et comme "valeur" le numéro de l'ontologie dont il est issu.
Pendant le parsing des instances des ontologies d'entrée, nous extrayons pour chaque instance sa définition qui consiste en ses annotations utilisées (ses labels, ses commentaires, et ses propriétés d'annotation), ses classes qui l'instancient, ses instances identiques et différentes, les propriétés d'objet/data qu'elle appelle et leurs valeurs (informations avec lesquelles nous créons les instances de notre future ontologie). Et nous remplissons au fur et à mesure le HMap des instances qui contiendra comme "clé" l'URI original de l'instance, et comme "valeur" le numéro de l'ontologie dont il est issu.
Pendant le parsing des propriétés d'annotation des ontologies d'entrée, nous extrayons pour chaque propriété sa définition qui consiste en ses labels, ses commentaires, ses superpropriétés, ses domaines, et ses images (informations avec lesquelles nous créons les propriétés d'annotation de notre future ontologie).
Pendant le parsing des individus anonymes des ontologies d'entrée, nous extrayons pour chaque individu (qui est sous forme d'un ID local unique) sa définition qui consiste en ses labels et ses commentaires, etc. (informations avec lesquelles nous créons les individus anonymes de notre future ontologie). § Ainsi, lors du parsing des ontologies originales, nous avons créé des entités propres à notre future ontologie, et en même temps, nous avons rempli les quatre HMaps correspondants à chaque type d'entité -classes, propriétés objet, propriété de données, et instances-(où l'URI original de l'entité forme la "clé", et le numéro de son ontologie forme la "valeur"), et tout cela pour remédier au problème de redondance des entités expliqué dans la section précédente.
Deuxième étape
Nous allons représenter les correspondances (entre les différentes entités des ontologies sources) par des axiomes OWL, car cette représentation est sémantiquement correcte et permet de réutiliser l'infrastructure et le vocabulaire du langage OWL.
En général
Nous parcourons les correspondances (les paires d'entités) de chaque alignement d'entrée (i.e. les cellules qui ont une mesure supérieure ou égale à un seuil que l'utilisateur a fixé), et au fur et à mesure, nous ajoutons à la nouvelle ontologie des axiomes de pont (des liens d'équivalence) traduisant ces correspondances entre les entités déjà créées dans notre ontologie.
En détail
Dans OWL API, nous ne pouvons pas lier les entités directement par des axiomes. En effet, il existe quatre types de méthodes de création d'axiomes, chacun destiné à un type d'entité (-classes, propriétés d'objet, propriétés de données, et instances-). Ceci s'applique entre autres pour les axiomes d'équivalence que nous allons utiliser dans notre cas. Les voici : Figure 3.4 -Création des axiomes d'équivalence dans OWL API Sachant que dans les alignements, nous ne pouvons pas savoir le type des entités mises en correspondance, et que les entités sont citées par leurs URIs originaux complets (comme elles ont été définies dans leur ontologie originale), nous avons eu recours aux quatre HMaps remplis déjà dans l'étape précédente, pour savoir le type de chaque entité, et son ID (le numéro de l'ontologie dont elle est issue), afin de pouvoir créer des "bridging" axiomes en liant les couples d'entités (citées dans les cellules des alignements) par des axiomes d'équivalence, en changeant leurs URIs de préfixe originaux par l'URI de notre ontologie + l'ID correspondant.
A la fin, dans notre ontologie de sortie, les supposés "bridging" axiomes créés ne vont plus être considérés comme ceci. En effet, selon nous, ils vont plutôt être perçus comme des axiomes d'équivalence normaux et originaux liant des entités d'une nouvelle ontologie indépendante (la nôtre), comme si celle-ci n'était pas le résultat d'une intégration ; car les entités la composant ont toutes un "URI de préfixe" propre à elle (les URIs des entités de notre nouvelle ontologie ne sont pas des URIs des ontologies sources déjà publiées). Autrement dit, nous avons fait un refactoring (une personnalisation) des URIs des entités sources que nous avons réutilisées pour former notre ontologie.
Démarche détaillée de la référence
Comme il n'y a pas de benchmark pour les approches d'intégration des ontologies, nous avons créé une autre version d'intégration avec laquelle nous pourrons nous comparer. Nous considérerons l'ontologie résultante comme notre ontologie de référence, car il s'agit d'une ontologie de pont sans perte de connaissances (i.e., complète). Nous appellerons cette version comme l'intégration de "référence" ou la "pseudo-référence". En principe, la démarche de référence consiste en la composition (l'union / l'intégration) automatique des ontologies sources et l'ontologie qui correspond aux alignements entre elles. Supposons que nous avons deux ontologies O 1 et O 2 à intégrer, et un alignement A entre elles. L'ontologie résultante serait O 3 = O 1 + O 2 + O A , après avoir converti A en une ontologie. En effet, puisque le format d'alignement est exprimé en RDF, ainsi il est librement extensible, l'"Alignment API" permet de convertir les correspondances (les cellules) d'un alignement en des axiomes OWL d'équivalence, de subsomption, et de disjonction (à l'aide de la méthode OWLAxiomsRendererVisitor(ObjectAlignment)) pour générer une ontologie comprenant à la fois les entités alignées et les axiomes OWL de pont. Malheureusement, cette tâche n'a pas pu être effectuée correctement, et nous n'avons pas pu transformer directement l'alignement en une ontologie. Pour ce faire, nous avons appliqué l'idée de notre approche (déjà expliquée).
Première étape
OWLOntologyMerger() est une méthode prédéfinie dans OWL API qui unit toutes les ontologies chargées (loaded) dans le OWLOntologyManager. Nous n'avons qu'à spécifier à la méthode createMergedOntology() le nouvel URI de l'ontologie que nous allons créer :
OWLOntologyMerger integration = new OWLOntologyMerger(manager) ; OWLOntology newOnto = integration.createMergedOntology(manager, newIRI) ; Il faut noter que les termes "Merger" et "MergedOntology" utilisés par OWL API sont faux et accentuent encore plus la mécompréhension du terme "fusion" dans la communauté. En effet, c'est une composition (union, intégration, association), ce n'est pas une fusion. D'ailleurs, Protégé fait exactement la même erreur avec le terme "Merge ontologies" dans le menu "refactor".
Nous aurons avec seulement cette étape une ontologie intégrée (composée, agrégé) qui ne manque aucune information des ontologies d'entrée, et qui maintient les URIs d'origine des entités sources en les mettant dans l'ontologie de sortie telles qu'elles sont originairement dans leurs ontologies d'entrée. Nous parcourons les correspondances de chaque alignement d'entrée (i.e. les cellules qui ont une mesure supérieure ou égale au seuil que nous avons fixé), et au fur et à mesure, nous ajoutons à la nouvelle ontologie des liens d'équivalence (des "bridging" axiomes) qui traduisent fidèlement ces correspondances entre les entités.
Deuxième étape
3.4. COMPARAISON ENTRE OIA2R ET LA RÉFÉRENCE § Sachant que dans OWL API, nous ne pouvons pas lier les entités directement par des axiomes, mais plutôt à travers quatre types de méthodes de création d'axiomes pour chacun des types d'entité (-classes, propriétés objet, propriétés de données, et instances-), et sachant que dans les alignements, nous ne pouvons pas savoir le type des entités correspondues, nous avons pu, à partir des quatre HSets déjà créés et remplis, savoir le type de chaque entité des cellules parcourues et créer des "bridging" axiomes (lier les entités citées dans les cellules des alignements par des axiomes d'équivalence en gardant leurs URIs originaux (tels qu'ils sont cités dans les alignements)).
Comparaison entre OIA2R et la référence
L'intégration de référence n'a absolument aucune perte d'informations des ontologies originales, pas le moindre axiome perdu, par contre la nôtre ne parvient pas à tout parser, nous perdons les entités anonymes et les restrictions, car toutes les entités que nous parsons sont nommées.
La seule différence entre ce travail et la référence, c'est que toutes les entités de notre ontologie résultante ont un URI de préfixe propre à nous, contrairement à l'intégration de référence qui garde les URIs originaux des entités et qui ne fait aucun refactoring. Ainsi notre ontologie est tout à fait originale et ne pointe pas sur des entités appartenant à des ontologies externes déjà existantes.
Conditions favorables pour de meilleurs résultats
3.5.1 Mapping (1-à-1) au lieu d'alignement (1-à-N) Comme expliqué dans le chapitre 1, le matching retourne un alignement ou un mapping. Dans l'alignement, une entité d'une première ontologie peut être mise en correspondance avec une ou plusieurs entités d'une deuxième ontologie (ces correspondances n'ont pas la même pertinence). Il s'agit de correspondances "1-à-N". Tandis que dans le mapping, une entité d'une première ontologie peut être mise en correspondance avec zéro ou une seule entité d'une deuxième ontologie. Il s'agit de correspondances "1-à-1". D'après les expérimentations (que nous détaillerons dans le chapitre 4), nous avons remarqué que, dans l'ontologie résultant d'une intégration qui utilise des alignements, le nombre de classes insatisfiables est beaucoup plus important que celui de l'ontologie résultant d'une intégration qui utilise des mappings.
Ci-dessous un exemple qui montre comment se forme l'insatisfiabilité d'une classe dans une ontologie de pont. La figure 3.6 montre les justifications que nous a affichées le debugueur de OWL API (à l'aide du raisonneur HermiT) pour une des classes insatisfiables (002#Tissue_Dissection) générées dans une de nos expérimentations.
La figure 3.6 est la représentation graphique de axiomes de justification générés par le debugueur, où les classes de couleur rouge sont les classes insatisfiables. figure 3.7 montre les deux correspondances qui ont causées toutes ces incohérences. La relation " ?" veut dire une relation d'équivalence "=" correcte mais qui génère des insatisfiabilités dans l'ontologie intégrée.
CONDITIONS FAVORABLES POUR DE MEILLEURS RÉSULTATS
Sachant que la relation d'équivalence (des "bridging" axiomes) est en réalité égale à deux relations de subsomption dans les deux sens, le schéma devient comme le montre la figure 3.8. Le pire avec les alignements, c'est que les entités cibles (ou sources) correspondues avec la même entité source (ou cible) sont généralement toutes proches (i.e., voisines) ainsi susceptibles d'avoir entre elles des relations de disjonction qui sont la première source des incohérences.
CONDITIONS FAVORABLES POUR DE MEILLEURS RÉSULTATS
La figure 3.9 montre ce que devient si nous ne gardons qu'une seule correspondance pour l'entité source "003#Clinical_finding". Dans notre approche, nous avons la possibilité de filtrer les correspondances ayant la même entité source ou la même entité cible en gardant uniquement la correspondance ayant la plus grande confiance (c.f., figure 3.10).
En premier lieu, nous créons deux HMaps : la première contiendra comme clé l'IRI de l'entité source de chaque cellule d'un alignement, et comme valeur l'IRI de l'entité cible. La deuxième contiendra comme clé l'IRI de l'entité source de chaque cellule d'un alignement, et comme valeur la mesure de confiance de la relation. Pendant le parsing des alignements d'entrée, nous remplissons ces deux HMaps au fur et à mesure, de telle sorte que si nous trouvons une cellule dont l'entité source est déjà existante comme clé dans les HMaps et dont la mesure de confiance est supérieure à celle rencontrée avant, nous mettons à jour les valeurs correspondantes à cette clé dans les deux HMaps ; sinon nous ne faisons rien (i.e. si la cellule dont l'entité source est déjà existante comme clé dans les HMaps et dont la mesure de confiance est inférieure ou égale à celle rencontrée avant, elle ne sera pas stockée, car nous avons celle qui est plus pertinente déjà enregistrée dans les HMaps).
En deuxième lieu, nous allons refaire la même chose, mais à l'envers. Nous créons deux HMaps "inverses" : la première contiendra comme clé l'IRI de l'entité cible de chaque entrée de la première HMap issue de l'étape précédente, et comme valeur l'IRI de l'entité source. La deuxième contiendra comme clé l'IRI de l'entité cible de chaque entrée de la première HMap issue de l'étape précédente, et comme valeur la mesure de confiance de la relation. Pendant le parcours des entrées de la première HMap déjà remplie dans l'étape 1, nous remplissons ces deux HMaps "inverses" au fur et à mesure, de telle sorte que si nous trouvons une entrée dont l'entité cible est déjà existante comme clé dans les HMaps "inverses" et dont la mesure de confiance est supérieure à celle rencontrée avant, nous mettons à jour les valeurs correspondantes à cette clé dans les deux HMaps "inverses".
Au lieu d'utiliser les alignements originaux (i.e., d'entrée), nous utiliserons le premier HMap "inverse" qui contiendra toutes les correspondances filtrées des alignements d'entrée. Ce HMap exprime les correspondances supposées former des mappings.
Réparation des alignements
La réparation des alignements ou des mappings (en supprimant les correspondances qui sont susceptibles d'engendrer des insatisfibilités lorsqu'elles seront associées aux ontologies d'entrée) aide à diminuer les incohérences dans l'ontologie résultante. D'après Cheatham and Pesquita (2017), actuellement, peu de systèmes de matching d'ontologies ne supportent la gestion de l'incohérence logique, et encore moins pour les grandes ontologies. L'approche la plus basique consiste à filtrer les correspondances qui violent une série de règles sémantiques (comme le fait YAM++ (2012)). Des approches plus sophistiquées reposent sur des procédures automatisées capables d'identifier les correspondances impliquées dans l'incohérence logique et de sélectionner celles à supprimer pour atteindre la cohérence, comme AML (2015) et LogMap (2011). Abbas and Berio (2013) • D'autres auteurs trouvent que les incohérences peuvent être causées soit par les alignements, soit par les ontologies (ContentMap de Jiménez-Ruiz et al. (2009)). Ils ont déduit que lorsque les correspondances sont celles qui sont prévues (sont correctes) et lorsque l'ontologie résultante contient quand même des incohérences logiques, alors ces incohérences doivent être forcément dues aux ontologies sources qui sont incompatibles à cause des différences de leurs conceptualisations. Ils proposent alors une solution pour réparer les ontologies (supprimer les axiomes qui causent des contradictions dans l'ontologie de sortie) à l'aide d'un ingénieur du domaine.
Dans notre approche, nous avons exploité les outils LogMap et ALCOMO qui prennent en entrée deux ontologies sources et un alignement entre eux, et génèrent un alignement réparé (après avoir fait un calcul des inférences entre eux pour décider quelles correspondances supprimer). Nous utilisons l'un de ces deux outils pour tous nos alignements d'entrée afin de minimiser au maximum les incohérences dans notre future ontologie résultante.
LogMap 1 est un système de matching d'ontologies basé sur la logique créé par Jiménez-Ruiz and Grau (2011). Il effectue une réparation des alignements (i.e., une transformation d'un alignement incohérent en un alignement cohérent) en exécutant un raisonnement (parfois incomplet). Il supprime ou modifie les correspondances qui causent l'apparition des classes insatisfiables.
Créé par Meilicke (2011), ALCOMO 2 est un système de debugage des alignements qui permet de transformer un alignement incohérent en un alignement cohérent en lui supprimant certaines correspondances. Il est complet car il détecte toute forme d'insatisfiabilité entre les ontologies causée par les alignements.
Nouvelle définition de la notion d'intégration
Dans la littérature, il n'y pas un accord général sur les définitions de l'intégration et la fusion des ontologies. Flouris et al. (2006), et Euzenat and Shvaiko (2013) ont essayé de faire une clarification et une désambiguïsation de toutes les terminologies de l'ingénierie des ontologies. Et Pinto (1999) a fait la même chose pour les termes "intégration" et "fusion". Mais malgré leurs efforts, les termes "intégration" et "fusion" sont toujours mal définis, mal compris, et mal placés.
Comme le dit Pinto (1999), l'intégration concerne des ontologies de différents ou de proches domaines pour former une ontologie de domaine plus large englobant tous les domaines sources ; et la fusion concerne des ontologies de même domaine pour former une ontologie décrivant mieux ce domaine-là. La confusion réelle réside dans le sens naturel de ces termes. En effet, dans la littérature, la plupart des auteurs parlent de fusion lorsqu'ils vont fondre les entités équivalentes pour les remplacer par une seule, ou lorsqu'ils vont changer et mêler les hiérarchies des ontologies sources en répartissant leurs entités autrement dans l'ontologie cible ; et parlent d'intégration ou de composition lorsqu'ils vont regrouper et assembler directement les ontologies, telles qu'elles sont, dans une autre ontologie, sans fusionner leurs entités équivalentes et sans toucher leurs hiérarchie originale. Les processus de fusion ou d'intégration peuvent s'appliquer concrètement à toute ontologie (de domaine = ou =). C'est seulement le but à atteindre qui différencie vraiment les deux définitions consensuelles. Autrement dit, le problème réside dans le fait que nous pourrons faire une fusion (au sens propre du mot) pour deux ontologies de domaines différents (car elles peuvent contenir quand même des chevauchements entre elles), et une composition / intégration (au sens propre du mot) pour des ontologies de même domaine. Ce qui est contradictoire aux définitions soi-disant standardisées.
Dans le cas d'une ontologie de pont créée à partir d'ontologies de même domaine, si nous nous conformons à ces définitions, nous sommes en train de faire une fusion des ontologies, car il s'agit bien d'ontologies de même domaine, mais réellement, nous ne fusionnons pas les entités, ne mélangeons pas leurs emplacements, et ne modifions pas leurs structures, nous faisons une ontologie de pont où les entités originales et leurs hiérarchies sont intactes. Pas de fusion dans un processus de fusion. En contre parti, notre travail respecte les règles de la définition de l'intégration des ontologies qui dicte que les parties provenant des ontologies sources soient identifiables facilement dans l'ontologie de sortie et qu'il s'agit juste d'une inclusion, d'une agrégation, ou d'un assemblage des ontologies sources pour former un tout. Avions-nous fait une intégration ou une fusion ?
Par conséquent, nous proposons que le terme "intégration des ontologies" soit le terme général de toutes les définitions rencontrées dans le chapitre 2, par analogie avec le terme "intégration des données", et nous proposons qu'il soit appliqué sur des ontologies de mêmes ou de différents sujets, ainsi pour de différents objectifs. Bien évidemment, les ontologies de même sujet seront les plus dures à intégrer ; les ontologies de très différents domaines n'auront pas (beaucoup) de correspondances entre elles, donc seront toujours plus faciles à intégrer. Nous distinguons cinq niveaux d'intégration selon le niveau d'interopérabilité sémantique. Nous expliquons chaque type avec le plus simple cas qui intègre seulement deux ontologies (c.f., figure 3.11) :
Alignement Défini par Noy and Musen (2000) (définition 1), il implique deux ontologies séparées et un alignement (deux mapping dans les deux sens, une articulation, ou une ontologie intermédiaire comme le nomme Kalfoglou and Schorlemmer (2003)) à travers lequel une ontologie peut interroger l'autre et vice-versa.
Interconnexion des données Nommée aussi "révisons de mapping" par Heflin and Hendler (2000), terme qui peut être confondu avec la notion de debugage et de réparation des mappings, elle consiste en l'ajout de correspondances d'un alignement ou d'un mapping dans les deux ontologies. En d'autres termes, c'est l'ajout des relations sémantiques entre les entités de l'ontologie en question et les entités de l'autre ontologie comme prescrit dans l'alignement ou le mapping entre elles. Réconciliation / Coévolution Définie par Euzenat and Shvaiko (2013), elle peut être une transformation des entités de l'une des ontologies par les entités de l'autre comme le prescrit l'alignement entre les deux ontologies, ou bien une transformation des entités des deux ontologies, nommée "intersection d'ontologies" par Heflin and Hendler (2000), après la standardisation des termes correspondus.
Ontologie de pont Introduite par De Bruijn et al. (2006), elle met les deux ontologies et les correspondances de leur alignement dans une même ontologie qui les englobe sans rien modifier.
Fusion / Unification Appelée par Pinto (1999) "Fusion", et appelée "unification" ou "compatibilité totale" par Sowa (1997), elle génère une ontologie en sortie et peut se faire de différentes manières ; la plus simple est d'unir les ontologies sources et de fusionner leurs entités équivalentes (comme décrites dans l'alignement) ; et la plus difficile est d'exploiter, en plus des correspondances d'équivalence et de disjonction, des correspondances de subsomption qui changeront énormément la hiérarchie originale des ontologies.
Selon Calvanese et al. (2001), dans le cas de plusieurs ontologies sources, l'intégration des ontologies peut impliquer soit une approche "global-centric", où les entités de l'ontologie globale sont mises en correspondance avec les entités des ontologies locales, soit une approche "localcentric", où les entités des ontologies locales sont mises en correspondance avec les entités de l'ontologie globale. Mais nous ajoutons une autre approche que nous nous permettons d'appeler "non-centric" où les entités des paires d'ontologies sont mises en correspondance. Ainsi, il n'existe pas d'ontologies globale et locales, elles ont toutes la même priorité.
Concernant l'ontologie de pont et l'ontologie de fusion, le processus d'intégration de plusieurs ontologies peut être fait soit d'une manière incrémentale, où il y a une ontologie cible prioritaire ou une ontologie vide (nommée ontologie globale) dans laquelle les autres ontologies sources (locales) seront intégrées l'une après l'autre (c.f., figure 3.12 and 3.13) ; soit d'une manière non incrémentale, où toutes les ontologies sources ont la même priorité et seront intégrées les unes avec les autres en même temps pour former ensemble l'ontologie cible.
Remarque
Rappelons que les termes "Merger" et "MergedOntology" utilisés par des méthodes dans OWL API, et "Merge ontologies" dans le menu "refactor" de Protégé sont faux, car ils font juste une composition/union/agrégation d'ontologies (c.f., figure 3.17); ils mettent les ontologies sources, telles qu'elles sont, dans une nouvelle ontologie qui les englobe, sans créer des liens de pont en elles et sans les fusionner. Nous n'avons pas ajouté ce simple processus dans les types d'intégration, car il ne permet aucune interopérabilité sémantique entre les agrégats (les sous-ontologies sources) de l'ontologie résultante. Conclusion L'ontologie de pont que nous allons implémenter est une intégration d'interopérabilité moyenne. Elle peut être exploitée réellement quand deux entreprises veulent coopérer, collaborer et intégrer leurs ontologies utilisées sans modifier les noms des entités et leurs descriptions, pour ne pas être obligés de modifier tout un système (ou une application) alimenté avec ces ontologies. Les liens de pont ajoutés dans l'ontologie de pont vont permettre l'interopérabilité sémantique entre elles.
En général, le type d'intégration choisi dépend des circonstances à faire face et des buts des applications. Tenons l'exemple des linked data dans le Web distribué et réparti, l'intégration dans ce contexte consiste à ajouter à chaque ontologie des liens d'équivalence et d'identité (sameAs) qui pointent vers des entités d'autres ontologies. C'est l'un des niveaux les plus bas d'interopérabilité, mais qui convient le mieux à cette situation.
Introduction
Dans ce chapitre, nous allons présenter notre environnement de travail, les bases de test utilisées dans les expérimentations, et les critères d'évaluation de la qualité de l'ontologie produite suite à l'intégration. Par la suite, nous allons étaler et évaluer les résultats de nos expérimentations faites sur des ontologies de différentes tailles. Ce volet d'expérimentations va nous permettre de valider notre méthode d'intégration qui s'est avérée efficace, et de prouver sa capacité de produire une ontologie de bonne qualité.
Environnement de réalisation
L'environnement de développement de notre méthode est constitué des outils suivants :
• Java : un langage de programmation orienté objet.
• Eclipse : un environnement de développement intégré (IDE) Java, libre, gratuit et multiplateforme.
• OWL API 1 (Version 4.1.4) : une interface de programmation pour le développement, la manipulation, et la sérialisation des ontologies OWL.
• HermiT 2 (Version 1.3.8) : un moteur d'inférence OWL 2 DL (Description Logic) créé à l'université d'Oxford et publié sous la licence LGPL. Il est supporté par OWL API et Protégé (qui est un outil de création et de gestion d'ontologies). Il permet de réaliser les services de raisonnement suivants : l'inférence, la classification, la satisfiabilité, et la consistance. Mais il ne fournit pas un diagnostic ou une solution pour les deux derniers problèmes.
• Alignment API 3 (Version 4.9) : une interface de programmation développée en java permettant d'exprimer, d'accéder et de manipuler des alignements ontologiques sous le format d'alignement (qui est le format le plus utilisé pour représenter les alignements). Les
CRITÈRES D'ÉVALUATION
fondateurs de cette API ont conçu le format d'alignement pour exprimer les alignements disponibles de manière uniforme et pouvoir les partager sur le Web. Ce format est écrit en langage RDF, ainsi il est librement extensible. Dans sa représentation, chaque correspondance entre deux ontologies (nommée "cellule") contient l'URI de l'entité source, l'URI de l'entité cible, la relation qui existe entre ces deux entités (égalité, subsumption, exclusion, ou instanciation etc.), et la force de cette relation (une valeur décimale comprise entre 0 et 1, inclusivement).
Les tests ont été effectués sur un PC doté d'un système d'exploitation Windows 10, d'une mémoire centrale de 4 Go, et d'une horloge possédant une fréquence de 2 GHz.
Critères d'évaluation
Selon Flouris et al. (2006), le problème de l'évaluation des techniques d'intégration ou de fusion des ontologies est encore ouvert. Une comparaison générale et objective est difficile, car nous ne savons pas comment l'évaluation de ces outils pourrait être mesurée.
En effet, déterminer la qualité d'un résultat d'intégration ou de fusion nécessiterait de le comparer avec un résultat parfait ou presque parfait. Mais ce résultat est impossible à obtenir manuellement pour les grandes ontologies, et même inexistant car il pourrait y avoir plus qu'un résultat idéal. Il n'y a pas de benchmark qui pourrait être utilisé pour évaluer la qualité de l'approche proposée, e.g., en utilisant des mesures de qualité telles que la précision, le rappel ou la F-Mesure Raunich and Rahm (2012).
Un benchmark de la fusion ou de l'intégration des ontologies devrait être en mesure d'évaluer équitablement la qualité des différents outils. Pour ce faire, Raunich and Rahm (2012) ont défini des métriques de qualité telles que :
• La qualité de l'ontologie de sortie : Elle se reflète par la quantité de ses chevauchements sémantiques qui peuvent être palliés en évitant l'introduction de chemins supplémentaires (relations redondantes). La qualité de l'ontologie dépend fortement de la qualité des ontologies d'entrée ; Idéalement, les ontologies d'entrée sont correctes et ne représentent pas (ou très peu) de conflits et d'incohérences ; idéalement, les alignements d'entrée sont aussi corrects bien que ce n'est pas évident d'en obtenir pour les grandes ontologies.
• La couverture (Préservation de l'information) : C'est une exigence clé, afin que toutes les informations représentées dans les ontologies d'entrée soient conservées dans l'ontologie résultante : * Pour le "Full Merge" où chaque paire d'entités équivalentes devient une entité fusionnée, la taille de l'ontologie résultante doit être égale à la somme du nombre d'entités des deux ontologies d'entrée, moins le nombre d'entités fusionnées, ou plutôt moins le nombre de correspondances d'équivalence (=) dans l'alignement d'entrée. § En dépit que ce soit considéré comme une perte d'information, le fait de ne pas couvrir toutes les entités d'entrée peut être un choix volontaire pour éviter les conflits qui sont dus à l'héritage multiple dans l'ontologie de sortie (ce qui est appelé "fusion asymétrique" par Raunich and Rahm (2012)). * Pour l'ontologie de pont (notre cas), la taille de l'ontologie résultante doit être égale à la somme du nombre d'entités des deux ontologies d'entrée.
• L'efficacité : C'est le temps d'exécution de l'algorithme d'intégration ou de fusion.
• L'effort manuel : C'est l'intervention de l'utilisateur ou de l'expert nécessaire pour le bon déroulement du processus. La base de test "Conference" est composée essentiellement de sept petites ontologies (cmt, conference, confOf, edas, ekaw, iasted, et sigkdd) décrivant le contexte de l'organisation des conférences. OAEI fournit un alignement de référence entre chaque paire de ces sept ontologies, pour avoir en tout, 21 alignements de référence.
Présentation des ontologies utilisées
La base de test "Anatomy" est composée de deux ontologies de taille moyenne : "mouse" qui décrit l'anatomie de la souris adulte, et "human" (une partie de NCIT) qui décrit l'anatomie humaine. OAEI fournit un alignement de référence entre elles.
La base de test "Large Biomedical Ontologies" est composée de trois ontologies volumineuses et sémantiquement riches : FMA (Foundational Model of Anatomy), SNOMED CT (Clinical Terms), et NCI (National Cancer Institute Thesaurus) contenant des dizaines de milliers de classes. La base Large Bio se subdivise en trois catégories de taille croissante (qu'on nommera 1, 2, et 3) dont la troisième est la complète. Pour FMA, il y a FMA1 (5%), FMA2 (13%), et FMA3 (100%). Pour NCI, il y a NCI1 (10%), NCI2 (36%), and NCI3 (100%). Et pour SNOMED, il y a SNOMED1 (5%), SNOMED2 (17%), et SNOMED3 (40%). OAEI fournit trois alignements de référence pour la troisième catégorie, i.e. entre chaque paire des trois ontologies complètes. Les relations "?" contenues dans les correspondances des alignements de référence veulent dire des relations d'équivalence "=" correctes mais qui génèrent des insatisfiabilités dans l'ontologie intégrée. Ces correspondances qui causent l'incohérence de l'alignement sont détectées par le système de débugage ALCOMO et/ou les systèmes de réparation de Logmap et/ou AML.
Nous n'avons pas testé notre Framework sur d'autres ontologies de plus grandes tailles, car il n'existe pas d'alignements disponibles publiés sur Internet pour de telles ontologies. Voici ce que donne l'exécution de tout le code (avec ses deux parties) qui réalise une intégration (i.e., une ontologie de pont avec -les "bridging" axiomes-) :
PRÉSENTATION DES ONTOLOGIES UTILISÉES
Pour la référence : les axiomes sont exactement identiques aux originaux, mais des axiomes d'équivalence (de pont) s'y ajoutent en plus (Figure 4.3). Pour OIA2R : les axiomes sont décrits exactement comme les originaux, mais des axiomes d'équivalence (de pont) s'y ajoutent, tout en personnalisant les IRIs de toutes les entités mentionnées (Figure 4.4). 4.5 Notions à clarifier 4.5.1 Insatisfiabilité C'est un terme dédié aux entités. Une classe insatisfiable est une classe ayant une description fausse (contradictoire), ce qui signifie qu'il n'est pas possible pour une instance de répondre à toutes les exigences requises pour être membre de cette classe. Elle ne peut et ne doit jamais avoir d'instances (tout à fait comme la classe "owl:Nothing"), car il n'existera aucune instance qui pourra la satisfaire Sattler et al. (2013).
Inconsistance
C'est un terme dédié aux ontologies. Une ontologie est consistante s'il lui existe une interprétation satisfaisante, e.g. une ontologie à partir de laquelle nous pouvons déduire que l'individu x est différent de l'individu y et qu'il est en même temps identique à lui, ne peut pas avoir une interprétation satisfaisante. L'inconsistance peut se manifester lorsqu'il y a au moins une violation des restrictions d'une classe, une instanciation d'une classe insatisfiable, une instanciation de deux classes disjointes, ou une contradiction sémantique entre les individus etc. Bail (2013).
Dans une ontologie inconsistante, toutes les classes sont insatisfiables, i.e. aucune de ses classes ne peut avoir d'individu. En effet, elle n'a pas de modèle. Elle est considérée comme une ontologie sévèrement endommagée contenant une grave erreur qui doit être réparée car aucune connaissance utile ne peut en être inférée. Elle ne peut pas être publiée et utilisée dans les applications.
Raisonneur
Un raisonneur est un composant clé dans le domaine des ontologies. Puisque la connaissance dans une ontologie OWL peut ne pas être explicite, la classification et l'interrogation d'une ontologie (qui sont les deux tâches basiques d'un raisonneur) doivent être faites par un raisonneur, pour pouvoir déduire les connaissances implicites et obtenir des résultats d'interrogation corrects. Les raisonneurs existants détectent l'inconsistance et l'incohérence, mais ne leur fournissent pas un diagnostic et une solution Sattler et al. (2013).
Voici les travaux qui ont été menés en collaboration avec notre laboratoire LIPAH concernant l'évaluation des performances des raisonneurs existants : Alaya et al. (2015dAlaya et al. ( ,a,c,b, 2016Alaya et al. ( , 2017.
Classification
Selon Sattler et al. (2013), un raisonneur détermine toutes les inférences de la forme "A subClassOf B" d'une ontologie donnée, i.e. il détermine sa hiérarchie, en appliquant les tests suivants :
-Si A = "owl: Table 4.11 -Qualité de l'ontologie résultant de l'intégration des ontologies de Anatomy
Anatomy
Nombre de classes insatisfiables Al originaux (1-à-N) Al filtrés (1-à-1) OIA2R
Réf OIA2R Réf Intégration 2-à-2 0 0 0 0 4.6. RÉSULTATS ET ÉVALUATION (366 467 + 20 881) § Ces axiomes d'équivalence vont aussi affecter la hiérarchie (la classification) des classes et des propriétés de l'ontologie résultante. En effet, le raisonneur pourra ne pas pouvoir s'arrêter (dans son calcul) et ainsi ne pas avoir un nombre précis de niveaux dans la hiérarchie.
Ci-dessous un exemple qui montre comment se forme l'insatisfiabilité d'une classe dans une ontologie de pont. La figure 4.5 montre les justifications que nous a affichées le debugueur de OWL API à l'aide du raisonneur HermiT pour une des classes insatisfiables (Cytoplasmic_Matrix) de l'ontologie résultant d'une intégration des ontologies FMA 1 (Ont1) et NCI 1 (Ont2). Nous remarquons qu'après l'ajout des "bridging" axiomes d'équivalence, la classe "002#Cy-toplasmic_Matrix" (provenant de l'ontologie NCI 1 (Ont2)) devient par inférence sous-classe des deux classes "001#Portion_of_body_structure" et "001#Anatomical_structure" qui sont disjointes (information extraite de l'ontologie FMA 1 (Ont1)). Ceci est contradictoire, car une classe ne peut pas être sous-classe de deux classes disjointes. La même chose s'applique pour l'autre classe coloriée en rouge.
La référence ne manque aucun axiome des ontologies d'entrée, alors que la nôtre a des pertes d'informations telles que les entités anonymes et les restrictions. C'est pour cette raison que le raisonneur infère plus d'informations et ainsi détecte plus de classes insatisfiables dans l'ontologie de référence. D'ailleurs, pour calculer toutes ses classes insatisfiables, le raisonnement HermiT prend beaucoup plus de temps pour terminer son calcul.
L'ontologie d'une intégration N-à-N produit beaucoup plus de classes insatisfiables que l'ontologie d'une intégration 2-à-2 ou 1-à-N à cause des relations redondantes. Plus il y a de relations redondantes (dans ce cas, des relations d'équivalence redondantes entre les entités sources), plus il y a d'incohérence. Les correspondances redondantes peuvent être déduites automatiquement par un raisonneur, ainsi elles sont inutiles, et surtout source de conflits sémantiques.
Il est important également de noter que la réparation de l'alignement est dédiée à l'intégration de deux ontologies seulement. Autrement dit, si nous intégrons deux ontologies en utilisant un alignement réparé entre elles, nous obtiendrons une ontologie consistante et cohérente sans aucune classe insatisfiable. Cependant, si nous intégrons plusieurs ontologies à l'aide de plusieurs alignements réparés (i.e., entre les paires d'ontologies), nous obtiendrons une ontologie comportant plusieurs classes insatisfiables. En effet, les systèmes actuels de réparation des alignement prennent en entrée deux ontologies (à intégrer ultérieurement) et un alignement entre elles. Ils ne sont pas en mesure de prendre en compte plusieurs ontologies et alignements entre elles pour but de les intégrer simultanément.
Atouts de OIA2R
Notre framework est automatique et générique. Il prend en entrée toute ontologie et tout alignement avec lesquels il produira une nouvelle ontologie qui les englobe tous. Ce processus est rapide même pour les plus grandes ontologies et les plus grands alignements. L'ontologie résultante est assez complète et cohérente.
Nous donnons la possibilité de convertir les alignements sources en des mappings, et également de les réparer à l'aide d'outils externes, afin de minimiser les erreurs dans l'ontologie de sortie.
Notre approche permet un refactoring (une personnalisation) de toutes les entités des ontologies et des alignements sources pour former une ontologie propre à nous (dont les entités ne pointent pas sur les URIs externes des ontologies sources déjà publiées). En effet, l'utilisateur n'a qu'à entrer l'URI qu'il désire pour la future ontologie, et par la suite toutes les entités l'auront comme URI de préfixe.
Temps d'exécution
Ce sont les temps d'exécution moyens d'une intégration complète N-à-N avec des alignements transformés en mappings, mais qui sont déjà réparés à l'avance. Nous voulons dire par "loading", le temps de chargement des ontologies dans le manager de OWL API, car pour les grandes ontologies, leur loading prend une bonne part du temps d'exécution (comme le montrera le tableau 4.15), et ce temps-là ne fait pas partie du temps effectif de notre intégration. Le temps "avec loading" est le temps d'exécution de tout le programme (du début jusqu'à la fin), et le temps "sans loading" est le temps d'exécution exact de notre framework. Rappelons que notre framework prend en entrée des alignements pré-établis, ainsi, les temps de d'exécution fournis ne comprennent pas le temps du matching. Les temps d'exécution CPU ne dépassent pas 0,7 min pour les plus grandes ontologies. Le temps global de l'intégration de référence est plus long, car la référence prend plus de temps pour sauvegarder tous les axiomes d'entrée (à la fin du programme) et créer l'ontologie de pont complète. Cependant, le temps global de l'intégration de OIA2R prend moins de temps pour sauvegarder les axiomes d'entrée, car OIA2R manque les axiomes complexes. Le temps effectif de l'intégration de référence prend moins de temps, car la référence ne perd pas du temps à parser, refactoriser les axiomes des ontologies d'entrée et créer de nouveaux axiomes refactorisés comme le fait OIA2R, elle assemble directement les axiomes des ontologies d'entrée et ajoute les axiomes de pont.
Pour découvrir le niveau d'intégration qui génère plus d'incohérences dans son ontologie résultante (soit l'ontologie de pont, soit la fusion), nous avons réalisé un autre travail qui fait une fusion de deux ontologies (uniquement deux), i.e. il fusionne les paires d'entités équivalentes en une seule entité. (2012)) que la fusion complète des ontologies génère toujours moins de conflits qu'une ontologie de pont (appelée "fusion directe" selon eux).
Ci-dessous un exemple qui montre comment se forme l'insatisfiabilité d'une classe dans une ontologie résultante d'un processus de fusion complète. Dans la figure 4.8, nous schématisons les justifications que nous a affichées le debugueur de OWL API (à l'aide du raisonneur HermiT) pour une des classes insatisfiables générées suite à la fusion de FMA 1 (Ont1) et SNOMED 1 (Ont2). Nous avons choisi le ID "/000" pour les entités issues de la fusion de deux entités équivalentes. Et nous avons choisi de leur donner comme noms, une concaténation des noms des paires d'entités fusionnées (juste pour pouvoir voir clairement dans l'ontologie résultante ce qui a été fusionné). Dans l'état de l'art, les auteurs choisissent généralement l'un des deux noms des entités fusionnées (peut-être après avoir défini une ontologie prioritaire), ou bien créent un code unique tout en ajoutant les deux noms originaux comme labels.
Dans la figure 4.9, nous modélisons la représentation graphique des axiomes de justification ci-dessus, où la classe en rouge est la classe insatisfiable. Nous remarquons qu'après la fusion des classes "001#Extracellular_space" provenant de FMA 1 (Ont1) et "002#Intercellular_space" provenant de SNOMED 1 (Ont2), la classe "000#Extracellular_space=Intercellular_space" devient par inférence sous-classe des deux classes "001#Immaterial_anatomical_entity" et "001#Material_anatomical_entity" qui sont disjointes (information extraite de l'ontologie FMA 1 (001)). Ceci est contradictoire, car une classe ne peut pas être sous-classe de deux classes disjointes.
Conclusion
Enfin, nous déduisons que si les ontologies modélisent des vues différentes et incompatibles du même domaine, il est impossible de les intégrer aveuglément et d'assurer à la fois la complétude et la cohérence dans l'ontologie résultante. Dans un contexte d'intégration d'ontologies, assurer la cohérence et la consistance est une priorité car l'ontologie résultante doit être logiquement correcte pour être réellement utile. Dans ce cas, nous ne pourrons jamais réaliser une interopérabilité sémantique complète entre les ontologies d'entrée car nous serons dans l'obligation d'abandonner des correspondances sémantiques. Et au cas où nous souhaiterions atteindre la complétude, les incompatibilités des ontologies sont insolvables automatiquement et l'intervention d'un expert devient nécessaire, ce qui est impossible pour les grandes ontologies. Dans l'ensemble, l'intégration des ontologies ayant des vues incompatibles reste toujours un problème ouvert.
Dans ce chapitre, nous avons présenté les expérimentations sur notre nouvelle approche d'intégration des ontologies OIA2R. L'analyse des résultats a montré les performances de notre approche et la validité de l'ontologie résultante. En effet, OIA2R a produit des résultats encourageants dans des temps minimes. De même, les expérimentations ont montré une possibilité d'amélioration de ces résultats pour avoir une qualité optimale de l'ontologie de sortie.
Conclusion générale
Les services Web et les moteurs de recherche peuvent améliorer leurs performances dans l'échange des informations et la précision des résultats de recherche en exploitant la représentation sémantiquement enrichie des informations qu'ils partagent à travers les ontologies. Actuellement, la recherche et le développement dans le domaine du Web sémantique (qui est un Web distribué et ouvert) ont atteint un stade où un grand nombre d'applications et de services tels que le commerce électronique, le renseignement gouvernemental, la médecine, la fabrication, etc, sont alimentés par des ontologies de toute taille, développées par différentes personnes, groupes de recherche, ou organisations, et contenant beaucoup de chevauchements (similarités) sémantiques entre elles. En effet, les différentes sources de données modélisent leurs ontologies de différentes manières selon leurs propres besoins, exigences, et buts, et n'utilisent pas nécessairement des ontologies déjà existantes. Par conséquent, il devient difficile de récupérer les informations provenant de différentes sources dans le Web.
Pour une représentation efficace et homogène des domaines de connaissances, il serait alors nécessaire d'intégrer (ou de fusionner) toutes les ontologies pour former de nouvelles ontologies plus complètes et mieux modélisées qui les remplacera.
Dans le premier chapitre, nous avons passé en revue les principales définitions des notions essentielles pour cerner le champ d'étude. Une étude bibliographique sur le Web Sémantique, l'ontologie, et l'ingénierie ontologique a été menée.
Nous avons établi au deuxième chapitre un bilan des définitions et des méthodes existantes qui s'appliquent dans le cadre de l'intégration des ontologies. Notamment, parmi ces méthodes ou définitions, il y a celles qui sont restées uniquement théoriques.
Dans le troisième chapitre, nous avons mis au point une nouvelle méthode qui permet d'intégrer deux ou plusieurs ontologies à l'aide des alignements entre elles, pour générer une nouvelle ontologie qui les englobe.
Dans le quatrième chapitre, nous avons décrit notre environnement de travail et les critères d'évaluation des outils d'intégration, nous avons appliqué et évalué notre approche dans la pratique, et nous avons prouvé qu'elle est générique, efficace et scalable.
Figure 1 . 1 -
11Fragment d'une ontologieCheatham and Pesquita (2017)
Formellement
, le processus de matching peut être vu comme une fonction f qui, à partir d'une paire d'ontologies O et O à mettre en correspondance, un ensemble de paramètres p, et un ensemble de ressources externes r, retourne en sortie un alignement A (éventuellement un mapping) entre ces deux ontologies : A = f (O, O , p, r).
Figure 1 . 2 -
12Matching De Bruijn et al. (2006)
Figure 1 . 3 -
13Processus général du matchingCheatham and Pesquita (2017)
Figure 1 . 4
14Noy and Musen (2000) pensent que dans l'alignement, les ontologies sources(généralement de domaines complémentaires) doivent être toujours séparées et consistantes les unes avec les autres, tout en ayant des liens entre elles. Les auteurs Zhu et al. (2009) le pensent aussi et définissent l'alignement par le processus qui combine deux ontologies et qui établit ensuite une collection de relations binaires (correspondances) entre elles.(a)Noy and Musen (2000) (b)Zhu et al. (2009)
Formellement
, étant donné deux ontologies O et O (ayant les langages L et L ) et un ensemble de relations d'un alignement A, une correspondance est un triplé (e, e , r), tel que e ∈ O, e ∈ O , et r ∈ Θ. La correspondance (e, e , r) déclare que la relation bidirectionnelle r relie les entités e et e ; mais elle est souvent accompagnée aussi par un identifiant et une confiance, ainsi, elle sera représentée généralement par un tuple (id, e, e , r, n) où id est son identifiant unique, et n est sa mesure de confiance
Figure 1 . 5 -
15Alignement Abels et al. (2005)
Figure 1
1Choi et al. (2006), le mapping des ontologies est utilisé principalement dans trois situations :
Formellement, la transformation des ontologies à l'aide d'un alignement (mapping) A entre deux ontologies O et O , génère une ontologie O qui transforme les entités de O par celles de O suivant les correspondances dans A. Elle peut être exprimée par l'opérateur suivant : T ransf orm(O, A) = O . Les opérations de transformation sont orientées, i.e. la transformation a une source et une cible identifiées, ainsi, à partir d'un alignement, il est possible de générer deux opérations (dans les deux sens) selon la source et la cible.
Figure 2 . 1 -
21Fusion dePinto (1999) interprétée parKeet (2004) Figure 2.2 -Fusion deAbels et al. (2005) Fusion comme étant une ontologie intermédiaire SelonKalfoglou and Schorlemmer (2003), la "forte" notion de fusion peut être détendue en prenant l'articulation (l'alignement des deux ontologies O et O ) avec laquelle une ontologie O pourrait être définie.Fusion de De Bruijn et al.D'après De Bruijn et al. (2006), la fusion des ontologies est la création d'une nouvelle ontologie qui unie deux ou plusieurs ontologies en se basant sur les correspondances entre elles. Selon eux, la nouvelle ontologie doit capturer toutes les connaissances des ontologies sources et refléter toutes les correspondances entre elles pour pouvoir les remplacer. Nous notons qu'ils n'évoquent pas les domaines des ontologies sources (différents ou similaires). Ils distinguent deux approches distinctes dans la fusion des ontologies :• Fusion complète (Full Merge) : Chaque paire d'entités équivalentes est fusionnée en une seule entité. • Ontologie de pont : Nous allons l'expliquer tout de suite.
Figure 2 . 3 -
23Fusion complète De Bruijn et al. (2006) Fusion dans la symétrie et l'asymétrie Selon Raunich and Rahm
et Zhang et al. (2017) utilisent les termes "fusion" et "intégration" comme des synonymes.
Figure 2 . 4 -
24Ontologie de pont De Bruijn et al. (2006) 2.1.2 Principaux outils de fusion et leurs limites Outils célèbres Les approches les plus connues de fusion des ontologies telles que PROMPT* Noy and Musen (2000), Chimaera McGuinness et al. (2000), et FCA-Merge Stumme and Maedche (2001) sont des Full Merge, semi-automatiques (nécessitant l'intervention d'experts et introduisant un effort manuel important, surtout pour les grandes ontologies) qui ne se basent pas sur les mappings, i.e. elles n'appliquent pas une séparation entre le matching et la fusion Raunich and Rahm (2012).
L
'outil de Chatterjee et al. Dans leur expérimentation, Chatterjee et al. (2017) ont choisi de créer une nouvelle ontologie dans le domaine de l'agriculture, en fusionnant des ontologies de sous-domaines (de la récolte, les engrais, la terre (le sol), et la météo). § Ce travail est en réalité une intégration (non pas une fusion), car les ontologies d'entrée appartiennent à différents domaines, et l'ontologie résultante est de domaine (interdisciplinaire) plus large qui englobe ces sous-domaines (c'est une composition de sous-domaines). Ils font le parsing des fichiers .owl des ontologies d'entrée et extraient leur ensemble d'entités (en utilisant la bibliothèque "Owlready" en Python), puis ils font le matching de chaque couple d'ontologies (en combinant plusieurs techniques de matching (i.e. de niveau élémentaire et structurel). A l'aide des alignements générés par le matching, ils appliquent une fusion complète des entités similaires et les mettent dans l'ontologie résultante O M , puis ils copient les entités restantes (non fusionnées) des ontologies sources dans O M , et génèrent un fichier .owl correspondant à O M .
et al. (2017), le processus de fusion des ontologies avec la méthode OIM-SM prend deux ontologies et retourne une nouvelle ontologie (sous forme d'arbre, i.e. sans héritage multiple). Il se compose des étapes suivantes : 1. Le matching d'équivalence sémantique entre les concepts des deux ontologies. 2. La fusion de toutes les paires de concepts équivalents, pour produire un nouveau concept à la place de chaque paire. Concernant les instances et les propriétés de chaque couple de concepts (A et B), ils ont proposé d'appliquer deux règles de fusion pour former le nouveau concept C : * L'ensemble des instances de C est l'union de l'ensemble des instances de A et de B. * L'ensemble des propriétés de C est l'intersection de l'ensemble des propriétés de A et de B.
Figure 2 . 5 -
25Correspondances entre deux ontologies Zhang et al. (2017)Figure 2.6 -Fusion initiale des fragments d'ontologies Zhang et al. (2017) Dans les expérimentations, ils ont fusionné l'ontologie BCO (Biological Collections Ontology) qui contient 127 concepts, avec l'ontologie ACO (Animal in Context Ontology) qui contient 510 concepts, dans 9 minutes ; et ils ont utilisé comme référence une fusion retournée artificiellement.
Figure 2 . 7 -
27Résultat final de la fusionde Zhang et al. (2017)
Figure 2 . 8 -
28Intégration des ontologiesMena et al. (1996) Intégrationde Sowa Selon Sowa (1997), l'intégration est "le processus de recherche de points communs entre deux ontologies A et B et de dérivation d'une nouvelle ontologie C facilitant l'interopérabilité entre les systèmes informatiques basés sur les ontologies A et B. La nouvelle ontologie C peut remplacer A ou B, ou peut être utilisée comme intermédiaire entre un système basé sur A et un autre basé sur B". Il n'a pas spécifié les domaines des ontologies à intégrer.
Intersection des ontologies où une nouvelle ontologie O N fusionne et standardise les termes des entités en correspondance de O 1 et O 2 , tout en les renommant dans O 1 et O 2 (qui sont des nouvelles versions de O 1 et O 2 ) par les termes fusionnés et standardisés. (C'est la transformation des termes des entités correspondues en des termes communs)
Figure 2 . 9 -
29Intégration deHeflin and Hendler (2000)
Figure 2 .
210 -Intégration de
et Zhang et al. (2017) utilisent les termes "fusion" et "intégration" comme des synonymes.Intégration comme étant une ontologie de pontSelonUdrea et al. (2007), l'intégration des ontologies est l'ajout des axiomes de l'alignement A (entre O1 et O2) à l'union de O1 et O2 produisant à la fin une ontologie consistante et cohérente. Les correspondances de A sont utilisées pour créer des liens logiques (des axiomes) qui représentent la sémantique des relations entre les différentes entités (l'équivalence, la subsumption, la disjonction etc.).Selon Euzenat and Shvaiko(2013), l'intégration des ontologies est l'inclusion dans une ontologie O d'une autre ontologie O et des assertions exprimant des liens entre ces deux ontologies (des axiomes de pont). L'ontologie résultante O est censée contenir la connaissance des deux ontologies initiales (O et O ). Il n'y a pas vraiment de différence entre leurs définitions de fusion et d'intégration, à part le fait que, selon eux, contrairement à la fusion qui ne modifie pas les ontologies d'entrée, dans l'intégration, l'ontologie source O est inchangée tandis que l'ontologie initiale O est modifiée (plutôt augmentée par O ). En d'autres termes, l'intégration, selon eux, se fait d'une manière incrémentale, alors que la fusion se fait d'une manière non incrémentale. § C'est l'approche que nous allons implémenter.
(Nous expliquerons plus les notions d'inconsistance et d'incohérence dans le chapitre 4).
L
'outil ContentMap (le plus proche de notre travail) Pour Jiménez-Ruiz et al. (2009), un ensemble de correspondances (d'un Mapping) est représenté par une ontologie M , où les correspondances sont des axiomes de la forme subClassOf (e, e ), equivalentClass(e, e ), et disjointW ith(e, e ) pour la relation de subsomption, d'équivalence, et de disjonction respectivement ; et les identifiants et les valeurs de confiance des correspondances sont des annotations d'axiomes qui n'ont aucun effet sur les inférences.
Dans leurs expérimentations, ils ont utilisé quatre petites ontologies qui décrivent toutes le domaine des références bibliographiques, mais qui sont développées séparément. Leur taille varie de 130 entités (58 classes, 46 propriétés d'objet, et 26 propriétés de données) à 49 entités (18 classes, 12 propriétés d'objet, et 19 propriétés de données) et de 235 axiomes à 96 axiomes. O-INR est l'ontologie avec laquelle les trois autres ontologies (O-MIT, O-UMBC, et O-AIFB) ont été intégrées chacune à part. Il existe trois alignements de référence : un alignement pour O-MIT et O-INR contenant 119 correspondances, un alignement pour O-UMBC et O-INR contenant 83 correspondances, et un alignement pour O-AIFB et O-INR contenant 98 correspondances. Ils ont intégré O-MIT, O-UMBC, et O-AIFB séparément avec O-INR en utilisant leurs alignements de référence correspondants, puis ils ont évalué les conséquences sémantiques de leurs ontologies résultantes. Dans tous les cas, ils ont trouvé un nombre signifiant d'inférences imprévues. Par exemple, lors de l'intégration de O-AIFB et O-INR, ContentMap a détecté 34 concepts insatisfiables (originaires des deux ontologies) pour lesquels il y a eu un nombre énorme de justifications (généralement complexes) qui ont rendu la réparation manuelle extrêmement difficile. Egalement, lors de l'intégration de O-MIT et O-INR, ContentMap a détecté des nouvelles subsomptions qui ont été identifiées et réparées automatiquement. D'un point de vue temps, le goulot d'étranglement est le calcul de toutes les justifications des inférences imprévues. Une fois les justifications calculées, le temps de réparation est, selon eux, relativement court (ils ne l'ont pas précisé). Ils ont remarqué aussi que l'utilisation des correspondances générées automatiquement a abouti à un plus grand nombre d'inférences imprévues, e.g. quand ils ont intégré O-AIFB et O-INR en utilisant l'outil de matching CIDER avec un seuil de confiance égale à 0.1, ils ont trouvé 55 concepts insatisfiables et 34 subsomptions imprévues qui sont des erreurs causées principalement par des correspondances incorrectes.Pour conclure, les auteurs ont fait une fusion (non pas une intégration), précisément une ontologie de pont, semi-automatique à de petites ontologies de même domaine, et malgré la réparation des alignements d'entrée, ils trouvent toujours énormément de classes insatisfiables dans l'ontologie de sortie. Ils n'évoquent pas le temps d'exécution de ces expérimentations. L'outil de Ziemba et al.L'algorithme d'intégration des ontologiesde Ziemba et al. (2015) utilise essentiellement les outils de refactoring et d'intégration de l'éditeur "Protégé" qui facilitent énormément leur processus d'intégration. Il est divisé en trois parties :1. L'intégration de la première ontologie :(a) Créer une nouvelle ontologie vide dans l'éditeur Protégé (Ils ont choisi de lui donner l'IRI (l'identificateur) : "Intégrée") ;
2 .
2La sélection, l'importation et le refactoring d'une nouvelle ontologie source dans l'ontologie cible, et faire l'alignement entre elles, en utilisant les dictionnaires, les thésaurus, et les outils de "Protégé", pour l'introduire ensuite sous forme de relations d'équivalence et de subsomption entre les entités des ontologies source et cible.
Figure 2 .
211 -Incohérence de la fusion de O1 etO2 Fahad et al. (2010) L'exemple de la figure 2.12 illustre une incohérence logique causée par deux correspondances entre l'ontologie "National Cancer Institute Thesaurus" (NCIT) et l'ontologie "Foundational Model of Anatomy" (FMA). Cela se produit car, lors de l'intégration, la classe Fibrillar_Actin devient (suite à l'équivalence) une sous-classe de Anatomic_Structure_System_or_Substance et de Gene_Product, qui sont deux classes disjointes. § Résoudre ces incohérences est loin d'être facile.
Figure 2 .
212 -Incohérence de l'ontologie de pont Cheatham and Pesquita (2017) Udrea et al. (2007) exigent l'exploitation de la sémantique des ontologies pendant la génération des correspondances entre elles (pendant le matching), pour parvenir à créer une ontologie consistante et cohérente suite au processus d'intégration (ou de fusion). Et Fahad et al. (2010) exigent de prêter une attention particulière aux conflits sémantiques générés à cause des relations disjointes dans les ontologies sources.
appelé notre algorithme d'intégration "OIA2R" (Ontology Integration : Alignment Reuse and Refactoring). Ce que notre algorithme génère est une ontologie de pont, i.e., l'union des ontologies d'entrée et des alignements entre eux. Puisque nous allons convertir les correspondances contenues dans les alignements d'entrée en des axiomes OWL, ces alignements sont considérés comme des ontologies OWL intermédiaires (constituées d'entités ayant des relations d'équivalence). Ainsi, implicitement, c'est une union des ontologies sources et des ontologies intermédiaires (l'articulation). Dans le cas de deux ontologies O 1 et O 2 , ayant un alignement A qui peut être vu comme une ontologie O A , le résultat sera une nouvelle ontologie O 3 de sorte que O 3 = O 1 + O 2 + A, ou plutôt O 3 = O 1 + O 2 + O A . Le schéma de la figure 3.3 illustre nos dires.
Figure 3 . 1 -
31Processus général de l'intégration des ontologies
Figure 3 . 2 -
32Processus général de notre méthode d'intégration des ontologies (OIA2R)
Figure 3 . 3 -
33Ontologie de pont (Ont3)
le parsing des classes (des ontologies d'entrée) et de leurs définitions (descriptions), et au fur et à mesure, nous créons les axiomes correspondants à ces classes et à leurs définitions dans notre nouvelle ontologie. Nous faisons le parsing des propriétés d'objet (des ontologies d'entrée) et de leurs définitions, et au fur et à mesure, nous créons les axiomes correspondants à ces propriétés d'objet et à leurs définitions dans notre nouvelle ontologie. Nous faisons le parsing des propriétés de données (des ontologies d'entrée) et de leurs définitions, et au fur et à mesure, nous créons les axiomes correspondants à ces propriétés de données et à leurs définitions dans notre nouvelle ontologie. Et, nous faisons le parsing des individus anonymes (des ontologies d'entrée) et de leurs définitions, et au fur et à mesure, nous créons les axiomes correspondants à ces individus et à leurs définitions dans notre nouvelle ontologie.
Nous parsons les classes des ontologies d'entrée, et nous remplissons au fur et à mesure le HSet des classes par tous les URIs originaux des classes. Nous parsons les propriétés d'objet des ontologies d'entrée, et nous remplissons au fur et à mesure le HSet des propriétés d'objet par tous les URIs originaux des propriétés d'objet. Nous parsons les propriétés de données des ontologies d'entrée, et nous remplissons au fur et à mesure le HSet des propriétés de données par tous les URIs originaux des propriétés de données. Nous parsons les individus des ontologies d'entrée, et nous remplissons au fur et à mesure le HSet des individus par tous les URIs originaux des individus.
Figure 3 . 5 -
35Debugage d'une classe insatisfiable dans une ontologie de pont
Figure 3
3Figure 3.6 -Formation des classes insatisfiables
Figure 3 . 7 -
37Deux correspondances ayant la même entité source
Figure 3 . 8 -
38Cause de l'incohérence d'une ontologie de pont nant de l'ontologie Ont3) avait été correspondue avec une seule classe de l'autre ontologie (002), précisément la classe avec laquelle elle a la plus grande mesure de similarité, nous aurons évité toutes ces incohérences.
Figure 3 . 9 -
39Résolution des insatisfiabilités
Figure 3 . 10 -
310Transformation d'un alignement (1-à-N) en un mapping(1-à-1)
Figure 3 .
311 -Nouvelle définition de l'intégration sémantique
Figure 3 .
312 -Intégration incrémentale(cas 1)
Figure 3 .
313 -Intégration incrémentale (cas 2)Nous proposons trois types d'intégration non incrémentale :• Intégration 2-à-2 : Les ontologies sont intégrées uniquement à l'aide des alignements entre les paires d'ontologies consécutives (c.f.,figure 3.14),• Intégration 1-à-N : Les ontologies sont intégrées à l'aide des alignements entre une ontologie choisie (préférée ou prioritaire) et les autres ontologies (c.f., figure 3.15), • Intégration N-à-N : Les ontologies sont intégrées à l'aide des alignements entre toute paire d'ontologies possible (c.f., figure 3.16). L'intégration N-à-N est la plus complète, par contre les deux autres types d'intégration (1-à-N et 2-à-2) ne le sont pas (i.e., n'assurent pas une interopérabilité complète). Tenons l'exemple de cinq ontologies appartenant au même domaine (O 1 , O 2 , O 3 , O 4 , and O 5 ) pour faire une intégration 2-à-2. Supposons que toutes les ontologies contiennent une classe A, à part l'ontologie O 4 . Si O 4 était dans la quatrième position, alors la classe A de l'ontologie O 5 ne va pas avoir une
Figure 3 Figure 3 .
3315 -Intégration non incrémentale(1-to-N)
Figure 3 .
316 -Intégration non incrémentale (N-to-N) correspondance d'équivalence avec une classe de l'ontologie O 4 . Ce qui fait qu'elle ne sera pas intégrée avec les autres classes A des autres ontologies (ayant la position 1, 2 et 3). L'intégration 1-à-N par contre résout ce problème. Tenons le même exemple en choisissant l'ontologie O 1 comme l'ontologie préférée, avec qui les quatre autres ontologies (O 2 , O 3 , O 4 , and O 5 ) seront alignées. Dans ce cas, la classe A de l'ontologie O 1 va être correspondue à toutes les classes A existantes, y compris celle de l'ontologie O 5 . Malheureusement, cette méthode ne va pas garantir une interopérabilité complète. Par exemple, si une classe B existe seulement dans l'ontologie O 3 et O 4 , ces deux classes ne vont pas être intégrées (parce que ce type d'intégration n'utilise pas l'alignement entre O 3 and O 4 ). Ces inconvénients sont tous palliés par l'intégration N-à-N. Mais dans le cas d'une ontologie de pont, cette dernière va générer de multiple redondances et cycles. Par exemple, parmi les cinq ontologies d'entrée, les ontologies O 1 , O 2 , et O 3 ont une entité A en commun. Dans une ontologie de pont, nous aurons des liens d'équivalence entre O1:A et O2:A, O2:A et O3:A, O1:A et O3:A. L'équivalence entre O1:A et O3:A peut être déduite des deux autres équivalences. Il s'agit donc d'un lien redondant. Et sachant qu'une relation d'équivalence est formellement composée de deux relations de subsumption (chacune dans un sens), il y aura deux cycles de subsomption entre ces trois entités (un cycle dans chaque direction).
Figure 3 .
317 -Agrégation des ontologies
Figure 4 . 2 -
42Agrégation de OIA2R
Figure 4 . 3 -
43Intégration de "référence"
Figure 4 . 4 -
44Intégration de OIA2R
Figure 4 . 5 -
45Debugage d'une classe insatisfiable dans une ontologie de pont Dans la figure 4.6, nous modélisons la représentation graphique des axiomes de justification ci-dessus, où les classes en rouge sont les classes insatisfiables.
Figure 4 . 6 -
46Formation des classes insatisfiablesSachant que la relation d'équivalence (des "bridging" axiomes) est en fait égale à deux relations de subsomption dans les deux sens, le schéma devient comme le montre la figure 4.7.
Figure 4 . 7 -
47Cause de l'incohérence d'une ontologie de pont
Figure 4 . 8 -
48Debugage d'une classe insatisfiable après une fusion
Figure 4 . 9 -
49Formation d'une classe insatisfiable après une fusion complète
Table des matières
desTable des figures ivListe des acronymes
ALCOMO
Applying Logical Constraints on Matching Ontologies
AML
AgreementMakerLight
API
Application Programming Interface
AROMA
Association Rule Ontology Matchinh Approach
CIDER
Context and Interface baseD ontology alignER
ContentMap
LogiC-based ONtology inTEgratioN Tool using MAPpings
DTD
Document Type Definition
FITON
Framework for InTegrating ONtologies
F-logic
Frame logic
FMA
Foundational Model of Anatomy
HTML
HyperText Markup Language
ILIADS
Integrated Learning In Alignment of Data and Schema
IRI
Internationalized Resource Identifier
KIF
Knowledge Interchange Format
LGPL
Lesser General Public Licence
LOD
Linked Open Data
LogMap
Logic-based Methods for Ontology Mapping
NCI
National Cancer Institute Thesaurus
OAEI
Ontology Alignment Evaluation Initiative
OIM-SM
Ontology Integration Method based on Semantic Mapping
OLA
OWL Lite Alignment
OWL
Ontology Web Language
RDF
Resource Description Framework
RDFS
RDF-Schema
SWRL
Semantic Web Rule Language
SNOMED CT
SNOMED Clinical Terms
URI
Uniform Resource Identifier
URL
Uniform Resource Locator
WWW
World Wide Web
W3C
WWW Consortium
XML
Extensible Markup Language
YAM++
Yet Another Matcher
Ontology Language) est un langage de représentation de connaissances qui permet d'écrire (de construire) des ontologies Web, et tout comme RDF, il est un langage profitant de l'universalité syntaxique de XML. OWL devient une recommandation du W3C en 2004, et OWL 2 le devient en 2009. A part sa capacité de définir et de décrire des classes, des propriétés, et des individus de classes, OWL permet aussi de définir des relations entre les classes (union, intersection, disjonction, équivalence, subsomption etc.), des contraintes de cardinalité pour les valeurs des propriétés (nombre minimum, maximum, ou exact), des relations spéciales pour les propriétés (transitive, symétrique, fonctionnelle, inverse, réflexive, etc.), et des restrictions sur le domaine et le co-domaine des propriétés, etc. Par conséquent, OWL possède une logique très développée qui permet le raisonnement sémantique sur ces règles. Comparé aux langages RDF et RDFS, OWL offre aux machines une plus grande capacité d'interprétation du contenu Web, grâce à son vocabulaire riche et sa sémantique formelle.Les classes définies par l'utilisateur sont toutes des enfants de la superclasse « owl:Thing » (qui représente l'ensemble de tous les individus) et des parents de la sous-classe « owl:Nothing » (qui représente l'ensemble vide).Les propriétés d'objet et de type de données définies par l'utilisateur sont toutes respectivement des enfants des super propriétés « owl:TopObjectProperty » et « owl:TopDataProperty », et des parents des sous-classes « owl:BottomObjectProperty » et « owl:BottomDataProperty ». Les propriétés d'annotation telles que « owl:versionInfo », « rdfs:label », « rdfs:comment », « rdfs:seeAlso », « owl:priorVersion » etc. sont des constructeurs intégrés dans OWL.
2.1. FUSION DES ONTOLOGIES * Le plugin de PROMPT est dépassé et non fonctionnel maintenant (il n'est plus disponible pour le téléchargement). L'outil de Caldarola et Rinaldi Le Framework de Caldarola and Rinaldi (2016) contient quatre blocs principaux : 1. Le bloc de récupération des ontologies 2. Le bloc de normalisation des ontologies 3. Le bloc de matching des ontologies : Ce bloc est responsable de l'obtention d'un ensemble d'alignements (A) qui sont des correspondances entre les entités des ontologies d'entrée et de l'ontologie cible. Le matcher implique trois types d'opérations de matching (à base de chaînes, sémantique, et linguistique) qui vont également aider à faire une analyse automatique qui évalue et découvre les ontologies d'entrée les plus similaires à l'ontologie cible (i.e. les ontologies pertinentes) parmi lesquels les ingénieurs de connaissances vont sélectionner les ontologies locales à réutiliser en les intégrant dans l'ontologie cible. 4. Le bloc de fusion des ontologies : Il est responsable de l'intégration des ontologies d'entrée sélectionnées dans une ontologie OWL globale qui sera plus riche. Selon les mesures des correspondances contenues dans l'ensemble des alignements (A), les opérations suivantes seront effectuées sur les entités appariées des ontologies :
). Il s'agit d'une nouvelle ontologie O M , positionnée entre les deux ontologies O 1 et O 2 , qui contient les règles / les axiomes (de transformation) pour mettre en correspondance des entités entre O 1 et O 2 . Révisions de Mapping où O 1 , une nouvelle version de O 1 , contient (à part les entités et les axiomes de O 1 ) les règles qui mettent en correspondance les entités de O 1 par rapport à O 2 , et O 2 , une nouvelle version de O 2 , contient (à part les entités et les axiomes de O 2
remarquent deux perceptions de réparation et de debugage dans les travaux de fusion ou d'intégration des ontologies :• Quelques auteurs considèrent que les ontologies (à intégrer ou fusionner) sont correctes et
toujours plus fiables que les alignements, et s'il y a d'incohérence ou d'inconsistance, c'est
3.6. NOUVELLE DÉFINITION DE LA NOTION D'INTÉGRATION
forcément à cause des alignements (LogMap et ALCOMO). Ils cherchent alors à trouver
l'ensemble minimal de conflits entraînant l'incohérence de l'alignement, et suppriment les
correspondances qui causent les insatisfiabilités dans les classes de l'ontologie résultante
pour minimiser leur impact.
L'expérimentation est réalisée à l'aide des bases de test Conference, Anatomy, et Large Biomedical disponibles dans le cadre de la compagne OAEI (Ontology Alignment Evaluation Initiative). Menée depuis 2004 par un groupe de chercheurs sur le matching des ontologies, l'initiative de l'évaluation des alignements d'ontologies (OAEI) est une plate-forme internationale standard d'évaluation des outils de matching. Elle vise à améliorer les différents matchers d'ontologies en évaluant et en comparant leurs forces et leurs faiblesses à l'aide d'une suite d'alignements de référence qu'elle fournit. Les résultats des campagnes d'évaluation de chaque année, ainsi que l'ensemble des bases et des alignements de référence peuvent être téléchargés sur le site Web de OAEI.
Table 4 .
41 -Caractéristiques des ontologies de la base ConferenceConference Classes Niv Prop Obj Niv Prop Data Niv Instances Axiomscmt
29
4
49
1
10
1
0
226
conference
59
7
46
2
18
1
0
285
confOf
38
3
13
1
23
1
0
196
edas
103
4
30
1
20
1
114
739
ekaw
73
6
33
2
0
0
0
233
iasted
140
6
38
1
3
1
4
358
sigkdd
49
4
17
1
11
1
0
116
Total/Max
491
7
226
2
85
1
118
2 153
Table 4 .
42 -Caractéristiques des ontologies de la base AnatomyAnatomy
Classes Niv Prop Obj Niv Prop Data Niv Instances Axioms
human
3 304
13
2
1
0
0
0 11 545
mouse
2 743
7
3
1
0
0
0
4 838
Total/Max
6 047
13
5
1
0
0
0 16 383
Table 4 .
43 -Caractéristiques des ontologies de la base LargeBioLargeBio
Classes Niv Prop Obj Niv Prop Data Niv Instances Axioms
FMA
78 988
21
0
0
54
1
0
79 218
NCI
66 724
17
123
6
67
1
0
96 046
SNOMED
122 464
34
55
3
0
0
0 191 203
Total/Max 268 176
34
178
6
121
1
0 366 467
Table 4 .
44 -Les alignements de référence de la base ConferenceTable 4.5 -Les alignements de référence de la base AnatomyTable 4.6 -Les alignemens de référence de la base LargeBioAlignment
Cellules
cmt-conference
15 (14)
cmt-confOf
16
cmt-edas
13
cmt-ekaw
11
cmt-iasted
4
cmt-sigkdd
12
conference-confOf
15
conference-edas
17
conference-ekaw
25
conference-iasted
14
conference-sigkdd
15
confOf-edas
19
confOf-ekaw
20 (19)
confOf-iasted
9
confOf-sigkdd
7
edas-ekaw
23
edas-iasted
19
edas-sigkdd
15
ekaw-iasted
10
ekaw-sigkdd
11
iasted-sigkdd
15
Total
305 (303)
() : filtré
Alignment
Nombre de cellules
Original (1-to-N) Filtré (1-to-1)
human-mouse
1 516
1 491
Alignment
Original (1-to-N)
Filtré (1-to-1)
=
? Taille
=
? Taille
FMA-NCI
2 686
338
3 024
2 337
170
2 507
FMA-SNOMED
6 026 2 982
9 008
5 186 2 568
7 754
SNOMED-NCI
17 210 1 634 18 844 13 358
740 14 098
Total
25 922 4 954 30 876 20 881 3 478 24 359
Thing", et B = "owl:Nothing", alors il s'agit d'un test de consistance. -Si A = "une classe", et B = "owl:Nothing", il s'agit d'un test de satisfiabilité. -Si A et B sont toutes les deux des classes, il s'agit d'un test de subsomption.Table 4.7 -Caractéristiques de l'ontologie résultant d'une intégration ou d'une agrégation Sortie = Ontologie résultante Classes Propriétés d'objet Propriétés data Individus4.6 Résultats et évaluation
4.6.1 Résultats
Entrées =
ontologies (+ alignements)
« Conference »
491
226
85
118
« Anatomy »
6 047
5
0
0
« Large Bio »
268 176
178
121
0
Table 4 .
48 -Qualité de l'ontologie résultant d'une agrégationTable 4.9 -Qualité de l'ontologie résultant de l'intégration des ontologies de ConferenceOntologies
d'entrée
Ontologie de sortie
Classes
insatisfiables
Axioms
logiques
Consistance
OIA2R
Réf OIA2R
Réf OIA2R Réf
Conference
0
0
1 860
2 153
Anatomy
0
0
6 635 16 383
LargeBio
0
0 244 942 366 467
Conference
Nombre des classes insatisfiables
Al originaux (1-à-N) Al filtrés (1-à-1)
OIA2R
Réf OIA2R
Réf
Intégration
2-à-2
0
5
0
5
Intégration
1-à-N
0
0
0
0
Intégration
N-à-N
54
54
Table 4 .
410 -Préservation des axiomes après l'intégration des ontologies de ConferenceConference
Nombre des axiomes logiques
Al originaux
Al filtrés
OIA2R
Réf Attendus OIA2R
Réf Attendus
Intégration
2-à-2
1 957 2 250
2 250
(2 153 +
97)
1 956 2 249
2 249
(2 153 +
96)
Intégration
1-à-N
1 931 2 224
2 224
(2 153 +
71)
1 930 2 223
2 223
(2 153 +
70)
Intégration
N-à-N
2 165 2 458
2 458
(2 153 +
305)
2 163 2 456
2 456
(2 153 +
303)
Table 4 .
412 -Préservation des axiomes après l'intégration des ontologies de AnatomyAnatomy
Nombre des axiomes logiques
Al originaux
Al filtrés
OIA2R
Réf Attendus OIA2R
Réf Attendus
Intégration
2-à-2
8 151 17 899
17 899
(16 383
+ 1 516)
8 126 17 874
17 874
(16 383
+ 1 491)
Table 4 .
413 -Qualité de l'ontologie résultant de l'intégration des ontologies de LargeBioLargeBio
Nombre de classes insatisfiables
Al originaux
Al filtrés
OIA2R
Réf OIA2R
Réf
Intég
2-à-2
Al
originaux
120 743 190 486
67 342 141 941
Al
réparés
11 978
-11 078
-
Intég
1-à-N
Al
originaux
58 608 118 579
27 773 65 043
Al
réparés
56
-
48
96
Intég
N-à-N
Al
originaux
136 301 206 232
80 320 157 121
Al
réparés
14 655
-12 919
-
Table 4 .
414 -Préservation des axiomes après l'intégration des ontologies de LargeBioLargeBio
Nombre des axiomes logiques
Al originaux
Al filtrés
OIA2R
Réf Attendus OIA2R
Réf Attendus
Intég
2-à-2
Al
originaux
266 810 388 335
388 335
(366 467
+ 21 868)
261 547 383 072
383 072
(366 467
+ 16 605)
Al
réparés
264 838 386 363
386 363
(366 467
+ 19 896)
260 637 382 162
382 162
(366 467
+ 15 695)
Intég
1-à-N
Al
originaux
256 974 378 499
378 499
(366 467
+ 12 032)
255 203 376 728
376 728
(366 467
+ 10 261)
Al
réparés
253 654 375 179
375 179
(366 467
+ 8 712)
252 465 373 990
373 990
(366 467
+ 7 523)
Intég
N-à-N
Al
originaux
275 818 397 343
397 343
(366 467
+ 30 876)
269 301 390 826
390 826
(366 467
+ 24 359)
Al
réparés
270 864 392 389
392 389
(366 467
+ 25 922)
265 823 387 348
387 348
Table 4 .
415 -Temps d'exécution d'une intégration N-à-NTps d'exécutionCPU (s)Notre intégration
La référence
+loading -loading +loading -loading
Conference
1,531
0,406
1,375
0,171
Anatomy
3,093
0,703
3,562
0,453
Large Bio
36,859
8,406
41,375
4,890
Table 4 .
416 -Qualité de l'ontologie intégrée (LargeBio OAEI Task 1) FMA1-NCI 1Table 4.17 -Qualité de l'ontologie intégrée (LargeBio OAEI Task 3)Table 4.18 -Qualité de l'ontologie intégrée (LargeBio OAEI Task 5)Table 4.19 -Qualité de l'ontologie intégrée (LargeBio OAEI Task 2)Nombre de classes insatisfiables
Al original
Al filtré
OIA2R Full merge OIA2R Full Merge
Al original
1 727
826
410
173
Al réparé
0
0
0
0
FMA2-SNOMED1
Nombre de classes insatisfiables
Al original
Al filtré
OIA2R Full merge OIA2R Full Merge
Al original
13 508
7 212 10 048
4 379
Al réparé
0
0
0
0
NCI 2-SNOMED2
Nombre de classes insatisfiables
Al original
Al filtré
OIA2R Full merge OIA2R Full Merge
Al original
34 639
19 132 25 637
12 990
Al réparé
0
0
0
0
FMA3-NCI 3
Nombre de classes insatisfiables
Al original
Al filtré
OIA2R Full merge OIA2R Full Merge
Al original
7 175
6 272
1 158
995
Al réparé
0
0
0
0
Table 4 .
420 -Qualité de l'ontologie intégrée (LargeBio OAEI Task 6) Nous remarquons (comme l'avaient ditRaunich and Rahm NCI 3-SNOMED3
Nombre de classes insatisfiables
Al original
Al filtré
OIA2R Full merge OIA2R Full Merge
Al original
92 149
76 280 49 825
42 331
Al réparé
0
0
0
0
§
.5. INGÉNIERIE ONTOLOGIQUE
.1. FUSION DES ONTOLOGIES
Dans la littérature, le problème de l'intégration des ontologies a été largement étudié au cours des dernières années, mais il reste toujours un défi si nous voulons réaliser une intégration de manière automatique, efficace, sur de grandes ontologies, en préservant toutes les données originales, et sans produire d'erreurs (conflits sémantiques / logiques).
Nous faisons le parsing des propriétés d'annotation (des ontologies d'entrée) et de leurs définitions, et au fur et à mesure, nous créons les axiomes correspondants à ces propriétés d'annotation et à leurs définitions dans notre nouvelle ontologie. Nous faisons le parsing des individus / instances (des ontologies d'entrée) et de leurs définitions, et au fur et à mesure, nous créons les axiomes correspondants à ces individus et à leurs définitions dans notre nouvelle ontologie.
Nous remarquons qu'après l'ajout des "bridging" axiomes d'équivalence, la classe "002#Tissue_Dissection" devient par inférence une sous-classe des deux classes "002#Fin-dings_and_Disorders_Kind" et "002#NCI_Kind" qui sont disjointes (information extraite de l'ontologie originale (Ont2)). Ceci est contradictoire, car une classe ne peut pas être une sous-classe de deux classes disjointes. Aucune instance ne peut la satisfaire. La même chose s'applique pour les autres classes coloriées en rouge. Si la classe "003#Clinical_finding" (prove-
. https://github.com/ernestojimenezruiz/logmap-matcher 2. http://web.informatik.uni-mannheim.de/alcomo/
Nous allons passer tout de suite à la concrétisation de notre approche décrite dans ce chapitre.
RemerciementsJe remercie Monsieur Sadok Ben Yahia, Professeur à la Faculté des Sciences de Tunis et directeur du Laboratoire d'Informatique en Programmation, Algorithmique et Heuristique (LIPAH), pour la confiance qu'il m'a accordée en acceptant de diriger mes travaux de mastère. Je remercie sa disponibilité continue et je voudrais lui éprouver toute mon admiration.RésuméCe travail est accompli dans le cadre d'un projet de mémoire de mastère de recherche. Le but est d'intégrer deux ou plusieurs ontologies (de mêmes ou de différents domaines) dans une nouvelle ontologie OWL consistante et cohérente pour assurer leur interopérabilité sémantique. Pour ce faire, nous avons choisi de créer une ontologie de pont qui inclut toutes les ontologies sources et leurs axiomes de pont dans une nouvelle ontologie. Par la suite, nous avons introduit un critère qui aide à obtenir une ontologie de meilleure qualité (ayant le minimum de conflits sémantiques / logiques). Nous avons proposé également une nouvelle terminologie qui clarifie les notions floues et mal placées utilisées dans les travaux de l'état de l'art. Enfin, nous avons testé et évalué notre outil OIA2R à l'aide des ontologies et des alignements de référence de OAEI. Il s'est avéré qu'il est générique, efficace, scalable, et assez performant.Mots clés: Ontologie, Intégration des ontologies, Fusion des ontologies, Matching, Alignement, Mapping, Consistance, Cohérence, Insatisfiabilité, OWL, Réparation des alignements, debugage des alignements.AbstractThis work is done as part of a research master's thesis project. The goal is to integrate two or more ontologies (of the same or different domains) in a new consistent and coherent OWL ontology to insure semantic interoperability between them. To do this, we have chosen to create a bridge ontology that includes all source ontologies and their bridging axioms in a new ontology. Subsequently, we introduced a new criterion for obtaining an ontology of better quality (having the minimum of semantic / logical conflicts). We have also proposed a new terminology that clarifies the unclear and misplaced notions used in state-of-the-art works. Finally, we tested and evaluated our OIA2R tool using OAEI ontologies and reference alignments. It turned out
Pour but de mettre en relief les axiomes d'équivalence ajoutés à l'union des ontologies sources et bien les montrer dans nos captures, nous avons choisi de faire une intégration N-à-N. Nous avons choisi d'imprimer le résultat de l'intégration des plus grandes ontologies pour prouver que notre Framework monte à l'échelle facilement. comme le montreront les temps d'exécutionPour but de mettre en relief les axiomes d'équivalence ajoutés à l'union des ontologies sources et bien les montrer dans nos captures, nous avons choisi de faire une intégration N-à-N. Nous avons choisi d'imprimer le résultat de l'intégration des plus grandes ontologies pour prouver que notre Framework monte à l'échelle facilement (comme le montreront les temps d'exécution).
La première ontologie insérée en entrée est. FMA. 3wholeLa première ontologie insérée en entrée est "FMA 3" (whole);
. La , NCI. 3wholeLa deuxième ontologie est "NCI 3" (whole);
. La , SNOMED 3" (wholeLa troisième ontologie est "SNOMED 3" (whole).
Voici ce que donne l'exécution de la première partie du code qui réalise une agrégation / composition simple des ontologies d'entrée (i.e., sans les "bridging" axiomes) : Pour la référence : les axiomes sont exactement identiques aux originaux. Figure 4.1Voici ce que donne l'exécution de la première partie du code qui réalise une agrégation / composition simple des ontologies d'entrée (i.e., sans les "bridging" axiomes) : Pour la référence : les axiomes sont exactement identiques aux originaux (Figure 4.1).
Pour OIA2R : les axiomes sont décrits exactement comme les originaux sauf que nous personnalisons les IRIs de toutes les entités mentionnées. Figure 4.2Pour OIA2R : les axiomes sont décrits exactement comme les originaux sauf que nous personnalisons les IRIs de toutes les entités mentionnées (Figure 4.2).
En effet, si nous ne gardons pas d'axiomes de disjonction, nous n'obtiendrons aucune classe insatisfaisable, et toutes nos ontologies de sortie seraient cohérentes et consistantes, mais incomplètes (i.e., manquant des informations de disjonction précieuses). Notez que toutes les classes insatisfiables sont causées par la préservation des connaissances de disjonction des alignements d'entrée. Nous concluons que, lorsque toutes les correspondances sont des correspondances d'équivalence, la seule cause de conflits est les relations. DisjointWith" issues des ontologies d'entréeNotez que toutes les classes insatisfiables sont causées par la préservation des connaissances de disjonction des alignements d'entrée. En effet, si nous ne gardons pas d'axiomes de disjonction, nous n'obtiendrons aucune classe insatisfaisable, et toutes nos ontologies de sortie seraient cohérentes et consistantes, mais incomplètes (i.e., manquant des informations de disjonction précieuses). Nous concluons que, lorsque toutes les correspondances sont des correspondances d'équivalence, la seule cause de conflits est les relations "DisjointWith" issues des ontologies d'entrée.
Nous remarquons aussi que dans l'ontologie résultant d'une intégration N-à-N, le nombre de classes insatisfiables est beaucoup plus important que celui de l'ontologie résultant d'une intégration 2-à-2 ou 1-à-N. L'ontologie de référence contient toujours plus de classes insatisfiables que notre ontologie. Par conséquent, nous serions dans le risque d'avoir une inconsistance possible si jamais il y avait un individu instancié par une des classes insatisfiables, ou si jamais des individus avaient un conflit entre eux suite à des axiomes de pont de type "sameAs". Dans notre cas, les ontologies sources utilisées ne contiennent pas d'instances, à part "edas" et "iasted" dont toutes les instances sont instanciées par des classes qui n'ont aucune correspondance avec d'autres classes, donc sont hors de danger. Nous constatons aussi qu'une intégration d'ontologies de différents domaines. Constatations Dans tous les cas d'intégration, notre ontologie finale est complète dans le sens où elle conserve toutes les entités et la hiérarchie des ontologies d'entrée, et toutes les correspondances des alignements d'entrée. Dans l'agrégation (sans "bridging" axiomes), notre ontologie n'aura aucun ajout de classe insatisfiable, et le nombre de niveaux de sa hiérarchie sera toujours égal au nombre maximal des niveaux de hiérarchie des ontologies d'entrée. Dans l'ontologie de pont, nous constatons que suite à l'ajout des "bridging" axiomes, le raisonneur HermiT génère beaucoup trop de classes insatisfiables. comme dans "Anatomy") génère toujours moins de conflits qu'une intégration d'ontologies de même domaine. comme dans "Conference" et "Large Bio")Constatations Dans tous les cas d'intégration, notre ontologie finale est complète dans le sens où elle conserve toutes les entités et la hiérarchie des ontologies d'entrée, et toutes les correspondances des alignements d'entrée. Elle ne parvient pas pourtant à préserver tous les axiomes des ontologies d'entrée, contrairement à l'ontologie de "référence". Dans l'agrégation (sans "bridging" axiomes), notre ontologie n'aura aucun ajout de classe insatisfiable, et le nombre de niveaux de sa hiérarchie sera toujours égal au nombre maximal des niveaux de hiérarchie des ontologies d'entrée. Dans l'ontologie de pont, nous constatons que suite à l'ajout des "bridging" axiomes, le raisonneur HermiT génère beaucoup trop de classes insatisfiables. Nous remarquons aussi que dans l'ontologie résultant d'une intégration N-à-N, le nombre de classes insatisfiables est beaucoup plus important que celui de l'ontologie résultant d'une intégration 2-à-2 ou 1-à-N. L'ontologie de référence contient toujours plus de classes insatisfiables que notre ontologie. Par conséquent, nous serions dans le risque d'avoir une inconsistance possible si jamais il y avait un individu instancié par une des classes insatisfiables, ou si jamais des individus avaient un conflit entre eux suite à des axiomes de pont de type "sameAs". Dans notre cas, les ontologies sources utilisées ne contiennent pas d'instances, à part "edas" et "iasted" dont toutes les instances sont instanciées par des classes qui n'ont aucune correspondance avec d'autres classes, donc sont hors de danger. Nous constatons aussi qu'une intégration d'ontologies de différents domaines (comme dans "Anatomy") génère toujours moins de conflits qu'une intégration d'ontologies de même domaine (comme dans "Conference" et "Large Bio").
nous ne parvenons pas toujours à avoir un nombre de niveaux fixe (un niveau maximal) dans la hiérarchie des classes de notre ontologie, car le raisonneur qui découvre les niveaux (et les classes de chaque niveau) ne termine pas son raisonnement. On dirait que, suite à l'ajout des "bridging" axiomes, le raisonneur rencontre une boucle infinie. un cercle vicieux) dans son raisonnementA part cela, nous ne parvenons pas toujours à avoir un nombre de niveaux fixe (un niveau maximal) dans la hiérarchie des classes de notre ontologie, car le raisonneur qui découvre les niveaux (et les classes de chaque niveau) ne termine pas son raisonnement. On dirait que, suite à l'ajout des "bridging" axiomes, le raisonneur rencontre une boucle infinie (un cercle vicieux) dans son raisonnement.
Interprétations Ces insatisfiabilités sont dues au fait que l'axiome d'équivalence entre deux entités est formellement équivaut à deux axiomes de subsomption réciproques : equivalentClass (C1 C2) = subClassOf (C1 C2) + subClassOf. C2 C1Interprétations Ces insatisfiabilités sont dues au fait que l'axiome d'équivalence entre deux entités est formellement équivaut à deux axiomes de subsomption réciproques : equivalentClass (C1 C2) = subClassOf (C1 C2) + subClassOf (C2 C1)
Perspectives : Dans nos prochains travaux, nous allons nous projeter sur la fusion des ontologies qui constitue le plus haut niveau d'interopérabilité sémantique entre les ontologies, et cela pour but de minimiser au maximum les erreurs de l'ontologie résultante de ce processus. En effet, la fusion génère toujours moins d'insatisfiablités que l. § Et l'ajout de ces subsomptions implicites aux équivalences infère de nouvelles connaissances qui peuvent être contradictoires. ontologie de pont que nous avons réalisée dans ce mémoire§ Et l'ajout de ces subsomptions implicites aux équivalences infère de nouvelles connaissances qui peuvent être contradictoires. Perspectives : Dans nos prochains travaux, nous allons nous projeter sur la fusion des ontologies qui constitue le plus haut niveau d'interopérabilité sémantique entre les ontologies, et cela pour but de minimiser au maximum les erreurs de l'ontologie résultante de ce processus. En effet, la fusion génère toujours moins d'insatisfiablités que l'ontologie de pont que nous avons réalisée dans ce mémoire.
Nous exploiterons aussi d'autres relations sémantiques à part la relation d'équivalence dans les alignements, telles que la subsomption et la disjonction, pour que l'interopérabilité soit maximale et que toute hétérogénéité soit traitée. Nous exploiterons aussi d'autres relations sémantiques à part la relation d'équivalence dans les alignements, telles que la subsomption et la disjonction, pour que l'interopérabilité soit maximale et que toute hétérogénéité soit traitée.
nous comptons exploiter le domaine de la fouille de données dans nos prochains travaux de fusion ou d'intégration des ontologies. En effet, les contributions de notre laboratoire LIPAH ont atteint un niveau avancé dans ce domaine, ce qui va énormément nous aider. Fca-Merge Suivant L'exemple De, Maedche Stumme, Citons en quelques travaux intéressants. Bouzouita et al.Suivant l'exemple de FCA-Merge Stumme and Maedche (2001), nous comptons exploiter le domaine de la fouille de données dans nos prochains travaux de fusion ou d'intégration des ontologies. En effet, les contributions de notre laboratoire LIPAH ont atteint un niveau avancé dans ce domaine, ce qui va énormément nous aider. Citons en quelques travaux intéressants : Bouzouita et al. (2006);
. Gasmi, Gasmi et al. (2007);
. Cellier, Cellier et al. (2008);
. Ben Othman, Yahia, Othman and Ben Yahia (2008);
. Hamrouni, Hamrouni et al. (2008);
. Ayouni, Ayouni et al. (2010, 2011);
. Brahmi, Brahmi et al. (2010, 2011);
. Hamdi, Hamdi et al. (2013);
. Bouker, Bouker et al. (2014)
Il faut également noter qu'un autre axe de recherche très intéressant et plus difficile se présente. C'est le domaine de réparation, de debugage, ou de révision des ontologies et des alignements. Ce domaine aidera énormément à avoir des ontologies de bonne qualité suite à l. intégration des ontologiesIl faut également noter qu'un autre axe de recherche très intéressant et plus difficile se présente. C'est le domaine de réparation, de debugage, ou de révision des ontologies et des alignements. Ce domaine aidera énormément à avoir des ontologies de bonne qualité suite à l'intégration des ontologies.
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Novel Machine Learning Approach for Predicting Poverty using Temperature and Remote Sensing Data in Ethiopia
Om Shah
Lakeside School
Krti Tallam
Department of Ecology
Stanford University
94305StanfordCA
Novel Machine Learning Approach for Predicting Poverty using Temperature and Remote Sensing Data in Ethiopia
Social SciencesSustainability Sciences Machine LearningPoverty ModelingClimate Change
In many developing nations, a lack of poverty data prevents critical humanitarian organizations from responding to large-scale crises. Currently, socio-economic surveys are the only method implemented on a large scale for organizations and researchers to measure and track poverty. However, the inability to collect survey data efficiently and inexpensively leads to significant temporal gaps in poverty data; these gaps severely limit the ability of organizational entities to address poverty at its root cause. We propose a transfer learning model based on surface temperature change and remote sensing data to extract features useful for predicting poverty rates. Machine learning, supported by data sources of poverty indicators, has the potential to estimate poverty rates accurately and within strict time constraints. Higher temperatures, as a result of climate change, have caused numerous agricultural obstacles, socio-economic issues, and environmental disruptions, trapping families in developing countries in cycles of poverty. To find patterns of poverty relating to temperature that have the highest influence on spatial poverty rates, we use remote sensing data. The two-step transfer model predicts the temperature delta from high resolution satellite imagery and then extracts image features useful for predicting poverty. The resulting model achieved 80% accuracy on temperature prediction. This method takes advantage of abundant satellite and temperature data to measure poverty in a manner comparable to the existing survey methods and exceeds similar models of poverty prediction.Significance StatementAccording to the United Nations' Sustainable Development Goals, humanity's first and foremost goal is the elimination of worldwide poverty. Accurate, frequent poverty data is necessary for humanitarian organizations and policy makers to address poverty, especially in developing countries where a lack of poverty data has contributed to the uneven allocation of stimulus and resources. Without correctly directing resources to the impoverished, we cannot uplift communities out of cycles of poverty and successfully eliminate economic status as an obstacle to humanity's long-term success. The novel method to predict poverty discussed in this paper is essential to the critical need for poverty data in developing countries.
Introduction
There is a pressing need for inexpensive, abundant poverty data in developing nations. The United Nations' (UN) World That Counts publication reports the repercussions of lacking data are serious, ranging from a neglect of human rights to rapid environmental degradation. Sub-annual data is needed for countries to combat poverty through policy decisions, NGO funding, and effective disaster response. While sufficient poverty data is available for wealthy countries, through a combination of active and passive data sources, to properly accommodate humanitarian services, many developing countries face data shortages that limit their ability to serve at-risk communities [1]. The current prevailing data collection method, surveys, are time-consuming and expensive due to a variety of factors. Inefficient questionnaires decrease the quality of data collected while driving costs up. Furthermore, substantial portions of the population live in inaccessible rural areas making survey logistics difficult to plan [2]. Governments with strict budgeting requirements may not be willing to spend funds on employing survey personnel, or local leadership could harbor dissent towards data collection associated with a particular government or organization [3]. There is no consistent method for high quality data collection as any number of factors could impact proper execution. However, recent efforts focus on the use of machine learning to create poverty prediction solutions that utilize publicly available datasets and increase efficiency. Stanford University's Ermon Lab produced a machine learning transfer model that utilized nightlights as a proxy for urbanization and satellite imagery based image classification to support a poverty prediction task in multiple African countries. We extend the remote sensing based poverty mapping work researched by the Ermon Lab to examine the causal temperature-consumption relationship [4].
Causal relationships between consumption and consumption-determinators such as temperature are often viewed as downstream tasks [5]. In most cases, consumption-determinators are used to inform policy decisions after a deep learning model has been trained to predict consumption. It can be useful, however, to exploit the causal relationship directly in model training rather than as a corroboration of findings. Examining a singular causal relationship doesn't convey the full picture of poverty rates, but allows for segmenting determinants by their ability to explain variation in poverty rates. For example, organizations with climate focuses can direct resources towards areas most vulnerable to climate change, as seen through a temperature-consumption model. Monetary policy can be targeted towards economic relief for communities bearing the brunt of rising temperatures.
An opportunity exists to solve the poverty data void through novel methods. The United Nations wrote in their 2020 World Social report that urbanization is linked to poverty: most of the world population in poverty live in rural areas. Migration from rural areas to urban areas can result in a reduction in poverty in many cases. However, the transfer of people between rural and urban areas is a long term effect and thus can only be measured through long term analysis [6]. We therefore look at a different cause of poverty linked to variance in regional poverty rates. For populations living in agricultural communities, climate change poses a greater threat. Rising global temperatures are drastically reducing crop harvest output in regions such as sub-saharan Africa where poverty rates exceed 40%, impacting families who rely on agricultural growth to escape poverty [7,8]. In addition to crop failures, high temperatures have also caused the evaporation of water sources and placed a financial burden on families to improve their roofing material [9,10]. What otherwise may have been a temporary period of low income and crop yields has transformed into long term financial distress.
Global average temperature data can statistically represent the progress of climate change in the context of deep learning. Not only is temperature data abundant, but advances in satellite resolution have produced highly accurate climate datasets. However, by directly relating temperature data to poverty, we cannot assign weights to specific patterns between temperature and poverty. For example, visual patterns such as evaporating water sources or crop color combined with a high temperature correlation may indicate higher poverty rates than roof material. Remote sensing data is a potential data source for finding the strongest spatial links between temperature and poverty because satellite imagery can be collected instantaneously and inexpensively. Satellite data can measure a variety of natural and human developments such as water sources, roofing material, and crops, but also micro-features that are only a few pixels wide. Recent developments in machine learning tools and technology have increased computing efficiency for analyzing sophisticated forms of data such as satellite imagery. Machine learning models can be trained through indicators of climate change -namely temperature -to extract features from satellite imagery and produce meaningful poverty predictions.
We propose using a transfer learning model trained on temperature data to extract features from satellite images and predict poverty in Ethiopia. While transfer learning is traditionally used to compensate for a lack of training data in a target problem, we utilize it as a way to introduce spatial observations of the indirect temperature-consumption relationship. The first step will predict temperature from satellite images to learn features useful in predicting poverty. The second step will extract a feature vector from the temperature model and use those features to linearly predict consumption, an economic indicator of poverty.
Our three primary data sources are the satellite images, temperature data, and survey data. Satellite images are downloaded from the Google Static Maps API at a 16 factor zoom resolution. Temperature data is aggregated from WorldClim, a large scale climate database, at a 30 degree arc second resolution (approximately 1km by 1km). In this paper, average temperature refers to the average delta temperature between 1980 and 2016 for Ethiopia. Consumption per capita data is collected by the Living Standards Measurements Study (LSMS) 2016 socio-economic survey for Ethiopia.
The first step of the transfer learning model predicts temperature from satellite images. A pretrained convolutional neural network (CNN) model predicts temperature from satellite images and outputs a trained model from which features can be extracted. The CNN model is pre-trained so it can skip over unnecessary training that learns basic image patterns recognized in most image recognition models [11]. The first layers of any CNN model will almost always find relationships in images such as edges and corners. To save time and energy on the computing device, we avoid retraining for elementary patterns.
Feature extraction extracts the most useful features from each image and compiles a feature vector for the trained model [12]. In most image classification cases, feature extraction must be used because the sheer size of features from a large dataset of images can lead to unpredictable issues in later stages. Without feature extraction, the second part of the model trains on a noisy feature set and therefore produces a less accurate result.
The second step of the model involves training a ridge regression model on the extracted feature set. Ridge regression, a form of linear regression, is used to fit the consumption per capita values to the feature set. Unlike standard linear regression, a ridge model adds a bias to the hypothesis function to reduce overfitting and create a function better suited for prediction [13]. This proves useful if we wish to implement the model in different geographic locations or with contrasting demographic data.
We test the accuracy of our model using a five-fold cross validation model. With a standard holdout validation system, a model is tested using a limited set of test data which may introduce bias. The alternative method is a k-fold cross validation. Cross validation is a process of testing a model iteratively based on subsections of training data to ensure limited bias [14]. We limit bias because the model may have performed differently based on distinct geographic data trends within Ethiopia. The correlation of actual and predicted consumption values can be measured with an R^2 value, also known as the coefficient of determination. The R^2 value, a common metric in the machine learning and statistics fields, will inform us of the percentage of poverty rates in Ethiopia explained by the temperature model. Temperature data and satellite images from Ethiopia can be transformed into highly accurate poverty predictions through machine learning pattern analysis techniques.
Methods
The transfer learning model consists of two parts: predicting temperature using satellite images and predicting consumption from specific features of satellite images trained on temperature. Temperature data became a potential variable due to its relationship to poverty as an indicator of climate change. Only a specific range of temperatures -especially in developing countries -can support profitable crop yields, provide an environment with adequate water resources, and allow for unobstructed living [8,9,10]. In many places, the window of viable agricultural temperature is quickly closing in and water sources are rapidly depleting. We use temperature as a proxy for climate change and its impacts on poverty. Global average temperatures have been tracked by satellites for decades and their accuracy is getting more precise by year. The temperature data used in this paper has a spatial resolution of 30 arc seconds which equates to approximately a 1km by 1km resolution.
While temperature data can be computed for any latitude and longitude in the world, consumption data can only be collected by various surveys that occur every couple of years on a household level. A survey that computes consumption per capita is the Living Standards Measurement Study (LSMS) that is conducted in numerous countries across the globe. Their initiative is linked with the World Bank making the dataset a reliable source of information. The data used in this paper is from the Socioeconomic Survey 2015-2016 in Ethiopia. Asset wealth was the targeted economic measure in other studies such as the one conducted by Yeh et al., where urbanization proxies such as nightlights are indicative of a net-positive collection of material resources by a population -roads, cars, building sizes. We chose to use consumption because the temperature-consumption relationship impacts the ability of households to achieve a net-positive income. Another benefit of using consumption data to test our model against is that we not only get the specific consumption values but also locations where those consumption values were collected. This is helpful because we don't have to find a separate list of latitudes and longitudes for where those consumption values may have been surveyed. Consumption is used as total consumption per capita, a popular metric of poverty in academia and industry applications [15]. We derive consumption per capita to normalize the consumption per individual which is a constant value in all locations instead of per household for which size can fluctuate. We calculate this by taking the total annual consumption of each household and dividing the value by the total number of household members.
Procuring temperature data involves manipulating GeoTIFF data types and superimposing them onto the consumption data. WorldClim is an online repository of climate data from which we used average global temperature in degrees Celsius. A GeoTIFF file consists of an underlying map with embedded metadata [16]. TIFF files cover an entire area instead of specific locations like the LSMS survey. Due to this, any location derived from the LSMS data can be found in the TIFF file with its corresponding temperature. To further normalize the temperature data going into the model, a 10km by 10km bounding box around each location is created. We take the average temperature for this 100km^2 area instead of a single point at the latitude longitude provided by the survey data. For each location, in the form of latitude and longitude, from the LSMS survey, a consumption per capita value and average temperature value is assigned. This aggregated data is used to create specific download locations for the satellite images. To reciprocate taking the average temperature of a 10km by 10km bounding box, multiple images from each bounding box are taken instead of one image per box. This makes sure that there are enough training images for the model to predict temperature from validation images and subsequently predict consumption.
Before downloading the images, a Gaussian mixture model is used to split the temperature data into three bins. Data binning is a pre-processing technique where data is placed into separate bins depending on their relation to measures of central tendency [17]. Each bin is represented by a central value of the data it covers, such as the mean. The mixture model segments any input data into n groups, similar to a k-means model. Each image location, for which an image will be downloaded, is assigned to a temperature bin based on its average temperature. This step will simplify the model so it only has to predict the temperature bin of a model instead of its exact temperature. Another benefit of using temperature bins is that they will remove any anomalies that may arise from the data due to isolated geographic events. This allows the long term temperature increase induced by climate change to shine through any noise. Alongside the original temperature and consumption data, the assigned temperature bin from the gaussian mixture model is added to the set of data points for each image.
To download the images, we used the Google Static Image API. The only parameters needed by the API are latitude, longitude, and the zoom for the images. The API doesn't allow queries for specific timestamps, so the images downloaded were the most recent images taken by satellites. These images are likely <1 year old. We assume that model performance would increase if 2016 satellite images were downloaded. Once this step is complete, all images are downloaded to their respective locations on the hardware.
The model used for predicting is a VGG-11 model pre-trained on ImageNet. The VGG CNN model achieved high accuracy at the 2014 ILSVRC and thus proved to be a viable model for predicting poverty [18]. We chose the VGG-11 model over newer architectures such as ResNet and VGG-19 as the experimental goal was to simply find notable features for classification into three bins. A more advanced model would not return an appropriate performance boost for the additional computing power needed. The numeral after VGG represents the number of weighted layers that each image will be passed through; in VGG-11, there are 11 weighted layers through which the satellite images will be passed. Any VGG model takes in an input image of 224 by 224 pixels. The first eight layers of the model are a combination of convolution and max pooling. These make up the convolutional layers of the VGG-11 model. Each convolutional layer throughout the entire course of the model uses 3x3 filters, the smallest group of pixels within the image, to train. Every layer, the number of filters doubles to increase the model's exposure to the image. The last three layers are dedicated to a fully connected neural network and a softmax activation function. The first two fully connected layers have 4096 channels each while the third layer has 1000 channels. The model outputted a temperature bin prediction for each image. We used a 20 epoch distribution for training the model. Out of the 20 epochs, ten will be used to train the last few layers while the rest will be used to train the entire model. We didn't have to dedicate all the layers because the first layers are pretrained. This highlights the benefit of using a pretrained model to efficiently utilize compute and memory. After the 20 epochs of training are complete, the next step is to extract features from the trained model. The model was trained on a batch size of 8.
Additionally, we introduced augmentation and normalization functions to the model to vary input data. Augmentation involves performing minor edits such as flipping, reflecting, or color grading on images [19]. This increases the number of unique training data that the model receives on which it can train. Normalization takes a set of data and fits it into a given range. We must use normalization because larger values intrinsically have a greater impact on the model than smaller values. Normalization ensures there is no imbalanced influence of the training data on the model. Feature extraction is a critical step to analyzing the output of the trained model. The VGG-11 CNN model generates thousands of features from satellite images it finds important for predicting temperature. However, many of these features are discardable and limit the efficiency of the predictions [12]. To select what features we want to use, we must pass the model through a feature extraction process. The model used to extract features is a sequential classifier with only the first four layers. From the first layer, 25,088 features are taken as an input and by the last layer, 4096 features are outputted for each image. After the sequential layers, all remaining features are aggregated and compiled into a single feature vector for predicting consumption.
Predicting consumption from the extracted features is conducted through ridge regression. We avoid optimizing the ridge model parameters and architecture as a performance boost to the training is unnecessary. The experiment focuses on measuring the linear relationship between temperature and poverty that inspired the use of ridge regression rather than pushing the boundaries on performance. Ridge regression models add penalties, called a bias, to the hypothesis to avoid overfitting the data and its outliers. By adding penalties, the model performs with greater accuracy on new data. This is ideal because there are still locations where poverty has not been predicted with the model. Ridge models consist of a cost function to calculate the mean squared error differences between predicted and actual output values for each training example. The squared magnitude of all coefficients is added to the overall cost function to skew any produced coefficients toward a higher cost [13]. It is important to note that the square magnitude is first multiplied by the optimal learning rate, alpha, before being added to the overall cost. This allows for faster fitting to the data. For each cluster of training images, multiple images from a similar location in Ethiopia, there is a 4096-feature vector. The feature vectors of all clusters are scaled to create a consistent set of training variables. The training variables are fed into a ridge regression model instantiated by pre-built machine learning libraries, which in this case is scikit-learn. The best alpha for the ridge model is found by iterating over a possible set of hard coded alphas and feeding them into the ridge model. The best alpha is the value which produces the highest R^2 value.
Finding the accuracy of predicting consumption to track poverty is the final piece of the transfer learning model. We use a five fold cross validation model to test the performance of the trained ridge model; the five fold cross validation model used is a variant of industry standard k-fold cross validation. Instead of validating the model on a part of the data reserved solely for validation purposes, the data is segmented into k chunks. Holdout is performed on each chunk iteratively and the mean squared error is averaged over each fold [13]. With k-fold cross validation, each piece of training data will be trained on k-1 times and validated with k times. The primary reason for using k-fold cross validation is to limit any selective bias that may occur when separating the training data from validation data. We used a five-fold model because it balances out computational time with the least bias from the training data. Finally, the results of the five fold cross validation are graphed out. The trained model displayed an accuracy of 80% over all iterations conducted in 20 epochs for predicting temperature. During the five fold cross validation phase, the model achieved an R^2 score of 0.20. The R^2 score was calculated by dividing the residual sum of squares by the total sum of squares and subtracting the resulting value from 1. As seen by the graph, the predicted function should be as close to the equation f(x)=x as possible; this shows that every predicted consumption value is as close as possible to the actual consumption value.
Results
The temperature model correctly identifies trends throughout Ethiopia where poverty is high. As a whole, the model matches the actual consumption data in spatial poverty mapping: the northern regions have higher poverty rates than southern regions with the exceptions of outliers.
The temperature model can be validated by established indicators of poverty such as NDVI [20] and population data. We ran two additional models using these variables to compare to the accuracy of the temperature model. Normalized difference vegetation index (NDVI), is calculated by measuring the difference between near-infrared light and red light. The data values have a range of -1 to 1. NDVI was used because it can serve as an indicator of land health, soil fertility, and rainfall. Due to this, it proves to be an indicator of poverty most similar to temperature data because both variables consider agriculture as a primary source of sustenance of families.
NDVI data was collected from the Google Earth Engine software in the form of a TIFF file. The data was imposed onto individual download locations and matched with consumption data in a similar process as detailed above. NDVI ran through the complete pipeline and achieved an accuracy of 71.07% for the temperature prediction task with an R^2 score of 0.04 for predicting consumption. Like NDVI, population data was also collected using the Google Earth Engine in the TIFF format. Training on population data takes a different approach to predicting poverty. Instead of looking for the impacts of climate change, it's an indicator of urbanization and migration. After running through 20 epochs, the model received an accuracy of 70.05% for the temperature prediction task with an R^2 score of 0.05 for predicting consumption. The results of both of these models demonstrates the validity of temperature data and its expertise in predicting poverty.
Conclusion
While NDVI and population data offer important insights into the performance of alternative models, average temperature still reigns in terms of model performance and its global links to poverty. NDVI has real world ties to crop output and climate change, but it may lead to incorrect model assumptions with a vastly different geographic setting. Despite being located in a desert, with little to no vegetation, many North-African and developed Middle Eastern countries have a poverty rate at or lower than 30%. The visible geographic differences are too literal for accurately predicting poverty across a variety of environments. With population, another issue may arise. Populations for individual regions are primarily calculated through state-run surveys that happen every decade or so. In the off-years when surveys are not being conducted, large migratory patterns could arise and disappear. Another problem is that timely and accurate population data from any given year cannot be fed into the model. This nullifies the purpose of switching to a remote sensing based model where images are available readily and through a variety of data sources.
In comparison to Yeh et al, our model solely focuses on the transfer learning method of poverty prediction. The transfer learning approach was intuitively thought to bolster the inherent benefits of using satellite imagery over a direct linear regression prediction. In Yeh et al, transfer learning was found to perform worse compared to a complete end-to-end model based on nightlights. The increased performance of an end-to-end model in the study points to the transfer learning discarding important spatial features critical to predicting poverty. In a future study, we wish to implement this approach to analyze the benefits of directly measuring poverty without a transfer step.
The results from the temperature model therefore represent the best version of poverty tracking conducted within this study and on track to achieving the results of nighttime imagery models. The model was applied to predict Ethiopia's poverty, but the model has the ability to be used in any geographic location due to the ubiquitous access of temperature data. Temperature data does have its own caveats: notably, climatic anomalies can impact short term poverty tracking. Additionally, surveys excel in raw performance compared to our temperature model because it collects absolute poverty statistics directly from households, without the added noise created by machine learning algorithms. However, the demonstrated use of tracking regional poverty trends proves that the temperature model approaches survey data's poverty tracking performance Furthermore, the model is reproducible because the only data needed is temperature data and satellite imagery, widely available through organizations such as NOAA or Google. The model tested in this study is a simpler and accurate alternative to the expensive surveys of today.
Given the shortcomings of a temperature model, we believe that the model performance may be increased through data collection improvements. While spatial average was conducted via a clustering system, temporal averaging can also be conducted by utilizing more data. WorldClim's averaged monthly datasets can be used to limit the effect of climatic anomalies on the model. Thus, the CNN model would train on an intra-annual subset of data. Additionally, the model's three data sources -satellite data, temperature data, and consumption data -have gaps in their collection time periods. Satellite data is the most recent, taken within 1 year, while temperature data and consumption data are from the same time periods. Shifting to the use of Google Earth Engine would allow us to control the time parameter of image queries to better align with the temperature and consumption data. These changes would increase the performance of our model when regressing.
In addition to altering the data collection methods, expanding the study to additional countries would allow us to test the temperature model's generalizability. In this study we prefer generalizing, both in CNN training and ridge training, as a way to reduce overfitting in Ethiopia's own distinct climate and procuring unbiased model results. When including other countries in a future study, an additional step would need to be taken to ensure that a variety of economic regions and climates are being counted to avoid a strict adherence to the high-temperature high-poverty scenario. There may be countries at risk from climate change but with resources available to actively fight against it or countries not affected by climate change but instead other poverty determinants such as access to education, healthcare, and a robust political system. Categorizing these scenarios and representing them through inclusive datasets is critical to extrapolating the predictions of the temperature model.
The ubiquitous nature of data collected actively and passively has the potential to build a greater understanding of demographics in countries where wealth and consumption data is lacking. However, the same data sources may fuel a struggle for data sovereignty and ethical implications. This warrants a minor discussion of the implications of global, instantaneous, data-driven poverty predictions. In this study, poverty is viewed through the lens of annual consumption which is a predominantly capital-driven view of community status. In certain communities, a welfare ranking may function as a more inclusive framework for analyzing poverty. Welfare-based studies also take into consideration agricultural communities that practice subsistence farming, growing only as much food needed to support their household. To properly acknowledge the various types of global lifestyles, it is important to present poverty and consumption predictions within the historical context of a community.
Using a transfer learning model utilizing high resolution remote sensing data and global average temperature data, we accurately predict poverty in Ethiopia. A convolutional neural network based on the advanced VGG-11 standard is trained on temperature data to intrinsically detect features in satellite images that could be useful for predicting poverty. These features are aggregated to produce fully-fledged poverty estimates comparable -and in some cases even exceeding -in accuracy to other established poverty tracking methods. This novel method cuts down on crucial time needed to collect survey data and enables a more efficient process for maintaining poverty standards in developing nations. This technology has the full potential to revolutionize how countries and organizations work across the globe to address poverty.
Figure 1 .
1The results of the cross validation model are shown with the actual consumption per values plotted on the x-axis and the predicted consumption per capita values plotted on the y-axis. The R^2 value represents the amount of variance of the dependent variable that can be explained by the independent variable.
Figure 2. The scale indicates normalized total consumption per capita for each administrative zone in Ethiopia for actual versus predicted consumption (left and right respectively) at LSMS survey locations. Model performance in administrative zones is important for organizations and committees to pinpoint specific regions where poverty needs to be addressed.
Competing InterestsWe declare no competing interests.Appendix: Code AvailabilityCode for this research was adapted from the pythonification work of Jean et al. by Jatin Mathur to examine the temperature-consumption relationship. All work is available at: https://github.com/omshah2006/Predicting-Poverty-Ethiopia
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| sample_37 | 0.5304 | arxiv | |
Effect of Rain Scavenging on Altitudinal Distribution of Soluble Gaseous Pollutants in the Atmosphere
Tov Elperin
Department of Mechanical Engineering
The Pearlstone Center for Aeronautical Engineering Studies
Ben-Gurion University of the Negev
P. O. B. 65384105Israel
Andrew Fominykh
Department of Mechanical Engineering
The Pearlstone Center for Aeronautical Engineering Studies
Ben-Gurion University of the Negev
P. O. B. 65384105Israel
Boris Krasovitov
Department of Mechanical Engineering
The Pearlstone Center for Aeronautical Engineering Studies
Ben-Gurion University of the Negev
P. O. B. 65384105Israel
Alexander Vikhansky
School of Engineering and Material Science
University of London
Mile End RoadE1 4NSLondonQueen MaryUK
Effect of Rain Scavenging on Altitudinal Distribution of Soluble Gaseous Pollutants in the Atmosphere
1
We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. It is shown that below-cloud gas scavenging is determined by non-stationary convective diffusion equation with the effective Peclet number. The obtained equation was analyzed numerically in the case of log-normal droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are performed for wet removal of ammonia (NH 3 ) and sulfur dioxide (SO 2 ) from the atmosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atmosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere.
Introduction
Predicting chemical composition of the atmosphere and elucidating processes which affect atmospheric chemistry is important for addressing problems related to air quality, climate and ecosystem health.
Wet deposition is very important in the removal of gaseous pollutants from the atmosphere, and thus strongly affects global concentration of gaseous pollutants in the atmosphere of Earth. Atmospheric composition is controlled by natural and anthropogenic emissions of gases, their subsequent transport and removal processes. Wet deposition, including below-cloud scavenging by rains, is one of the most important removal mechanisms that control the distribution, concentration and life-time of many gaseous species in the atmosphere. Rains, through the below-cloud scavenging and aqueous-phase processes, alter the chemical composition of the atmosphere on a global scale (see, e.g. Zhang et al. 2006). Inorganic nitrogen in wet deposition is a significant source of nutrients for phytoplankton and has a direct impact on the health of estuaries and coastal water bodies (see, e.g. Mizak et al. 2005).
Negative impact of 2 SO on visibility was indicated, e.g. by Watson (2002), Green et al. (2005) and by Tsai et al. (2007). NH in a sea water whereby the ocean acts as a sink of soluble gases (see Georgii and Müller 1974;Georgii 1978). Information scavenging of these gases by rains. Hales (1972Hales ( , 2002, Hales et al. (1973) and Slinn (1974) considered removal of soluble pollutant gases from gas plumes. Hales (1972Hales ( , 2002 and Hales et al. (1973) assumed that concentration of the dissolved gas in a droplet is equal to concentration of saturation in liquid, corresponding to concentration of a trace soluble gas in the atmosphere at a certain height. Hales (1972) showed that if a drop falls through a plume and emerges into a clean air before reaching the ground, it may release most of the soluble gaseous pollutants that has been removed from more polluted regions. The significance of this effect is lowering the altitude of the regions with increased concentration of soluble gaseous pollutants under the influence of rain.
Hales (2002) Stefan and Mircea (2003), Slinn (1977), Calderon et al. (2008), Asman (1995), Mircea et al. (2000Mircea et al. ( , 2004, Kumar (1985), Levine and Schwartz (1982), Dana et al. (1975), Elperin and Fominykh (2005). Asman (1995) investigated absorption of highly soluble gases by rain using the approximation of infinite solubility of absorbate in the absorbent and assuming that distribution of soluble gas in the atmosphere during the rain is time-dependent and uniform. The latter assumption allowed calculating numerically the dependence of the scavenging coefficient on the rainfall rate in the atmosphere.
Power law dependence of the scavenging coefficient on the rainfall rate for ammonia absorption by rain, which was predicted by Asman (1995) theoretically, was confirmed experimentally by Mizak et al. (2005).
All the above studies did not account for the dependence of scavenging coefficient on height, time and initial profile of soluble gas in the atmosphere. In this study we investigate the influence of the altitude absorbate inhomogenity in a gaseous phase on the rate of soluble gas scavenging by falling rain droplets.
The problem is reduced to the equation of nonstationary convective diffusion with the effective Peclet number that depends on droplets size distribution (DSD). The obtained equation was solved numerically for log-normal DSD with Feingold-Levin parameterization (Feingold and Levin, 1986), and time and altitude dependence of the scavenging coefficient was analyzed.
Description of the model
In this study we consider absorption of a moderately soluble gas from a mixture containing inert gas by falling rain droplets. At time t = 0 rain droplets begin to fall and absorb gaseous pollutants (trace gases) from the atmosphere. It is assumed that the initial concentration of the dissolved trace gas in rain droplets is equal to the concentration of saturation in liquid corresponding to concentration of a trace soluble gas in a cloud and that the initial distribution (at time t = 0) of soluble trace gas in the atmosphere is known.
It must be noted that for moderately soluble gases, only a small fraction of the gas dissolves in the cloud water. Therefore the concentration of the moderately soluble gas in the interstitial air in a cloud is close to the concentration of the soluble gas in the below-cloud atmosphere immediately adjacent to the cloud. Since the residence time of droplets in the cloud is large, the equilibrium is established between the concentration of a moderately soluble gas in the interstitial air and concentration of the dissolved gas in the cloud droplets (see Asman 1995).
The goal of this study is to determine an evolution of concentration distribution of soluble trace gases in the atmosphere below the cloud under the influence of gas scavenging by falling rain droplets. Our analysis is not restricted to gases with low solubility and is valid for all gases which obey
Henri's law. The suggested model is not constrained by a magnitude of a gradient of the soluble trace gas concentration in a gaseous phase. Following the approach suggested by Hales (1972Hales ( , 2002 and Hales et al. (1973), time derivative of the mixed-average concentration of the dissolved gas in a falling droplet can be written as follows:
( ) ( ) ( ) ( ) L G D L c mc dt dc − = τ 1 ,(2)⋅ ⋅ + = ,(3)where G d u ν / Re ⋅ = , G G D / Sc ν = . For small D τ Eq.
(2) yields:
( ) ( ) ( ) − = t d c d c m c G D G L τ .(4)
Total concentration of soluble gaseous pollutant in gaseous and liquid phases reads:
( ) ( ) ( ) L G c c c φ φ + − = 1(5)
As can be seen from the Eq. (4) in the case when
( ) ( ) 1 << t d c d c G G D τ
Eqs (4)-(5) yield:
( ) [ ] φ φ m c c G + − = ) 1 ( ,(6)
where φ -volume fraction of droplets in the air. The total flux of the dissolved gas transferred by rain droplets is determined by the following expression:
( ) L c u q c ⋅ ⋅ = φ ,(7)
where u -velocity of a droplet, ( ) L c -concentration of dissolved gas in a droplet. Using Eqs. (4) and (7) we obtain:
( ) ( ) − = t d c d c u m q G G D c τ φ .(8)
Equation of mass balance for soluble trace gas in the gaseous and liquid phases is as follows:
z q t c c ∂ ∂ − = ∂ ∂ .(9)
Combining Eqs. (4) -(9) we obtain the following convective diffusion equation:
( ) ( ) ( ) 2 2 z c D z c U t c G G G ∂ ∂ = ∂ ∂ + ∂ ∂ ,(10)0 = t , ( ) ) (z f c G = (11) 0 = z , ( ) ( ) G G c c c 0 , = ,(12)L z = , ( ) 0 = ∂ ∂ z c G ,(13)
where L -distance between the ground and the lower and U is the "wash-down" front velocity.
Equation (10) implies that trace gas in the atmosphere is scavenged with a "wash-down" velocity U and is smeared by diffusion. Equations (10) -(13) can be rewritten in the following form:
( ) ( ) ( ) 2 2 Pe 1 η η ∂ ∂ ⋅ = ∂ ∂ + ∂ ∂ G G G C C T C (14) 0 = T , ( ) ) (η f C G = ,(15)0 = η , ( ) 1 = G C ,(16)1 = η , ( ) 0 = ∂ ∂ η G C ,(17)
Where
D UL / Pe = , L tU T / = , ( ) ( ) ( ) G G G c c c C 0 , = .
Assuming that the dependence of the terminal fall velocity of a liquid droplet depends on its diameter is as follows (see Kessler, 1969):
2 1 1 d c u ⋅ = ,(18)0 = T , ( ) ( ) ( ) ( ) η ⋅ − + = 1 1 0 , 0 , G G G c gr c c C .(20)
Results and discussions
The cloud. Note that for gaseous pollutants their concentration at the ground is always larger than the concentration in a cloud (see e.g., Georgii and Müller, 1974;Georgii, 1978;Gravenhorst et al., 1978). Figs. 1-2 shows that the thickness of the layer "washed down" by precipitation strongly depends on the rainfall amount and also depends on the gas solubility.
Inspection of
Using the obtained numerical solution of the equation (14) with the boundary conditions (15)- (17) we also calculated the scavenging coefficient for soluble trace gas absorption from the atmosphere:
8 ( ) ( ) t c c G G ∂ ∂ − = 1 Λ .(22)
The dependence of the scavenging coefficient vs.
altitude in the case of ammonia wash out is shown in intensity are plotted for the early stage of rain (Fig. 5) as well as for the advanced stage of rain (Fig. 6).
Figs. 3 -4.
As can be seen from these plots the scavenging coefficient increases with rain intensity increase. In spite of the numerous theoretical calculations and measurements of scavenging coefficient available in the literature (see e.g., Beilke, 1970;Sperber and Hameed, 1986;Shimshock and De Pena, 1989;Renard et al., 2004;Mizak et al., 2005) the In particular, for wet deposition of ammonia very different values of scavenging coefficient are reported in the literature, in the range from less that 10 -5 (s -1 ) (Sperber and Hameed, 1986) to larger than 10 -3 (s -1 ) (in Mizak et al., 2005) are reported. This large scatter of data is mentioned in several studies and reviews (see e.g., Renard et al., 2004).
Conclusions
In this study we developed a model for scavenging of soluble trace gases in the atmosphere by rain. It is shown that gas scavenging is determined by non-
about the evolution of the vertical profile of soluble gases with time allows calculating fluxes of these gases in an the ABL. Vertical transport of soluble gases in the ABL is an integral part of the atmospheric transport of gases and is important for understanding the global distribution pattern of soluble trace gases. An improved understanding of the cycle of soluble gases is also essential for the analysis of global climate change. Clouds and rains play essential role in vertical redistribution these gases. At the same time the existence of vertical gradients of the soluble gases in the atmosphere affects the rate of gas absorption by rain droplets (see Elperin et al. 2009). Note that the existing models of global transport in the atmosphere do not take into account the influence of rains on biogeochemical cycles of different gases. In spite of a large number of publications devoted to soluble gases scavenging by clouds (see, e.g., Elperin et al. 2007 and Elperin et al. 2008 and references therein) there are only a few studies on
U u >> . The term in the right-hand side of Eq. (10) arises because we do not make a simplifying assumption about equality between the instantaneous concentration of the dissolved gas in a droplet and concentration of saturation in liquid corresponding to the concentration of a trace soluble gas in an atmosphere at a given height. In other words, Eq. (10) is valid when a characteristic diffusion time and a characteristic time of concentration change in a gaseous are of the same order of magnitude. For examplethe soluble gaseous species are molecularly dissolved in water droplets, and the molecules of these species do not dissociates into ions in the liquid phase (see Seinfeld and Pandis 2006, Chapter 7). The initial and boundary conditions for Eq. (10) are as follows:
boundary of a cloud. Equation of non-stationary convective diffusion (10) with initial and boundary conditions (11) -(13) (see, e.g. Leij and Toride 1998) describes evolution of solvable trace gas distribution in the atmosphere under the influence of rain. Equation (13) is a condition of ground impermeability for soluble gases. The volume fraction of a liquid phase φ in Eq. (10) determines the intensity of rain, φ u R =
Pe . If the initial distribution of a trace gas in the atmosphere is linear, the boundary condition given by Eq. (15) becomes
Fig. 1 .
1above model of atmospheric trace gases scavenging by liquid precipitation was applied to study the evolution of trace soluble gas concentration in the atmosphere caused by rain. Results of numerical solution of Eqs. (14) -(17) with linear initial distribution of soluble trace gas in Evolution rain. Wet removal of soluble gases from the atmosphere strongly depends on the raindrops diameter that is determined by droplet size distribution (DSD). In our calculations we assumed the log-normal size distribution of raindrops with Feingold and Levin parameterization (Feingold and Levin, 1986) based on the long-time measurements of rain drops size spectra in Israel: Figs. 1 and 2 shows that the larger is the solubility of the trace gas in water, the smaller it is the quantity of precipitation required to washout it. For instance, inspection of Fig. 1 reveals that approximately 600 mm of precipitation can wash out 1 km of atmosphere from the ammonia gas. At the same time for wet removal of sulfur dioxide from the atmosphere of the same altitude the considerably higher amount of precipitation is required.
Fig. 2 .
2Evolution of sulfur dioxide distribution in the atmosphere caused by rain scavenging In the calculations the initial concentration of dissolved trace gas in rain drops is assumed equal to the concentration of saturation in a liquid corresponding to the concentration of a trace soluble gas in a cloud. Therefore the soluble gas in the belowcloud atmosphere can be washed down only up to the concentration of soluble gas in the interstitial air in a
Fig. 3 .
3Dependence of scavenging coefficient vs. altitude for ammonia wash out (linear initial distribution of ammonia in the atmosphere studies have showed that the scavenging coefficient which is measured or calculated under the assumption of the uniform soluble trace gas distribution may not accurately predict wet deposition of soluble trace gases in the presence of a gradient of concentration of trace gases in the atmosphere (see e.g. Assman, 1995; Mizak et al., 2005; Calderon et al., 2008). The suggested model takes into account the initial concentration gradient of soluble species in trace gas concentration in the atmosphere.
Fig. 4 .
4Dependence of scavenging coefficient vs. altitude for ammonia wash out (linear initial distribution of ammonia in the atmosphere be seen from these plots the scavenging coefficient increases with the increase of the soluble species concentration gradient. The analysis of the plots on Figs. 3 -4 shows that the high values of the scavenging coefficient Λ in the below-cloud atmosphere immediately adjacent to the cloud at the early stage of a rain is explained by high rates of gas absorption by falling rain droplets. High rates of mass transfer between the rain droplets and soluble gas are caused by thin concentration boundary layers in droplets and in a gaseous phase at the initial stage of gas-liquid contact. For linear profile of soluble gas in the atmosphere, at the early stage of a rain, the scavenging coefficient increases with height. in an atmosphere with a non-uniform initial concentration profile of soluble gas is constant. Therefore the rate of change of concentration in a gaseous phase ( ) t c G ∂ ∂ / is constant. At the same height at the early stage of rain whereby the initial concentration profile of the soluble gas in the atmosphere is not disturbed significantly. Scavenging of soluble gas begins in the upper atmosphere and the front of scavenging propagates downwards with the "wash down" velocity that is proportional to Henry's constant and rain intensity (see Eq. 10). Concentration of a soluble gas in the below-cloud layer decreases to the concentration of a soluble gas in the interstitial air in a cloud. The subsequent rain droplets fall in the below-cloud atmosphere without absorbing soluble gas. This explains the decrease of the scavenging coefficient in the upper below-cloud layers of the atmosphere at the later stages of rain whereby the initial concentration profile of the soluble gas in the atmosphere changes significantly. Note that the soluble gas in the below-cloud layer is washed out only to the concentration of the soluble gas in the interstitial air in a cloud. At the ground the value of the scavenging coefficient increases with time because the concentration at the ground decreases faster than the rate of concentration change. Dependences of scavenging coefficient on the rate of precipitation are shown in Figs. 5 and 6. The dependences of the scavenging coefficient on rain
Fig. 5 .
5Dependence of scavenging coefficient vs. rain intensity for ammonia wash out at the early stage of rain the predicted values of scavenging coefficient with those calculated from the measured concentrations of ammonia in rainwater reveals large discrepancies.
Fig. 6 .
6Dependence of scavenging coefficient vs. rain intensity for ammonia wash out at the later stage
The wide range of variation of the magnitude of scavenging coefficient is caused by dependence of scavenging coefficient on the altitude, time, initial gradient of the soluble gas concentration in the below-cloud atmosphere, droplet size distribution as well as on meteorological conditions (wind, temperature etc.) and difficulties associated with evaluating scavenging coefficient from the experiments.
stationary convective diffusion equation with the effective Peclet number that depends on droplet size distribution (DSD). The obtained equation was analyzed numerically in the case of log-normal DSD with Feingold-Levin parameterization (Feingold and Levin, 1986). The simple form of the obtained equation allows analyzing the dependence of the rate of soluble gas scavenging on different parameters, e.g. rain intensity, gas solubility, gradient of absorbate concentration in a gaseous phase etc. Using the developed model we calculated scavenging coefficient and the rates of scavenging of different trace gases (SO 2 and NH 3 ). The obtained results can be summarized as follows: 1. It is demonstrated that scavenging coefficient for the wash out of soluble atmospheric gases by rain is time-dependent. It is shown that value of scavenging coefficient at the ground increases with time whereas the value of scavenging coefficient in the below-cloud atmosphere immediately adjacent to the cloud decreases with the amount of precipitation. 2. It is shown that scavenging coefficient in the atmosphere is height-dependent. Scavenging of soluble gas begins in the upper atmosphere and scavenging front propagates downwards with "wash down" velocity and is smeared by diffusion. We have found that in the case of linear initial distribution of concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient c Λ increases with height at an early stage of rain. At the advanced stage of rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere. 3. It is found that scavenging coefficient strongly depends on the initial distribution of soluble trace gas concentration in the atmosphere. Calculations performed for linear distribution of the soluble gaseous species in the atmosphere show that the scavenging coefficient increases with the increase of soluble species gradient. The developed model can be used for the analysis of precipitation scavenging of hazardous gases in the atmosphere by rain and for validating advanced models for predicting scavenging of soluble gases by rain.
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| sample_41 | 0.5301 | arxiv | |
Effective radiative forcing in the aerosol-climate model CAM5.3- MARC-ARG
Benjamin S Grandey
Center for Environmental Sensing and Modeling
Singapore-MIT Alliance for Research and Technology
Singapore
Daniel Rothenberg
Center for Global Change Science
Massachusetts Institute of Technology
CambridgeMassachusettsUSA
Alexander Avramov
Center for Global Change Science
Massachusetts Institute of Technology
CambridgeMassachusettsUSA
Department of Environmental Sciences
Emory University
AtlantaGeorgiaUSA
Qinjian Jin
Center for Global Change Science
Massachusetts Institute of Technology
CambridgeMassachusettsUSA
Hsiang-He Lee
Center for Environmental Sensing and Modeling
Singapore-MIT Alliance for Research and Technology
Singapore
Xiaohong Liu
Department of Atmospheric Science
University of Wyoming
LaramieWyomingUSA
Zheng Lu
Department of Atmospheric Science
University of Wyoming
LaramieWyomingUSA
Samuel Albani
Department of Earth and Atmospheric Sciences
Cornell University
IthacaNew YorkUSA
LSCE/IPSL
Laboratoire des Sciences du Climat et de l'Environnement
CEA-CNRS-UVSQ
Gif-sur-YvetteFrance
Chien Wang
Center for Environmental Sensing and Modeling
Singapore-MIT Alliance for Research and Technology
Singapore
Center for Global Change Science
Massachusetts Institute of Technology
CambridgeMassachusettsUSA
Effective radiative forcing in the aerosol-climate model CAM5.3- MARC-ARG
Correspondence to: Benjamin S. Grandey (benjamin@smart.mit.edu)
We quantify the effective radiative forcing (ERF) of anthropogenic aerosols modelled by the aerosol-climate model CAM5.3-MARC-ARG. CAM5.3-MARC-ARG is a new configuration of the Community Atmosphere Model version 5.3 (CAM5.3) in which the default aerosol module has been replaced by the two-Moment, Multi-Modal, Mixing-stateresolving Aerosol model for Research of Climate (MARC). CAM5.3-MARC-ARG uses the default ARG aerosol activation scheme, consistent with the default configuration of CAM5.3. We compute differences between simulations using year-1850aerosol emissions and simulations using year-2000 aerosol emissions in order to assess the radiative effects of anthropogenic aerosols. We compare the aerosol column burdens, cloud properties, and radiative effects produced by CAM5.3-MARC-ARG with those produced by the default configuration of CAM5.3, which uses the modal aerosol module with three lognormal modes (MAM3). Compared with MAM3, we find that MARC produces stronger cooling via the direct radiative effect, stronger cooling via the surface albedo radiative effect, and stronger warming via the cloud longwave radiative effect.The global mean cloud shortwave radiative effect is similar between MARC and MAM3, although the regional distributions differ. Overall, MARC produces a global mean net ERF of W m -2 , which is stronger than the global mean net ERF of W m -2 produced by MAM3. The regional distribution of ERF also differs between MARC and MAM3, largely due to differences in the regional distribution of the cloud shortwave radiative effect. We conclude that the specific representation of aerosols in global climate models, including aerosol mixing state, has important implications for climate modelling.IntroductionAerosol particles influence the earth's climate system by perturbing its radiation budget. There are three primary mechanisms by which aerosols interact with radiation. First, aerosols interact directly with radiation by scattering and absorbing solar and thermal infrared radiation(Haywood and Boucher, 2000). Second, aerosols interact indirectly with radiation by perturbing clouds, by acting as the cloud condensation nuclei on which cloud droplets form and the ice nuclei that facilitate freezing of cloud droplets (Fan et al., 2016; Rosenfeld et al., 2014): for example, an aerosol-induced increase in cloud cover would lead to increased scattering of "shortwave" solar radiation and increased absorption of "longwave" thermal infrared radiation. Third, aerosols can influence the albedo of the earth's surface (Ghan, 2013): for example, deposition of absorbing aerosol on snow reduces the albedo of the snow, causing more solar radiation to be absorbed at the earth's surface. The "effective radiative forcing" (ERF) of anthropogenic aerosols, defined as the top-of-atmosphere radiative effect caused by anthropogenic emissions of aerosols and aerosol precursors, is often used to quantify the radiative effects of aerosols (Boucher et al., 2013). The anthropogenic aerosol ERF is approximately equivalent to "the radiative flux perturbation associated with a change from preindustrial to present-day [aerosol emissions], calculated in a global climate −1.75 ± 0.04 −1.57 ± 0.04 ! 1 model using fixed sea surface temperature" (Haywood and Boucher, 2000). This approach "allows clouds to respond to the aerosol while [sea] surface temperature is prescribed" (Ghan, 2013). The primary tools available for investigating the anthropogenic aerosol ERF are state-of-the-art global climate models. However, there is widespread disagreement among these models, especially regarding the magnitude of anthropogenic aerosol ERF (Quaas et al., 2009; Shindell et al., 2013). Of particular importance are model parameterizations related to aerosol-cloud interactions, such as the aerosol activation scheme (Rothenberg et al., 2017), the choice of autoconversion threshold radius (Golaz et al., 2011), and constraints on the minimum cloud droplet number concentration (Hoose et al., 2009). The detailed representation of aerosols also likely plays an important role, because the aerosol particle size and chemical composition determine hygroscopicity and hence influence aerosol activation (Petters and Kreidenweis, 2007).The magnitude of the ERF of anthropogenic aerosols is highly uncertain: estimates of the global mean anthropogenic aerosol ERF range from to W m -2(Boucher et al., 2013). Since the present-day anthropogenic aerosol ERF partially masks the warming effects of anthropogenic greenhouse gases, the large uncertainty in the anthropogenic aerosol ERF is a major source of uncertainty in estimates of equilibrium climate sensitivity and projections of future climate(Andreae et al., 2005). Furthermore, the anthropogenic aerosol ERF is regionally inhomogeneous, adding another source of uncertainty in climate projections (Shindell, 2014). The regional inhomogeneity of the anthropogenic aerosol ERF has likely also influenced rainfall patterns during the 20 th century (Wang, 2015). In order to improve understanding of current and future climate, including rainfall patterns, it is necessary to improve understanding of the magnitude and regional distribution of the anthropogenic aerosol ERF.In this manuscript, we investigate the uncertainty in anthropogenic aerosol ERF associated with the representation of aerosols in global climate models. In particular, we assess the aerosol radiative effects produced by a new configuration of the Community Atmosphere Model version 5.3 (CAM5.3). In this new configuration -CAM5.3-MARC-ARG -the default modal aerosol module has been replaced with the two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC). We compare the aerosol radiative effects produced by CAM5.3-MARC-ARG with those produced by the default modal aerosol module in CAM5.3. 2 Methodology 2.1 Modal aerosol modules (MAM3 and MAM7) The Community Earth System Model version 1.2.2 (CESM 1.2.2) contains the Community Atmosphere Model version 5.3 (CAM5.3). Within CAM5.3, the default aerosol module is a modal aerosol module which parameterizes the aerosol size distribution with three log-normal modes (MAM3), each assuming a total internal mixture of a set of fixed chemical species (Liu et al., 2012). Optionally, a more detailed modal aerosol module with seven log-normal modes (MAM7) (Liu et al., 2012) can be used instead of MAM3. More recently, a version containing four modes (MAM4) (Liu et al., 2016) has also been coupled to CAM5.3, but we do not consider MAM4 in this study.The seven modes included in MAM7 are Aitken, accumulation, primary carbon, fine soil dust, fine sea salt, coarse soil dust, and coarse sea salt. Within each of these modes, MAM7 simulates the mass mixing ratios of internally-mixed sulfate, ammonium, primary organic carbon, secondary organic carbon, black carbon, soil dust, and sea salt .In MAM3, four simplifications are made: first, the primary carbon mode is merged into the accumulation mode;second, the fine soil dust and fine sea salt modes are also merged into the accumulation mode; third, the coarse soil dust and coarse sea salt modes are merged to form a single coarse mode; and fourth, ammonium is implicitly included via sulfate and is no longer explicitly simulated. As a result, MAM3 simulates just three modes: Aitken, accumulation, and coarse. This reduces the computational expense of the model.
The two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC)
The two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC), which is based on the aerosol microphysical scheme developed by Ekman et al. (2004Ekman et al. ( , 2006 and Kim et al. (2008), simulates the evolution of mixtures of aerosol species. Previous versions of MARC have been used both in cloud-resolving model simulations (Ekman et al., 2004(Ekman et al., , 2006(Ekman et al., , 2007Engström et al., 2008;Wang, 2005aWang, , 2005b and in global climate model simulations (Ekman et al., 2012;Kim et al., 2008Kim et al., , 2014. Recently, an updated version of MARC has been coupled to CAM5.3 within CESM1.2.2 .
In contrast to MAM, MARC tracks the number concentrations and mass concentrations of both externally-mixed and internally-mixed aerosol modes with assumed lognormal size distributions. The externally-mixed modes include three pure sulfate modes (nucleation, Aitken, and accumulation), pure organic carbon, and pure black carbon. The internallymixed modes include mixed organic carbon plus sulfate and mixed black carbon plus sulfate. In the mixed organic carbon plus sulfate mode, it is assumed that the organic carbon and sulfate are mixed homogeneously within each particle; in the mixed black carbon plus sulfate mode, it is assumed that each particle contains a black carbon core surrounded by a sulfate shell. Sea salt and mineral dust are represented using sectional single-moment schemes, each with four size bins (Albani et al., 2014;Mahowald et al., 2006;Scanza et al., 2015).
Sea salt emissions follow the default scheme used by MAM , based on simulated wind speed and sea surface temperature. Dust emissions follow the tuning of Albani et al. (Albani et al., 2014), based on simulated wind speed and soil properties, including soil moisture and vegetation cover. Emissions of sulfur dioxide, dimethyl sulfide, primary sulfate aerosol, organic carbon aerosol, black carbon aerosol, and volatile organic compounds (such as isoprene and monoterpene) are prescribed.
The aerosol removal processes represented by MARC -including nucleation scavenging by both stratiform and
Simulations
In order to compare results from MAM3, MAM7, and MARC, five CAM5.3 simulations are performed:
1. "MAM3_2000", which uses MAM3 with year-2000 aerosol (including aerosol precursor) emissions; 2. "MAM7_2000", which uses MAM7 with year-2000 aerosol emissions;
3. "MARC_2000", which uses MARC with year-2000 aerosol emissions;
4. "MAM3_1850", which uses MAM3 with year-1850 aerosol emissions; and 5. "MARC_1850", which uses MARC with year-1850 aerosol emissions.
The three simulations using year-2000 emissions, referred to as the "year-2000 simulations", facilitate comparison of aerosol fields and cloud fields; the two simulations using year-1850 emissions, referred to as the "year-1850 simulations", further facilitate analysis of the aerosol radiative effects produced by MAM3 and MARC. There is no MAM7 simulation using year-1850 aerosol emissions, due to a lack of year-1850 emissions files for MAM7. The only difference between the year-2000 simulations and the year-1850 simulations is the aerosol (including aerosol precursor) emissions. In the figures and discussion of results, "2000-1850" and "! " both refer to differences between the year-2000 simulation and the year-1850 simulation for a given aerosol module (e.g. MARC_2000-MARC_1850).
The prescribed emissions for both MAM and MARC follow the default MAM emissions files, described in the Supplement of Liu et al. (2012), based on Lamarque et al. (2010). This differs from , who used different emissions of organic carbon aerosol, black carbon aerosol, and volatile organic compounds. In this study, we deliberately use identical emissions for MAM and MARC so that the influence of emissions inventories can be minimised when the results are compared.
For the MAM simulations, the aerosol emissions from some sources follow a vertical profile . For the MARC simulations, sulfur emissions follow the same vertical profile as for MAM; but all organic carbon, black carbon, and volatile organic compounds are emitted at the surface. 2.5% of the sulfur dioxide is emitted as primary sulfate. Mineral dust and sea salt emissions are not prescribed, being calculated "online". Each simulation is run for 32 years, and the first two years are excluded as spin-up. Hence, a period of 30 years is analysed.
Diagnosis of radiative effects
Pairs of prescribed-SST simulations, with differing aerosol emissions, facilitate diagnosis of anthropogenic aerosol ERF via the "radiative flux perturbation" approach (Haywood et al., 2009). When "clean-sky" radiation diagnostics are available, the ERF can be decomposed into contributions from different radiative effects (Ghan, 2013). (We use the term "radiative forcing" only when referring to ERF, defined as the radiative flux perturbation between a simulation using year-1850 emissions and a simulation using year-2000 emissions; we use the term "radiative effect" more generally.)
The shortwave effective radiative forcing (! ) can be decomposed as follows:
! (1)
where ! refers to the 2000-1850 difference, ! is the direct radiative effect, ! is the clean-sky shortwave cloud radiative effect, and ! is the 2000-1850 surface albedo radiative effect. These components are defined as follows:
! (2) ! (3) ∆ E R F SW E R F SW = ∆ DR E SW + ∆ C R E SW + ∆ SR E SW ∆ DR E SW C R E SW ∆ SR E SW E R F SW = ∆ F DR E SW = (F − F clean ) ! 4 ! (4) !(5)
where ! is the net shortwave flux at top-of-atmosphere (TOA), ! is the clean-sky net shortwave flux at TOA, and ! is the clean-sky clear-sky net shortwave flux at TOA. ("Clear-sky" refers to a hypothetical situation where clouds do not interact with radiation; "clean-sky" refers to a hypothetical situation where aerosols do not directly interact with radiation.)
The longwave effective radiative forcing (! ) is calculated as follows:
! (6)
where ! is the net longwave flux at TOA, ! is the clear-sky net longwave flux at TOA, and ! is the longwave cloud radiative effect. Eq. (6) assumes that aerosols and surface albedo changes do not influence the longwave flux at TOA, so that ! .
The net effective radiative forcing (! ) is simply the sum of ! and ! :
! .(7)
All the quantities mentioned in Eqs.
(1)-(7) are calculated at TOA.
We also consider absorption by aerosols in the atmosphere (! ), defined as follows:
! (8)
where ! is the net shortwave flux at the earth's surface, and ! is the clean-sky net shortwave flux at the earth's surface.
Results
We focus on model output fields relating to different components of the ERF, taking each component in turn: the direct radiative effect, the cloud radiative effect, and the surface albedo radiative effect. When discussing each of these components, we also discuss related model field; for example, in the section discussing the direct radiative effect we also consider other fields related to direct aerosol-radiation interactions. But first, to provide context for the discussion of the radiative effects, we examine the aerosol column burdens.
Aerosol column burdens
An aerosol column burden, also referred to as a loading, reveals the total mass of a given aerosol species in an atmospheric column. The advantage of column burdens is that they are relatively simple to understand, facilitating comparison between the different aerosol modules. However, when comparing the column burdens, it is important to remember that information about aerosol size distribution and aerosol mixing state is hidden. Information about the vertical distribution is also hidden, because the burdens are integrated throughout the atmospheric column. Oceania. For both MAM3 and MARC, global mean ! accounts for more than half of global mean year-2000 ! , indicating that anthropogenic sulfur emissions are responsible for more than half of the global burden of sulfate aerosol. unchanged so these species are unlikely to contribute to ! . S8e, f) likely also influence ! , because precipitation efficiently removes sea salt aerosol from the atmosphere.
Total sulfate aerosol burden
C R E SW = (F clean − F clean,clear ) ∆ SR E SW = ∆ F clean,clear F F clean F clean,clear E R F LW E R F LW = ∆ L ≈ ∆ ( L − L clear) = ∆ C R E LW L L clear C R E LW ∆ L clear ≈ 0 E R F SW+LW E R F SW E R F LW E R F SW+LW = ∆ (F + L) = E R F SW + E R F LW ≈ E R F SW + ∆ C R E LW A A A SW A A A SW = ( F − F clean) − (F surface − F surface clean ) F surface F surface clean B u r de n SO4
Total organic carbon aerosol burden
Total black carbon aerosol burden
However, it should be noted that the 2000-1850 differences in ! , surface wind speed, and precipitation rate are both relatively small and often statistically insignificant across most of the world. If an interactive dynamical ocean were to be used, allowing SSTs to respond to the anthropogenic aerosol ERF, it is likely that we would find much larger 2000-1850 differences in surface wind speed, precipitation rate, and ! . play a role. As we noted above when discussing the sea salt burden, if an interactive dynamical ocean were to be used, it is likely that we would find much larger 2000-1850 differences in surface wind speed, precipitation rate, and ! .
Total dust aerosol burden
Aerosol-radiation interactions and the direct radiative effect
Aerosol optical depth
Aerosols scatter and absorb shortwave radiation, leading to extinction of incoming solar radiation. Before considering the direct radiative effect, we first look at aerosol optical depth (! ), a measure of the total extinction due to aerosols in an atmospheric column. have also previously noted that the ! for MARC is generally lower than that retrieved from the MODerate Resolution Imaging Spectroradiometer (MODIS; Collection 5.1); but it should be noted that differences in spatial-temporal sampling (Schutgens et al., 2017(Schutgens et al., , 2016 have not been accounted for.
The differences between the aerosol burdens for MAM3 and MARC, discussed above, are insufficient to explain the differences in year-2000 ! . Hence it is likely that differences in the optical properties of the MARC aerosols and the MAM3 aerosols are responsible for the fact that MARC generally produces lower values of ! .
∆ B u r de n salt B u r de n salt B u r de n salt B u r de n salt B u r de n salt B u r de n dust B u r de n dust B u r de n dust B u r de n dust B u r de n dust ∆ B u r de n dust B u r de n dust B u r de n dust B u r de n dust B u r de n dust B u r de n dust AOD AOD AOD AOD AOD AOD AOD AOD ! 7
Positive 2000-1850 differences in ! , ! , and ! , discussed above, drive positive values of ! , the 2000-1850 difference in ! ( Fig. 6d-f). As was the case for year-2000 ! , ! produced by MARC is generally much lower than ! produced by MAM3.
Direct radiative effect
Figure 7a-c shows the direct radiative effect (! ) for the year-2000 simulations. ! reveals the influence of direct interactions between radiation and aerosols on the net shortwave flux at TOA (Eq. (3)). Aerosols that scatter shortwave radiation efficiently, such as sulfate, generally contribute to negative values of ! , indicating a cooling effect on the climate system; aerosols that absorb shortwave radiation, such as black carbon, generally contribute to positive values of ! , indicating a warming effect on the climate system. Other factors, such as the presence of clouds, the vertical distribution of aerosols relative to clouds, and the albedo of the earth's surface, also play a role in determining ! (Stier et al., 2007). Due to these factors -especially the differing impact of scattering and absorbing aerosols and
Absorption by aerosols in the atmosphere
Figure 8a-c shows the absorption of shortwave radiation by aerosols in the atmosphere (! ; Eq. (8)
∆ AOD AOD AOD ∆ AOD ∆ AOD DR E SW DR E SW DR E SW DR E SW DR E SW AOD DR E SW DR E SW AOD DR E SW DR E SW ∆ DR E SW DR E SW −0.02 ± 0.01 ∆ DR E SW ∆ DR E SW −0.18 ± 0.01 A A A SW A A A SW DR E SW A A A SW B u r de n dust A A A SW A A A SW B u r de n BC A A A SW B u r de n dust B u r de n BC A A A SW A A A SW ∆ A A A SW A A A SW ∆ B u r de n BC ∆ A A A SW A A A SW ∆ A A A SW A A A SW ∆ A A A SW ! 8
3.3 Aerosol-cloud interactions and the cloud radiative effects
Cloud condensation nuclei concentration
Many aerosol particles have the potential to become the cloud condensation nuclei (CCN) on which water vapour condenses to form cloud droplets. Figure 9a- When we look in more detail at the regional distribution of year-2000 ! for MAM3, and compare this to the column burden results, we notice that locations with high ! have either high ! or high ! . This suggests that, for MAM3, the organic carbon aerosol -internally-mixed with other species with high hygroscopicitycontributes to efficient CCN, consistent with two previous MAM3-based studies that found that organic carbon emissions from wildfires can exert a strong influence on clouds (Grandey et al., 2016a;Jiang et al., 2016).
In contrast, for MARC, the regional distribution of year-2000 ! closely resembles that of ! but does not resemble that of ! . This suggests that, for MARC, the organic carbon aerosol -much of which remains in a pure organic carbon aerosol mode with very low hygroscopicity -is not an efficient source of CCN.
If we look at the results for ! , the 2000-1850 difference in ! (Figs. 9d-f, S1d-f, and S2d-f), similar deductions about sulfate aerosol and organic carbon aerosol can be made as were made above. For MAM3, the regional distribution of ! reveals that changes in the availability of CCN are associated with both ! and ! . For MARC, the regional distribution of ! is associated with ! , but is not closely associated with ! . For both MAM and MARC, ! is generally positive, revealing increasing availability of CCN between year-1850 and year-2000. The absolute increase is smaller for MARC than for MAM.
It is important to note that these ! results are for a fixed supersaturation of 0.1%; but as pointed out by Rothenberg et al. "all aerosol [particles] are potentially CCN, given an updraft sufficient enough in strength to drive a highenough supersaturation such that they grow large enough to activate" . Furthermore, the number of CCN that are actually activated is influenced by competition for water vapour among various types of aerosol particles, which depends on the details of the aerosol population including size distribution and mixing state. When aerosol particles with a lower hygroscopicity rise alongside aerosol particles with a higher hygroscopicity in a rising air parcel, the latter would normally be activated first at a supersaturation that is much lower than the one required for the former to become activated; the consequent condensation of water vapour to support the diffusive growth of the newly formed cloud particles would effectively lower the saturation level of the air parcel and further reduce the chance for the lower hygroscopicity aerosol particles to be activated Wang, 2016, 2017). In other words, ! at a fixed supersaturation is not necessarily a good indicator of the number of CCN that are actually activated, because activation depends on specific environmental conditions and the details of the aerosol population present. In an aerosol model such as MAM3 that includes only internally-mixed modes, the hygroscopicity of a given mode is derived by volume weighting through all the included aerosol species and is therefore not very sensitive to changes in the chemical composition of the mode. In contrast, MARC explicitly handles mixing state and thus hygroscopicity of each individual type of aerosol.
Column-integrated cloud droplet number concentration
The availability of CCN influences cloud microphysics via the formation of cloud droplets. Figure 10a- : there appears to be no influence from organic carbon aerosol, consistent with the ! results discussed above; and the influence of sulfate aerosol appears weaker than for MAM. Interestingly, there is good agreement between MAM and MARC over the Southern Ocean: for both MAM and MARC, sea salt appears to have a substantial influence on year-2000 ! .
When we look at ! , the 2000-1850 difference in ! (Fig. 10d-f), we see that anthropogenic emissions generally drive increases in ! , as expected. The absolute increase is smaller for MARC than for MAM.
Grid-box cloud liquid and cloud ice water paths
In addition to influencing cloud microphysical properties (such as cloud droplet number concentration), the availability of CCN and ice nuclei influence cloud macrophysical properties (such as cloud water path). Figure 11a-c shows grid-box cloud liquid water path (! ) for the year-2000 simulations.
Year-2000 ! is highest in the tropics and midlatitudes. The regional distribution of year-2000 ! is similar to that of total cloud fractional coverage (Fig. S4a-c). increases in ! over Europe, East Asia, Southeast Asia, South Asia, parts of Africa, and northern South America -the regional distribution of ! is similar to the regional distributions of ! and ! . MARC produces large increase in ! over the same regions, and additionally over Australia and North America. Overall, ! is larger for MARC than for MAM3, especially over the Northern Hemisphere mid-latitudes. For MARC, in comparison with MAM3, the relatively strong ! response contrasts with the relatively weak ! response and ! response.
Globally, for both MAM3 and MARC, the ! response is relatively weak (Fig. 12d-f). However, relatively large values of ! , both positive and negative, are found regionally. This regional response differs between MAM3
and MARC. For both MAM3 and MARC, it appears that decreases in ! correspond to increases in ! (Fig. 2e, f); but this relationship is likely spurious, because organic carbon aerosol does not directly influence ice processes in either aerosol module. The same applies to ! , the 2000-1850 difference in ! (Fig. 13d-f), which is strongly negatively correlated with ! and ! : increases in ! and ! drive a stronger shortwave cloud cooling effect. For both MAM3 and MARC, the cooling effect of ! is strongest in the Northern Hemisphere, particularly regions with high anthropogenic sulfur emissions, especially East Asia, Southeast Asia, and South Asia. Compared with MAM3, MARC produces a slightly stronger ! response in the mid-latitudes and a slightly weaker ! response in the sub-tropics. Another difference between MAM3 and MARC is the land-ocean contrast: compared with MAM3, MARC often produces a slightly stronger ! response over land but a weaker ! response over ocean.
Shortwave cloud radiative effect
When globally averaged, the global mean for MARC ( W m -2 ) is very similar to that for MAM3 ( W m -2 ). Considering the differences between MAM3 and MARC, we find it somewhat surprising that the two aerosol modules produce such a similar global mean response, although we have noted differences in the regional distribution.
Longwave cloud radiative effect
The cooling effect of ! is partially offset by the warming effect of ! (Eq. (6)), the longwave cloud radiative effect which arises due to absorption of longwave thermal infrared radiation.
The surface albedo radiative effect
In addition to interacting with radiation both directly and indirectly via clouds, aerosols can influence the earth's radiative energy balance via changes to the surface albedo. The surface albedo radiative effect (! ; Eq. (5)), "includes effects of both changes in snow albedo due to deposition of absorbing aerosol, and changes in snow cover induced by deposition and by the other aerosol forcing mechanisms" (Ghan, 2013). For both MAM and MARC, deposition of absorbing aerosol is enabled via the coupling between CAM5 and the land scheme in CESM; and "other aerosol forcing mechanisms" include aerosol-induced changes in precipitation rate. Aerosol-induced changes in column water vapor can also influence the calculation of ! , because ! is sensitive to near-infrared absorption by water vapour; but the contribution from such changes in column water vapour is small.
W P liquid W P total W P liquid W P total ∆ C R E SW C R E SW ∆ W P liquid ∆ W P total W P liquid W P total ∆ C R E SW ∆ C R E SW ∆ C R E SW ∆ C R E SW ∆ C R E SW ∆ CR E SW −2.11 ± 0.03 −2.09 ± 0.04 ∆ CR E SW C R E SW C R E LW C R E LW C R E LW W P ice ∆ C R E LW C R E LW ∆ C R E LW ∆ C R E LW ∆ C R E LW + 0.54 ± 0.02 + 0.66 ± 0.02 ∆ C R E LW ∆ C R E SW ∆ SR E SW ∆ SR E SW F clean,clear ∆ SR E SW ∆ SR E SW ∆ SR E SW ∆ SR E SW + 0.00 ± 0.02 ∆ SR E SW −0.12 ± 0.02 ! 11
The ! response is associated with 2000-1850 changes in snow cover over both land and sea-ice ( Fig. S10d-f): increases in snow cover lead to negative ! values, while decreases in snow cover lead to positive ! values. Changes in snow rate (Fig. S11d-f) likely play a major role, explaining much of the snow cover response.
Changes in black carbon deposition (Fig. S12d-f), contributing to changes in the mass of black carbon in the top layer of snow ( Fig. S13d-f), may also play a role. The mass of black carbon in the top layer of snow is much lower for MARC compared with MAM ( Fig. S13a-c); the 2000-1850 difference in the mass of black carbon in the top layer of snow is also much lower for MARC compared with MAM ( Fig. S13d-f).
Net effective radiative forcing
The net effective radiative forcing (! ) -the 2000-1850 difference in the net radiative flux at TOA (Eq. (7)) -is effectively the sum of the radiative effect components we discussed above. Figure 16 shows ! ; Table 1 summarises the global mean contribution from the different radiative effect components.
In general, the cloud shortwave component, ! , dominates, resulting in negative values of ! across much of the world. In particular, strongly negative values of ! , indicating a large cooling effect, are found near regions with substantial anthropogenic sulfur emissions. The cooling effect is far stronger in the Northern Hemisphere than it is in the Southern Hemisphere. If coupled atmosphere-ocean simulations were to be performed, allowing SSTs to respond, the large inter-hemispheric difference in ! would likely impact inter-hemispheric temperature gradients and hence rainfall patterns (Chiang and Friedman, 2012;Grandey et al., 2016b;Wang, 2015).
Across much of the globe, the net cooling effect of ! produced by MARC is similar to that produced by MAM. However, in the mid-latitudes, MARC produces a stronger net cooling effect, especially over North America, Europe, and northern Asia. Another difference is that MARC appears to exert more widespread cooling over land than MAM does, while the opposite appears to be the case over ocean. These differences in the regional distribution of ! are largely due to differences in the regional distribution of ! . As mentioned in the previous paragraph, rainfall patterns are sensitive to changes in surface temperature gradients. Therefore, if SSTs were allowed to respond to the forcing, the differences in the regional distribution of ! between MARC and MAM may drive differences in rainfall patterns.
When averaged globally, MAM3 produces a global mean of W m -2 ; MARC produces a stronger global mean of W m -2 . The produced by CAM5.3-MARC-ARG is particularly strong compared with many other global climate models (Shindell et al., 2013). However, the global mean ! may become weaker if the inter-annual variability in the wildfire emissions of organic carbon were to be carefully accounted for (Grandey et al., 2016a).
Summary and conclusions
The specific representation of aerosols in global climate models, especially the representation of aerosol mixing state, has important implications for aerosol hygroscopicity, aerosol lifetime, aerosol column burdens, aerosol optical properties, and cloud condensation nuclei availability. For example, in addition to internally-mixed modes, MARC also includes a pure organic carbon aerosol mode and a pure black carbon aerosol mode both of which have very low hygroscopicity. The low hygroscopicity of these pure organic carbon and pure black carbon modes likely leads to increased aerosol lifetime compared with the internally-mixed modes. Therefore, far away from emissions sources, the column burdens of organic carbon aerosol and black carbon aerosol are higher for MARC compared with MAM3, which contains only internally-mixed aerosol modes.
Furthermore, the representation of aerosol mixing state, and the associated implications for hygroscopicity, strongly influences the ability of the aerosol particles to act as cloud condensation nuclei.
We have demonstrated that changing the aerosol module in CAM5.3 influences both the direct and indirect radiative effects of aerosols. Standard CAM5.3, which uses the MAM3 aerosol module, produces a global mean net ERF of
∆ SR E SW ∆ SR E SW ∆ SR E SW E R F SW+LW E R F SW+LW ∆ C R E SW E R F SW+LW E R F SW+LW E R F SW+LW E R F SW+LW E R F SW+LW ∆ C R E SW E R F SW+LW E R F SW+LW −1.57 ± 0.04 E R F SW+LW −1.75 ± 0.04 E R F SW+LW E R F SW+LW ! 12
W m -2 associated with the 2000-1850 difference in aerosol (including aerosol precursor) emissions; CAM5.3-MARC-ARG, which uses the MARC aerosol module, produces a stronger global mean net ERF of W m -2 , a particularly strong cooling effect compared with other climate models (Shindell et al., 2013). As summarised below, the difference in the global mean net ERF is primarily driven by differences in the direct radiative effect and the surface albedo radiative effect; but indirect radiative effects via clouds contribute to differences in the regional distribution of ERF produced by MAM3 and MARC.
By analysing the individual components of the net ERF, we have demonstrated that:
1. The global mean 2000-1850 direct radiative effect produced by MAM3 ( W m -2 ) is close to zero due to the warming effect of black carbon aerosol opposing the cooling effect of sulfate aerosol and organic carbon aerosol. In contrast, the 2000-1850 direct radiative effect produced by MARC is W m -2 , with the cooling effect of sulfate aerosol being larger than the warming effect of black carbon aerosol.
2. The global mean 2000-1850 shortwave cloud radiative effect produced by MARC ( W m -2 ) is very similar to that produced by MAM3 ( W m -2 ). However, the regional distribution differs: for MAM3, the cooling peaks in the Northern Hemisphere subtropics; while for MARC, the cooling peaks in the Northern
Hemisphere mid-latitudes. The land-ocean contrast also differs: compared with MAM3, MARC often produces stronger cooling over land but weaker cooling over ocean. For both MAM3 and MARC, the 2000-1850 shortwave cloud radiative effect is closely associated with changes in liquid water path.
3. The global mean 2000-1850 longwave cloud radiative effect produced by MARC ( W m -2 ) is stronger than that produced by MAM3 ( W m -2 ). For both MAM3 and MARC, the 2000-1850 longwave cloud radiative effect is closely associated with changes in ice water path and high cloud cover.
4. The global mean 2000-1850 surface albedo radiative effect produced by MARC ( W m -2 ) is also stronger than that produced by MAM3 ( W m -2 ). The 2000-1850 surface albedo radiative effect is associated with changes in snow cover.
If climate simulations were to be performed using a coupled atmosphere-ocean configuration of CESM, these differences in the radiative effects produced by MAM3 and MARC would likely lead to differences in the climate response.
In particular, the differences in the regional distribution of the radiative effects would likely impact rainfall patterns (Wang, 2015).
In light of these results, we conclude that the specific representation of aerosols in global climate models has important implications for climate modelling. Important interrelated factors include the representation of aerosol mixing state, size distribution, and optical properties.
Appendix A: Computational performance
In order to assess the computational performance of MARC, in comparison with MAM, we have performed six timing simulations. The configuration of these simulations is described in the caption of Table S1.
Before looking at the results, it is worth noting that the default radiation diagnostics differ between MARC and MAM. As highlighted by Ghan (Ghan, 2013), in order to calculate the direct radiative effect of aerosols, a second radiation call is required in order to diagnose "clean-sky" fluxes -in this diagnostic clean-sky radiation call, interactions between aerosols and radiation are switched off. In MARC, these clean-sky fluxes are diagnosed by default. However, in MAM, these clean-sky fluxes are not diagnosed by default, although simulations can be configured to include the necessary diagnostics. The inclusion of the clean-sky diagnostics increases computational expense. Hence, in order to facilitate a fair comparison between MARC and MAM, we have performed two simulations for each aerosol module: one with clean-sky diagnostics switched on, and one with clean-sky diagnostics switched off.
The results from the timing simulations are shown in Table S1. When clean-sky diagnostics are switched off, as would ordinarily be the case for long climate-scale simulations, using MARC increases the computational cost by only 6% condensation nuclei concentration (Figs. S1 and S2), cloud water path and fraction (Figs. S3-S7), total precipitation rate ( Fig. S8), wind speed (Fig. S9), snow cover and rate (Figs. S10 and S11), and black carbon deposition (Figs. S12 and S13). Table Table S1: Results from the six timing simulations. Each of these simulations consists of "20-day model runs with restarts and history turned off" (CESM Software Engineering Group, 2015), repeated five times in order to assess variability. The repetition of each simulation allows the standard error to be calculated via calculation of the corrected sample standard deviation. For consistency, all runs have been submitted on the same day. For each run, 720 processors, spread across 20 nodes on Cheyenne
) E R F SW+LW Δ surface albedo radiative effect (! ) ∆ SR E SW Δ longwave cloud radiative effect (! ) ∆ C R E LW Δ shortwave cloud radiative effect (! ) ∆ C R E SW Δ direct radiative effect (! ) ∆ DR E SW ! 19
Supplementary
CESM 1.2.2, with CAM5.3, is used for all simulations. Greenhouse gas concentrations and sea surface temperatures (SSTs) are prescribed using year-2000 climatological values, based on the "F_2000_CAM5" component set. CAM5.3 is run at a horizontal resolution of 1.9°×2.5° with 30 levels in the vertical direction. Clean-sky radiation diagnostics are included, facilitating diagnosis of the direct radiative effect. The Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP) (Bodas-Salcedo et al., 2011) is switched on, although the COSP diagnostics are not analysed in this manuscript.
Figure
Figure 1a-c shows the total sulfate aerosol burden (! ) for the year-2000 simulations. For all three aerosol
Figure 1d-f shows !
Figure 2a -
2ac shows the total organic carbon aerosol burden (! ) for the year-2000 simulations. For both MAM3 and MARC, year-2000 ! peaks in the tropics, especially sub-Saharan Africa and South America, due to emissions from wildfires. The impact of anthropogenic emissions of organic carbon aerosol is evident over South Asia and East Asia. Biogenic emissions of isoprene and monoterpene also contribute to ! . In general, year-2000 ! is higher for MARC than it is for MAM. This suggests that the organic carbon aerosol lifetime is longer for MARC compared with MAM, consistent with the differing representations of mixing state influencing wet removal efficiency: MAM3 assumes that all organic carbon aerosol is internally-mixed with other species, whereas MARC also includes a pure organic carbon aerosol mode with very low hygroscopicity. Over the major emissions regions of organic carbon aerosol, MAM3 and MARC both produce positive values of ! , the 2000-1850 difference in ! (Fig. 2d-f). However, negative values of ! are found over North America, especially for MAM3. These 2000-1850 differences arise due to changes in both wildfire emissions and anthropogenic emissions of organic carbon aerosol between year-1850 and year-2000. Although emissions of some volatile organic compounds do change between year-1850 and year-2000, emissions of isoprene and monoterpene remain
Figure 3a -
3ac shows the total black carbon aerosol burden (! ) for the year-2000 simulations. For both MAM3 and
Figure 5a -
5ac shows the total dust aerosol burden (! ) for the year-2000 simulations. Dust emission primarily occurs over desert areas, especially the Sahara Desert, so year-2000 ! is highest directly over and downwind of these desert source regions. Year-2000 ! is much larger for MARC, which follows Albani et al., (2014), compared with MAM. The largest differences between MAM3 and MARC appear to occur directly over the desert source regions, suggesting that differences in dust emission drive the differences in year-2000 ! -if this is the case, dust emission is far higher for MARC compared with MAM over the Sahara, Middle East, and East Asian deserts, while the opposite may be true over southern Africa and Australia. However, differences in the lifetime of dust aerosol may also contribute to the differences in year-2000 ! between MAM and MARC. We expect the dust aerosol lifetime to be longer for MARC compared with MAM3, because MAM3 assumes internal mixing of dust with sulfate and sea salt within the coarse mode, thereby increasing the wet removal rate (Liu et al., 2012), while MARC assumes that dust aerosol remains pure (with no internal mixing).! , the 2000-1850 difference in ! (Fig. 5d-f), reveals that ! decreases between year-1850 and year-2000, especially over the Sahara Desert. Both MAM3 and MARC produce a similar zonal mean decrease in ! . The reasons for the 2000-1850 changes in ! are unclear, although changes in surface wind speed (Fig. S9d-f), influencing emission, and changes in precipitation rate (Fig. S8d-f), influencing lifetime, likely
Figure 6a -
6ac shows ! for the year-2000 simulations. For both MAM and MARC, zonal mean year-2000 ! peaks in the Northern Hemisphere subtropics, driven by emission of dust from deserts, especially the Sahara Desert. Over other regions, both anthropogenic aerosol emissions and natural aerosol emissions, including emissions of sea salt, contribute to year-2000 ! . The year-2000 ! values for MARC are often much lower than those for MAM3, especially over subtropical ocean regions.
Figure 12a -
12ac shows grid-box cloud ice water path (! ) for the year-2000 simulations. As with ! , year-2000 ! is highest in the tropics and mid-latitudes. The regional distribution of year-2000 ! is similar to that of high-level cloud fractional coverage (Fig. S7a-c), and is similar between MAM and MARC. However, year-2000 ! is consistently lower for MARC than for MAM. Although MARC and MAM3 are coupled to the same ice and mixed-phase cloud microphysics scheme (Gettelman et al., 2010; Liu et al., 2007), differences in the availability of ice nuclei can arise due to differences in dust and sulfate number concentrations and size distributions. Differences in tuneable parameters, for which observational constraints do not exist, may also play a role: the uncertainties associated with ice nucleation are very large (Garimella et al., 2017). The 2000-1850 differences in ! and ! are shown in Figs. 11d-f and 12d-f. MAM3 produces large
Figure 13a -
13ac shows the clean-sky shortwave cloud radiative effect (! ; Eq. (4)) for the year-2000 simulations. Clouds scatter much of the incoming solar radiation, exerting a strong cooling effect on the climate system. This cooling effect is strongest in the tropics and mid-latitudes. The regional distribution of year-2000 ! is strongly negatively correlated
Figure 14a -
14ac shows ! for the year-2000 simulations. As with the shortwave cooling effect, the longwave warming effect is strongest in the tropics and mid-latitudes, for both MAM and MARC. The regional distribution of year-2000 ! is positively correlated with ! (Fig. S12ac) and high-level cloud fraction (Fig. S7a-c) -high-level ice cloud drives the longwave warming effect. The same is true for ! , the 2000-1850 difference in ! (Fig. 14d-f): changes in high-level ice cloud cover drive changes in the longwave cloud warming effect. For both MAM3 and MARC, ! is positive over much of Southeast Asia, South Asia, the Indian Ocean, the Atlantic Ocean, and Pacific Ocean; ! is negative over much of Africa and parts of South America. When averaged globally, MAM3 produces a global mean ! of ! W m -2 , while MARC produces a stronger global mean of W m -2 . Hence offsets approximately one quarter to one third of the ! cooling effect.
(! does not include changes in land use, because the only difference between the year-1850 and year-2000 simulations is the aerosol emissions.) Figure 15 shows ! , the 2000-1850 surface albedo radiative effect. In the Arctic and high-latitude land regions of the Northern Hemisphere, ! can be relatively large. MAM3 produces a mixture of positive and negative values, averaging out to approximately zero globally ( W m -2 ). However, MARC tends to produce mainly negative values, averaging out to a global mean of W m -2 .
FiguresFigure 1 :Figure 2 : 21 !Figure 3 : 22 !Figure 4 : 23 !Figure 5 : 24 !Figure 6 :Figure 7 : 26 Figure 8 : 27 Figure 9 : 28 Figure 10 : 29 Figure 11 :Figure 12 : 31 Figure 13 : 32 Figure 14 :Figure 15 :Figure 16 :
1221322423524672682792810291112311332141516Annual mean total sulfate aerosol burden (! ). For the zonal means (a, d), the standard errors, calculated using the annual zonal mean for each simulation year, are indicated by shading; but this shading is not visible inFig. 1, because the standard errors are smaller than the width of the plotted lines. For the maps (b, c, e, f), the area-weighted global mean and associated standard error, calculated using the annual global mean for each simulation year, are shown below each map. For the maps showing 2000-1850 differences (e, f), white indicates differences with a magnitude less than the threshold value in the centre of the colour bar ( mg m -2 ). For locations where the magnitude is greater than this threshold value, stippling indicates differences that are statistically significant at a significance level of 0.05 after controlling the false discovery rate (Benjamini and Hochberg, 1995; Wilks, 2016); the two-tailed p values are generated by Welch's unequal variances t-test, using annual mean data from each simulation year as the input; the approximate p value threshold, ! , which takes the false discovery rate into account, is written underneath each map. The analysis period is 30 years. Annual mean total organic carbon aerosol burden (! ). MARC does not directly diagnose total organic carbon aerosol burden, so we have used the mass-mixing ratios diagnosed by MARC in order to calculate the total organic carbon aerosol burden -the errors associated with this post-processing step are estimated to be less than 1% for all grid-boxes, and the errors are far smaller when global mean averaging is applied. The figure components are explained in theFig. 1caption.B u r de n OC! Annual mean total black carbon aerosol burden (! ). MARC does not directly diagnose total black carbon aerosol burden, so we have used the mass-mixing ratios diagnosed by MARC in order to calculate the total black carbon aerosol burden. The figure components are explained in theFig. 1 caption.B u r de n BC! Annual mean total sea salt aerosol burden (! ). MARC does not directly diagnose sea salt aerosol burden, so we have used the mass-mixing ratios diagnosed by MARC in order to calculate the total sea salt aerosol burden. The figure components are explained in theFig. 1 caption.B u r de n salt! Annual mean dust aerosol burden (! ). MARC does not directly diagnose dust aerosol burden, so we have used the mass-mixing ratios diagnosed by MARC in order to calculate the total dust aerosol burden. The figure components are explained in theFig. 1 caption.B u r de ndust ! Annual mean aerosol optical depth (! ). The figure components are explained in the Fig. 1 caption. Annual mean direct radiative effect (! ; Eq. (3)). The figure components are explained in the Fig. 1 caption. For all four maps, white indicates differences with a magnitude less than the threshold value in the centre of the corresponding colour bar. DR E SW ! Annual mean absorption by aerosols in the atmosphere (! ; Eq. (8)). The figure components are explained in the Fig. 1 caption. For all four maps, white indicates differences with a magnitude less than the threshold value in the centre of the corresponding colour bar. A A A SW ! Annual mean cloud condensation nuclei concentration at 0.1% supersaturation (! ) in model level 24 (in the lower troposphere). The figure components are explained in the Fig. 1 caption. Corresponding results, showing ! near the surface and in the mid-troposphere (model level 19), are shown in Figs. S1 and S2 of the Supplement. C C N conc C C N conc ! Annual mean column-integrated cloud droplet number concentration (! ). The figure components are explained in the Fig. 1 caption. C DNC column ! Annual mean grid-box cloud liquid water path (! ). The figure components are explained in the Fig. 1 caption. Annual mean grid-box cloud ice water path (! ). The figure components are explained in the Fig. 1 caption. W P ice ! Annual mean clean-sky shortwave cloud radiative effect (! ; Eq. (4)). The figure components are explained in the Fig. 1 caption. For all four maps, white indicates differences with a magnitude less than the threshold value in the centre of the corresponding colour bar. C R E SW ! Annual mean longwave cloud radiative effect (! ; Eq. (6)). The figure components are explained in the Fig. 1 caption. For all four maps, white indicates differences with a magnitude less than the threshold value in the centre of the corresponding colour bar. Annual mean 2000-1850 surface albedo radiative effect (! ; Eq. (5)). The figure components are explained in the Fig. 1 caption. Annual mean 2000-1850 net effective radiative forcing (! ; Eq. (7)). The figure components are explained in the Fig. 1 caption. When comparing the relative contributions of the different radiative effect components to ! Introduction This document contains a supplementary table and supplementary figures for the manuscript titled "Effective radiative forcing in the aerosol-climate model CAM5.3-MARC-ARG". The supplementary figures are grouped thematically: cloud
(doi:10.5065/D6RX99HX), have been used. As with the year-2000 and year-1850 simulations (Section 2.3 of the main manuscript), a model resolution of 1.9° × 2.5° is used, SSTs and greenhouse gas concentrations are prescribed using year-2000 climatological values, and aerosol and aerosol precursor emissions follow year-2000 emissions. In contrast to the simulations described in the main manuscript, COSP has not been used in these timing simulations. The simulation costs shown represent the total cost of all model components, including non-atmospheric components such as the land scheme.
Figure S1 :Figure S2 :Figure S3 : 4 !Figure S4 :Figure S5 :Figure S6 :Figure S7 :Figure S8 :Figure S9 :Figure S10 :Figure S11 :Figure S12 :Figure S13 :
S1S2S34S4S5S6S7S8S9S10S11S12S13Annual mean cloud condensation nuclei concentration at 0.1% supersaturation (" ) in the bottom model level. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean cloud condensation nuclei concentration at 0.1% supersaturation (" ) in model level 19 (in the mid-troposphere). The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean grid-box total cloud water path (" ). The figure components are explained in the caption of Fig. 1 in the main manuscript. W P total = W P liquid + W P ice ! Annual mean total cloud fraction (" ). The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean low-level cloud fraction (" ). The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean mid-level cloud fraction (" ). The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean high-level cloud fraction (" ). The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean total precipitation rate. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean 10-m wind speed. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean fraction of the earth's surface covered by snow. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean total snow rate. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean total black carbon deposition over land. The figure components are explained in the caption of Fig. 1 in the main manuscript. Annual mean mass of black carbon in the the top layer over snow over land. The figure components are explained in the caption of Fig. 1 in the main manuscript.
Hemisphere, especially over the remote Southern Ocean and Antarctica. In general, there is close agreement between MAM and MARC over the Northern Hemisphere tropics and the Southern Hemisphere. However, over the Northern Hemisphere subtropics and mid-latitudes, year-2000 ! is generally lower for MARC compared with MAM3. Interestingly, over the Northern Hemisphere subtropics, the zonal means are very similar between MAM7 and MARC.1a-c shows the total sulfate aerosol burden (!
) for the year-2000 simulations. For all three aerosol
modules, year-2000 !
is highest in the Northern Hemisphere subtropics and mid-latitudes, especially near source
regions with high anthropogenic emissions of sulfur dioxide. Year-2000 !
is much lower in the Southern
than that for MAM, especially over remote regions far away from sources. This suggests that the black carbon aerosol lifetime is longer for MARC than it is for MAM, likely due to the low hygroscopicity of the pure black carbon aerosol modeMARC, year-2000 !
is high over sub-Saharan Africa and South America, as was the case for !
, due to
large emissions of black carbon aerosol from wildfires. However, in contrast to !
, the peak in zonal mean
year-2000 !
occurs in the Northern Hemisphere subtropics and mid-latitudes, due to anthropogenic emissions of
black carbon aerosol over East Asia, South Asia, Europe, and North America. In the tropics, year-2000 !
is
generally similar between MAM and MARC. Outside of the tropics, year-2000 !
for MARC is generally higher
in MARC.
MAM3 and MARC produce similar increases in !
between year-1850 and year-2000, as indicated by
positive values of !
(Fig. 3d-f). For MARC, positive values of !
are found over even remote
ocean regions, consistent with a longer black carbon lifetime for MARC compared with MAM3.
3.1.4 Total sea salt aerosol burden
Figure 4a-c shows the total sea salt aerosol burden (!
) for the year-2000 simulations. For both MAM3 and
MARC, year-2000 !
is highest over ocean areas with strong surface wind speeds (Fig. S9b, c). Over land,
year-2000 !
is very low, suggesting that the sea salt aerosol generally has a relatively short lifetime, as expected
due to the large particle size and high hygroscopicity. Year-2000 !
is very similar between MAM3 and MARC.
This is not surprising, because MARC uses the same sea salt emissions parameterization as MAM3 does.
∆ B u r de n SO4
B u r de n SO4
∆ B u r de n SO4
∆ B u r de n SO4
B u r de n SO4
B u r de n OC
B u r de n OC
B u r de n OC
B u r de n OC
∆ B u r de n OC
B u r de n OC
∆ B u r de n OC
∆ B u r de n OC
B u r de n BC
B u r de n BC
B u r de n OC
B u r de n OC
B u r de n BC
B u r de n BC
B u r de n BC
B u r de n BC
∆ B u r de n BC
∆ B u r de n BC
B u r de n salt
B u r de n salt
B u r de n salt
B u r de n salt
! 6
For both MAM3 and MARC, !
, the 2000-1850 difference in !
(Fig. 4e, f), appears to be
positively correlated with the 2000-1850 difference in surface wind speeds (Fig. S9e, f). Changes in precipitation rate (Fig.
variations in the albedo of the earth's surface -large values of ! may not necessarily correspond to large values of ! . Having said that, for both MAM3 and MARC, the regional distribution of year-2000 ! shares some similarities with that of year-2000 ! . Over dark ocean surfaces in the subtropics, scattering by aerosols drives negative values of year-2000 ! . The impact of dust on year-2000 ! differs between MAM3 and MARC, likely due to differing optical properties: for MAM3, absorption by dust drives positive values over the bright surface of the Sahara Desert, while little radiative impact is evident downwind over the dark surface of the tropical Atlantic Ocean; for MARC, scattering by dust drives negative values over the tropical Atlantic Ocean, while little radiative impact is evident over the Sahara Desert.For MAM3, , the 2000-1850 difference in , is relatively weak at all latitudes(Fig. 7d, e), with a global mean of only W m -2 , due to the cooling effect of anthropogenic sulfur emissions being offset by the warming effect of increased black carbon aerosol emissions. In contrast, for MARC, reveals a relatively strong cooling effect across much of the Northern Hemisphere(Fig. 7d, f), especially near anthropogenic sourcesof sulfur emissions, leading to a global mean
of
W m -2 .
) for the year-2000 simulations. Consideration of ! , which reveals heating of the atmosphere by aerosols, complements consideration of ! . For example, over the Sahara Desert, we noted above that the dust aerosol in MARC exerts only a weak direct radiative effect at TOA (Fig. 7c); however, Fig. 8c reveals that the dust aerosol in MARC leads to strong heating of the atmosphere. For both MAM and MARC, year-2000 ! is largest near emission sources of dust, especially over the Sahara Desert where year-2000 ! is particularly high, showing that dust is the primary driver of year-2000 ! . Further away from the dust emission source regions, year-2000 ! is spatially correlated with year-2000 ! , showing that black carbon aerosol also contributes to year-2000 ! . Despite the fact that year-2000 ! and ! are larger for MARC compared with MAM, year-2000 ! is generally weaker for MARC compared with MAM3: this difference in year-2000 ! is likely due to differences in the aerosol optical properties, associated with different handling of dust and black carbon aerosol mixing state between MAM3 and MARC.!
, the 2000-1850 difference in !
(Fig. 8d-f), generally follows the same regional distribution as
!
, showing that changes in emissions of black carbon aerosol dominate !
. Although dust dominates
year-2000 !
, changes in dust emission exert only a relatively small influence on !
. As with year-2000
!
, !
is generally weaker for MARC compared with MAM3.
B u r de n SO4 B u r de n OC
B u r de n BC
c shows the CCN concentration at a fixed supersaturation of 0.1% (! ) in the lower troposphere for the year-2000 simulations. Corresponding results showing year-2000 ! near the surface and in the mid-troposphere are shown in Figs. S1a-c and S2a-c of the Supplement. Looking at year-2000 ! across these different vertical levels, we make two initial observations: first, for both MAM and MARC, year-2000 ! is generally higher in the Northern Hemisphere; second, year-2000 ! is generally much lower for MARC compared with MAM.
Table 1 :
1DR, and HHL analysed the results. BSG produced the figures shown in this manuscript. BSG wrote the manuscript, with contributions from all other co-authors. CW provided supervisory guidance throughout the project. Area-weighted global mean radiative effects. Combined standard errors are calculated using the annual global mean for each simulation year. The regional distributions of these radiative effects are shown inFigs. 7, 13, 14, 15, and 16. ! is the sum of the other radiative effect components.−1.57 ± 0.04
−1.75 ± 0.04
−0.02 ± 0.01
−0.18 ± 0.01
−2.11 ± 0.03
−2.09 ± 0.04
+ 0.66 ± 0.02
+ 0.54 ± 0.02
−0.12 ± 0.02
+ 0.00 ± 0.02
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DISCUSSION OF: A STATISTICAL ANALYSIS OF MULTIPLE TEMPERATURE PROXIES: ARE RECONSTRUCTIONS OF SURFACE TEMPERATURES OVER THE LAST 1000 YEARS RELIABLE?
2011
Gavin A Schmidt
NASA Goddard Institute for Space Studies
Pennsylvania State University and Roger Williams University
Michael E Mann
NASA Goddard Institute for Space Studies
Pennsylvania State University and Roger Williams University
Scott D Rutherford
NASA Goddard Institute for Space Studies
Pennsylvania State University and Roger Williams University
DISCUSSION OF: A STATISTICAL ANALYSIS OF MULTIPLE TEMPERATURE PROXIES: ARE RECONSTRUCTIONS OF SURFACE TEMPERATURES OVER THE LAST 1000 YEARS RELIABLE?
The Annals of Applied Statistics
512011Received September 2010.Main article
McShane and Wyner (2011) (henceforth MW) analyze a dataset of "proxy" climate records previously used byMann et al. (2008)(henceforth M08) to attempt to assess their utility in reconstructing past temperatures. MW introduce new methods in their analysis, which is welcome. However, the absence of both proper data quality control and appropriate "pseudoproxy" tests to assess the performance of their methods invalidate their main conclusions.We deal first with the issue of data quality. In the frozen 1000 AD network of 95 proxy records used by MW, 36 tree-ring records were not used by M08 due to their failure to meet objective standards of reliability. These records did not meet the minimal replication requirement of at least eight independent contributing tree cores (as described in the Supplemental Information of M08). That requirement yields a smaller dataset of 59 proxy records back to AD 1000 as clearly indicated in M08. MW's inclusion of the additional poor-quality proxies has a material affect on the reconstructions, inflating the level of peak apparent Medieval warmth, particularly in their featured "OLS PC10" (K = 10 PCs of the proxy data used as predictors of instrumental mean NH land temperature) reconstruction. The further elimination of four potentially contaminated "Tiljander" proxies [as tested in M08; M08 also tested the impact of removing tree-ring data, including controversial long "Bristlecone pine" tree-ring records. Recent work [cf. Salzer et al. (2009)], however, demonstrates those data to contain a reliable longterm temperature signal], which yields a set of 55 proxies, further reduces the level of peak Medieval warmth(Figure 1(a); cf. Figure 14 in MW; see
McShane and Wyner (2011) (henceforth MW) analyze a dataset of "proxy" climate records previously used by Mann et al. (2008) (henceforth M08) to attempt to assess their utility in reconstructing past temperatures. MW introduce new methods in their analysis, which is welcome. However, the absence of both proper data quality control and appropriate "pseudoproxy" tests to assess the performance of their methods invalidate their main conclusions.
We deal first with the issue of data quality. In the frozen 1000 AD network of 95 proxy records used by MW, 36 tree-ring records were not used by M08 due to their failure to meet objective standards of reliability. These records did not meet the minimal replication requirement of at least eight independent contributing tree cores (as described in the Supplemental Information of M08). That requirement yields a smaller dataset of 59 proxy records back to AD 1000 as clearly indicated in M08. MW's inclusion of the additional poor-quality proxies has a material affect on the reconstructions, inflating the level of peak apparent Medieval warmth, particularly in their featured "OLS PC10" (K = 10 PCs of the proxy data used as predictors of instrumental mean NH land temperature) reconstruction. The further elimination of four potentially contaminated "Tiljander" proxies [as tested in M08; M08 also tested the impact of removing tree-ring data, including controversial long "Bristlecone pine" tree-ring records. Recent work [cf. Salzer et al. (2009)], however, demonstrates those data to contain a reliable longterm temperature signal], which yields a set of 55 proxies, further reduces the level of peak Medieval warmth (Figure 1 The MW "OLS PC10" reconstruction has greater peak apparent Medieval warmth in comparison with M08 or any of a dozen similar hemispheric temperature reconstructions [Jansen et al. (2007)]. That additional warmth, as shown above, largely disappears with the use of the more appropriate dataset. Using their reconstruction, MW nonetheless still found recent warmth to be unusual in a long-term context: they estimate an 80% probability that the decade 1997-2006 is warmer than any other for at least the past 1000 years. Using the more appropriate 55-proxy dataset with the same (K = 10) estimation procedure, we calculate a higher probability of 86% that recent decadal warmth is unprecedented for the past millennium [ Figure 1
(b)].
However K = 10 principal components is almost certainly too large, and the resulting reconstruction likely suffers from statistical over-fitting. Objective selection criteria applied to the M08 AD 1000 proxy network (see Supplementary Figure S4), as well as independent "pseudoproxy" analyses discussed below, favor retaining only K = 4 ("OLS PC4" in the terminology of MW). Using this reconstruction, we observe a very close match [e.g., Figure 1(a)] with the relevant M08 reconstruction and we calculate considerably higher probabilities up to 99% that recent decadal warmth is unprecedented for at least the past millennium [ Figure 1(c)]. These posterior probabilities imply substantially higher confidence than the "likely" assessment by M08 and IPCC (2007) (a 67% level of confidence). Indeed, a probability of 99% not only exceeds the IPCC "very likely" threshold (90%), but reaches the "virtually certain" (99%) threshold. However, since these posterior probabilities do not take into account potential systematic issues in the source data, are sensitive to methodological choices, and vary by a few percent depending on the MCMC realization, we maintain that a "likely" conclusion is most consistent with the balance of evidence [IPCC (2007)].
There are additional methodological weaknesses in the techniques employed by MW that require discussion. MW mix incommensurate (decadal vs. annual resolution) proxy data in their procedure, a problem that is avoided by the "hybrid" frequency band calibration method used by M08. Using a version of the proxy data that was consistently low-pass filtered to retain only decadal features shows even better agreement with the M08 reconstruction (supplementary Figure S3).
Furthermore, methods using simple Ordinary Least Squares (OLS) regressions of principal components of the proxy network and instrumental data suffer from known biases, including the underestimation of variance [see, e.g., Hegerl et al. (2006)]. The spectrally "red" nature of the noise present in proxy records poses a particular challenge [e.g., Jones et al. (2009)]. A standard benchmark in the field is the use of synthetic proxy data known as "pseudoproxies" derived from long-term climate model simulations where (We note that the term "pseudoproxy" was misused in MW to instead denote various noise models.) In contrast to the MW claim that their methods perform "fairly similarly," these tests show dramatic differences in model performance ( Figure 2). Indeed, the various flavors of OLS and, particularly, the "Lasso" method (used only in the first half of MW), suffer from serious underestimation biases in comparison with, for example, the hybrid RegEM approach of M08 (see also Table S1).
Taken together, these points demonstrate that any conclusions regarding the utility of proxies in reconstructing past climate drawn by MW were, at best, overstated. Assessing the skill of methods that do not work well (such as Lasso) and concluding that no method can therefore work well, is logically flawed. Additional problems exist in their assessment procedurereducing the size of the hold out periods to 30 years from 46 years in M08, for instance, makes it more difficult to meaningfully diagnose statistical skill.
Problems in climate research, such as statistical climate reconstruction, require sophisticated statistical approaches and a thorough understanding of the data used. Moreover, investigations of the underlying spatial patterns of past climate changes, rather than simply hemispheric mean temperature estimates, are most likely to provide insights into climate dynamics [e.g., Mann et al. (2009), Schmidt (2010]. Further progress in this area will most likely arise from continuing collaboration between the statistics and climate science communities, such as fostered since 1996 by the joint NSF/NCAR Geophysical Statistics Project.
(a); cf. Figure 14 in MW; see also Supplementary Figures S1-S2 [Schmidt, Mann and Rutherford (2011a, 2011b)]).
Fig. 1 .
1Reconstructions of mean Northern Hemisphere land temperatures over the past millennium for various methodological choices (cf. MW Figure 14). (a) Results using the M08 frozen AD 1000 network of 59 minus 4 "Tiljander" proxy records (corresponding results based on all 59 records are shown in Supplementary Figure S1). Shown for comparison are the original MW results and the Mann et al. (2008) "EIV" decadal "CRU" NH land temperature reconstruction based on the identical proxy data. The OLS reconstructions have been filtered with a loess smoother (span = 0.05) to emphasize low-frequency (greater than 50 year) variations. Associated annual reconstructions are shown in Supplementary Figure S2. (b) Comparison of Monte Carlo ensemble (and mean) reconstructions using "OLS PC10" as in MW Figure 16. Labeled reconstructions are in color, grey lines are the total set of MW reconstructions after allowing for uncertainties in the coefficients.
Fig. 1 .
1(c) As in (b) above but instead using "OLS PC4." the true climate history is known, and the skill of the particular method can be evaluated [see, e.g.,Mann et al. (2007);Jones et al. (2009) and numerous references therein].
Fig. 2 .
2Pseudoproxy tests of reconstruction methodologies used by MW and comparison with the hybrid and nonhybrid RegEM EIV methods used by M08. The pseudoproxy networks are defined by a randomly selected set of gridboxes using two different coupled ocean-atmosphere general circulation model (OAGCM) simulations subjected to estimated natural and anthropogenic forcing over the past millennium. Pseudoproxies are constructed assuming "red" proxy noise [AR(1)with ρ = 0.32] yielding mean signal-to-noise amplitude ratio of SNR = 0.4, characteristics which are consistent with estimates from actual proxy data networks [see Mann et al. (2007)]. All reconstructions use a calibration interval of 1856-1980. Figure shows results for a 59-location network including (a) NCAR CSM and (b) GKSS simulations and a network with 104 locations for (c) CSM and (d) GKSS.Labeled reconstructions are in color, grey lines are the total set of MW reconstruction techniques. Note that uncertainties are reduced for the larger network, where the underestimation bias becomes negligible for the hybrid RegEM EIV method.
Acknowledgments. We thank Sonya Miller for substantial technical assistance. The JAGS/rjags code used in the Bayesian modeling was adapted from http://probabilitynotes.wordpress.com/.Supplementary figures and tables, data used, and scripts for performing all analyses are all available at: http://www.meteo.psu.edu/~mann/ supplements/AOAS/DISCUSSION7Schmidt, G. A.,Mann, M. E. and Rutherford, S. D. (2011b). Supplement to "Discussion on A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?" DOI: 10.1214/10-AOAS398DSUPPB.
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Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Ipcc, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. MillerCambridge Univ. PressCambridgeIPCC (2007). Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. Miller, eds.). Cambridge Univ. Press, Cambridge.
Palaeoclimate. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. E Jansen, J Overpeck, K R Briffa, J.-C Duplessy, F Joos, V Masson-Delmotte, D Olago, B Otto-Bliesner, W R Peltier, S Rahmstorf, R Ramesh, D Raynaud, D Rind, O Solomina, R Villalba, D Zhang, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. MillerCambridge Univ. PressCambridgeJansen, E., Overpeck, J., Briffa, K. R., Duplessy, J.-C., Joos, F., Masson- Delmotte, V., Olago, D., Otto-Bliesner, B., Peltier, W. R., Rahmstorf, S., Ramesh, R., Raynaud, D., Rind, D., Solomina, O., Villalba, R. and Zhang, D. (2007). Palaeoclimate. In Climate Change 2007: The Physical Science Basis. Contri- bution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. Miller, eds.). Cambridge Univ. Press, Cambridge.
High-resolution paleoclimatology of the last millennium: A review of current status and future prospects. P D Jones, K R Briffa, T J Osborn, J M Lough, T D Van Ommen, B M Vinther, J Luterbacher, E R Wahl, F W Zwiers, M E Mann, G A Schmidt, C M Ammann, B M Buckley, K M Cobb, J Esper, H Goosse, N Graham, E Jansen, T Kiefer, C Kull, M Küttel, E Mosley-Thompson, J T Overpeck, N Riedwyl, M Schulz, A W Tudhope, R Villalba, H Wanner, E Wolff, E Xoplaki, Holocene. 19Jones, P. D., Briffa, K. R., Osborn, T. J., Lough, J. M., van Ommen, T. D., Vinther, B. M., Luterbacher, J., Wahl, E. R., Zwiers, F. W., Mann, M. E., Schmidt, G. A., Ammann, C. M., Buckley, B. M., Cobb, K. M., Esper, J., Goosse, H., Graham, N., Jansen, E., Kiefer, T., Kull, C., Küttel, M., Mosley- Thompson, E., Overpeck, J. T., Riedwyl, N., Schulz, M., Tudhope, A. W., Villalba, R., Wanner, H., Wolff, E. and Xoplaki, E. (2009). High-resolution paleoclimatology of the last millennium: A review of current status and future prospects. Holocene 19 3-49.
Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millenia. M E Mann, Z Zhang, M K Hughes, R S Bradley, S K Miller, S Rutherford, F Ni, Proc. Natl. Acad. Sci. USA. 105Mann, M. E., Zhang, Z., Hughes, M. K., Bradley, R. S., Miller, S. K., Ruther- ford, S. and Ni, F. (2008). Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millenia. Proc. Natl. Acad. Sci. USA 105 13252-13257.
Robustness of proxy-based climate field reconstruction methods. M E Mann, S Rutherford, E Wahl, C Ammann, J. Geophys. Res. 11212109Mann, M. E., Rutherford, S., Wahl, E. and Ammann, C. (2007). Robustness of proxy-based climate field reconstruction methods. J. Geophys. Res. 112 D12109.
Global signatures and dynamical origins of the "Little Ice Age" and "Medieval Climate Anomaly. M E Mann, Z Zhang, S Rutherford, R S Bradley, M K Hughes, D Shindell, C Ammann, G Falugevi, F Ni, Science. 326Mann, M. E., Zhang, Z., Rutherford, S., Bradley, R. S., Hughes, M. K., Shin- dell, D., Ammann, C., Falugevi, G. and Ni, F. (2009). Global signatures and dy- namical origins of the "Little Ice Age" and "Medieval Climate Anomaly." Science 326 1256-1260.
A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?. B B Mcshane, A J Wyner, Ann. Appl. Statist. 5McShane, B. B. and Wyner, A. J. (2011). A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? Ann. Appl. Statist. 5 5-44.
Recent unprecedented tree-ring growth in bristlecone pine at the highest elevations and possible causes. M W Salzer, M K Hughes, A G Bunn, K F Kipfmueller, Proc. Natl. Acad. Sci. USA. 106Salzer, M. W., Hughes, M. K., Bunn, A. G. and Kipfmueller, K. F. (2009). Recent unprecedented tree-ring growth in bristlecone pine at the highest elevations and possible causes. Proc. Natl. Acad. Sci. USA 106 20348-20353.
Enhancing the relevance of palaeoclimate model/data comparisons for assessments of future climate change. G A Schmidt, J. Quaternary Sci. 25Schmidt, G. A. (2010). Enhancing the relevance of palaeoclimate model/data compar- isons for assessments of future climate change. J. Quaternary Sci. 25 79-87.
Discussion on A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable. G A Schmidt, M E Mann, S D Rutherford, 10.1214/10-AOAS398DSUPPASupplement toSchmidt, G. A., Mann, M. E. and Rutherford, S. D. (2011a). Supplement to "Discussion on A statistical analysis of multiple temperature proxies: Are re- constructions of surface temperatures over the last 1000 years reliable?" DOI: 10.1214/10-AOAS398DSUPPA.
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Analyzing 50 years of major fog events across the central coastal plain of Israel
Noam David
AtmosCell
Israel (www.atmoscell.com) 2. The Israeli Meteorological ServiceTel Aviv, Beit-DaganIsrael
Asaf Rayitsfeld
H Oliver Gao
The School of Civil and Environmental Engineering
Cornell University
IthacaNY*Correspondence
Analyzing 50 years of major fog events across the central coastal plain of Israel
This report presents an analysis of 152 major fog events that have been occurring for five decades across the central coastal plain of Israel. Analysis of the meteorological data shows that fog events in the experimental area predominantly occur under two sets of synoptic conditions -Red Sea Trough (44%) and Ridge (41%), while the incidence of fog events peaks between March and June. In particular, the results obtained indicate a decreasing trend in the number of fog events and their duration over time where the frequency of radiation fog has decreased over time when compared to the incidence of advection fog. This note provides a long-term analysis of data in a region that lacks reliable time series of this length, and highlight important insights for future research.
Introduction
According to the American Meteorological Society, fog is defined as a state where water droplets suspended in the air near the Earth's surface reduce visibility below 1 km (AMS, 2020). The economic damages caused due to fog can be vast, and on a scale comparable to the damages from winter storms, as a result of the disruption to flight schedules, for example, or even the shutting down of airports in severe cases (Gultepe et al., 2009). By way of demonstration, research has found that accurate timing of the onset and ending of capacity limiting situations such as fog could save busy air terminals around New York City approximately $480,000 per event (Allan et al., 2001).
Additional negative effects related to the phenomenon include acid fog that can cause damage to vegetation and structures, and smog, which presents a health risk, particularly for people suffering from respiratory illnesses (e.g. Tanaka et al., 1996;Wichmann et al., 1989).
However, the phenomenon also has positive contributions. Thus, for instance, in areas with low water availability, fresh water for afforestation, gardening, and even potable water can be harvested from fog (Klemm et al., 2012). Additionally, fog plays an important role in scrubbing the atmosphere through particle scavenging and drop deposition processes (Herckes et al., 2007).
Tools for monitoring fog include a variety of ground level sensors, human observers and satellite systems (David et al., 2013).
Human observers estimate the visibility during fog based on the appearance or obscuring of objects located at predetermined distances from the observers location.
The observations derived by this method, though, are not objective, since one observer's visibility estimate might be different from another observer's estimate.
Satellites provide wide spatial coverage and map areas where fog exists (e.g. Lensky, and Rosenfeld, 2008), but, at times, do not provide sufficient response, for example, due to obscuring of the fog from the satellite's viewpoint as a result of high altitude cloud cover. Additionally, satellite systems cannot, at times, differentiate, for example, between a low stratus cloud, at an elevation of several tens of meters above ground level, that does not endanger drivers, and fog that lies in immediate proximity to the ground (e.g. Gultepe et al., 2007;David, 2018).
On the other hand, specialized sensors such as visibility meters, Runway Visual Range (RVR) sensors and particle monitors can provide precise and reliable fog observations near ground level, however these instruments can only provide a local measurement, that does not reliably represent the entire space.
Hence, reliable monitoring of the phenomenon, over a wide geographic area, is still currently a challenge, and efforts are being made to develop tools for mapping fog in high temporal and spatial resolution using alternative and complimentary solutions (e.g. David et al., 2015;2019).
Categorizing broadly, fog can be classified as either radiation fog or advection fog, based on the physical processes that cause it to develop (Ziv and Yair, 1994). The first is caused as the result of radiative cooling of the surface, and the optimal conditions for its creation including a clear night, allowing for efficient radiative cooling, light wind (less than 5 knots), stability, and humid air. Advection fog is caused by relatively warm air being cooled to saturation as a result of it being carried by a light wind over a cold surface. The optimal conditions for its creation include a 5-10 knot wind and atmospheric stability. At times, a combination of both of these processes can cause the creation of fog, for example in cases where the surface is not cold enough to cause the condensing of droplets in the air traveling over it alone, but where the addition of radiative cooling can lead to the completion of the process.
As has been extensively reviewed by Klemm and Lin (2015), the frequency and intensity of fog events vary greatly over time. Broadly, the majority of research reports, from different locations across the world, indicate a major decrease in the frequency of fog formation, and its intensity. In most of the measuring stations where observations were carried out (e.g. Chen et al., (2006); Vautard et al. (2009); LaDochy and Witiw (2012); Williams et al. (2015)). In some cases an increase was observed (e.g. Syed et al., (2012)).
Trends in fog frequency and intensity can be a result of changes in regional climactic conditions. Urban Heat Island (UHI) effect, or changes in predominant circulation patterns, can lead to increasing air temperatures and a resulting decrease in Relative Humidity (RH), and as long as there are no feedback mechanisms overriding the temperature effect, may alter fog trends. Changes in the number of cloud condensation nuclei (CCN) has been discussed as a potential cause for fog trends, though there has yet to be a discussion of the relevant physical processes behind this reasoning (Klemm and Lin, 2015).
In this study, we present an analysis of fog measurements taken over 5 decades (1967 -2017) in Israel's central coastal region. Based on analysis of this data, we report a meaningful decrease in the frequency of fog creation and their duration. Additionally, we point out the key synoptic conditions that comprise the mechanism for the creation of fog in the area and analyze some of the characteristics of the phenomenon.
Classification for advection and radiation fog
In order to distinguish between the two types of fog we examined the vertical structure of the temperature and the dew point in the lower tropospheric levels up to 850 mb. The classification process was performed on the basis of the radiosonde measurements, launched from Bet Dagan station every night between 23:00 to 00:00 UTC ( Figure 1). Depending on the two different profile types, two types of fog were observed.
Radiation fog was typically characterized by a deep temperature inversion which extended from the surface level up to a pressure level of about 950 mb (~500 m above sea level). Simultaneously, the dew point was increasing with the increasing temperature, conditions that created a stable moist layer. While under the above conditions winds on the lower two levels were measured to be less than 4 knots (i.e. at ground level and at a height of 1000 millibars), the fog was classified as an radiation fog type. The fog was classified as advection fog when measured wind speed was higher than 4 knots (an up to 10 knots) during a low marine inversion and / or a weak ground inversion.
Results
We studied 152 fog major events which took place between March 1967 to March 2017 across the test site located in the central coastal plain of Israel. Figure 1 shows the experiment site where meteorological measurements and visibility estimates, acquired by professional human observers, were taken from Beit Dagan surface station. Additional visibility estimates were taken by observers located at Ben Gurion airport. database -based on visibility data, relative humidity, wind velocity, radiosonde records and synoptic conditions. The measurements that were available for the entire period were stored in SYNOP code, and accordingly, are available at a sampling frequency of once every three hours. The set of radiosonde measurements analyzed was gathered from nightly releases from the Beit Dagan station. We also note that events documented in the database at only one specific hour were considered as events of 1 hour duration in the calculations. The analysis of the results focused on fog events that we defined as significant, that is, events that were observed by both stations in the same time frame. Thus, an event was defined as a fog event when visibility was estimated by the professional observers at Beit Dagan and Ben Gurion Airport to be less than 1 km simultaneously, or, at times where visibility was estimated to be less than 1 km at one station, under the condition that fog was also detected at the other station within a 6 hour time interval from when it was detected at the first station. Figure 2 presents general details regarding the fog events that took place across the experiment site between 1967 and 2017, and particularly, the frequency of fog creation given a certain synoptic condition (Fig. 2a), the total number of fog events occurring per month (Fig. 2b) and the distribution of average visibility estimates at each station (Fig. 2c). It can be seen, then, that most of the fog evets in the experiment area occur under conditions of Red Sea Trough (44%) and Ridge (41%), where the incidence of events in the area peaking between March and June. In the major percentage of fog events (observed by both stations, as defined here) average visibility is lower than 600 meters. Figure 3 shows the total number of radiation fog events (Fig. 3a), advection fog ( Fig. 3b) and the distribution of the total number of events combined divided into three equal periods. (Fig. 3a), number of advection fog events (Fig. 3b), and total number of fog events (Fig. 3c)
divided into 3 equal periods.
From analysis of the data we found that 64% of fog events analyzed had radiation fog characteristics, while 36% had characteristics of advection fog.
We note, in the overall view, that while the incidence of radiation fog has decreased over time, the incidence of advection fog has increased when compared to the first third of the experiment period. We note that the total number of fog events decreased measurably over time.
We focus, then, on this aspect. Figure 4 shows the trend of fog creation frequency and duration. The linear fit approximations of the fog event records are listed at the top right of each panel. It can be seen that the total number of events per year has generally decreased over time (Fig. 4a) and that the total number of hours where fog existed per year has decreased as well. Fig. 4c, which was constructed from Figures 4b and 4a shows the average duration of a single fog event. The linear fit calculated, indicates a more or less constant (an overall very small decreasing trend) in the average duration of each single event.
Discussion
It has been shown that a temperature increase of a few tenths of a degree can strongly affect the visual range (Klemm and Lin, 2015). In particular, the temperature increase (and a decrease of the aerosol concentrations) can lead to increased visual range, i.e. a decrease of fog.
Previous climate change observations have already shown temperature increases of a few tenths of a degree over vast parts of the terrestrial surface (Stocker et al., 2013). Zhang et al. (2005) analyzed data from 75 stations across 15 countries in the Middle East region for the period 1950-2003. Their data analysis showed statistically significant, and spatially coherent, trends in temperature indices pointing to a warming trend in that area. They also reported a significant increase in the frequency of warm days which has been observed towards the 1990s, while, since the 1970s, the frequency of cold days has gradually decreased significantly. More specifically to the experimental area discussed here, recent research conducted on extreme temperature (and precipitation) indices in Israel between 1950 and 2017a period that covers the entire period of research of this workfound that temperatures (specifically, the daily minimum / maximum temperatures) are trending upwards (Yosef et al., 2019).
Due to the relationship between the increase in temperature and the increase in visibility range, it is reasonable to assume that the decrease in fog is driven by climate change (Klemm and Lin, 2015). That being said, we note that this is a general statement, and downscaling it to the specific case reviewed here is non-trivial, and requires future research.
Moreover, the observation stations of this study are located in Israel's central coastal plain, a region with temperate weather, at an elevation of between 30-40 meters above sea level. These days, the area where the stations are located is urban, but includes agricultural fields spread within it.
We note that over the years since the experiments beginning and until the writing of this paper, major changes have occurred in the land surface due to intensive construction in the area, and the region has transformed from one with a more rural character, where building, vehicle and population densities were relatively low, to an area where a major transportation intersection is located, one where population and building densities have, accordingly, dramatically increased over time. We note that the specific location where the measuring station is situated (a sand lot) has not changed meaningfully over the years, however the changes in area land surfaces are clearly apparent.
Importantly, vegetation gave way to concrete and asphalt roads, buildings, and other structuresall surfaces that absorb, rather than reflect, solar energy. As a result, surface temperatures, as well as overall ambient temperatures have risen. Thus, the urbanization process in the area, i.e. the UHI effect is also a probable cause for the temperature increase (Rotem-Mindali et al., 2015), and the meaningful reduction in the creation of fog, as a result.
When mentioning UHI, it is important to note that urbanization influences fog in different ways (Klemm and Lin, 2015). An increase in the UHI effect is associated with air temperature increases especially at night, thus resulting in a decreased tendency for formation of radiation fog, as we also observe in the current research ( Figure 3a). Further, UHI is often associated with decreased water vapor content in the air, which results in the same effect. In rural, or agricultural areas, though, the issue is more complex -Increased temperatures may lead to a decrease in fog creation due to the reduction in RH. On the other hand, enhanced evapotranspiration caused by those higher temperatures may lead to an increase in fog. Regardless, the verification of the process based on meteorological data is extremely challenging, as the temperature changes involved are quite small, and the associated variations of RH unmeasurably so (within the 99% < RH < 100% range). Moreover, prior research has shown that under the assumption of equilibrium conditions, both increase in air temperature, and decrease in concentration of aerosol particles lead to a reduction in development of fog and its intensity. Klemm and Lin (2015) have shown that in their case study, an increase of 0.1 percent in temperature had an equivalent effect to a decrease of 10% in aerosol concentration, where reductions of fog were concerned. If urbanization, as was observed in the experimental area (Fig. 5), is associated with increased air pollution, then fog formation can be enhanced. As comprehensive air pollution measurements for the entire experiment period were not available to us, as part of this research, this aspect was not investigated. A recent research has shown, though, that when urbanization and aerosol-pollution act together, the inhibiting effect of urbanization on fog dominants the much weaker aerosol-promoting effect (Yan et al., 2020).
We note that the literature data as reviewed (e.g. Klemm and Lin, 2015) indicates that, overall, as urbanization increases, decreases in fog occur more frequently than increases, as was also the case here.
Summary
In this paper 5 decades of fog data from Israel's central coastal plain was analyzed.
The measurements indicate a decrease in the incidence of fog creation and a decrease in the frequency of radiation fog when compared to advection fog events. The decreasing fog trends detected here are in line with fog trends that have been widely observed across different parts of the world (Chen et al., (2006); Vautard et al., (2009); Van Schalkwyk (2012)). An in-depth investigation of the possible reasons for the decreasing fog trends in the experimental area is beyond the scope of this work, and is left for future research. However, we have indicated several factors that may have a role in creating the trends we report here.
Naturally, there are uncertainty factors in carrying out the observations. Thus, for example, we note that for the database we used, the measurements were stored every 3 hour interval. It is possible, then, that relatively shorter fog events might have occurred in between these sample times, and therefore were not tallied in this research. Additionally, it is important to note that the instruments measuring the different parameters were updated over time. It is possible that the location of the instruments was changed slightly, that different human observers carried out visibility observations, etc.
The results of this work can form the basis for future research that could be conducted on fog life cycles in the area, and indicate, for the first time, the trend of reductions of fog in this region.
Over the last decade numerous studies point to the potential that lies in the use of data from prevalent technologies and the 'Internet of Things' (IoT) to enhance the ability to measure various environmental phenomena (Overeem et al., 2013;Mass et al., 2014;Harel et al., 2015;Alpert et al., 2016;Price et al., 2018;David, 2019;Kumah et al., 2020), improve weather prediction capabilities (e.g. Kawamura et al., 2017) including fog in particular (e.g. David and Gao, 2016;2018). However, the precise forecasting of this phenomenon remains an unsolved challenge (Koračin, 2017). Achieving better insight into the different mechanisms of fog formation, maintenance, and dissipation may lead to better forecasting capabilities, and, as a result, better capacity to contend with the dangers associated with this phenomenon.
Figure 1 :
1The experiment site situated in the central costal plain of Israel. The asterisks mark the locations of the surface stations, in the vicinity of the city of Tel Aviv. Fog events were determined according to the Israeli Meteorological Service (IMS)
Figure 2 :
2Analysis of fog events between 1967 and 2017. (a) Frequency during different synoptic conditions. (b) Total major fog events per month. (c) Distribution of average visibility estimates for the Beit Dagan station (red) and Ben Gurion (black).To produce graph (c), the average visibility was calculated for each station separately, from the visibility observations taken during each fog event.
Figure 3 :
3Radiation and Advection fog. Number of radiation fog events
Figure 4 :
4Incidence and duration of fog per year for the experimental area. Number of meaningful fog events per year (a), total number of fog event hours in every year (b), average duration of fog event per year.
Figure 5 (
5a) shows a photograph of the experiment area from the early 1960s vs Figure 5 (b) -a photograph of the area from the year 2017.
Figure 5 .
5The experiment area, early 60's (a) vs 2017 (b) (Credit: IMS).
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| sample_122 | 0.6612 | arxiv | |
Regularized Fingerprinting in Detection and Attribution of Climate Change with Weight Matrix Optimizing the Efficiency in Scaling Factor Estimation
Yan Li
Department of Statistics
University of Connecticut
CTU.S.A
Kun Chen
Department of Statistics
University of Connecticut
CTU.S.A
Jun Yan
Xuebin Zhang
Department of Statistics
University of Connecticut
CTU.S.A
Environment and Climate Change Canada
QC, CA
Regularized Fingerprinting in Detection and Attribution of Climate Change with Weight Matrix Optimizing the Efficiency in Scaling Factor Estimation
Measurement errorNonlinear shrinkage estimatorTotal least squares *
The optimal fingerprinting method for detection and attribution of climate change is based on a multiple regression where each covariate has measurement error whose covariance matrix is the same as that of the regression error up to a known scale. Inferences about the regression coefficients are critical not only for making statements about detection and attribution but also for quantifying the uncertainty in important outcomes derived from detection and attribution analyses. When there is no errorsin-variables (EIV), the optimal weight matrix in estimating the regression coefficients is the precision matrix of the regression error which, in practice, is never known and has to be estimated from climate model simulations. We construct a weight matrix by inverting a nonlinear shrinkage estimate of the error covariance matrix that minimizes loss functions directly targeting the uncertainty of the resulting regression coefficient estimator. The resulting estimator of the regression coefficients is asymptotically optimal as the sample size of the climate model simulations and the matrix dimension go to infinity together with a limiting ratio. When EIVs are present, the estimator of the regression coefficients based on the proposed weight matrix is asymptotically more efficient than that based on the inverse of the existing linear shrinkage estimator of the error covariance matrix. The performance of the method is confirmed in finite sample simulation studies mimicking realistic situations in terms of the length of the confidence intervals and empirical coverage rates for the regression coefficients. An application to detection and attribution analyses of the mean temperature at different spatial scales illustrates the utility of the method.
Introduction
Detection and attribution analyses of climate change are critical components in establishing a causal relationship from the human emission of greenhouse gases to the warming of planet Earth (e.g., Bindoff et al., 2013). In climate science, detection is the process of demonstrating that a climate variable has changed in some defined statistical sense without providing a reason for that change; attribution is the process of evaluating the relative contributions of multiple causal factors to a change or event with an assignment of statistical confidence (e.g., Hegerl and Zwiers, 2011). Casual factors usually refer to external forcings, which may be anthropogenic (e.g., greenhouse gases, aerosols, ozone precursors, land use) and/or natural (e.g., volcanic eruptions, solar cycle modulations). By comparing simulated results of climate models with observed climate variables, a detection and attribution analysis evaluates the consistency of observed changes with the expected response, also known as fingerprint, of the climate system under each external forcing.
Optimal fingerprinting is the most widely used method for detection and attribution analyses (e.g., Hasselmann, 1997;Allen and Stott, 2003;Hegerl et al., 2010). Fingerprinting is a procedure that regresses the observed climate variable of interest on the fingerprints of external forcings, and checks whether the fingerprints are found in and consistent with the observed data. The central target of statistical inferences here is the regression coefficients, also known as scaling factors, which scale the fingerprints of external forcings to best match the observed climate change. Historically, the method was "optimal" in the context of generalized least squares (GLS) when the precision matrix of the regression error is used as weight, such that the resulting estimator of the scaling factors have the smallest variances.
It was later recognized that the fingerprint covariates are not observed but estimated from climate model simulations. This leads to an errors-in-variables (EIV) issue, which has been approached by the total least squares (TLS) (Allen and Stott, 2003) with both the response and the covariates "prewhittened" by the covariance matrix of the error. The covariance matrix represents the internal climate variation. In practice, it is unknown and has to be estimated from climate model simulations (Allen and Tett, 1999;Ribes et al., 2013), which is generally handled preliminarily and independently from the regression inference (e.g., Hannart et al., 2014).
Estimating the error covariance matrix in fingerprinting is challenging because the available runs from climate model simulations are small relative to the dimension of the covariance matrix. The dimension of the covariate matrix is often reduced by considering averages over 5-year or 10-year blocks in time and/or over aggregated grid-boxes in space. For example, decadal average over a 110-year period in 25 grid-boxes would lead to a dimension of 275 × 275. The sample size from climate model simulations that can be used is, however, at most a few hundreds. The sample covariance matrix is not invertible when the sample size of climate model simulations is less than its dimension. Earlier methods project data onto the leading empirical orthogonal functions (EOF) of the internal climate variability (Hegerl et al., 1996;Allen and Tett, 1999). More recently, the regularized optimal fingerprinting (ROF) method avoids the projection step by a regularized covariance matrix estimation (Ribes et al., 2009), which is based on the linear shrinkage covariance matrix estimator of Ledoit and Wolf (2004). The ROF method has been shown to provide a more accurate implementation of optimal fingerprinting than the EOF projection method (Ribes et al., 2013).
The uncertainty in estimating the error covariance matrix has important implications in optimal fingerprinting. The optimality in inferences about the scaling factor in optimal fingerprinting was historically based on the assumption that the error covariance matrix is known. The properties of the scaling factor estimator obtained by substituting the error covariance matrix with an estimate have not been thoroughly investigated in the literature.
For example, it is not until recently that the confidence intervals for the scaling factors constructed from asymptotic normal approximation (Fuller, 1980;Gleser, 1981) or bootstrap (Pesta, 2013) were reported to be overly narrow when the matrix is only known up to a scale (DelSole et al., 2019) or completely unknown (Li et al., 2019). A natural, fundamental question is: when the error covariance matrix is estimated, are the confidence intervals constructed using the optimal approach under the assumption of known error covariance matrix still optimal? Since optimality under unknown error covariance matrix is practically infeasible, to be precise, we term fingerprinting for optimal fingerprinting and regularized fingerprinting (RF) for ROF in the sequel.
The contributions of this paper are two-fold. First, we develop a new method to construct the weight matrix in RF by minimizing directly the uncertainty of the resulting scaling factor estimators. The weight matrix is the inverse of a nonlinear shrinkage estimator of the error covariance matrix inspired by Ledoit and Wolf (2017a). We first extend the validity of their nonlinear shrinkage estimator to the context of RF via GLS regression with no EIV.
We show that the proposed method is asymptotically optimal as the sample size of climate model simulations and the matrix dimension go to infinity together with a fixed ratio. When there is EIV, as is the case in practice, we show that the proposed weight is more efficient than the existing weight in RF (Ribes et al., 2013) in terms of the asymptotic variance of the scaling factor estimator when RF is conducted with generalized TLS (GTLS). This is why we refer to the current practice by RF instead of ROF. The second contribution is practical recommendations for assumptions about the structure of the error covariance matrix under which the sample covariance is estimated before any shrinkage in RF based on findings of a comparison study under various realistic settings. An implementation of both linear shrinkage and nonlinear shrinkage estimators is publicly available in an R package dacc (Li et al., 2020) for detection and attribution of climate change.
The rest of this article is organized as follows. After a review of RF in Section 2, we develop the proposed weight matrix and the theoretical results to support the asymptotic performance of proposed method in Section 3. A large scale numerical study assessing the performance of the proposed method is reported in Section 4. In Section 5, we demonstrate the proposed method with detection and attribution analysis on global and regional scales. A discussion concludes in Section 6. The technical proofs of the theoretical results are relegated in the Supplementary Materials.
Regularized Fingerprinting
Fingerprinting takes the form of a linear regression with EIV
Y = p i=1 X i β i + ,(1)X i = X i + ν i , i = 1, . . . , p,(2)
where Y is a N × 1 vector of the observed climate variable of interest, X i is the true but unobserved N ×1 fingerprint vector the ith external forcing with scaling factor β i , is a N ×1
vector of normally distributed regression error with mean zero and covariance matrix Σ,X i is an estimate of X i based on n i climate model simulations under the ith external forcing, and ν i is a normally distributed measurement error vector with mean zero and covariance matrix Σ/n i , and ν i 's are mutually independent and independent of , i = 1, . . . , p. The covariance matrices of ν i 's and only differ in scales under the assumption that the climate models reflect the real climate variation. No intercept is present in the regression because the response and the covariates are centered by the same reference level. The primary target of inference is the scaling factors β = (β 1 , . . . , β p ) .
The "optimal" in optimal fingerprinting originated from earlier practices under two assumptions: 1) the error covariance matrix Σ is known; and 2) X i 's are observed. The GLS estimator of β with weight matrix W iŝ
β(W ) = (X W X) −1 X W Y,
where X = (X 1 , . . . , X p ). The covariance matrix of the estimatorβ(W ) is
V(β(W )) = (X W X) −1 X W ΣW X(X W X) −1(3)
The optimal weight matrix is W = Σ −1 , in which case,β(Σ −1 ) is the best linear unbiased estimator of β with covariance matrix X Σ −1 X. Since Σ is unknown, a feasible version of GLS uses W =Σ −1 , whereΣ is an estimator of Σ obtained separately from controlled runs of climate model simulations.
Later on it was recognized that, instead of X i 's, only their estimatesX i 's are observed and that usingX i 's in place of X i 's leads to bias in estimating β (Allen and Stott, 2003). If Σ is given, the same structure (up to a scale 1/n i ) of the covariance matrices of ν i 's and allows precise pre-whitening of both Y andX i 's . Then the TLS can be applied to the pre-whitened variables. Inferences about β can be based on the asymptotic normal distribution of the TLS estimator of β (Gleser, 1981) or nonparametric bootstrap (Pesta, 2013), as recently studied by DelSole et al. (2019). Similar to the GLS setting, a feasible version of the GTLS procedure relies on an estimator of Σ.
The current practice of fingerprinting consists of two separate steps. First, estimate Σ from controlled runs of climate model simulations under the assumption that the climate models capture the internal variability of the real climate system. Second, use this estimated matrix to pre-whiten both the outcome and covariates in the regression model (1)-(2), and obtain the GTLS estimator of β on the pre-whitened data. Nonetheless, estimation of Σ in the first step is not an easy task. The dimension of Σ is N × N , with N (N + 1)/2 parameters if no structure is imposed, which is too large for the sample size n of available climate model simulations (usually in a few hundreds at most). The sample covariance matrix based on the n runs is a start, but it is of too much variation; when N > n it is not even invertible.
The linear shrinkage method of Ledoit and Wolf (2004) regularizes the sample covariance matrixΣ n to in the form of λΣ n + ρI, where λ and ρ are scalar tuning parameters and I is the identity matrix. This class of shrinkage estimators has the effect of shrinking the set of sample eigenvalues by reducing its dispersion around the mean, pushing up the smaller ones and pulling down the larger ones. This estimator has been used in the current RF practice (Ribes et al., 2009(Ribes et al., , 2013.
Substituting Σ with an estimator introduces an additional uncertainty. The impact of this uncertainty on the properties of resulting ROF estimator has not been investigated when the whole structure of Σ is unknown (Li et al., 2019). The optimality of the optimal fingerprinting in its original sense is unlikely to still hold. Now that the properties of the resulting estimator of β depends on an estimated weight matrix, can we choose this weight matrix estimator to minimize the variance of the estimator of β? The recently proposed nonlinear shrinkage estimator Wolf, 2017a, 2018) has high potential to outperform the linear shrinkage estimators.
Weight Matrix Construction
We consider constructing the weight matrix by inverting a nonlinear shrinkage estimator of Σ (Ledoit and Wolf, 2017b) in the fingerprinting context. New theoretical results are developed to justify the adaptation of this nonlinear shrinkage estimator of Σ to minimize the uncertainty of the resulting estimatorβ of β. Assume that there are n replicates from climate model simulations (usually pre-industrial control runs) that are independent of Y andX i 's. Let Z i , Z 2 , . . . , Z n ∈ R N be the centered replicates so that the sample covariance matrix is computed asΣ n = n −1 n i=1 Z i Z i . Our strategy is to revisit the GLS setting with no EIV first and then apply the result of the GTLS setting to the case under EIV, the same order as the historical development.
GLS
Since the target of inference is β, we propose to minimize the "total variation" of the covariance matrix V(β) of the estimated scale factorsβ(W ) in (3) with respect to W =Σ −1 . Two loss functions are considered that measure the variation ofβ, namely, the summation of the variances ofβ (trace of V(β)) and the general variance ofβ (determinant of V(β)), denoted respectively as L 1 (Σ, Σ, X) and L 2 (Σ, Σ, X). In particular, we have
L 1 (Σ, Σ, X) = Tr (X Σ −1 X) −1 X Σ −1 ΣΣ −1 X(X Σ −1 X) −1 , L 2 (Σ, Σ, X) = Tr(X X) pN p det X Σ −1 ΣΣ −1 X N det −2 X Σ −1 X N ,
where the first loss function directly targets on the trace of V(β(W )) and the second loss function is proportional to the determinant of V(β(W )) (up to a constant scale {Tr(X X)/p} p ).
The theoretical development is built on minimizing the limiting forms of the loss functions as n → ∞ and N → ∞. The special case of p = 1 has been approached by Ledoit and Wolf (2017b). We extend their result to multiple linear regressions with p > 1.
Lemma 1. The loss functions L 1 (Σ, Σ, X) and L 2 (Σ, Σ, X) remain unchanged after orthogonalization of design matrix X via the singular value decomposition.
The proof of Lemma 1 is in Appendix A.
Lemma 1 implies that, without loss of generality, we only need to consider orthogonal designs in the regression model (1). In other words, we may assume that the columns of the design matrix X are such that X i X j = 0 for any i = j.
Consider the minimum variance loss function
L mv (Σ, Σ) = Tr(Σ −1 ΣΣ −1 )/N (Tr(Σ −1 )/N ) 2(4)
derived in Engle et al. (2019). We have the following result.
Theorem 1. As dimension N → ∞ and sample size n → ∞ with N/n → c for a constant c, minimizing lim n,N →∞ L 1 (Σ, Σ, X) or lim n,N →∞ L 2 (Σ, Σ, X) is equivalent to minimizing lim n,N →∞ L mv (Σ, Σ).
The proof for Theorem 1 is presented in Appendix B.
LetΣ n = Γ n D n Γ n be the spectral decomposition of the sample covariance matrixΣ n , where D n = diag(λ 1 , . . . , λ N ) is the diagonal matrix of the eigenvalues and Γ n contains the corresponding eigenvectors. Consider the rotation invariant class of the estimatorsΣ = Γ nDn Γ n , whereD n = diag δ(λ 1 ), . . . , δ(λ N ) for a smooth function δ(·). Then, under some regularity assumptions on the data genration mechanism (Ledoit and Wolf, 2017a,
Assumptions 1-4), we can get the asymptotically optimal estimatorΣ which minimizes the limiting form of proposed two loss functions as n → ∞ and N → ∞.
Let with the shrinkage form of the eigenvalues given by
δ oracle (λ i ) = λ i [πcλ i f (λ i )] 2 + [1 − c − πcλ i H f (λ i )] 2 .(5)
A feasible nonlinear shrinkage estimator (bona fide counterpart of the oracle estimator)
can be based on a kernel estimator of f , which is proposed and shown by Ledoit and Wolf (2017a) to perform as well as the oracle estimator asymptotically. Let c n = N/n, which is a estimator for the limiting concentration ratio c. The feasible nonlinear shrinkage δ(λ i ), i = 1, . . . , N , of the sample eigenvalues is defined as following results for both cases of c n ≤ 1 and c n > 1.
Case 1 If c n ≤ 1, that is, the sample covariance matrix is nonsingular, then
δ(λ i ) = λ i [π N n λ if (λ i )] 2 + [1 − N n − π N n λ i Hf (λ i )] 2 ,
wheref (·) is a kernel estimator of the limiting sample spectral density f , and Hf is the Hilbert transform off . Various authors adopt different conventions to define the Hilbert transform. We follow Ledoit and Wolf (2017a) and apply the same semicircle kernel func-tion and Hilbert transform because of the consistency of the resulting feasible estimator.
Specifically, we havẽ
f (λ i ) = 1 N N j=1 [4λ 2 j h 2 n − (λ i − λ j ) 2 ] + 2πλ 2 j h 2 n , Hf (λ i ) = 1 N N j=1 sgn(λ i − λ j ) [(λ i − λ j ) 2 − 4λ 2 j h 2 n ] + − λ i + λ j 2πλ 2 j h 2 n ,
where h n = n −γ is the bandwidth of the semicircle kernel with tuning parameter γ, and a + = max(0, a). For details on the Hilbert transform and the mathematical formulation of Hilbert transform for commonly used kernel functions, see Bateman (1954).
Case 2 In optimal fingerprinting applications, the case of c n > 1 is more relevant because the number n of controlled runs that can be used to estimate the internal climate variation is often limited, much less than the dimension N of the problem. If c n > 1, we have N − n null eigenvalues. Assume that (λ 1 , . . . , λ N −n ) = 0. In this case, we only consider the empirical cumulative distribution function F N of the nonzero n eigenvalues. From Silverstein (1995), there existing a limiting function F such that lim N,n→∞ F N = F , and it admits a continuous derivative f . The oracle estimator in Equation (5) can be written as
δ oracle (λ i ) = λ i π 2 λ 2 i [f (λ i ) 2 + H f (λ i ) 2 ]
.
Then the kernel approach can be adapted in this case. Letf and Hf be, respectively, the kernel estimator for f and its Hilbert transform H f . The our feasible shrinkage estimator is
δ(0) = 1 π N −n n Hf (0) , i = 1, . . . , N − n, δ(λ i ) = λ i π 2 λ 2 i [f (λ i ) 2 + Hf (λ i ) 2 ] , i = N − n + 1, . . . , N,
where
Hf (0) = 1 − 1 − 4h 2 n 2πnh 2 n N j=N −n+1 1 λ j , f (λ i ) = 1 n N j=N −n+1 [4λ 2 j h 2 n − (λ i − λ j ) 2 ] + 2πλ 2 j h 2 n , Hf (λ i ) = 1 n N j=N −n+1 sgn(λ i − λ j ) [(λ i − λ j ) 2 − 4λ 2 j h 2 n ] + − λ i + λ j 2πλ 2 j h 2 n ,
and h n = n −γ is the bandwidth with tuning parameter γ.
In both cases, the pool-adjacent-violators-algorithm (PAVA) in isotonic regression can be used to ensure the shrunken eigenvalues to be in ascending order. The bandwidth parameter γ can be selected via crossvalidation on the estimated standard deviation of the scaling factors or other information criteria. The feasible optimal nonlinear shrinkage estimator is the resultingΣ MV = Γ nDn Γ n .
GTLS
For the GTLS setting, which is more realistic with EIV, we propose to pre-whiten Y and X i 's byΣ MV and then apply the standard TLS procedure (Gleser, 1981) to estimate β.
The resulting estimator of the β will be shown to be more efficient than that based on pre-whitening with the linear shrinkage estimatorΣ LS (Ribes et al., 2013).
Consider the GTLS estimator of β obtained from prewhitening with a class of regularized covariance matrix estimatorΣ from independent control runs. In the general framework of GTLS, the measurement error vectors usually have the same covariance matrix as the model error vector for the ease of theoretical derivations. This assumption can be easily achived in the OF setting (1)-(2) by multiplying each observed fingerprint vectorX i by √ n i . Therefore, without loss of generality, in the following we assume n i = 1 to simplify the notations. LetX = (X 1 , . . . ,X p ). The GTLS estimator based onΣ iŝ
β(Σ) = arg β min Σ − 1 2 (Y −Xβ) 2 2 1 + β β ,(6)
where a 2 is the 2 norm of vector a. The asymptotic properties ofβ(Σ) are established for a class of covariance matrix estimatorsΣ including bothΣ MV andΣ LS .
Assumption 1. lim N,n→∞ X Σ −1 X/N = ∆ 1 exists, where ∆ 1 is a non-singular matrix.
Assumption 2. lim N,n→∞ Tr(Σ −1 Σ)/N exists and is a positive constant.
Assumption 3. lim N,n→∞ Tr{(Σ −1/2 ΣΣ −1/2 ) 2 }/N = K exists with K > 0.
Remark 1. Assumptions 1 originates from Gleser (1981), which is needed for the consistency ofβ(Σ). Assumptions 2-3 are from Wolf (2018, 2017a). The proof for Lemma 2 is in Appendix C.
The asymptotic normality ofβ(Σ) is established with additional assumptions.
Assumption 4. lim N,n→∞ X Σ −1 ΣΣ −1 X/N = ∆ 2 exists for a non-singular matrix ∆ 2 .
Assumption 5. The regression error and measurement errors ν i 's, i = 1, . . . , p, are mutually independent normally distributed random vectors.
Remark 2. Assumption 4 originates from Gleser (1981) for the asymptotic noramlity of the GTLS estimator. Assumption 5 is commonly used in the context of climate change detection and attribution for mean state climate variables.
Theorem 2. Under Assumptions 1-5, as N, n → ∞ with N/n → c for some c > 0,
√ N (β − β 0 ) D → N (0, Ξ), where Ξ = ∆ −1 1 ∆ 2 + K(I p + β 0 β 0 ) −1 (1 + β 0 β 0 )∆ −1 1 .(7)
The proof of Theorem 2 is in Section C.2 of Appendix C.
The higher efficiency of the resulting estimator for β from the proposed weight matrix in comparison with that from the existing weight is summarized by the following result with proof in Section C.3 of Appendix C.
Theorem 3. Let Ξ(Σ) be the asymptotic covariance matrix in Equation (7) for a rotation invariant estimatorΣ under Assumptions 1-5. Then Tr Ξ(Σ MV ) ≤ Tr Ξ(Σ LS ) .
In our implementation, a 5-fold cross validation is used to select the optimal bandwidth parameter γ ∈ (0.2, 0.5).
Simulation Studies
The finite sample performance of the proposed method in comparison with the existing practice in RF needs to be assessed to make realistic recommendations for detection and attribution of climate change. We conducted a simulation study similar to the setting of a study in Ribes et al. (2013). The observed climate variable of interest is 11 decadal mean temperatures over 25 grid-boxes, a vector of dimension N = 275. Two N ×1 fingerprints were considered, corresponding to the anthropogenic (ANT) and natural forcings (NAT), denoted by X 1 and X 2 , respectively. They were set to the average of all runs from the CNRM-CM5 model as in Ribes et al. (2013). To vary the strength of the signals, we also considered halving X 1 and X 2 . That is, there were two levels of signal-to-noise ratio corresponding to the cases of multiplying each X i , i ∈ {1, 2}, controlled by a scale λ ∈ {1, 0.5}. The true scaling factors were β 1 = β 2 = 1. The distribution of the error vector was multivariate normal MVN(0, Σ). The distribution of the measurement error vector ν i , i ∈ {1, 2}, was MVN(0, Σ/n i ), with (n 1 , n 2 ) = (35, 46) which are the values in the detection and attribution analysis of annual mean temperature conducted in Section 5.
Two settings of true Σ were considered. In the first setting, Σ was an unstructured matrix Σ UN , which was obtained by manipulating the eigenvalues but keeping the eigenvectors of the proposed minimum variance estimate from the same set of climate model simulations as
in Ribes et al. (2013). Specifically, we first obtained the eigen decomposition of the minimum variance estimate, and then restricted the eigenvalues to be equal over each of the 25 gridboxes (i.e., only 25 unique values for the N = 25×11 eigenvalues) by taking averages over the decades at each grid-box. The pattern of the resulting eigenvalues is similar to the pattern of the eigenvalues of a spatial-temporal covariance matrix with variance stationarity and weak dependence over the time dimension. Finally, the eigenvalues were scaled independently by a uniformly distributed variable on [0.5, 1.5], which results in a more unstructured covariance matrix setting similar to the simulation settings in Hannart (2016). In the second setting, Σ was set to be Σ ST whose diagonals were set to be the sample variances from the climate model simulations without imposing temporal stationarity; the corresponding correlation matrix was set to be the Kronecker product of a spatial correlation matrix and a temporal correlation matrix, both with autoregressive of order 1 and coefficient 0.1.
The observed mean temperature vector Y and the estimated fingerprints (X 1 ,X 2 ) were generated from Models (1) Number of control runs n in estimating Σ Scaling factor estim Figure 1: Boxplots of the estimates of the scaling factors in the simulation study based on 1000 replicates. accurate estimation Σ; a higher λ means stronger signal; a more structured Σ means an easier task to estimate Σ. In the case of Σ = Σ UN , the M2 estimates have smaller variations than the M1 estimate, since the eigenvalues were less smooth and, hence, favored the nonlinear shrinkage function. For the case of Σ = Σ ST where the covariance matrix is more structured, both methods estimate the true covariance matrix much more accurately, and the differences between methods are less obvious. More detailed results are summarized in Table D.1 and Table D.2, the latter of which had smaller ensembles in estimating the fingerprints with (n 1 , n 2 ) = (10, 6). The standard deviations of the M2 estimates are over 10% smaller than those of the M1 estimates for both cases.
Confidence intervals are an important tool for detection and attribution analyses. It would be desirable if the asymptotic variance in Theorem 2 can be used to construct confidence intervals for the scaling factors. Unfortunately, it has been reported that the confidence intervals for the scaling factors based onΣ LS have coverage rates lower than, sometimes much lower than, their nominal levels (Li et al., 2019). The under-coverage issue remains for the estimator based onΣ MV . To give confidence intervals with correct coverage rates, Li et al.
(2019) proposed a calibration procedure which enlarges the confidence intervals based on the asymptotic normality of the estimators by an appropriate scale tuned by a parametric bootstrap to achieve the desired coverage rate. We applied this calibration to both M1 and M2 estimators. Figure 2 shows the empirical coverage rates of the 95% confidence intervals after the calibration. The coverage rate of a naive confidence interval could be as low as 70% (not Europe (SEU), where the spatio-temporal correlation structure is more likely to hold.
In each regional analysis, we first constructed observation vector Y from the HadCRUT4 dataset (Morice et al., 2012). The raw data were monthly anomalies of near-surface air temperature on 5 • × 5 • grid-boxes. At each grid-box, each annual mean temperature was computed from monthly temperatures if at least 9 months were available in that year; otherwise, it was considered missing. Then, 5-year averages were computed if no more than 2 annual averages were missing. To reduce the spatial dimension in the analyses, the 5 • × 5 • grid-boxes were aggregated into larger grid-boxes. In particular, the grid-box sizes were 40 • × 30 • for GL and NH, 40 • × 10 • for NH 30-70, 10 • × 20 • for EA, and 10 • × 5 • for NA. For the subcontinent regions, no aggregation was done except for SCA, in which case 10 • × 10 • grid-boxes were used. Details on the longitude, latitude and spatio-temporal steps of each regions after processing can be found in Table 1.
Two external forcings, ANT and NAT, were considered. Their fingerprints X 1 and X 2 were not observed, but their estimatesX 1 andX 2 were averages over n 1 = 35 and n 2 = 46 runs from CIMP5 climate model simulations. The missing pattern in Y was used to mask the simulated runs. The same procedure used to aggregate the grid-boxes and obtain the 5-year averages in preparing Y was applied to each masked run of each climate model under each forcing. The final estimatesX 1 andX 2 at each grid-box were averages over all available runs under the ANT and the NAT forcings, respectively, centered by the average of the observed annual temperatures over 1961-1990, the same center used by the HadCRUT4 data to obtain the observed anomalies.
Estimation of Σ was based on n = 223 runs of 60 years constructed from 47 pre-industrial control simulations of various length. The long-term linear trend was removed separately from the control simulations at each grid-box. As the internal climate variation is assumed to be stationary over time, each control run was first split into non-overlapping blocks of 60 years, and then each 60-year block was masked by the same missing pattern as the Had-CRUT4 data to create up to 12 5-year averages at each grid-box. The temporal stationarity of variance at each grid implies equal variance over time steps at each observing grid-box, which is commonly incorporated in detection and attribution analyses of climate change (e.g., Hannart, 2016). Both M1 and M2 estimates based on linear and nonlinear shrinkage, respectively, were obtained for comparison. Pooled estimation of the variance at each gridbox was considered in each of the shrinkage estimation to enforce the stationary, grid-box specific variance.
Discussion
Optimal fingerprinting as the most commonly used method for detection and attribution analyses of climate change has great impact in climate research. Such analyses are the basis for projecting observationally constrained future climate (e.g., Jones et al., 2016) and esti-q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Figure 3: Estimated signal scaling factors for ANT and NAT required to best match observed 1950 -2010 annual mean temperature for different spatial domains, and the corresponding 95% confidence intervals from different methods. For weight matrix construction, "M1" denotes the linear shrinkage approach and "M2" denotes the minimum variance approach. For confidence interval, the calibration method is used.
mating important properties of the climate system such as climate sensitivity (e.g., Schurer et al., 2018). The original optimality of optimal fingerprinting, which minimizes the uncertainty in the resulting scaling factor estimator, is no longer valid under realistic settings where Σ is not known but estimated. Our method constructs a weight matrix by inverting a nonlinear shrinkage estimator of Σ, which directly minimizes the variation of the resulting scaling factor estimator. This method is more efficient than the current RF practice (Ribes et al., 2013) as evident from the simulation study. Therefore, the lost optimality in fingerprinting is restored to a good extent for practical purposes, which helps to reduce the uncertainty in important quantities such as attributable warming and climate sensitivity.
There are open questions that we have not addressed. It is of interest to further investigate how the asymptotic results under N, n → ∞ and N/n → c can guide the RF practice.
The temporal and spatial resolution that controls N can be tuned in RF practice, which may lead to different efficiencies in inferences and, hence, different results in detection and attribution. Is there an optimal temporal/spatial resolution to obtain the most reliable result? Goodness-of-fit check is an important element in detection and attribution analyses.
The classic approach to check the weighted sum of squared residuals against a chi-squared distribution under the assumption of known Σ is not valid when Σ has to be estimated.
Can a test be designed, possibly based on parametric bootstrap, to take into account of the uncertainty in regularized estimation of Σ? These questions merit future research.
Supplementary Materials
A Sufficiency to Assume Orthogonal Covariates
Consider the singular value decomposition of N × p design matrix X:
X = U DV ,
where U is a N × N orthogonal matrix, D is a N × p matrix with p non-negative singular values on the diagonal, and V is a p × p orthogonal matrix.
Let X * = U D = XV = (X * 1 , . . . , X * p ) and β * = V β = (β * 1 , . . . , β * p ). The columns of X * are orthogonal. The linear regression can be expressed as
Y = p i=1 X * i β * i + . The estimator of β * isβ * = (X * Σ −1 X * ) −1 X * Σ −1 Y = (V X Σ −1 XV ) −1 V X Σ −1 Y = V (X Σ −1 X) −1 X Σ −1 Y
and the corresponding covariance matrix is
V(β * ) = V (X Σ −1 X) −1Σ−1 ΣΣ −1 X(X Σ −1 X) −1 V.
The orthogonality of V ensures that Tr(V(β)) = Tr(V(β * ) and det(V(β)) = det(V(β * ).
Therefore, we only need to consider the orthogonal design in the regression model. In other words, we may assume that the columns of the design matrix have columns such that X i X j = 0 for any i = j.
B Justification of Method M2 in the GLS Case
It is critically important to estimate the covariance matrix precisely as the covariance matrix ofβ depends onΣ. In the estimation of the covariance matrix, an important question is how to quantify the quality of the covariance matrix estimator. We use loss functions to measure the quality of the covariance matrix estimator. For example, one loss function is the Frobenius norm of the bias of the estimator
L(Σ, Σ) = Σ − Σ F ,
and another loss function is Stein's loss
L(Σ, Σ) = Tr(ΣΣ −1 ) − log det(ΣΣ −1 ) − N,
which is the Kullback-Leibler divergence under the normal assumption.
B.1 Minimum Variance Loss Function
Considering the purpose of the fingerprinting, we construct a loss function directly related to the variance of the scaling factor estimator. In other words, we minimize the summation of the variances of the estimated scaling factors
L 1 (Σ, Σ, X) = Tr((X Σ −1 X) −1 X Σ −1 ΣΣ −1 X(X Σ −1 X) −1 ).
From the random matrix theory (Marcenko and Pastur, 1967), we have the following results under the assumption that all limiting forms exist. Consider an N × 1 random vector x = (x 1 , . . . , x N ) whose entries are independent and identically distributed with mean zero, positive variance, and finite 12th moment. Let A be a given N ×N matrix. Then there exists a constant K > 0 independent of N and x such that (Ledoit and Péché, 2011;Silverstein and Bai, 1995) E|x Ax − Tr(A)| 6 ≤ K A 6 N 3 ,
or E|x Ax/N − Tr(A)/N | 6 ≤ K A 6 N −3 ,
where A is the spectral norm of A. In other words, if A < C for some constant C, then as N → ∞,
x Ax/N − Tr(A)/N a.s. → 0.
Similarly, for two independent random vector x and y,
x
Ay N = (x + y) A(x + y) 2N − x Ax 2N − y Ay 2N a.s. → 0. Now let X = (x 1 , x 2 , .
. . x p ) be an N × p matrix with independent columns. Then, for
any N × N matrix A with A < C, the p × p matrix X AX N − Tr(A) N I p a.s. → 0,
where the righthand side is a p×p matrix of zeroes. In other words, X AX/N and Tr(A)I p /N have the same limit.
In optimal fingerprinting, letΣ n be the sample covariance matrix estimated from ensemble runs representing the internal climate variation. Suppose that the eigendecomposition ofΣ n isΣ n = Γ n D n Γ n , where D n = diag(λ 1 , . . . , λ N ) is the diagonal matrix of the eigenvalues and Γ n contains the corresponding eigenvectors. Consider the rotation invariant class of the estimatorsΣ = Γ nDn Γ n , whereD n = diag(δ(λ i )), i = 1, 2, . . . , N for a smooth function δ(·).
Under the same Assumptions 1-3 of the main text, we have both Σ −1 and Σ −1 ΣΣ −1 bounded. Then the assumptions of almost sure convergence are satisfied.
Consider the loss functioñ
L 1 (Σ, Σ, X) = Tr(X X) p 2 L 1 (Σ, Σ, X) = Tr(X X) p 2 Tr((X Σ −1 X) −1 X Σ −1 ΣΣ −1 X(X Σ −1 X) −1 ) = Tr(X X) p 2 N Tr X Σ −1 X N −1 X Σ −1 ΣΣ −1 X N X Σ −1 X N −1 .
Under the orthogonality assumption of X, Tr(X X)/(pN ) a.s.
→ 1. Therefore, we can consider a loss function with the same limit,
L(Σ, Σ) = 1 p Tr Tr(Σ −1 ) N I p −1 Tr(Σ −1 ΣΣ −1 ) N I p Tr(Σ −1 ) N I p −1 = Tr(Σ −1 ΣΣ −1 )/N (Tr(Σ −1 )/N ) 2 ,
which has the same form as what Ledoit and Wolf (2017b) got. We have, as N → ∞,
L(Σ, Σ) −L 1 (Σ, Σ, X) a.s. → 0.
B.2 Minimum General Variance Loss Function
Instead of considering the trace, we can use the determinant of V(β) as the objective loss function. Then the loss function is
L 2 (Σ, Σ, X) = det((X Σ −1 X) −1 X Σ −1 ΣΣ −1 X(X Σ −1 X) −1 ) = det(X Σ −1 ΣΣ −1 X) det(X Σ−1 X) 2 .
It is asymptotically equivalent to loss functioñ
L 2 (Σ, Σ, X) = Tr(X X) p p L 2 (Σ, Σ, X) = Tr(X X) pN p det X Σ−1 ΣΣ −1 X N det X Σ−1 X N 2 .
Similar to the minimum variance loss function, we can consider the loss function with the same limiting form:
L(Σ, Σ) = det Tr(Σ −1 ) N I p −1 Tr(Σ −1 ΣΣ −1 ) N I p Tr(Σ −1 ) N I p −1 = Tr(Σ −1 ΣΣ −1 )/N (Tr(Σ −1 )/N ) 2 p .
In other words, as N → ∞,
L(Σ, Σ) −L 2 (Σ, Σ, X) a.s. → 0.
That is, minimizing the limiting forms of two loss functions are asymptotically equivalent to minimize the limiting form of
L mv (Σ, Σ) = Tr(Σ −1 ΣΣ −1 )/N (Tr(Σ −1 )/N ) 2 .
This concludes the proof of Theorem 1 of the main text.
N −1 W = δI p+1 + (I p , β 0 ) ∆ 1 (I p , β 0 ), (C.8)
which is in the same form of Lemma 3.1 in Gleser (1981). Consider the eigen decomposition of the matrix W = GDG , where D = diag(d 1 , . . . , d p , d p+1 ), and the (p + 1) 2 matrix G is partitioned as
G = G 11 G 12 G 21 G 22
with p×p matrix G 11 . Then following the results of Lemma 3.3 by Gleser (1981), (G 11 , G 21 ) converges to the eigenvectors corresponding to the p largest eigenvalues of the limiting matrix of δI p+1 + (I p , β 0 ) ∆ 1 (I p , β 0 ), denoted by (H 11 , H 21
= I p β 0 ψ, H 21 H −1 11 = β 0 .
The estimator from Equation (6)
C.2 Proof of Theorem 2 of the Main Text
Proof. In the context of general asymptotics, i.e., N, n → ∞ with fixed ratio, consider the eigendecomposition of matrixΣ −1/2 ΣΣ −1/2 = U ΛU , where Λ = diag(λ i ) is the diagonal matrix of eigenvalues, and U is the corresponding matrix of eigenvectors. Let
Y * = U Σ − 1 2 Y, X * = U Σ − 1 2 X, * = U Σ − 1 2 , X * = U Σ − 1 2X , V * = U Σ − 1 2 V. (C.9)
Then from Equation (6) of the main text, the generalized total least squares estimatorβ solves equation
S(β) =X * (y * −X * β) N + β y * −X * β 2 F N (1 + β β) = 0,
where S(β) = (S 1 (β), . . . , S p (β)) is a p dimensional vector. By Taylor's theorem there exists a series of β * j on the line segment betweenβ and β 0 for j = 1, . . . , p such that S j (β) = S j (β 0 ) + [∇S j (β * j )] (β − β 0 ) = 0, j = 1, 2, ..., p S(β) = S(β 0 ) + H(β − β 0 ) = 0, H = (∇S 1 (β * 1 ), . . . , ∇S p (β * p )).
It follows that
H √ N (β − β 0 ) = − √ N S(β 0 ) = − 1 √ N N i=1 ( * i − v * i β 0 )(x * i + v * i ) + β 0 ( * i − v * i β 0 ) 2 (1 + β 0 β 0 ) := − 1 √ N N i=1 f i (β 0 ),
where for i = 1, . . . , N , * i is the ith element of vector , v * i is the ith row vector of V * and
x * i is the ith row vector of X * .
From Assumption 5 in the main text and Equation (C.9), * i ∼ N (0, λ i ), v * i ∼ N (0, λ i I p ), and f i (β 0 ) are mutually independent vectors with finite covariance matrices
V(f i (β 0 )) = λ i x * i x * i (1 + β 0 β 0 ) + λ 2 i (I p + I p β 0 β 0 + 2β 0 β 0 ) − 3λ 2 i β 0 β 0 = [λ i x * i x * i + λ 2 i (I p + β 0 β 0 ) −1 ](1 + β 0 β 0 ), such that lim N →∞ 1 N N i=1 V(f i (β 0 )) = ∆ 2 + K(I p + β 0 β 0 ) −1 (1 + β 0 β 0 ).
Then from Lemma 4.1 of Gleser (1981) and Assumption 3 and 4 of the main text,
√ N S(β 0 ) D → M V N (0, Ξ 1 ), where Ξ 1 = ∆ 2 + K(I p + β 0 β 0 ) −1 (1 + β 0 β 0 ).
It remains to show that as N → ∞,
H = (∇S 1 (β * 1 ), . . . , ∇S p (β * p )) P → ∆ 1 . (C.10)
Consider the derivative of the score function S(β) at any value of β
∇S(β) = −X * X * N + y * −X * β 2 F N (1 + β β) I p + β ∂ y * −X * β 2 F /{N (1 + β β)} ∂β = −X * X * N + y * −X * β 2 F N (1 + β β) I p + β{S(β)} 1 + β β . Since S(β) → 0 as N → ∞ and β P → β 0 , we have lim N →∞,β→β 0 ∇S(β) = lim N →∞,β→β 0 −X * X * N + y * −X * β 2 F N (1 + β β) I p = −∆ 1 − lim N →∞ Tr(Σ −1 Σ) N I p + lim N →∞ Tr(Σ −1 Σ) N I p + lim N →∞,β→β 0 (β − β 0 ) ∆ 1 (β − β 0 ) (1 + β β) I p = −∆ 1 .
Thus from the Lemma 2 of the main text and the fact that {β * j } is a sequence on the line segment betweenβ and β 0 for j = 1, . . . , p, Equation (C.10) holds. With this, we complete the proof of Theorem 2.
C.3 Proof of Theorem 3 of the Main Text
Proof. Here we sketch the proof in the context of optimal fingerprinting. More rigorous derivations are to be established for the more general setting. As mentioned in Section 3.2 of the main text, without loss of generality, we adjust the Model (2) to make the covariance matrix of the errors in the covariartes and in the response the same. Consider model
Y = p i=1 X * i β * i + , X * i = X * i + ν * i , i = 1, . . . , p,
where ν * i is a normally distributed measurement error vector with mean zero and covariance matrix Σ/n i . Here for the ease of illustration, we consider n 1 = . . . = n p = n 0 . Usually in the above model, the magnitudes of fingerprints are comparable to the noise in the sense that the values of Tr{(X * ) X * } and Tr(Σ) are comparable, i.e., Tr{(X * ) X * }/p Tr(Σ) = O(1)
as N → ∞.
LetX i = √ n 0X * i , X i = √ n 0 X * i , ν i = √ n 0 ν * i and β i = β * i / √ n 0 .
Then the model can be rewritten as
Y = p i=1 X i β i + , (C.11) X i = X i + ν i , i = 1, . . . , p, (C.12)
which is exactly in the form of Models (1)-(2) of the main text with n i = 1. Then the theoretical results in Section 3.2 of the main text are directly applied to the adjusted model.
The coefficient estimations and corresponding variance estimations of the original model can be easily obtained from the results of above adjusted model. That is, in the context of optimal fingerprinting, the original model is equivalent to fit models with relative large magnitudes of fingerprints X i and small values of true coefficients β 0 .
Consider the trace of asymptotic covariance matrix for the estimated coefficient vector
in Model (C.11) given by
Tr(Ξ) = Tr(∆ −1 1 ∆ 2 + K(I p + β 0 β 0 ) −1 (1 + β 0 β 0 )∆ −1 1 ) (C.13) = Tr(∆ −1 1 ∆ 2 ∆ −1 1 ) + (1 + β 0 β 0 ) Tr(∆ −1 1 K(I p + β 0 β 0 ) −1 ∆ −1 1 ) (C.14)
from the Theorem 2 of the main text.
The first term Tr(∆ −1 1 ∆ 2 ∆ −1 1 ) on the right hand side of (C.13) is the same as the loss function proposed in Appendix B.1. In the context of general asymptotics, i.e., N, n → ∞ with fixed ratio, the first term is equivalent to N p 2 Tr(X X)
Tr(Σ −1 ΣΣ −1 )/N (Tr(Σ −1 )/N ) 2 ,
as X AX/N is asymptotically equivalent to {Tr(A)I p /N }{Tr(X X)/N p} for properly defined matrices X and A (See Appendix B.1).
As for the second term (1 + β 0 β 0 ) Tr(∆ −1 1 K(I p + β 0 β 0 ) −1 ∆ −1 1 ), we need to show that it is dominated by the first term. Given the information on the magnitudes of fingerprints X and coefficients β 0 from the above illustrations, with appropriate large choice for the value of n 0 (which is fairly reasonable in real fingerprinting studies), the small values of β 0 can be omitted in the second term. Then the second term can be approximated by Tr(∆ −1 1 K∆ −1 1 ).
We further note that K = lim N,n→∞ Tr{(Σ −1/2 ΣΣ −1/2 ) 2 }/N and Tr{(Σ −1/2 ΣΣ −1/2 ) 2 }/N ≤ {Tr(Σ −1 ΣΣ −1 ) Tr(Σ)}/N . Then we have in the general asymptotics
Tr(∆ −1 1 K∆ −1 1 ) ≤ N 2 p 3 Tr(X X) 2 {Tr(Σ −1 ΣΣ −1 ) Tr(Σ)}/N (Tr(Σ −1 )/N ) 2 = N p 2 Tr(X X) {Tr(Σ −1 ΣΣ −1 )}/N (Tr(Σ −1 )/N ) 2 Tr(Σ) Tr(X X)/p ,
where Tr(Σ)/(Tr(X X)/p) = O(1/n 0 ) as N → ∞ based on the adjustment in Model (C.11).
That is, with fairly large value of the number of climate simulations to obtain the estimated fingerprintsX i , the second term on the right hand side of (C.13) can be dominated by the first term, i.e., as N → ∞ we have
(1 + β 0 β 0 ) Tr(∆ −1 1 K(I p + β 0 β 0 ) −1 ∆ −1 1 ) ≤ δ Tr(∆ −1 1 ∆ 2 ∆ −1 1 ),
for an arbitrary small value δ with large enough magnitude of X i in Model (C.11), i.e., large enough number of climate simulations for computing the fingerprints in the original model.
Thus the proposed covariance matrixΣ MV which is the optimal choice regarding the first term in general asymptotics is expected to outperform the linear shrinkage estimatorΣ LS in the sense that
Tr Ξ(Σ MV ) ≤ Tr Ξ(Σ LS ) ,
which is consistent with the fact that as the number of climate simulations to estimate the fingerprints becomes larger, the effects of measurement error diminish.
This completes the proof.
D Detailed Results on Simulation Studies
The results of simulation studies in Section 4 of the main text are detailed in Table D Table D.2: Scaling factor estimates and 95% confidence interval. Two structures of covariance matrix is considered: Σ UN for proposed shrinkage estimator from ensemble simulations and Σ ST for separable spatio-temporal covariance matrix. λ is the scale to control the signalto-noise ratio. Error terms are generated from multivariate normal distribution. Number of ensembles for two forcings are n 1 = 10 and n 2 = 6. Two constructions of weight matrix are compared. "M1" denote for linear shrinkage estimator and "M2" denote for proposed approach. Existing formula-based method (N) and calibration method (CB) are used to construct 95% confidence intervals. Bias and standard deviation (SD × 100) of scaling factors and average length of confidence intervals (CIL) and corresponding empirical rate (CR) from 1000 replicates are recorded. Figure D.1: Calibrated 95% confidence intervals for the scaling factors in the simulation study based on 1000 replicates. The numbers of runs for two forcings are n 1 = 10 and n 2 = 6 respectively.
F
N be the empirical cumulative distribution function of sample eigenvalues. Silverstein (1995) showed that the limiting form F = lim N,n→∞ F N exists under the same assumptions. The oracle optimal nonlinear shrinkage estimator minimizing the limiting form of proposed loss function under general asymptotics depends only on the derivative f = F of F and its Hilbert transform H f , and the limiting ratio c of N/n (Ledoit and Wolf, 2017a),
the average of the variances of the components of the pre-whitened error vectors converge to positive constant. For the class of rotation invariant estimators defined in Ledoit and Wolf (2017b,a), which includes bothΣ MV andΣ LS , Assumptions 2 and 3 are satisfied. Lemma 2. Under Assumptions 1-3,β(Σ) P → β 0 , as N, n → ∞ with a N/n → c for some c > 0.
-(2). The control runs used to estimate Σ were generated from MVN(0, Σ) with sample size n ∈ {50, 100, 200, 400}. For each replicate, the two GTLS estimators of β in Theorem 3 were obtained. For each configuration, 1000 replicates were run.
Figure 1
1displays the boxplots of the estimates of the ANT scaling factor β 1 from the two TGLS approaches based on pre-whitening withΣ LS (denoted as M1) andΣ MV (denoted as M2) and, respectively. Both estimators appear to recover the true parameter values well on average. The variations of both estimators are lower for larger n, higher λ, and more structured Σ (the case of Σ ST ). These observations are expected. A larger n means more
Σ 5 ΣΣFigure 2 :
52Setting 1: Σ UN , λ=0.Setting 1: Σ UN , λ=1 Σ Setting 2: Σ ST , λ=0.5 Σ Setting 2: Σ ST , Setting 1: Σ UN , λ=0.5 Σ Setting 1: Σ UN , λ=1 Σ Setting 2: Σ ST , λ=0.5 Σ Setting 2: Σ ST , Calibrated 95% confidence intervals for the scaling factors in the simulation study based on 1000 replicates.shown). After the calibration, the coverage rates are much closer to the nominal levels. The agreement is better for larger n and more structured Σ. The calibrated confidence intervals from M2 are about 10% shorter to those from M1 overall in both settings of true Σ, except for the case of Σ = Σ UN and sample size n = 50 where the confidence intervals suffer from under-coverage issue..5 Fingerprinting Mean Temperature ChangesWe apply the proposed approach to the detection and attribution analyses of annual meantemperature of 1951-2010 at the global (GL), continental, and subcontinental scales. The continental scale regions are Northern Hemisphere (NH), NH midlatitude between 30 • and 70 • (NHM), Eurasia (EA), and North America (NA), which were studied in (Zhang et al., 2006). The subcontinental scale regions are Western North American (WNA), Central North American (CNA), Eastern North American (ENA), southern Canada (SCA), and southern
Figure 3
3summarizes the GTLS estimates of the scaling factorsβ 1 andβ 2 for the ANT and NAT forcings, respectively. The estimates from pre-whitening weight matrix Σ LS and Σ MV are denoted again as M1 and M2, respectively. The 95% confidence intervals were obtained with the calibration approach ofLi et al. (2019). The point estimates from M1 and M2 are similar in all the analysis. The confidence intervals from the M2 method are generally shorter than those from the M1 method in the analyses both at continental and subcontinental scale. More obvious reduction in the confidence interval lengths is observed at the subcontinental scales, e.g., the ANT scaling factor in EA/NA/SCA and the NAT scaling factor in NA/WNA/SCA. This may be explained by that signals at subcontinental scale are weaker and that the error covariance matrix has non-smooth eigenvalues that form some clustering patterns due to weak temporal dependence, as suggested by the simulation study. Although the detection and attribution conclusions based on the confidence intervals remain the same in most cases, the shortened confidence intervals means reduced uncertainty in the estimate of the attributable warming(Jones et al., 2013) and other quantities based on detection and attribution analysis, such as future climate projection and transient climate sensitivity(Li et al., 2019).
The results are direct extensions of those in Gleser (1981), we only briefly sketch the proof. Consider the observed data matrixà =Σ − 1 2 [X, Y ] which is obtained by binding the columns ofX and Y . Under the Assumption 1, 2 and 3, let W =à à and δ = lim N →∞ Tr(Σ −1 Σ)/N , we have lim N →∞
is given byβ = {G 21 G −1 11 } = −G 12 /G 22 . With the above results, we haveβ P → β 0 , as N, n → ∞ with N/n → c > 0.
. 1 ,
1Table D.2 and Figure D.1.
Table 1 :
1Summaries of the names, coordinate ranges, ideal spatio-temporal dimensions (S and T '), and dimension of observation after removing missing values of the 5 regions analyzed in the study.Acronym Regions
Longitude Latitude Grid size S T n
( • E)
( • N) (1 • × 1 • )
Global and Continental Regions
GL
Global
−180 / 180 −90 / 90 40 × 30 54 11 572
NH
Northern Hemisphere
−180 / 180 0 / 90 40 × 30 27 11 297
NHM
Northern Hemisphere 30 • N to 70 • N −180 / 180 30 / 70 40 × 10 36 11 396
EA
Eurasia
−10 / 180 30 / 70 10 × 20 38 11 418
NA
North America
−130 / −50 30 / 60 10 × 5 48 11 512
Subcontinental Regions
WNA
Western North America
−130 / −105 30 / 60
5 × 5 30 11 329
CNA
Central North America
−105 / −85 30 / 50
5 × 5 16 11 176
ENA
Eastern North America
−85 / −50 15 / 30
5 × 5 21 11 231
SCA
Southern Canada
−110 / −10 50 / 70 10 × 10 20 11 220
SEU
South Eupore
−10 / 40
35 / 50
5 × 5 30 11 330
Table D .
D1: Scaling factor estimates and 95% confidence interval. Two structures of covariance matrix is considered: Σ UN for proposed shrinkage estimator from ensemble simulations and Σ ST for separable spatio-temporal covariance matrix. λ is the scale to control the signalto-noise ratio. Error terms are generated from multivariate normal distribution. Number of ensembles for two forcings are n 1 = 35 and n 2 = 46. Two constructions of weight matrix are compared. "M1" denote for linear shrinkage method and "M2" denote for proposed approaches. Existing formula-based method (N) and calibration method (CB) are used to construct 95% confidence intervals. Bias and standard deviation (SD × 100) of scaling factors and average length of confidence intervals (CIL) and corresponding empirical rate (CR) from 1000 replicates are recorded.ANT
NAT
N
CB
N
CB
size method Bias
SD CIL
CR CIL
CR Bias
SD CIL
CR CIL
CR
Σ Setting 1: Σ UN ; SNR λ = 0.5
50
M1
0.02 19.0 0.41 69.8 0.53 82.0
0.01 57.0 1.47 78.5 1.89 89.9
M2
0.02 17.3 0.38 69.2 0.55 84.7
0.01 49.7 1.23 76.3 1.79 92.6
100 M1
0.01 13.6 0.36 76.8 0.47 89.9 -0.02 36.9 1.12 85.8 1.46 94.0
M2
-0.00
9.7 0.29 83.4 0.40 97.0 -0.02 26.8 0.81 86.1 1.13 95.6
200 M1
0.00
9.0 0.30 89.4 0.39 96.2 -0.01 24.4 0.87 92.4 1.08 97.5
M2
-0.00
6.7 0.23 91.3 0.26 95.4 -0.01 18.7 0.64 89.1 0.76 94.8
400 M1
0.00
6.1 0.26 93.7 0.30 96.7 -0.01 18.9 0.72 93.2 0.83 97.0
M2
-0.00
5.6 0.20 93.2 0.22 94.0 -0.00 16.1 0.57 92.1 0.64 94.3
Σ Setting 1: Σ UN ; SNR λ = 1
50
M1
0.00
9.0 0.20 71.9 0.25 80.7 -0.01 20.4 0.63 87.2 0.73 92.4
M2
0.00
8.5 0.18 72.5 0.26 83.9 -0.00 19.2 0.55 80.9 0.68 89.6
100 M1
0.00
6.6 0.18 79.8 0.23 90.7 -0.01 14.8 0.51 91.0 0.59 96.2
M2
0.00
4.5 0.14 85.6 0.19 96.5 -0.01 12.0 0.38 86.9 0.46 94.6
200 M1
0.00
4.5 0.15 88.6 0.19 95.9 -0.00 10.2 0.41 95.4 0.46 97.5
M2
0.00
3.3 0.12 92.1 0.13 95.6
0.00
8.7 0.31 93.2 0.35 95.9
400 M1
0.00
3.2 0.13 94.0 0.14 96.5 -0.00
8.3 0.34 95.6 0.37 96.7
M2
0.00
2.8 0.10 92.4 0.11 94.0 -0.00
7.8 0.28 91.3 0.30 95.4
Σ Setting 2: Σ ST ; SNR λ = 0.5
50
M1
-0.00
3.2 0.10 87.7 0.11 91.8
0.00
8.7 0.33 91.8 0.39 96.7
M2
0.00
3.1 0.09 85.6 0.11 91.0
0.00
8.5 0.30 89.9 0.35 95.1
100 M1
-0.00
2.2 0.08 93.2 0.10 96.7
0.00
7.1 0.26 91.3 0.30 95.6
M2
-0.00
2.0 0.07 91.6 0.08 95.6
0.00
7.0 0.23 87.7 0.26 91.6
200 M1
-0.00
1.6 0.07 95.6 0.08 97.3
0.00
5.9 0.22 94.0 0.25 96.5
M2
-0.00
1.6 0.06 94.0 0.06 95.4
0.00
5.6 0.19 90.5 0.21 93.7
400 M1
-0.00
1.5 0.06 94.8 0.06 96.5
0.00
5.1 0.19 91.0 0.21 93.7
M2
-0.00
1.4 0.05 92.4 0.05 93.5 -0.00
4.8 0.17 88.8 0.18 90.7
Σ Setting 2: Σ ST ; SNR λ = 1
50
M1
-0.00
1.6 0.05 84.2 0.06 90.5
0.00
4.4 0.16 93.5 0.18 94.8
M2
-0.00
1.6 0.04 80.7 0.05 89.6
0.00
4.5 0.15 90.2 0.16 91.6
100 M1
-0.00
1.1 0.04 92.4 0.05 97.3
0.00
3.2 0.13 95.4 0.14 97.8
M2
-0.00
1.0 0.04 89.4 0.04 95.4
0.00
3.2 0.11 92.6 0.12 95.9
200 M1
-0.00
0.8 0.03 94.0 0.04 97.0
0.00
2.8 0.11 94.8 0.12 96.7
M2
0.00
0.7 0.03 93.7 0.03 95.4
0.00
2.7 0.10 92.6 0.10 94.6
400 M1
0.00
0.7 0.03 96.7 0.03 97.5
0.00
2.3 0.09 95.9 0.10 97.8
M2
0.00
0.6 0.03 95.4 0.03 95.4
0.00
2.3 0.08 92.4 0.09 94.6
Σ Setting 1: Σ UN , λ=0.5 Σ Setting 1: Σ UN , λ=1 Σ Setting 2: Σ ST , λ=0.5 Σ Setting 2: Σ ST , λ=1Number of control runs n in estimating Σ Average length of CIANT
NAT
N
CB
N
CB
size method Bias
SD CIL
CR CIL
CR Bias
SD CIL
CR CIL
CR
Σ Setting 1: Σ UN ; SNR λ = 0.5
50
M1
0.00 24.6 0.53 74.9 0.71 90.7 -0.00 130.9 2.08 66.8 3.07 85.8
M2
0.00 22.8 0.47 71.9 0.72 92.6
0.05 115.2 1.77 64.9 3.22 92.1
100 M1
-0.00 17.4 0.44 82.3 0.59 95.1
0.06
97.1 1.90 70.0 2.90 90.7
M2
-0.00 11.5 0.34 86.4 0.50 98.1
0.02
53.3 1.29 76.6 2.28 94.6
200 M1
0.01 11.4 0.36 89.1 0.47 96.7
0.03
47.0 1.37 83.7 2.02 94.6
M2
0.00
7.4 0.27 92.1 0.32 95.6
0.00
29.9 0.91 88.8 1.24 97.5
400 M1
0.00
7.5 0.30 94.3 0.35 97.3
0.02
30.5 1.09 90.5 1.41 96.2
M2
0.00
6.5 0.23 91.8 0.25 93.7
0.01
21.3 0.79 92.4 0.95 96.2
Σ Setting 1: Σ UN , λ=0.5
Σ Setting 1: Σ UN , λ=1
Σ Setting 2: Σ ST , λ=0.5
Σ Setting 2: Σ ST , λ=1
50
100
200
400 50
100
200
400 50
100
200
400 50
100
200
400
85
90
95
100
Coverage rate
50
100
200
400
50
100
200
400
50
100
200
400
50
100
200
400
0.03
0.04
0.05
0.06
0.06
0.08
0.10
0.12
0.15
0.20
0.25
0.30
0.3
0.4
0.5
0.6
0.7
Method
M1
M2
. Σ Setting. Σ ST2Σ Setting 2: Σ ST ;
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| sample_149 | 0.805 | arxiv | |
Learning Inter-Annual Flood Loss Risk Models From Historical Flood Insurance Claims and Extreme Rainfall Data
Joaquin Salas
CICATA Querétaro
Instituto Politécnico Nacional
Cerro Blanco 141
Colinas del Cimatario
QuerétaroQuerétaroMéxico. 76090
Earth, Atmospheric and Planetary Sciences
Earth Signals and Systems Group
Massachusetts Institute of Technology
77 Massachusetts Avenue02139-4307CambridgeMA
Anamitra Saha
Earth, Atmospheric and Planetary Sciences
Earth Signals and Systems Group
Massachusetts Institute of Technology
77 Massachusetts Avenue02139-4307CambridgeMA
Sai Ravela
Earth, Atmospheric and Planetary Sciences
Earth Signals and Systems Group
Massachusetts Institute of Technology
77 Massachusetts Avenue02139-4307CambridgeMA
Learning Inter-Annual Flood Loss Risk Models From Historical Flood Insurance Claims and Extreme Rainfall Data
1Generative Adversarial NetworksExtreme Gradient BoostingGaussian ProcessesFeature SelectionFlood LossNFIP datasetBias CorrectionNatural Hazards
Flooding is one of the most disastrous natural hazards responsible for substantial economic losses. A predictive model for flood-induced financial damages is helpful for many applications, such as climate change adaptation planning and insurance underwriting. This research assesses the predictive capability of regressors constructed on the National Flood Insurance Program (NFIP) dataset using neural networks (Conditional Generative Adversarial Networks), decision trees (Extreme Gradient Boosting), and kernel-based regressors (Gaussian Process). The assessment highlights the most informative predictors for regression. A Burr distribution with a bias correction scheme to increase the regressor's predictive capability effectively enables inference for claim amount distributions. Aiming to study the impact of physical variables, we incorporate Daymet rainfall estimation to NFIP as an additional predictor. A study of the coastal counties in the eight US South-West states resulted in an R 2 = 0.807. Further analysis of 11 counties with a significant number of claims in the NFIP dataset reveals that Extreme Gradient Boosting provides the best results, that bias correction significantly improves the similarity with the reference distribution, and that adding the rainfall predictor strengthens the regressor performance.
Introduction
Between 1998 and 2017, climate-related disasters caused economic losses of USD 2,245 trillion, affecting an estimated 4.4 billion people (CRED, 2018). While 43.4% of the disaster events corresponded to flooding, making them the most significant natural hazard to people's lives and properties (Hallegatte et al., 2016), the expectation is that the cost associated with them will grow. In its latest assessment, the United Nations (UN) Intergovernmental Panel on Climate Change (IPCC) (2021) concludes that the responsibility for climate change resides in human activity. Furthermore, it notices that nothing is arresting the planet from warming 1.5 • C above pre-industrial levels in the next two decades, not even stopping greenhouse gas emissions right now. As a result, we anticipate more significant weather events, including extreme droughts, heatwaves, and floods (Frame et al., 2020). Therein lies the need to improve flood loss risk modeling to enable rapid, up-to-date, and reliable projections for adaptation and mitigation strategies, reduce human vulnerability, and advance sustainable decision-making.
Even at a shorter time scale, for example, underwriting insurance at interannual timescales, it has been argued that it is essential to account for climate change 1 that has already occurred. This paper's approach to the problem involves learning an adaptive flood loss model from historical claims and meteorological data. As time evolves, so does the model; thus, a static model does not forecast the distant future. Results indicate that the dynamic data-driven modeling strategy is quite effective at short interannual horizons. At longer time horizons, e.g., decadal time scales, using numerical climate model projections is arguably essential for modeling flood loss risk.
In September 1965, Hurricane Betsy hit the US on the coast of Louisiana after traveling around the Florida peninsula, where it caused catastrophic damage in the Florida Keys (Perkins and Enos, 1968). The USD 8.5 billion (in the year 2000 dollars) in estimated costs (Emanuel, 2005) prompted the US Congress to create the National Flood Insurance Program (NFIP) in 1968 (Elliott, 2021). The program, run by the US government, permits homeowners to buy flood insurance at reduced premiums. The insurance is required for all the buildings receiving a loan and located in a Special Flood Hazard Area (SFHA), an area with a one percent chance of flooding in a given year (Lea and Pralle, 2022). Recently, NFIP released a censored dataset containing 2,546,311 claims and 4,034,086 policies (FEMA, 2019), providing a rich source of valuable information. The claims may be geospatially aggregated by latitude and longitude up to 0.1 • or politically by county. The dataset offers a glimpse into a vast market to learn about the financial impacts of flooding events. In particular, this research studies the capacity of the dataset to support the construction of flood loss risk models based on machine learning (ML) to predict the amount paid on flooding claims using the NFIP dataset.
In this study (see Figure 1), we utilize the NFIP dataset to evaluate different regressors in counties with many claims. Among the regressors, we include neural networks ( Conditional Generative Adversarial Networks), decision trees (Extreme Gradient Boosting), and kernel-based regressors (Gaussian Processes). Also, we identify the most significant features for estimating claims' cost and introduce a scheme to improve the predictability power of the ML regressors through bias correction in the resulting distributions. The contributions of this research include the following:
• Evaluation of the predictive skill of ML regressors to infer the amount paid on building flooding claims using the NFIP dataset. That includes a benchmark with a battery of regressors, including neural network, kernel, and decision tree-based methods.
• A distribution bias correction scheme is introduced, which boosts the resulting determination coefficient inference on the amount paid on building flooding claims.
• A study is conducted on the benefit of including rainfall as a meteorological variable. That includes information on the expected improvements in inference from an extension of NFIP to external variables, including hydrological, geological, and social.
• For interannual flood loss modeling, assess the performance of using the entire historical record vis a vis the record at only a fixed lag relative to the present time. Does forgetting the past improve effectiveness in the face of the already-changed climate?
The rest of this document develops as follows: We provide an overview of the literature related to flood cost assessment. After describing the NFIP dataset, we detail the benchmarked ML algorithms. After that, we explain how to postprocess the results of the regression prediction to correct for estimation bias, incorporate the rainfall and evaluate the performance. Finally, we present and discuss the approach's experimental outcomes and summarize the contributions and delineate future lines of research.
Related Literature
This section reviews related literature on flood-risk assessment, NFIP data analysis, characterizing flooding using ML, and established approaches to predicting flood loss.
Statistical-Physical Flood Risk Assessment
In contrast to event-wise flood forecasting (Basha et al., 2008) using real-time data, long-term flood risk assessment is a relatively well-developed approach in certain areas. Our prior work, for example, downscales reanalysis and climate models simulated under various scenarios (IPCC, 2021) to produce a synthetic catalog of extreme events. This includes tropical cyclones (Emanuel et al., 2006;Ravela and Emanuel, 2010;Emanuel and Ravela, 2012) and, more recently precipitation extremes (Saha and Ravela, 2022). The winds and rain from synthetic events then drive storm surge and flood inundation models that predict water depths (heights). The vulnerability of exposed regions to the flood hazard projections calculates damage and loss distributions using characteristic damage and loss curves (FEMA, 2022;Scawthorn et al., 2006). The methodology has been used to estimate economic impacts and adaptation strategies (Neumann et al., 2015a,b). Although flood risk projections are rapidly maturing through modeling, there is a substantial gap in carrying forward to projecting loss distributions. This gap is largely due to the difficulty of scaling damages and losses, and direct data at scale appears essential. The role of artificial intelligence (AI) has been highlighted in addressing problems relating to geosciences (Gil et al., 2018;Karpatne et al., 2019), even in data paucity regimes. Here we use ML approaches with NFIP to construct a loss model. Although NFIP is a redacted and granular data set, it still provides a vast trove of data for constructing time-dependent dynamic data-driven loss models (Blasch et al., 2018). When paired with short-term or long-term climate projections and downscaling (Saha and Ravela, 2022), the corresponding short-and long-term risks can be estimated for various applications beyond insurance.
Analysis of the NFIP Dataset
Sun et al. (2020) present an overview of AI applications in disaster management, particularly during the phases of mitigation, preparedness, response, and recovery. They highlight the availability of datasets for analysis, including the NFIP dataset (FEMA, 2019). Dombrowski et al. (2021) explore this dataset and integrate it with Zillow and American Community Survey data to research factors leading to flooding insurance take-up.
Some of the NFIP dataset's current uses include assessing flood probability. For instance, Mobley et al. (2021) introduce a Random Forest (RF) classifier that predicts flood probability along the Texas Gulf Coast. They employ the NFIP dataset to obtain insured flood loss and high-resolution geospatial topography and hydrology data at 10 m resolution. Similarly, Zarekarizi et al. (2021) produces continuous probabilities for flooding improving over the FEMA discrete assessments. Yang et al. (2021) present an RF regressor that predicts the number of claims in 589 flooding events. Besides the NFIP dataset, they employ satellite-based flood extent, precipitation, coastal weather, building location, land use, topography, geomorphology, and policy count. Similarly, Lin and Cha (2021) develop a neural network and gradient boosting-based statistical model to predict hurricane freshwater flood loss. Their model predicts flood depth, which they input to stage damage curves to estimate the loss by aggregating over the census tracts for the hurricane event and the residential categories.
Flooding Characterization through ML
Some research effort has focused on predicting flood susceptible areas. For instance, employing Landsat satellite images, Wang et al. (2021) assess hybridized Multi-Linear Perceptrons (MLP) to construct a flood susceptibility map. They identify the elevation, slope angle, and soil as important features. Saha et al. (2021) propose an ensemble of "hyper-pipes" and support vector regression (SVR) to infer flood susceptibility from satellite images, from which they extract topography and hydro-climatological predictors. Also, Janizadeh et al. (2021) identify areas prone to flooding by comparing Bayesian Additive Regression Trees, Naive Bayes, and RF. Siam et al. (2021a) perform a comparison between MIKE (Patro et al., 2009), a hydrodynamic model for flood forecasting, and hybridized SVR optimized with Genetic Algorithms, extracting important features with RF.
Lin and Billa (2021) implement a predictor of flood-prone areas employing Geographically Weighted Regression (GWR). Feature selection results in stream order, drainage texture, relief ratio, bifurcation ratio, and topographic wetness position indices. Lee and Kim (2021) predict in real-time the flood extent by estimating the amount of runoff caused by rainfall. Using past precipitation and rainfall-runoff inundation data, they employ the return period, duration, and time distribution and predict whether each grid point will flood for the simulated or observed runoff amount based on logistic regression. Finally, Persiano et al. (2021) compare generalized least squares (GLS) regression and top-kriging (TK) to predict at-site flood quantiles. They use the maximum annual flood in 20 catchments. Ramasamy et al. (2022) compare the Linear Log Regression (LLRM) and Gumbel's Analytical (GAM) methods to assess the flood magnitude at a given return period. Their data correspond to 24 years of annual daily peak flood flow value at the Vaigai reservoir gauging station from 1995 to 2018. Parizi et al. (2021) study the driver factors of discharges (FPD) at different return periods. Their analysis of more than 30 years of data from 206 gauging stations indicates that FPD increases with drainage area, heavy precipitation, and slope while decreasing with elevation and NDVI. Costache et al. (2021) identify slope surfaces with potential for flash flooding. Their approach ensemble techniques include deep learning neural networks, naive Bayes, gradient boosting, and classification and regression trees. Choi (2021) study the construction of flood damage risk assessment using the rainfall for 6 and 24 hours as the input for four types of nonlinear functions. Choi regresses over two rainfall datasets, including district size, topographic features, and urbanization rate. Meanwhile, Siam et al. (2021b) study the effect of noise in the labels employed for regression with ML algorithms to map the spatial flood susceptibility. They examine different kinds of noise and explore the optimal hyper-parameter values for different hybridized ML algorithms relevant to model spatial flood susceptibility.
Predicting Flood Loss
The relationship between flooding and climate change is of interest. For instance, Liu et al. (2021) combined future climate scenarios with a quantitative assessment model of natural disaster risk to obtain the response to flooding events in China to 1.5 and 2 • C of global warming assessing socio-economic risks of the floods, and determining the integrated risk levels. Hu et al. (2021) identifies the influence of precipitation on economic flood risk by developing a linear regression model to predict precipitation patterns. They estimate financial loss risk several months in advance.
Economic loss analysis further segregates into urban and rural sectors. For instance, Basnayake et al. (2021) assess flood loss and damage in agricultural fields by evaluating the farmers' crop production outcome. Their results are robust across crop types and flood severity and independent of household characteristics. Mohammadi et al. (2021) studied water loss in agricultural products after damage by flooding by employing water footprint and farming statistics. In urban settings, Schoppa et al. (2021) use a dataset corresponding to company loss data for 545 buildings to construct multivariate flood loss models. They tried RF, Bayesian networks, and Bayesian regression, with the first one outperforming the others. Mohor et al. (2021) introduce a Bayesian multilevel model to estimate residential flood loss based on a dataset of 1,812 observations. Also, Nofal et al. (2021) model the impact of early warning systems on the reduction of flood loss. They evaluate building-level flood mitigation measures by constructing fragility functions, , i.e., relationships that allow the propagation of uncertainty over the damage modeling process. Finally, Chen et al. (2021a) fit diverse actuarial models to insurance claims data on flood damage in Taiwan transportation construction projects. Chen et al. (2021b) present a systematic analysis of whether risk analysis translated to loss in flood cost assessment in southern China. Maiwald et al. (2021) extend the Earthquake Damage Analysis Center (EDAC) flood damage model refining the description and analysis over inundation level, flow velocities, building type, and the number of building floors. To assess flood risk, Scawthorn et al. (2006) proposed to employ the flood loss rate function, with the inundated depth and loss rate as the independent and dependent variables, respectively. For places for which there is not enough data, Lv et al. (2021) introduce a method to transfer the flood loss rate data from cities with models constructed with enough information to others lacking data.
NFIP Dataset
The NFIP dataset (FEMA, 2019) consists of 2,547,311 records, from which we utilize 22 discrete and nine continuous variables (see Table A.3). As a response variable, we use the amount paid on building claims.
Missing Data in the NFIP Dataset
The NFIP database has missing data in some of its records. For instance, out of its original 40 features, three predictors have between 15% and 55% of their entries with missing values, while seven have more than 55%. The field about the amount paid on the increased cost of compliance has 97.42% of missing values across the dataset. Only seven of the variables have no missing values. Overall, each record in the data set has an average number of missing fields of about 6.7, with one standard deviation of about 2.53. Figure 2 illustrates the distribution of missing data across features. For this research, we separately imputed the dataset for each county before using it as input for the regression models. We employed a different strategy depending on whether the variable was continuous, categorical, or a date-type. For continuous variables, we used Expectation-Maximization (EM) to fill the missing values because it has proved to be an effective method in different tasks (Malan et al., 2020;Taghavi-Shahri et al., 2020). The EM algorithm (Moon, 1996) obtains maximum likelihood parameter estimators in probabilistic models using hidden variables. Incorporating them as observable in the EM algorithm's expectation stage (step E) generates the likelihood expectation. The maximization step (step M) maximizes the likelihood parameters obtained in the E-step. The parameters from the M-step start a new E-step, and the procedure repeats itself until convergence or for an arbitrary maximum number of iterations. For categorical variables, we defined a new category for the missing values. We impute date fields by splitting them into year and day of the year, a numeric value ranging from 1 to 365 (or 366 in leap-years). Afterward, we filled in the missing values with the records median for the year and day of the year and converted the completed values to a date format.
Preprocessing
We adjust for inflation the amounts in dollars for the monetary features considering the Consumer Price Index from the US Bureau of Labor Statistics (U.S. Bureau of Labor Statistics, 2021) and express them in 2020 dollars. Similarly, we create a time index variable that counts the months since January 1, 1960. Using the date of loss and original construction date to estimate the house age at the event may be interesting. However, NFIP contains some erroneous entries where the date of loss occurs before the date of construction. In this study, we subtracted 100 years from the construction date whenever this case occurred. Before constructing the regressors, we expand categorical variables using a one-hot representation. That is, discrete values transform into binary variables where the value one indicates its presence and a zero of absence. The incorporation of dummy variables results in a dataset of 332 predictors. The dataset splits into learning (70%) and testing (30%) subsets. Continuous predictors are normalized using the learning dataset to have zero mean and unitary variance.
Inferring Flood Loss
We investigate representative regressors by studying the inference capability embedded in the NFIP dataset. Ensuing, we introduce a scheme for bias correction of the resulting inference distribution.
ML Regressors
To assess the amenability of the NFIP data set for predicting the amount paid on building claims, we tried kernel, decision trees, and neural networks-based methods. Here, we describe the ML regression algorithms employed in the benchmarking. Gaussian Processes (GP) is a type of stochastic process relying on the assumption that every subset of the collection of random variables follows a multivariate normal distribution, starting from a dataset of observations X n×m = [x 1 , . . . , x n ] T , x i ∈ R m , containing n observations of m variables, and the corresponding responses y = [y 1 , . . . , y n ] T . The problem is to compute the parameters φ= {φ 1 , . . . , φ κ }, including the model's variance σ 2 , which best map the observations with the response variable. GP is a Bayesian approach that estimates the parameters φ as
P (φ | X, y) = P (y | X, φ)P (φ) P (y | X) .(1)
Once the parameters are estimated, for each new observation x * , we could estimate the response variable y * marginalizing over the parameters as
P (y * | x * , X, y) = φ P (y * | x * , φ)P (φ | X, y)dφ.(2)
The assumption about a Gaussian nature of the individual components in (2) permits obtaining the result in closed form. Furthermore, the inverse in the mean value and the variance can be expressed in a computationally amenable form employing the Sherman-Morrison-Woodbury relationship (Guttman, 1946). In addition, once we use a nonlinear transformation z = f (x) on the input data, we may express the result with kernels as (Prince, 2012)
P (y * | x * , X, y) = N σ 2 p σ 2 K[x * , X]y − σ 2 p σ 2 K[x * , X] K[X, X] + σ 2 σ 2 p I −1 K[X, X]y, σ 2 p K[x * , x * ] − σ 2 p K[x * , X] K[X, X] + σ 2 σ 2 p I −1 K[X, x * ] + σ 2 ,(3)
where σ 2 p is the prior covariance, I is the identity matrix, and K[x, x], an entry in the kernel matrix, computes implicitly the product f (x) T f (x), and can be chosen among the expressions meeting the Mercer criteria (Ghojogh et al., 2021). Extreme Gradient Boosting (XGB) is constructed as a forest of decision trees. Given a loss function, such as (Chen and Guestrin, 2016)
L(F ) = n i=1 (y i − F (x i )) 2 + M m=1 Ω(F m ), where Ω(F m ) = γT m + 1 2 λ || ω m || 2 .(4)
Here y i is one of the n reference values,
F (x i ) = M m=1 F m (x i )
represents the outcome of the tree ensemble model, for F m (x i ) being one of the M regression trees with T m leaves and ω m leave weights, and Ω(F m ) is a regularization term that penalizes the complexity of the model with corresponding weights γ and λ. Gradient boosting creates incremental models based on previous iterations and focuses on the most challenging examples. That is, given a model prior, F m , the new approximation to y can be achieved by incorporating a new function h m such that
F m+1 (x) = F m (x) + h m (x) = y,(5)
is employed, i.e., h m can be expressed as
h m (x) = y − F m (x).(6)
Residuals h m (x) keep some resemblance to the negative of the gradient
h m (x) ∝ − ∂L ∂F = 2 n (y − F m (x)) + ∂ ∂F Ω(F m ).(7)
Furthermore, XGB computes a measure of importance for each feature by estimating its contribution to the overall performance. The importance measure considers how each attribute split point improves each tree's performance. The final estimation of importance is the average over all the decision trees in the model. Conditional Generative Adversarial Networks (CGAN) extend the capability of generative adversarial network models. CGAN typically produce data with similar characteristics to the training data by utilizing the response variable y as input, along with a random variable z, for both the generator G(z | y) and the discriminator D(x | y). For regression, the predictor X is employed instead of the response variable. During training, the discriminator updates its parameters using the gradient of the cross-entropy. In CGAN regression, the generator and discriminator functions are optimized by gradient descent using expressions to modify the parameters as (Goodfellow et al., 2020)
θ + d ← θ − d − ρ d ∇ θ d 1 m m i=1 log D x i | y i + log 1 − D G z i | y i | y i ,(8)
while the generator employs just the portion affected by the random variable z i , as (Goodfellow et al., 2020)
θ + g ← θ − g − ρ g ∇ θg 1 m m i=1 log 1 − D G z i | y i | y i ,(9)
for suitable learning rates ρ d and ρ g .
Bias Correction
Once observations infer response values, a parametric model fit to the distribution extracts the properties embedded in the predictions, which may be critical for assessing flood loss. As it is common in econometrics and risk statistics analysis, we approximate the distribution of the resulting predictions of the regression models using Burr (otherwise known as Burr Type XII, Burr, or Singh-Maddala) (Chen et al., 2021a). The Burr distribution has a probability density function (pdf) given as
f (y; c, k, λ) = ck λ y λ c−1 1 + y λ c −k−1 ,(10)
with parameters k, c for shape and λ for scale. Given the Burr's cumulative probability function (CDF) F for the predicted values
F (y p ; c p , k p , λ p ) = 1 − 1 + y cp λ p −kp ,(11)
one could approximate a reference distribution F (y g ; c g , k g , λ g ) by assuming equality for corresponding response values y p and y g as F (y g ; c g , k g , λ g ) = F (y p ; c p , k p , λ p ). One may correct for bias using the expression
y g = λ g 1 − F (y p ; c p , k p , λ p ) −1/kg − 1 1/cg ,(12)
for predicted and reference values, y p and y g , respectively. The parameters for the Burr distribution may be fit using Maximum-Likelihood. When Maximum-Likelihood fails to converge, a Weibull distribution is fit instead. The definition of Weibull distribution is
g(y; k, λ) = k λ y λ k−1 e −(y/α) k ,(13)
with parameters k for shape and λ for scale. Given the Weibull's CDF G p for the predicted values
G(y p ; k p , λ p ) = 1 − e −(yp/λp) kp ,(14)
one can approximate a reference distribution G(y g ; k g , λ g ) by assuming equality for corresponding response values y p and y g as G(y g ; k g , λ g ) = G(y p ; k p , λ p ). Using that assumption, one may correct for bias using the following closed-form expression
y g = α g − log 1 − G(y p ; k p , λ p ) 1/kg ,(15)
for predicted and reference values, y p and y g , respectively.
Experimental Setup
We analyze the NFIP by shifting and expanding periods to assess the regressors developed. We also study how significant physical variables could enrich NFIP. Finally, we detail the performance metric employed for assessment.
Analysis Periods
In many applications of ML regression, we start with a dataset split into training and testing partitions. The assumption is that the elements in the test split constitute a faithful representation of the data distribution where the learning has to occur, i.e., the task of the ML method is to perform well within the distribution defined by the dataset. This approach is not practical for predicting losses in general. In this problem, we want to learn from the past and assess events in the future. Thus, simulating flooding and claims can generate inferences about these possible scenarios.
To build a regressor for a county, we train with the claims covering the period from years b + δ to b + o + k − 1, inclusive, and test with claims from year b + o + k, the immediate next one. Here, b represents a baseline year, o is an offset, and k is an iterator for integer variables where k ≥ 0 and o ≥ 1. The variable δ has two possible values. For shifting periods of analysis, δ = k, meaning that the period of o years employed for training shifts with new intervals. For expanding analysis periods, δ = 0, the claims considered start on year b and end on year b + o + k, for the k-th iteration considered.
Incorporating Physical Variables
Rainfall may strongly influence economic loss (Hu et al., 2021), which we aim to quantify within the context of NFIP. To that end, we incorporated the Daymet (Thornton et al., 2020) dataset, a daily estimation from 1980 to 2021 of weather and climatology variables. The variables are available in a 1 km × 1 km regular grid (see Figure 5). They include the maximum and minimum temperature, precipitation, shortwave radiation, vapor pressure, snow water, and day length.
Since NFIP has a lower resolution, we incorporate the Daymet precipitation by aggregating the estimates around the geolocation of the claim at ±0.05 • of longitude and ±0.05 • of latitude. We tried six aggregation schemes, including Σ 3 , Σ 5 , Σ 7 , max 3 , max 5 , and max 7 , corresponding to the sum of rain two, four, and six days before, and the maximum for the two, four and six days earlier, in all cases including the day of the event. Once added to the predictors, the precipitation is normalized to have zero mean and unitary variance, just as the other continuous variables.
Performance Evaluation
To assess the performance of the different ML regressors, we utilize metrics reflecting the pointwise evaluation of inferences and the results we obtain by modeling the distributions of predictions.
Pointwise Performance Evaluation
To measure the pointwise similarity between the predictions for the response variable and the corresponding reference values, we employ indicators including the root-mean-squared error (RMSE), the RMSE divided by the standard deviation σ of the response value, and the coefficient of determination. Given a data set {X, y}, the unbiased estimation for the variance of the ground truth response variable is given by
σ 2 = 1 n − 1 (y − µ) T (y − µ),(16)
where µ is its mean value and n the number of elements in y. In regression, a common metric is RMSE, which measures the difference between the predicted values y p and the reference values y g using
RMSE = 1 n (y p − y g ) T (y p − y g ).(17)
Since the RMSE corresponding to different counties may result in a wide range of values, it is convenient to RMSE relative to the standard deviation as RMSE/σ. If this ratio is more than one, using the mean as the resulting inference would result in better performance than the outcome of the ML algorithm, while if it is below one, it is better to use the ML method.
Comparison between Distributions
Once a parametric continuous distribution approximates the data, there is a need to verify the goodness of fit. Among the several options available (Rayner et al., 2009), we select the Kolmogorov-Smirnov (K-S) test because it can be applied to continuous distributions and works best when the number of observations is in the order of thousands. For two CDFs P r and Q p , corresponding to the reference and prediction CDFs, the test employs the supreme of the difference to construct its test statistic, i.e.,
D n = max x | P r (x) − Q p (x) | .
In the K-S test, the null hypothesis H 0 claims that the observations under consideration come from the same underlying distribution. One rejects the null hypothesis whenever √ nD n is larger than a certain critical value K α , where n is the number of samples, and α reflects a level of confidence, i.e., the area of the Kolmogorov pdf p K beyond the threshold K α is smaller than α. Otherwise, we are assuming that p K √ nD n ≤ K α = 1 − α. In practice, one rejects the null hypothesis when the p-value of the test is smaller than the significance level α.
After testing the goodness of fit of the parametric pdf, we assess the difference between the reference and prediction distributions using the Kullback-Leibler (KL) divergence as
D(p || q) = x p r (x) log p r (x) q p (x) dx,(18)
where p r (x) and q p (x) correspond to the reference and inferred pdfs. Another performance measure consists of constructing a classifier to distinguish the distributions as considered different classes. Let the classification space C = {P, Q} for the reference and the prediction classes, respectively, with corresponding characterization p r (x) and q p (x). In the classification problem, given the observation of the predictor x, the objective is to assign it to the right class. In general, the classifier has to define whether an observation belongs to class P with probability p or to class Q with probability 1 − p. To indicate similarity between the distributions, we rely on regression gradient boosting trees (Friedman, 2001). Another insightful measure of performance is the determination coefficient R 2 , representing the proportion of the variability of the independent variable that is explainable in terms of the dependent ones. After bias correction, when there is a parametric representation of the reference p r (x) and prediction q p (x) distributions, we express R 2 as
R 2 = 1 − S r S v = 1 − x p r (x) − q p (x) 2 dx x p r (x) − µ r 2 dx ,(19)
where S r is the difference between the reference and prediction distributions, and S v is the deviation of the reference distribution from its mean value µ r . Chicco et al. (2021) argue that since the interval [0, 1] bounds the range of R 2 and because its value reflects the number of correctly-predicted elements, its use should be preferred based on its informative capability.
Results
To assess the predictive capabilities of the NFIP dataset, we implemented the method described in the previous sections and tested them on several scenarios. We standardized the continuous predictors using the training dataset, dividing the difference from its mean by the standard deviation, and created one-hot representations of the categorical variables. To assess the different regressors, we selected 11 US counties with many claims in the NFIP dataset for comparison (see Table 1). Fig. 3: Dataset protocol. The dataset partitions into training (70%) and testing (30%) partitions. The training dataset further has a learning (70%) and validation partition (30%). The first split is employed to fine-tune the hyperparameters. After training, performance results p i are obtained using the testing partition. Repeating this exercise 30 times estimates performance statistics.
Setting Up, Fine Tuning and Comparing the Regressors
Initially, we compared the regressors using the claims dataset corresponding to each of the counties under analysis. In this stage (see Figure 3), we took 70% of the data for training and 30% for testing. Then, we split the training dataset into learning (70%) and validation (30%) subsets. After evaluating the testing split, we obtained a performance assessment p i for this partition. After repeating this procedure 30 times, we estimated the performance statistics for each regressor in each county.
XGB. For this regressor, we used the XGBoost version 1.4.1.1 in R. The parameters to fine-tune include 1. η ∼ U(0.0001, 1), the information from a new tree employed during boosting. 2. c s ∼ U(0.1, 1), the fraction of the variables considered during branch splitting. 3. d m ∼ U(2, 10), the maximum depth of the trees; 4. s s ∼ U(0.1, 1), the percentage of the data employed to grow the tree, in what is known as stochastic boosting; and 5. γ ∼ U(0.01, 100), the minimum reduction in the loss function that is needed to create a tree.
We find these hyperparameters via a uniform random search over a range. Using a particular set of parameters, we trained an XGB regressor using the first split of the training/testing datasets taking 70% of the training samples for learning and validating with the remaining 30%. We kept the parameters for which, after 50 rounds, the root-meansquare error was relatively insignificant. A random search for the best parameters during 1,000 cycles for each county. Afterward, we trained for 100 iterations with the hyperparameters providing the best performance.
GP. In this case, we optimized the hyperparameter using the Matlab fitrgp method, selecting the basis function among a constant, linear, and quadratic. We sought the optimal kernel scale between r · (10 −3 , 1), where r is the maximum predictor range. The value of sigma was sought in the range (10 −4 , max(10 −3 , 10 · σ y )), for σ y being the standard deviation of the response. Also, we determined whether to standardize or not. In the former case, we divided the difference between the predictor and its mean by standard deviation. For the optimization, we employed five-fold cross-validation on the training dataset.
CGAN. We defined a fixed learning rate for the discriminator and generator of 0.001, trained with Adam the latter and Stochastic Gradient Descend the former. We employed the Exponential Linear Unit (ELU) as the activation function, training for 20 epochs with a batch size of 128. The stochastic input has a length of one. Our discriminator receives as input the predictors and is fully connected to a layer with 100 units, as does the stochastic value. Then, there are four fully connected layers, each with 50 units, ending with a single output with a sigmoid activation function. The generator and discriminator use a cross-validation loss function. The generator has the same architecture except for a linear output layer.
After training the regressors, we computed the prediction for the elements in the training set and assessed the performance using the testing partition (see Figure 4). We notice that the XGB was the only regressor consistently providing results below one for the ratio RMSE/σ for almost all the counties under consideration. The exceptions were Fig. 4: Comparison of regressor performance. XGB generated regressors with a ration RMSE/σ below 1.0, albeit with at least one partition above it for Ocean and Nassau counties. The shaded area delimits the best and worst performance observed during the 30 dataset splits. GP and CGAN produced regressors with RMSE/σ ratios above 1.0, except for Broward and Miami-Dale, for which counties the methods did not converge to create a regressor.
Ocean (NJ) and Nassau (NY) counties, for which XGB obtained a mean value of 0.8147 and 0.9382 but a maximum of 1.1227 and 2.4937. On the contrary, neither CGAN nor GP converged to a value smaller than one for the ratio RMSE/σ. Furthermore, they could not converge on a solution for Broward and Miami-Dade. For instance, the best results for GP were Jefferson Parish, Ocean, Nassau, and Suffolk, with an RMSE/σ ratio of 1.0. Based on these results, for the rest of the article, we will focus on the description of the predictive capabilities of the XGB regressor.
Bias Correction
During bias correction, we aim to fit a Burr distribution to the set of predictions, trying a Weibull when the minimization procedure fails to converge. In Figure 7, the method is illustrated for Harris county (48201) using the shifting period between 2000 and 2009, where the test dataset corresponded to 2010. For the predictions resulting from the evaluation of the training dataset, containing 47,160 claims, we fit a Burr distribution to the reference and predicted resulting in parameters α = 444, 293, c = 0.99, and k = 10.42 and α = 31, 832.9, c = 6.18, and k = 0.47. With a p-value of 6.5 × 10 −35 and 1.37 × 10 −19 , we reject the null hypothesis between the parametric model and the data distribution using the K-S test. We estimated the transformation between the reference and prediction-adjusted parametric distributions using the CDF and transformed the predicted values. Again, we fit a Burr distribution to these values, resulting in the parameters α = of 9, 294, c = 1.00, and k = 6.38. In this case, the K-S test resulted in a p-value of 5.43 × 10 −15 .
During testing, with a dataset of 297 claims, we modeled the reference and prediction distribution, finding the parameters A = 28, 570.6, B = 0.78 and α = 36, 950.7, c = 6.87, and k = 1.04. Note that for the reference distribution, a Weibull distribution was fit. The function learned during training transforms observations corresponding to the predictions. The resulting distribution was fit using a Burr distribution with parameters α = 131, 763, c = 1.37, and k = 7.68. This time the K-S test resulted in a p-value of 0.83. Hence, we did not reject the null hypothesis. The initial distribution had a KL divergence of 0.0123, while the final distribution had a KL divergence of 0.0015. Similarly, the initial ROC AUC had a value of 0.85, while the final ROC AUC had a value of 0.58.
Analysis Periods
We studied the behavior of the XGB regressor under shifting and expanding periods. In both cases, 2000 was the baseline employed, while 2020 was the last analysis year. For expanding periods, we initially took ten years, i.e., used the period from 2000 to 2009 for training and 2010 for testing. Then, we selected the period from 2000 to 2010 for training and 2011 for testing. We kept doing this until we ultimately chose the period from 2000 to 2019 for training and tested with the claims in 2020. We repeated this exercise for the 11 counties under study. For shifting periods, we initially took the period from 2000 to 2009 for training and tested it in 2010. Contrasting with expanding periods, in the next iteration, we took from 2001 to 2010 for training and tested it in 2011. In the last iteration, we trained with data from (a) Daymet geospatial coverage (b) NFIP (blue) and Daymet (red) geolocations for Cook county, IL (black polygonal shape). Shifting and Expanding Periods with Rainfall. To study the incorporation of Daymet, we obtained the rain for two, four, and six days before, including the date of loss for Cook county (17031), and characterized it with their sum and the maximum over the period. To aggregate rainfall, we incorporated Daymet rainfall for the area, including ±0.05 • in latitude and longitude around the NFIP claim location. Then, we constructed six regressors, incorporating rain's corresponding characterization as a predictor. For the sums, we obtain an R 2 = 0.516, and for the maximums, R 2 = 0.515. Thus, we arbitrarily decided to use the sum of the millimeters of rain falling around the claim's location for the two days before, including the date of loss. Then, we decided to study the implications of using the rainfall information for the other counties under study. Figures A.8 A.9 illustrate the results. For shifting periods, XGB could fit a regressor with a ration RMSE/σ for all the test years in Orlean Parish county. Although it fit ten regressors for three counties, it fit nine regressors for nine counties. Using the weighted with the claims R 2 values, we obtain a linear correlation coefficient of 0.096 between the shifting and expanded periods of analysis with Daymet information included; a correlation of 0.056 between the shifting without Daymet and expanding with it; and a correlation of -0.215 between the shifting periods with Daymet and expanding periods without it. The p-value was generally good, with few cases per county rejecting the null hypothesis of the goodness of fit with the parametric Burr distribution. In the case of the shifting period plus Daymet, the only exception was Jefferson Parish (22051), where the p-value was larger than 0.05 through the analysis period. In the case of expanding periods plus Daymet, we observed p-values below 0.05 for Nassau (36059), Suffolk (36103), Galveston (48167), and Harris (48201) counties. Weighting by the number of claims for each county in a given year, the R 2 value for the shifting and expanding period with Daymet information included was 0.61 and 0.7, respectively.
Comparing with Alternatives
Research on the NFIP dataset to predict loss has been scarce. An exception is a work by Lin and Cha (Lin and Cha, 2021). In their approach, Lin and Cha start simulating hurricane storm tracks. Then, they use a rainfall prediction model to simulate rainfall intensity, predicting the stream stage increment and the flood depth at the centroid of census tracts. Finally, they aggregate flood loss using stage-damage curves, obtaining an R 2 value of 0.3382. To assess, they employ FEMA-classified significant flooding events, those generating at least 1,500 claims, in the eight coastal states in the US South-West, from Texas to North Carolina for the period from 1980 (hurricane Allen) to 2017 (hurricane Maria) (see Figure 6 (a)). These eight states include 121 counties on the shoreline generating 1,246,888 claims on NFIP.
Tracing the trajectories of hurricanes, we detected the counties affected by significant flooding events. Using a leave-one-out (LOO) training strategy with cross-validation (CV), we took one storm for testing and the remaining for training. Thus, the number of claims for testing varies for each county regressor, depending on the hurricane employed. Figure 6(b) shows the maximum, minimum and average number of claims used for testing. We observe a surge of claims in Orlean Parish (22071) and Harris (48201) counties originating from Katrina (2005) and Harvey (2017) (see Figure 6(c)). Considering the number of claims, the average R 2 after bias correction is 0.807 (see Figure 6(d)).
Feature Importance
An important by-product of regressors such as XGB is their ability to rank importance for the employed variables. Table 2 depicts the results for the counties under analysis. Most counties' predictors, such as BFE (base flood elevation), rank high, but it is only sometimes the most important. It stands out that each county has a particular set of essential features with different relative importance. Also, most of the highest-ranked features are continuous, but some discrete features, such as RM (rate method) with value 5, are the second most important feature for the county with code 36103 (Suffolk, NY). 2: Ten most important features by county, as estimated by XGB. The value represents the fractional gain of a feature concerning the total gain of the feature's split (Chen and Guestrin, 2016). Acronyms stand for BFE (baseFloodElevation), ED (elevationDifference), PC (policyCount), TCI (totalContentsInsuranceCoverage), LAG (lowestAdjacentGrade), LFE (lowestFloorElevation), LAT (latitude), MO (months), LON (longitude), CI (condominiumIndicator), RZ (reportedZipcode), RM (rateMethod), OT (occupancyType), BE (basementEn-closureCrawlspace), ECI (elevationCertificateIndicator), EBI (elevatedBuildingIndicator), CRS (communityRatingSystemDiscount), NFB (numberOfFloorsInTheInsuredBuilding), OT (obstructionType
Discussion
As the effects of climate change spread across the globe Hu et al., 2021), the occurrence of more frequent and extreme flood events is anticipated, which will cause a significant economic (Basnayake et al., 2021) set back in urban (Mohor et al., 2021;Nofal et al., 2021) and rural (Mohammadi et al., 2021) settings. Thus, there is a need for novel models to estimate flood risk (Chen et al., 2021a) and estimate loss (Maiwald et al., 2021). This research sheds light on a data-driven estimation of flood loss in the US, where a considerable data-gathering infrastructure is readily available, as opposed to other nations where this effort still needs to take place (Lv et al., 2021).
This research on the NFIP dataset (FEMA, 2019) shows that it is possible to construct regressors to infer the amount paid on building claims. This work adds to the current body of research on NFIP, enriching it to produce continuous probability for flooding (Zarekarizi et al., 2021), predict the number of claims (Yang et al., 2021) and in general assess risk (Lin and Cha, 2021). The regression results show significant progress over the employment of flood depth and damage curves (Lin and Cha, 2021), while the bias correction stage improves the overall estimation of the amount paid distribution, extending Chen et al. (2021a) analysis on risk models.
The assessment of classic decision tree, kernel, and neural networks-based nonlinear regression methods highlights the potential of ML techniques and is similar to current efforts aimed to assess susceptibility Saha et al., 2021;Janizadeh et al., 2021;Siam et al., 2021a;, estimate the spatial extent (Lin and Billa, 2021;Lee and Kim, 2021), compare flood regions (Persiano et al., 2021). NFIP is a challenging dataset offering ample opportunities for ML techniques, e.g., consider the uncertainty quantification in the labeling process for predictors (Siam et al., 2021b).
An emerging argument is that the already-changed climate renders the extended historical record ineffective for modeling future risk. To make matters worse, since extremes are rare, a short history is also insufficient. Thus, the argument goes, we may no longer rely on the historical record to assess risk, even in the near future! Figures A.8 A.9 show models with considerable skill at projecting interannual flood loss risk using the historical record. We posit that this is primarily because they adapt in a dynamic data-driven manner. The model adapts faster as the horizon of future interest shrinks. Further, performance is similar between the expanding and shifting window modes of adaptation. This empirical evidence implies that it is neither true that the record is too short for the present flood loss modeling problem nor that using the entire history per se makes risk assessment less skillful. We posit that accelerating climate change at longer horizons will require better models through physics, but the issue remains unsettled at short horizons. (a), we obtain the distribution of its outputs and fit a parametric probability density function (pdf). We adjust the distribution to match the reference and training output prediction (b). The alignment relies in the inverse cumulative density function method (c). The method is then applied to the test split of the dataset (d)-(e). A possible form to assess the resulting match is by constructing a classifier to distinguish between the populations before (f) and after (g) bias correction.
Conclusion
The evaluation of flood risk is complex due to its multidimensionality characteristics that touch social, economic, political, territorial, and scientific dimensions (Elliott, 2021). Nevertheless, the quantitative assessment of the amount paid on insurance claims offers a glimpse of the challenges ahead and could serve as a solid guide for decision-making. This research explores the censored NFIP dataset by studying diverse classic ML techniques covering kernel, neural network, and decision tree-based approach. For a sample of some counties with the most significant number of claims, we demonstrate that it is possible to construct regressors that offer a critical predictive ability beyond the conventional approach of water depth and damage risk maps. Furthermore, we showed that incorporating meteorological variables can enhance performance. We also demonstrate that feature importance varies by county, which justifies the need for regional analysis.
We will incorporate relevant predictors into the regressor mix, as the related literature has highlighted their relevance. These include digital elevation maps, slopes, and climatological variables. Furthermore, current advances in ML techniques, such as oblique decision trees (Carreira-Perpiñán and Hada, 2021), are interesting to study in the light of the NFIP dataset.
Data Availability Statement
The data and code generated or used during the study are available upon request.
Appendix A. The NFIP Dataset
Fig. 1 :
1Predicting flood loss. Using the NFIP dataset, we construct and compare regressors based on decision trees, kernels, and neural networks to predict the flooding loss and select the most critical variables for estimation.
Fig. 2 :
2Visual representation of the missing values in the NFIP dataset. Columns and rows represent features and records, respectively. Gray spaces represent missing values.
Fig. 5 :
5Daymet is a dataset with daily weather parameters for North America, Hawaii (not shown), and Puerto Rico (not shown) (a). The resolution for Daymet is 1 km × 1 km, while NFIP has a resolution of 0.1 • (b). We incorporate Daymet precipitation by aggregating within non-overlapping squares around the NFIP location.2010 to 2019 and tested with 2020. To assess the R 2 performance of the XGB regressor, we weighted the value of the performance indicator by the number of claims employed for testing.Shifting and Expanding Periods. For shifting periods (seeFigure A.8 in the additional material section), the combination of XGB and bias correction produced regressors most of the time except in 2012 for Orlan Parish (22071). For five counties, they fail to generate a regressor for one year, different in each case. R 2 varies within a county. It can be as low as 0.15 for Cook county in 2014 or as high as 0.98 in 2015 for Nassan (36059). Correspondingly, the parametric fit was, in general adequate. For instance, the p-value did not fall below α = 0.05 for Jefferson Parish (22051), Orlean Parish (22071), and St Tammany Parish (22103), but it fell below α = 0.05 for Harris county (48201). The performance for expanding periods was lower (seeFigure A.9 in the additional material section). For instance, Jefferson Parish (22051) had only five useful regressors in the analysis period. The resulting values are uncorrelated with a linear correlation coefficient of -0.064 between the corresponding R 2 values of shifting and expanding periods. However, weighting by the number of claims per county in a given year, the R 2 value for the shifting and expanding window was 0.61 and 0.7, respectively.
Maximum, minimum and average number of claims in the LOO-CV construction of regressors. (c) Maximum, minimum and average R 2 in the LOO-CV construction of regressors (d) R 2 by county and hurricane. The circled cells signal places that lack a useful regressor.
Fig. 6 :
6Construction of regressors by the county during the analysis of significant flooding events due to hurricanes. Hurricanes affect shoreline counties (a) and generate significant flooding events (b). Using Leave-One-Out (LOO) Cross-Validation (CV), we selected one hurricane affecting a county and the remaining ones for testing (c). The resulting mean R 2 value is 0.807 (d).
Fig. A. 9 :
9Expanding Window. Resulting in R 2 (*.1) and corresponding p-value (*.2) for the counties under analysis for the testing period between 2010 and 2020. For the p-value figures, the horizontal dotted line signals the reference value for α = 0.05, rejecting values below the null hypothesis of suitable goodness of fit. The blue line shows the results for NFIP, and the red line for the combination NFIP+Daymet.
Table 1 :
1Counties employed in assessing ML regressors because of their large number of claims.n code
name
claims
n code
name
claims
1 12011
Broward, FL
31,059
7 34029
Ocean, NJ
52,436
2 12086
Miami-Dade, FL
61,197
8 36059
Nassau, NY
50,067
3 17031
Cook, IL
15,180
9 36103
Suffolk, NY
33,130
4 22051
Jefferson Parish, LA
133,162 10 48167 Galveston, TX
60,224
5 22071
Orlean Parish, LA
126,405 11 48201
Harris, TX
171,202
6 22103 St Tammany Parish, LA
37,514
Table
).county
1
2
3
4
5
6
7
8
9
10
1
12011
BFE
TBI
ED
PC
LAG
MO
TCI
RZ.33009
LFE
PR.1
1.00
0.90
0.49
0.41
0.34
0.29
0.21
0.19
0.16
0.14
2
12086
TBI
BFE
PC
MO
LFE
ED
LON
LAG
TCI
FZ.A14
1.00
0.92
0.59
0.39
0.37
0.29
0.16
0.16
0.13
0.13
3
17031
BFE
TCI
MO
CI.A
TBI
OT.4
LAT
LAG
ECI.1
ED
1.00
0.13
0.10
0.08
0.07
0.05
0.03
0.03
0.02
0.02
4
22051
TBI
BFE
MO
LFE
TCI
RZ.70006
LAG
ED
PC
LAT
1.00
0.94
0.68
0.28
0.17
0.14
0.11
0.10
0.10
0.09
5
22071
BFE
TBI
MO
ED
PC
TCI
LAG
LFE
BE.4
LON
1.00
0.89
0.57
0.27
0.27
0.25
0.21
0.14
0.03
0.03
6
22103
MO
TBI
BFE
LAT
LAG
TCI
LFE
ED
LON
RZ.70461
1.00
0.93
0.82
0.40
0.37
0.35
0.31
0.31
0.07
0.07
7
34029
BFE
LAG
MO
TBI
LFE
ED
TCI
LAT
PC
CRS.5
1.00
0.40
0.38
0.37
0.36
0.34
0.27
0.20
0.13
0.07
8
36059
PC
RM.5 BFE
TBI
LAG
MO
ED
TCI
LFE
NFB.6
1.00
0.76
0.48
0.39
0.21
0.16
0.10
0.04
0.03
0.03
9
36103
BFE
MO
LFE
TBI
TCI
ED
LAG
LAT
LON
RM.1
1.00
0.57
0.43
0.37
0.20
0.19
0.18
0.10
0.09
0.06
10
48167
TBI
BFE
TCI
MO
PC
LAG
ED
LFE
EBI.1
LON
1.00
0.44
0.33
0.31
0.25
0.22
0.20
0.19
0.14
0.12
11
48201
BFE
TBI
MO
LAG
PC
TCI
ED
LFE
LAT
LON
1.00
0.55
0.35
0.23
0.18
0.15
0.06
0.05
0.04
0.03
Fig. 7: Bias Correction. Once the regressor trains(a) XGB initial
(b) XGB final
(c) CDF matching
(d) XGB test initial
(e) XGB test final
(f) ROC initial
(g) ROC final
Table A .
A3 describes the structure of the NFIP dataset, while Figures A.8 and A.9 provide further detail for the results of fitting regressors to each county.
Table A .
A3: NFIP dataset. Here, we describe the 22 discrete and nine continuous variables employed in this research and the range of values each takes in the dataset. A01,. . . , A30, A99, A; AE, A1 . . . A30; A99 AH, AHB, AO,AOB,X, B,X, C ; D; V; VE, V1-V30; AE, VE, X, V1-V30, B,C; AR; AHB, AOB, ARE, ARH, ARO, and ARA12 Number of Floors in the Insured Building Y, N 13 Non Profit Indicator Y, N 14 Obstruction Type 10, . . . , 98 15 Occupancy Type 1, . . . , 4 16 Original Construction Date 1950.01.01 to 2048.07.25 17 Post-FIRM Construction Indicator Y, N 18 Rate Method 1,. . . , 9, A, B, E, F, G, P,. . .Fig. A.8: Shifting Window. Resulting in R 2 (*.1) and corresponding p-value (*.2) for the counties under analysis for the testing period between 2010 and 2020. For the p-value figures, the horizontal dotted line signals the reference value for α = 0.05, rejecting values below the null hypothesis of suitable goodness of fit. The blue line shows the results for NFIP and the red line for the combination NFIP+Daymet.Discrete
Continuous
1
Agriculture Structure Indica-
tor
Y, N
23 Amount Paid On
Building Claim
R ≥ 0
2
Basement
Enclosure
Crawlspace Type
0, . . . , 4
24 Base Flood Eleva-
tion
elevation feet for a 1%
chance/year of flooding
3
Community Rating System
Discount
1,. . . , 10
25 Elevation
Differ-
ence
R
4
Condominium Indicator
N, U, A, H, L, T;
26 Latitude
−90 • ≤ R ≤ 90 •
5
Date Of Loss
1970-08-31, . . . , 2021-09-08
27 Longitude
−180 • ≤ R ≤ 180 •
6
Elevated Building Indicator
Y, N
28 Lowest
Adjacent
Grade
R
7
Elevation Certificate Indica-
tor
Y, N
8
Flood Zone
A, 29 Lowest Floor Ele-
vation
R
9
House of Worship
Y, N
30 Policy Count
1, . . . , Z
10 Location Of Contents
1, . . . , 7
31 Total Building In-
surance Coverage
R ≥ 0
11 Lowest Adjacent Grade
1, . . . , 6
32 Total Contents In-
surance Coverage
R ≥ 0
, T,
W
19 Primary Residence
Y, N
20 Small Business Indicator
Building
Y, N
21 Year of Loss
1970, . . . , 2021
22 Zip Code
5-digit Postal Zip Code
(a.1) 12011
(b.1) 12086
(c.1) 17031
(d.1) 22051
(e.1) 22071
(f.1) 22103
(g.1) 34029
(h.1) 36059
(i.1) 36103
(j.1) 48167
(k.1) 48201
(a.2) 12011
(b.2) 12086
(c.2) 17031
(d.2) 22051
(e.2) 22071
(f.2) 22103
(g.2) 34029
(h.2) 36059
(i.2) 36103
(j.2) 48167
(k.2) 48201
(a.1) 12011
(b.1) 12086
(c.1) 17031
(d.1) 22051
(e.1) 22071
(f.1) 22103
(g.1) 34029
(h.1) 36059
(i.1) 36103
(j.1) 48167
(k.1) 48201
(a.2) 12011
(b.2) 12086
(c.2) 17031
(d.2) 22051
(e.2) 22071
(f.2) 22103
(g.2) 34029
(h.2) 36059
(i.2) 36103
(j.2) 48167
(k.2) 48201
Kerry Emanuel, personal communication
AcknowledgementsThis work was funded in part by Liberty Mutual (029024-00020), ONR (N00014-19-1-2273), and the two MIT Climate Grand Challenge projects, namely, "Preparing for a New World of Weather and Climate Extremes" and "Reinventing Climate Change Adaptation with the Climate Resilience Early Warning System (CREWSnet)." SIP-IPN partly supported Joaquin Salas under grant 20220583 and by SECTEI CDMX under grant 910C21. The article's content is solely the responsibility of the authors and does not necessarily represent the official views of the sponsors and funding sources. The authors thank Dagoberto Pulido for providing routines for inferring the missing values and Goran Zivanovic for data analysis assistance.
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| sample_170 | 0.9523 | arxiv | |
The energy return on investment of whole-energy systems: application to Belgium
Jonathan Dumas
Antoine Dubois
Paolo Thiran paolo.thiran@uclouvain.be
Institute of Mechanics
Materials and Civil Engineering
Catholic University of Louvain
Place de l'Université 1, Ottignies-Louvain-la-Neuve1348Belgium
Pierre Jacques p.jacques@uclouvain.be
Institute of Mechanics
Materials and Civil Engineering
Catholic University of Louvain
Place de l'Université 1, Ottignies-Louvain-la-Neuve1348Belgium
Francesco Contino francesco.contino@uclouvain.be
Institute of Mechanics
Materials and Civil Engineering
Catholic University of Louvain
Place de l'Université 1, Ottignies-Louvain-la-Neuve1348Belgium
Bertrand Cornélusse bertrand.cornelusse@uliege.be
Gauthier Limpens gauthier.limpens@uclouvain.be
Institute of Mechanics
Materials and Civil Engineering
Catholic University of Louvain
Place de l'Université 1, Ottignies-Louvain-la-Neuve1348Belgium
Departments of Computer Science and Electrical Engineering
Liege University
Place du 20-Août, 7B-4000Liege, StateBelgium
The energy return on investment of whole-energy systems: application to Belgium
Springer Nature 2021 L A T E X templateEnergy return on energy investmentenergy transitionwhole-energy systemsensitivity analysisEnergyScope TDpolynomial chaos expansion
Planning the defossilization of energy systems while maintaining access to abundant primary energy resources is a nontrivial multi-objective problem encompassing economic, technical, environmental, and social aspects. However, most long-term policies consider the cost of the system as the leading indicator in the energy system models to decrease the carbon footprint. This paper is the first to develop a novel approach by adding a surrogate indicator for the social and economic aspects, the energy return on investment (EROI), in a whole-energy system optimization model. In addition, we conducted a global sensitivity analysis to identify the main parameters driving the EROI uncertainty. This method is illustrated in the 2035 Belgian energy system for several greenhouse gas (GHG) emissions targets. Nevertheless, it can be applied to any worldwide or country energy system. The main results are threefold when the GHG emissions are reduced by 80%: (i) the EROI decreases from 8.9 to 3.9; (ii) the imported renewable gas (methane) represents 60 % of the system primary energy mix; (iii) the sensitivity analysis reveals this fuel drives 67% of the variation of the EROI. These results raise questions about meeting the climate targets without adverse socioeconomic impact, demonstrating the importance of considering the EROI in energy system models.
Introduction
To limit climate change and achieve the ambi- This study addresses this issue by considering a comprehensive indicator: the energy return on investment (EROI). It better encompasses the technical and social challenges of the energy transition than the cost. The field of net energy analysis was first developed following the 1970s oil crises, to assess how much energy is made available to society (Cleveland et al, 1984). Then, various metrics have been introduced in the past few decades, including the energy profit ratio, energy gain, energy payback time, and the most wellknown, the EROI. Expressed as a ratio between energy outputs and energy inputs of a given system or process (Hall et al, 1979), the EROI captures the extent to which helpful energy is yielded from that system or process. The lower the EROI of an energy source, the more input energy is required to produce the output energy, which results in less net energy available for the rest of the economy. Thus, the EROI can be understood as the ease with which the energy system can extract energy sources and transform them into a form beneficial to society. The work of Mulder and Hagens (2008) established a theoretical framework for EROI analysis that encompasses the various methodologies in the literature.
Access to abundant and affordable primary energy resources has been recognized as an essential element for the prosperity of human societies, and the concept of EROI is commonly used to measure their quality. The literature about EROI is abundant and, without being exhaustive, concerns three main fields of research, which are reviewed in the following paragraphs: (1) the link between EROI and societal well-being; (2) estimation of the EROI of an energy resource or technology; (3) the estimation of a global EROI at the level of an economy or a society, and a lower bound below which a prosperous lifestyle would not be sustainable.
The potential connections between societal well-being and net energy availability are investigated by Lambert et al (2014). The results for a large sample of countries point out that the estimated societal EROI is correlated with the Human Development Index (HDI), which is a standard of living indicator. However, for a few countries with a high level of development, i.e., HDI above 0.75, there is a saturation point where increasing the EROI above 20 is not associated with further improvement in society. In addition, the relationship between societal EROI and HDI is non-linear as the HDI increases less and less rapidly with societal EROI.
The characteristics of the primary energy sources, including the standard EROI of each fuel, are investigated by Hall et al (2014) 1,2 . They conclude that: (i) overall, the standard EROI of conventional fuels, such as oil and gas, has been declining over the last decades for all nations examined (United States, Canada, Norway, Mexico, and China), reducing from 10% to 50%, 1 The EROI values presented in Hall et al (2014) refer to standard EROI, which only considers energy inputs required for the extraction of the energy resource. Other EROI metrics exist, such as the final stage EROI or the societal EROI. The final stage EROI considers not only the energy inputs used for extracting, but also for processing and delivering an energy carrier.
2 The mean and standard error values of EROI provided are estimated based on several published studies, and the references are listed in Lambert et al (2 November 2012).
depending on the location of production. The study of Gagnon et al (2009) as PV with an average EROI value of 10, than traditional conventional fossil fuels. However, wind power energy seems competitive, with a mean EROI value of 20. Another more recent study (Brockway et al, 2019) calculates the EROI of fossil fuels at both primary and final energy stages.
Their results suggest that the current EROI of fossil fuels may not differ from the EROI of renewables when computed at the final stage, which illustrates the difficulty of adequately assessing the EROI of resources or technologies.
Several attempts to determine a lower bound of the societal EROI below which a prosperous lifestyle would not be sustainable have been performed over the past few years. However, the estimation of this threshold differs from one study to the other, as listed in Dupont et al (2021): (i) the study of Hall et al (2009) provides an educated guess of a minimum societal EROI value of around culation; ii) the work of Fizaine and Court (2016) focuses on the USA by conducting an econometric equation linking growth rates, energy expenditures, capital formation, and population. It results in an estimated EROI value of 11 to maintain the economic growth of the USA; iii) the paper of Brandt (2017) provides an estimated minimum societal EROI of 5 by using a simple template economy with four sectors and inputs for each sector defined at an order-of-magnitude level using data for the US; iv) the study of Court (2019) indicates that this lower bound decreases as technical change improves the conversion efficiency of primary-to-final and final-to-useful exergy processes. They estimated that the minimum sustainable societal EROI of the world has declined from 20 in 1900 to 6 in 1970 to remain constant so far.
Finally, a few studies have attempted to estimate the societal EROI at a country or world level. The work of Dupont et al (2021) provides an estimate of the societal EROI using a macroeconomic model with two sectors, an energy sector and a final sector aggregating the rest of the economy. In addition, they use the net energy ratio, which is more comprehensive than the EROI, to assess the energy embodied in the intermediate and capital consumptions of the entire economy.
The model estimates a net worldwide EROI of 8.5
for 2018, and the sensitivity analysis performed on the model parameters demonstrates the robustness of the model. However, the model of Dupont et al (2021) focuses only on the current EROI and does not assess how it would evolve with a transition towards an energy system based mainly on intermittent renewable energy sources to meet the IPCC targets.
The papers presented above illustrate the difficulty of assessing the EROI of a given resource, technology, or society. However, they depict the key elements which have contributed to the increased attention paid to the EROI and the field of net energy analysis: (1) the standard EROI of the main fuels, in particular fossil fuels, has been declining due to depletion of finite resources Lambert et al, 2013); (2) the estimated EROI values for renewable energy sources in comparison to conventional fossil fuels are often controversial and vary significantly depending on the adopted methodology Brockway et al, 2019). This matter raises concerns that the renewables-led energy transition required to meet climate targets may have adverse socioeconomic impacts (Sers and Victor, 2018); (3) the EROI captures the efficiency of energy conversion technologies and provides some macro-economic perspective because of its link to the well-being of society .
We provide two reasons to assess the EROI of a whole-energy system instead of a set of technologies and resources of a given subsystem of the energy sector, such as the electricity grid.
First, it is not relevant to compare the EROI of renewable resources or technologies independently. For instance, solar and wind energies are intermittent and non-dispatchable. Gas and nuclear power plants are adjustable and can meet fluctuating demand. Thus, comparing the EROI of solar vs. nuclear without taking into account storage systems and other assets to balance the system is not pertinent. Second, a whole-energy system comprises several sectors (mobility, heat, electricity, industry) that use several technologies and resources that can be imported or extracted.
These resources are transported, stored, and converted by energy conversion technologies to supply end-use demands such as electricity, transport, heating, and the production of goods. Assessing an energy system as a whole opens the opportunity for the full deployment of synergies and can generate unexpected results (Contino et al, 2020).
Thus, the EROI of the system cannot be simply the sum of the EROIs of each of its components.
The literature comprises a large variety of energy models (based on optimization and simulation). We refer the reader to the reviews proposed by Limpens et al (2019); Borasio and Moret (2022), which compare models according to the following features: open-source, time resolution (from monthly to hourly), exhaustivity (i.e., considering the electricity sector only, or also mobility and heat supply). While there are many studies devoted to planning a whole-energy system based on the cost indicator, those that consider the EROI are much rarer. MEDEAS-World (Capellán-Pérez et al, 2019, a global, one-region energy-economy-environment model, is one of the few models which take into account the evolution of the societal EROI. MEDEAS is a policy-simulation dynamic-recursive model that has been designed using the theory of System Dynamics. The EROI of the system is estimated, based on a detailed review of the life cycle analyses of the different energy sources, including the ancillary structures required to handle the intermittency of renewable energies. For 2015, using aggregated data at the world level, the model estimated a global societal EROI of 12. Then, the results indicate that a fast transition to reach a 100% renewable electric system by 2060, consistent with the Green Growth narrative, could cause a decrease of the EROI of the system from 12 to 3 by mid-century.
In the present work, we focus on optimization models that reveal optimal configurations among many available options and degrees of freedom. They are suitable for analyzing complex systems, where many combined alternatives need to be explored. However, the study of Borasio and Moret (2022) illustrates that there is no perfect energy model capable of addressing all case studies and research topics. It is improbable that a Springer Nature 2021 L A T E X template single modeling framework will ever be able to capture all the relevant and interlinked dynamics of the energy transition, which is a complex and interdisciplinary challenge (Contino et al, 2020).
Various models can answer different research questions and can be complementary. However, selecting a particular model among the wide range of available energy models is a difficult task. Thus, building on existing and consolidated frameworks can be advantageous rather than developing new case-specific models from scratch.
We decided to use EnergyScope Typical Days (EnergyScope TD) (Limpens et al, 2019), an opensource model for the strategic planning of urban and regional energy systems. Compared to other existing energy models, which are often proprietary, computationally expensive, and primarily focused on the electricity sector, EnergyScope TD optimizes both the investment and operating strategy of an entire energy system, including electricity, heating, mobility, and the non-energy demand (NED) 3 . Therefore, the EnergyScope TD model offers several benefits compared to other modeling approaches and can easily be extended to include new indicators such as the EROI. In the following section, we focus on the recent works related to EnergyScope TD.
3 The NED comprises energy products used as raw materials in different sectors, not consumed as a fuel or transformed into another fuel (Rixhon et al, 2021a). The NED amounts to 20% of the total energy demand in the case of Belgium and 10% of the world final energy consumption.
Related work
A first attempt to study the Belgian energy system using the EROI metric was conducted by Limpens and Jeanmart (2018). The study focuses on the mix of energy storage technologies to allow a high penetration of intermittent renewable energies. A simplified hourly-based model optimizes the renewable energy and storage assets by maximizing the EROI while respecting energy balance constraints. The results indicate that depending on the deployment of renewable energies and on the nuclear share in the energy mix, the EROI of the system ranges from 5 to 10.5. However, one of the main limitations of this study is related to the model, which is not a whole-energy system model. This issue is addressed with EnergyScope TD (Limpens et al, 2019), a more advanced model of the Belgian energy system. First, the EnergyScope TD model was applied to analyze the 2035 Belgian energy system for different carbon emissions targets (Limpens et al, 2020). Choosing the year 2035 constitutes a tradeoff between a long-term horizon shaped by policy choices and a horizon short enough to be able to define the future of the energy sector with a group of known technologies. The results indicate a lack of endogenous renewable resources in Belgium of 275.6 [TWh/y], amounting to 30-40% of the primary energy demand. Several recommendations are proposed to obtain additional potential such as importing renewable fuels and electricity or deploying geothermal energy. In the study from Limpens et al (2020), a mix of solutions is the most cost-effective for reaching low carbon emissions.
Second, a further step is achieved by considering the importance of renewable fuels in a low-carbon energy system (Rixhon et al, 2021b).
This study performs an uncertainty quantification on a whole-energy system model by considering the total annualized cost of the system (which is the objective function of EnergyScope TD).
The polynomial chaos expansion method is implemented to perform the sensitivity analysis and to highlight the influence of the critical parameters on the cost of the system. This approach is applied to study the case of Belgium in 2050 4 , and the results indicate: (i) when considering uncertain parameters, the average value of the system cost is 17% higher at carbon neutrality than in a deterministic setting; (ii) the standard deviation of the cost increases when decreasing the GHG emissions; (iii) the price of renewable fuels is the primary driver of the uncertainty on the system's cost with 53% of the cost variation.
Finally, a preliminary implementation of a multi-criteria approach in the EnergyScope TD model, which is currently a single objective optimization model, is proposed by Muyldermans and 4 EU strives to be a climate-neutral continent in 2050 with the European Green Deal (European Commission, Secretariat-General, 2019), which sets a target of zero net GHG emissions.
Nève (2021). Given the challenges associated with the energy transition, this work allows to assess an energy system including economic, environmental, technical, and social aspects. The case study is similar to Limpens et al (2020) with the 2035
Belgian energy system. The analysis emphasizes the environmental impacts of the energy system depending on the weights associated with each criterion in the objective function: the total system cost, EROI, and global warming potential. The authors conclude that considering multiple criteria leads to a more nuanced and robust solution than a single criterion approach. However, this work is introductory, and the results must be consolidated with a more extensive analysis. In addition, it does not: (i) consider several GHG emissions scenarios; (ii) assess the uncertainty of the model input parameters. Nevertheless, it paves the way for this paper.
Research gaps and scientific contributions
To the best of our knowledge, the research gaps motivating this paper are four-fold:
1. Many studies using the EROI are focused on specific technologies and resources. There have been several attempts to estimate the EROI of society in the economic and social sciences (Court, 2019;Dupont et al, 2021), but none Springer Nature 2021 L A T E X template have considered a whole-energy system using a With these research gaps in mind, the main contributions of this paper, built on the previous studies (Limpens and Jeanmart, 2018;Limpens et al, 2019;Rixhon et al, 2021b;Muyldermans and Nève, 2021) (Limpens et al, 2020;Rixhon et al, 2021b) References of the models: PRIMES (European Commission, 2022); CSG (Artelys, 2022); TIMES (Fishbone and Abilock, 1981); Antares (Doquet et al, 2008;RTE, 2022); EnergyScope TD ( The motivation of this definition is that energy enters the productive economy at the final energy stage. Figure
EROI definition
EROI formulation of EnergyScope TD
This study uses the open-source energy system optimization model EnergyScope TD (Limpens et al, 2019), built on previous works (Moret, 2017;Codina Gironès et al, 2015). EnergyScope TD is a linear programming (LP), multi-sector, and multi-carrier model for a regional whole-energy system such as a country. This model has been validated for the 2035 Belgian whole-energy system by Limpens et al (2020), which is the case study of interest. Furthermore, the model has been used for several regions 7 including Italy (Borasio and Moret, 2022), Spain (Martinez and Maria, 2021), Switzerland (Moret, 2017), and Europe-26 (Dommisse and Tychon, 2020). In addition, Thiran et al (2020) developed a multi-regional version, called EnergyScope Multi-Cell, which was applied to Western Europe (Cornet et al, 2021) and Italy (Thiran et al, 2021
E constr (j) lifetime(j) + i∈RES E op (i),(3)
with T ECH and RES the sets of all the technologies and resources, respectively, and lifetime(j) the lifetime of the technology j. E constr (j) is the energy invested by the system in the construction of technology j over its entire lifetime. This total energy invested is then allocated between years based on the technology lifetime lifetime(j).
E op (i) is the energy invested by the system annually in the operation of resource i. They are defined as follows
E constr (j) = e constr (j)F(j) ∀j ∈ T ECH, (4a) E op (i) = t∈T |{h,td}∈T H T D(t) e op (i)F t (i, h, td)t op (h, td) ∀i ∈ RES,(4b)GWP tot = j∈T ECH GWP constr (j) lifetime(j) + i∈RES GWP op (i), (5a) GWP constr (j) = gwp constr (j)F(j) ∀j ∈ T ECH,(5b)GWP op (i) = t∈T |{h,td}∈T H T D(t) gwp op (i)F t (i, h, td)t op (h, td) ∀i ∈ RES.(5c)
Similarly to the energy invested, the total emissions related to the construction of technologies are the product of the specific emissions gwp constr and the installed capacity F. The total emissions of resources operation are the emissions associated with fuels from cradle to combustion and imports of electricity gwp op multiplied by the quantities of resources used F t (i, h, td) and the period duration
t op .
The GHG emissions scenario or target is defined by setting a limit, gwp limit , on the annual system GHG emissions GWP tot as follows Fig. 3: EROI -GHG emissions (GWP tot ) optima with primary energy mix and technologies implementation. The energy transition is composed of seven main steps illustrated with the red circles. Abbreviations: natural gas (NG), electric cars (elec. cars), electricity import (elec import), renewable gas (Gas-RE), renewable methanol (Methanol-RE). energy invested objective. This is another rationale to account for uncertainties in such a research field, which is investigated in Section 5.
GWP tot ≤ gwp limit .(6)
Scenarios analysis of the EROI for several GHG emissions targets
This Section conducts an analysis of the Belgian energy system in 2035 by forcing the total annual emissions of the system to decrease by reducing its upper limit, i.e., gwp limit in Eq. (6). In practice, 5% steps of GWP tot reduction were made from the GWP op (94.9 [MtCO 2 -eq./y]) of the "reference scenario-100%" presented in Section 4.1.
First, a summary of the evolution of the EROI of the system is presented. Then, the focus is set on the evolution of GHG emissions in the system. Finally, the evolution of the primary energy uses is depicted. Appendix C provides additional results presented in terms of installed capacities, energy invested, and final energy consumption for the different GHG emissions targets. Table 6: Reference scenario-100%: major technologies used to supply the demands of Table 5 in terms of production and installed capacity. The private mobility accounts for 50% of the passengers mobility. Units: production of electricity and all types of heat in [TWh], the private and public mobility in [Mpass.
-km], the freight mobility in [Mt-km], and the production capacity of electricity and all types of heat in [GW]. Abbreviations: end-use demand (EUD), high temperature (HT), decentralized heat low temperature (DEC heat LT), combined cycle gas turbine (CCGT), combined heat and power (CHP), centralized heat low temperature (DHN heat LT), passenger (pass.), heat pump (HP), natural gas (NG). The system shifts from high emissions to low emissions; however, this is a view of the mind because the solutions of each GHG emissions target scenario do not represent a transition path and must be analyzed individually. In the following, we comment on the energy transition in seven steps, the circles depicted on Figure 3.
System evolution summary
Step 0 -"reference scenario-100%" -dark circle depicted in Figure 3: GWP tot reaches 100.3
[MtCO 2 -eq./y], and the system's primary energy mix relies on 71% of NG and the related technologies to satisfy the electricity, heat, and mobility demand (see Section 4.1).
Step 1 -gwp limit = 90.1 [MtCO 2 -eq./y]: the system is partially electrified with a shift from NG to electric cars for private mobility. In addition, a part of the electricity production shifts from CCGT to electricity import, reaching 7% of the primary energy mix. The NG share in the primary energy mix dropped by 10% and reached 61%.
Step 2 -gwp limit = 80.6 [MtCO 2 -eq./y]:
wet biomass is introduced and achieves 10% of the primary energy mix. Centralized biomass co-generation technology supplies the centralized heat low-temperature demand instead of centralized gas co-generation. There is an additional decrease of 10% of the NG share in the primary energy mix.
Step 3 Thermal seasonal and daily storage are introduced to cope with the solar and wind seasonal and daily intermittency.
Step 4 -gwp limit = 56.9 [MtCO 2 -eq./y]:
synthetic renewable gas (gas-RE) begins to be imported. Then, when gwp limit = 33.2 [MtCO 2eq./y], the NG disappears from the primary energy mix, and the gas-RE import amounts to 30% of the primary energy mix.
Step 5 -gwp limit = 19.0 [MtCO 2 -eq./y]:
the imported methanol and the waste resource (gwp limit = 14.2 [MtCO 2 -eq./y]) disappear from the primary energy mix.
Step 6 -gwp limit = 9.5 [MtCO 2 -eq./y]: the imported ammonia and electricity vanish from the primary energy mix. The gas-RE import amounts to 60% of the primary energy mix. CCGT technology replaces the electricity imports to produce electricity by using the gas-RE.
Step 7 They amount to 10.4% of the primary energy mix. The wood represents 5.7% of the primary energy and is also used at its maximum capacity of 23.4 [TWh/y]. Finally, the PV capacity is 3.9 [GWe] and amounts to only 1% of the primary energy mix. Indeed, the energy invested in constructing offshore and onshore wind capacities is approximately two times lower than the PV capacity. Figure 6 displays the evolution of the system's primary energy mix broken down between nonrenewable and renewable resources. The following comments explain the main steps of the decrease in non-renewable resources.
System primary energy evolution
Step 1 -gwp limit = 90.1 [MtCO 2 -eq./y]: the decrease of NG in the primary energy mix is balanced with electricity import 9 , which reaches the maximum importation limit of 27.5 [TWh/y]. The other non-renewable and renewable resources are stable in volume compared to the "reference scenario-100%".
Step 2 -gwp limit = 80.6 [MtCO 2 -eq./y]: wet biomass and solar renewable resources balance the NG decrease. The wet biomass is used at its maximal capacity of 38.9 [TWh/y]. The PV capacity starts to increase and reaches a capacity of 11.2
[GWe]. Then, from 80.6 to 61.7 [MtCO 2 -eq./y], the NG decrease is balanced with increased waste and PV in the primary energy mix. The latter reaches the maximal installed capacity of 59.2
[GWe].
Step 3 -gwp limit = 61.7 [MtCO 2 -eq./y]:
NG amounts to 28.1%, PV 16.8%, wind offshore and onshore 11.7%, wood 6.4%, biomass 10.6%, and waste 4.9% of the primary energy mix. Steps 4 to 6 -from 61.7 to 9.5 [MtCO 2 -eq./y]: the decrease in NG, methanol, waste, and electricity imports is progressively balanced by importing renewable gas (gas-RE).
Step 7 -gwp limit = 4.7 Then, the EROI of the system is analyzed through its mean, variance, and probability density function (pdf). Appendix D provides the details about the GSA approach and additional results concerning the first and second-order PCE. Table 11 in Appendix D.4 lists all the critical parameters with their total-order Sobol values. Figure 9 (Bureau, 2015), 80% of the passenger mobility is expected to be supplied by private cars in the future. Therefore, it supports half of the passenger mobility, and the other half is supplied by public transport modes, i.e., buses, trains, and tramways.
Critical parameters
Thus, the uncertainty on the maximal share of public mobility % public mob max is likely to impact significantly private mobility and the EROI of the system.
EROI probability density functions
The PCE coefficients allow estimating the statistical moments, e.g., mean µ and variance σ 2 , of the EROI of the system, without additional [GWe] of maximal installed nuclear capacity are considered. They correspond to the extension of 2 and all out of the seven current nuclear reactors, respectively. Table 8 presents the mean, the standard deviation of the EROI, and the coefficient 11 On Friday, 18 March 2022, the Belgian government decided to extend the two most recent nuclear reactors (Doel 4 and Tihange 3) in operation for another ten years until 2035, corresponding to 2 GWe (Federal nuclear control agency, 2022). NUC-0, NUC-2, and NUC-5.6. Finally, Figure 11 presents the EROI pdf for each GHG emissions target using the Monte Carlo approach along with the mean depicted by the dashed vertical line. 9.0 9.7 11.6 10.5
Discussion
Overall, this study provides the following primary outcomes when maximizing the EROI of the system: (1) renewable energies (either domestic such as solar and wind, or imported with renewable fuels) are required massively to reach ambitious GHG emissions targets; (2) nuclear energy is not the primary driver of the EROI variance.
Concerning the first point, renewable fuels play an increasingly key role in the Belgian energy transition to satisfy the mobility and heating end-use demands when decreasing GHG emissions. They represent the major part of the system primary Springer Nature 2021 L A T E X template energy when GWP tot ≈ 10 [MtCO 2 -eq./y]. However, given the limited domestic renewable potential compared to the end-use demands, Belgium has to import energy-intensive renewable fuels to decrease GHG emissions. The uncertainty in the required operational energy for renewable fuels drives up the variance of the EROI. This result is similar to the simulations with the minimization of the system cost (Rixhon et al, 2021b;Limpens et al, 2020), where the uncertainties of the renewable fuels prices are responsible for the increase of the system cost variance. Figure for the parameters not related to the energy invested in construction and operation. However, these ranges could be updated based on the last data and publications releases. In addition, due to the significant uncertainty of the energy invested in the construction and operation of technologies and resources, we adopted an arbitrary uncertainty range of minus/plus 25%. Further work should be dedicated to refining this range and adapting it to specific technology and resource.
Conclusion
Most long-term policies to decrease the carbon footprint of our societies consider the cost of the system as the leading indicator in the energy system optimization models. However, the energy transition encompasses economic, technical, environmental, and social aspects. We consider a more comprehensive indicator to address this issue: the EROI of a whole-energy system.
The primary outcomes of this paper are:
(1) the development of a novel and open-source approach by adding the EROI in EnergyScope TD (Limpens et al, 2019), a whole-energy system optimization model, and providing open access to the Python code and the database; (2) the illustration of this approach in a real-world case study: the energy transition of the 2035 Belgian energy system. However, the novel model can be applied to any energy system at the country, regional or world level; (3) the comparison of the results obtained when minimizing the cost and maximizing the EROI; (4) the global sensitivity analysis of the EROI of the system by applying a polynomial chaos expansion method (Sudret, 2014). It provides the critical drivers of the variation of the system's EROI; (5) the estimation of the probability density functions of the EROI of the system for several GHG emissions targets.
The main results are five-fold. First, the EROI of the Belgian system decreases from 8.9 to 3.9
for GHG emissions targets going from 100 to 19
[MtCO2-eq./y]. These values can be put into perspective with estimated values of: (i) lower bound on the societal EROI, e.g., 5 Brandt, 2017) Fig. 12). It was designed to represent the minimum EROI required for conventional oil to be able to perform various tasks required for civilization. Making such a pyramid with the minimum levels of EROI of a carbon-free society to perform these services would greatly help policy-makers.
Thus, we hope this paper will encourage policymakers, industries, and academia to: (i) dedicate more research to assess whole-energy systems with the EROI indicator; (ii) spend more time and energy improving the knowledge about renewable fuels, mainly to decrease the uncertainties related to their cost, availability, and energy invested.
Future works should address the model limitations, e.g., drawing a continuous plan of strategies from today to the carbon neutrality of 2050 instead of the snapshot approaches. They will also focus on refining the data and reducing the uncertainties of the main drivers, i.e., the renewable fuels, of the variation of the EROI of the system.
In addition, this novel model could be extended to:
(i) assess the EROI of a system composed of several inter-connected countries using EnergyScope Multi-Cell (Thiran et al, 2020), such as Europe, to better take into account the domestic complementarity of renewables. Indeed, as previously stated, the developed EROI-based approach is not lim- Finally, the comparative study of maximizing the EROI of the system vs. minimizing the cost indicates that the EROI of the system remains higher by at least one point when using it as an indicator to plan the system, but with a cost between 5 % and 15 % higher. It raises the question: is this additional cost worth it? Indeed, a decline in EROI implies that less energy is available to fuel society due to a decreased efficiency of the energy system. A lower-EROI society requires more sober ways of living and more rational use of energy. Optimizing the EROI instead of the cost makes this sobriety imperative slightly less stringent, to the extent that it still needs to be better characterized and quantified. In addition, it is not easy to assess how the economy of society could be when reducing the EROI significantly. The price is a human concept dependent on the economy, and a financial cost depends on the system economy and energy. However, the EROI does not depend on the economic system but only on the energy system. Two societies with the same energy system, thus the same EROI, could have two different economic systems. With the energy available in excess, society makes choices to use this energy to provide some services and goods. With a decreasing EROI, the field of economic possibilities may also decrease. Thus, the EROI should be taken into account by policymakers when planning the transition as a metric for energy sobriety.
The trade-off between EROI decrease, i.e, more sobriety, and economic cost would require further investigation by researchers from several research fields, including social sciences.
Acronyms
Name Description
Ammonia-RE Synthetic renewable ammonia.
CCGT
Variables (bold) and parameters
The snapshot approach implicitly considers vari-
Sets and indices
Name Description j Technology index.
i Resource index.
h Hour index.
td Typical day index.
eud End-use demand index.
T H T D(t)
Hour h and typical day td associated to the time period t.
T ECH Set of technologies.
RES
Set of resources.
T Set of all periods of the year.
Appendix A Table 1 justifications projects the impact of macro-economic, fuel price, and technology trends and policies on the evolution of the EU energy system, transport, and GHG emissions. However, this study considers only one scenario, i.e., the "Reference scenario". In addition, this study does not consider the EROI, and there is no sensitivity analysis.
In the study (Devogelaer and Gusbin, 2021), The studies (Limpens et al, 2020;Rixhon et al, 2021b)
the
Appendix B FEC calculation
This appendix provides the details to derive the FEC from the simulation results to be used to calculate the EROI of the system following Eq.
(1).
The set of end-use demands EUD comprises:
(1) electricity; (2)
Then, for a given end-use demand (eud) the energy balance is
eud + i∈I c i (eud) = j∈J p j (eud),(8)
If j is a technology, it produces p j (eud) and possibly other outputs, such as electricity or hydrogen, by consuming gas, electricity, or biomass. Then, FEC j (eud) is defined as follows
FEC j (eud) = p j (eud) p j (eud) + outputs j inputs j .(10)
If j is a resource such as methanol or ammonia, then FEC j (eud) = p j (eud).
For instance, the methanol end-use demand can be partially satisfied with imports.
Let us consider the case where at least one technology uses this end-use demand as input material: I = ∅. Then, the consumptions c i (eud)
are taken into account as follows to estimate the FEC correctlỹ
p j (eud) = p j (eud) − i∈I c i (eud) p j (eud) j∈J p j (eud) .(13)
Finally, the different FEC j (eud) are estimated as previously described by replacing p j (eud) in Eq.
(10) and Eq. (12)
C.3 FEC evolution
D.2 Uncertainty characterization
Accounting for uncertainties in energy system long-term planning is crucial (Mavromatidis et al, 2018) to obtain robust designs against uncertainty.
However, the insufficient quantity and quality of available data is frequently a limitation. This challenge is addressed in Moret et al (2017) by developing an application-driven method for uncertainty characterization, allowing the definition of ranges of variation for the uncertain parameters.
These ranges were initially defined for the Swiss energy system and have been adapted for Belgium (Limpens, 2021;Rixhon et al, 2021b). Similarly, this study assumes that all the uncertain parameters are independent and uniformly distributed between their lower and upper bounds.
D.3 First-order PCE results
The second step, depicted in Figure 18, consists of using the first-order PCE to build shorter lists of uncertain parameters for the second-order PCE.
This selection is performed for each GHG emissions target considered in the sensitivity analysis.
It relies on good practice (Turati et al, 2017), by selecting the parameters which have at least, over the five runs, i.e., to ensure redundancy, one total-order Sobol index above the threshold = 1/d, where d = 138 is the number of uncertain parameters at the pre-selection phase. These
D.4 Second-order PCE results
The final step, depicted in Figure 18, consists of using the second-order PCE on the parameters short-listed to limit the error below 1% (Coppitters et al, 2020) on the EROI statistical moments: mean µ and variance σ. Figure 20 depicts the selection of the critical parameters using the second-order PCE for the GHG emissions targets considered. Table 10 Springer Nature 2021 L A T E X template presents the number (#) of short-listed and critical parameters using the first-order and secondorder PCE. Finally, Table 11
an inevitable increase in the share of renewable generation in the energy mix. Integrating these new energy resources and technologies will lead to profound structural changes in energy systems, such as an increasing need for storage and radical electrification of the heating and mobility sectors. Therefore, energy planners face the double challenge of transitioning towards more sustainable fossil-free energy systems, including high penetration of renewables, while preserving access to abundant and affordable primary energy resources. In the literature, a large variety of energy system models exists. Limpens et al (2019) has conducted an extensive review of 53 energy system models and tools. They all consider a cost-based objective function with sometimes a greenhouse gas emissions target. However, designing an optimal energy system is a multi-objective problem as it encompasses economic, technical, environmental, and social aspects. Thus, new flexible and open-source optimization modeling tools are required to capture the increasing complexity of future energy systems.
. In addition, alternatives to conventional fossil fuels such as tar sands and oil shale have a lower standard EROI, with mean values of 4 and 7 (Hall et al, 2014), respectively; (ii) various renewable and non-conventional energy alternatives have substantially lower EROI values, such
Limpens et al, 2019) : criteria fully satisfied, ∼: criteria partially satisfied, ×: criteria not satisfied. Multi-sectors: wholeenergy system considered; Multi-scenario: several scenarios of GHG emissions; EROI: EROI-based objective function; Sensitivity analysis: uncertainty analysis of the model parameters; Open dataset: the data used are in open-access; Open-access code: the code used to conduct the experiments is in openaccess. Abbreviations: European Commission (EU), Federal Planning Bureau of Belgium (FPB), EnergyVille (EV), France's transmission system operator (RTE), Belgium's transmission system operator (ELIA), UCLouvain (UCL), ULiège (ULG), Price-Induced Market Equilibrium System (PRIMES), Crystal Super Grid (CSG), The Integrated MARKAL-EFOM System (TIMES). Appendix C. Supplementary material), and the code repository with the data is open-access.
2 depicts the differences between primary energy production and final energy consumed with the concept of energy cascade. It illustrates the EROI of the system at the final stage. The numerator is the sum of all the types of final energy consumption considered in the system, such as electricity, heat, mobility, and non-energy. The denominator is the sum of all the indirect and direct energy invested for each step of the energy conversion from the primary energy production to the conversion and storage of the final energy into final energy consumption (FEC). Direct energy is required for the conversion energy process, such as the energy to extract and produce gas and oil in the field. Indirect energy is related to the products used at each step of the conversion process, such as the infrastructure used to extract and produce gas and oil in the field. Note that the FEC definition adopted in this study is provided by European Commission -Eurostat (2022): it excludes energy used by the energy sector, including distribution and transformation, and it is the energy that reaches the final consumer's door, such as households or industries.Therefore, EROI fin defined in Eq. (1) corresponds to the net external energy return (NEER) from the nomenclature ofBrandt and Dale (2011).
Fig. 2 :
2The energy cascade illustrates the EROI of the system at the final stage (EROI fin ), considered in this study, with the direct and indirect energy invested at each step of the energy conversion required to produce final energy and satisfy the final energy consumption. ThisFigurewas adapted from Brockway et al (2019). country as a single node where transmissions constraints within the country are not considered. Energy demand is balanced by energy generation without considering the flows between the producers and the consumers. However, the heating and electricity grid costs are considered, including an extra electricity network investment related to the integration of intermittent renewable energies. These costs are proportional to the installed capacity of electricity production and heating technologies; (v) achieving a short computational time, typically a few minutes, due to the use of typical days, and a mapping method to represent the storage over a year with an hourly resolution.
with e constr (j) [GWh/GW] the specific value of energy invested in construction of technology j which is the cumulative energy demand associated to the construction of one GW of this technology, e op (i) [GWh/GWh fuel ] the specific value of energy invested in operation of resource i which includes energy inputs for extraction/production/transportation and combustion, F(j) [GW] ([GWh] for storage technologies) the installed capacity of the technology j, F t (i, h, td) [GWh] the quantity of the resource i that is used at the hour h of the typical day td, t op (h, td) (1h by default) the time period duration, T the set of all the periods of the year, i.e., 8760 hours, and T H T D(t) the hour h and the typical day td associated to the period t. In Eq. (4b) summing over the different typical days and the hours of typical days, using the set T H T D(t), is equivalent to summing over the 8760 hours of the year. of the system GWP tot are defined as the sum of: (1) the emissions related to the construction and end-of-life of the energy conversion technologies GWP constr , allocated to one year based on the technology lifetime; (2) the emissions related to the operation of resources GWP op which accounts for extraction, transportation and combustion. They are defined as follows
2 (
2Therefore, the method relies on a snapshot approach (Codina Gironès et al, 2015) where for two different GHG emissions targets specified in Eq. (6), two different strategies result from the optimization of the system in the year 2035 without any dependence on the state of the system at any previous year. The two obtained strategies are thus totally independent from each other. GWP data (gwp op and gwp constr ) are estimated by using a life cycle assessment (LCA) approach taken from the Ecoinvent database v3.Wernet et al, 2016) using the "allocation at the point of substitution", i.e., taking into account emissions of technologies and resources "from the cradle to the grave" and following the indicator "GWP100a-IPCC2013" developed by the Intergovernmental Panel on Climate Change (IPCC) (Stocker et al, 2013). The "Input Data" section of the online documentation provides the input data to apply the EnergyScope TD model to the Belgian energy system in 2035.
Figure 3
3depicts a summary of the EROI optimum values for each GHG emissions scenario with primary energy mix and main technologies changes.
Fig. 4 :
4GWP constr and GWP op of the system, broken down by technologies and resources for several yearly GHG emissions targets in 2035.
Figure 5
5Figure 5 depicts the evolution of the system's primary energy mix for several yearly GHG emissions targets in 2035, broken down by resource categories. Step 0 -"reference scenario-100%": the primary energy mix comprises mainly NG with
[Fig. 5 : 3 [
53MtCO 2 -eq./y]: below 9.5 [MtCO 2 -eq./y], there are no more non-renewable resources. GHG emissions targets force the system to decrease the construction GHG emissions as the operation GHG emissions are approximately 0 [MtCO 2eq./y]. Renewable fuels almost completely replace the PV and wind resources, and the system is partially un-electrified to use them. For instance, electric vehicles (mobility private and freight) are replaced by vehicles using synthetic fuels. That case is purely hypothetical because it assumes that: (1) imported renewable fuels imply lower GHG emissions than renewable resources such as solar and wind. However, the GWP data on renewable fuels are not mature enough to draw such conclusions; (2) importing such large quantities of renewable fuels (approximately 510 [TWh/y]) may be unrealistic. Evolution of the system's primary energy mix for several yearly GHG emissions targets in 2035, broken down by resource categories. Abbreviations: non-RE: waste, methanol, and ammonia; Fossil: NG; RE-fuels: gas-RE, methanol-RE, and ammonia-RE; Biomass: wood, and wet biomass.4.3 Comparison of the EROI and cost of the systemWhen minimizing the total cost of the system instead of the EROI, without limiting the GHG emissions, EnergyScope TD gives an EROI for the Belgian energy system in 2035 at around 6.3 and a GWP tot of 94.5 [MtCO 2 -eq./y]. This can be compared with the EROI of 8.9 and GWP tot of 100.MtCO 2 -eq./y] for the "reference scenario-100%"where the EROI is maximized.
Figure 7
7depicts the evolution of the cost and EROI of the 2035 system for several GHG emissions scenarios when minimizing the cost and maximizing the EROI. The trends are similar.However, the primary energy mix differs, as illustrated byFigure 8. When minimizing the system
relies on numerical input data, which are sometimes highly uncertain, such as the energy invested in the operation of renewable fuels. This uncertainty could influence the key messages of the previous deterministic results. To nuance these messages, two actions are proposed: (i) being transparent on the dataset used (refer to the online documentation), (ii) assessing the impact of uncertainty of the system's EROI for several GHG emissions targets through global sensitivity analysis (GSA), and the Monte Carlo method. This section is an extension of the works of Limpens (2021); Rixhon et al (2021b) by assessing the uncertainty of the EROI of the system with a GSA using the polynomial chaos expansion (PCE) method (Sudret, 2014). The PCE approach emphasizes the critical parameters by using Sobol indices and extracting statistical moments, mean and variance, of the EROI of the system. The implementation of this approach is conducted by using the RHEIA 10 (Coppitters et al, 2020) Python library.This section is organized into two parts. First, the most critical uncertain parameters for the EROI of the system are listed according to their respective Sobol indices based on the GSA results.
Fig. 7 :
7Comparison of the evolutions of the system's cost and EROI for several scenarios of GHG emissions, when, respectively, minimizing the cost and maximizing the EROI.
illustrates the evolution of the critical parameters as a function of GHG emissions constraints. More precisely, the evolution of the total-order Sobol values of the top-5 parameters for the GHG emissions constraints of 28.5 [MtCO 2 -eq./y] (Figure 9a) and 85.4 [MtCO 2 -eq./y] (Figure 9a) are represented. It is expected that e Gas-RE op becomes the primary driver of the variation of the EROI of the system when GHG emissions targets decrease, given the increasing share of renewable gas in the primary energy mix. In the model, the value of the energy invested in the operation of renewable gas is 4.4 times greater than its fossil equivalent, making it less competitive; thus, unused with no restrictions on GHG emissions. However, it becomes the most-impacting parameter, up to 67.1% of the variance of the EROI of the system for the GHG emissions target of 19.0 [MtCO 2eq./y]. The lower part of Figure 9 illustrates the opposite trend for NG. Given its low energy invested in operation, it is a critical resource when the GHG emissions targets are not compelling.
Fig. 8 : 4 [ 0 [
840Comparison of the system's primary energy mix when minimizing the cost (left) and maximizing the EROI (right), for several scenarios of GHG emissions. The mix is broken down between non-renewable resources (upper) and renewable resources (lower)The energy invested in the construction of gas cars and NG operation substantially impacts the EROI variance with 39.2% and 25.5%, respectively, when the GHG emissions are weakly constrained (85.MtCO 2 -eq./y]).Then, the energy invested in the construction of electric cars e Elec. cars constr is the second parameter to play a key role in the variance of the EROI of the system with the decrease of GHG emissions. It is the most-impacting parameter on the EROI with 18.0%, for the target of 56.9 [MtCO 2 -eq./y]. Then, it is the second most-impacting parameter with 4.8% and 6.1%, for the targets of 28.5 and 19.MtCO 2 -eq./y].Figure 16in Appendix C depicts the essential impact on the system's EROI of the private mobility for GHG emissions between 61.7
for GWP tot =28.5 [MtCO 2 -eq./y]. (b) Top-5 parameters for GWP tot =85.4 [MtCO 2 -eq./y].
Fig. 9 :
9Evolution of the total-order Sobol values of the Top-5 critical parameters for GHG emissions of 28.5 and 85.4 [MtCO 2 -eq./y]. Abbreviations: energy invested in the operation of gas-RE cars (e Gas-RE op ), energy invested in the construction of electric cars (e Elec. cars constr ), nuclear maximal installed capacity (f NUC max ), wood maximal availability (avail Wood ), maximal share of public mobility (% public mob max ), energy invested in the construction of NG cars (e NG cars constr ), energy invested in the operation of NG cars (e NG op ), energy invested in the operation of wet biomass (e Wet biomass op ).
computational cost. Furthermore, based on the obtained surrogate model and with a few supplementary seconds of computational time, the pdf of the EROI can be estimated by a Monte Carlo approach.
Figure 10 depicts
10, for the GHG emissions targets considered, the EROI mean µ (EROI [GSA]) and the evolution of the 95% (±2σ in gray) confidence interval, along with the EROI values from the deterministic approach EROI [Deterministic] NUC-0, where the maximal installed capacity of nuclear power plants is 0 [GWe]. Based on the 2021 policies, Belgium planned to phase out coal and nuclear. However, the 2022 policies 11 reconsider the progressive shutdown of the nuclear power plants. Thus, two deterministic scenarios in 2035 with 2 (EROI [Deterministic] NUC-2) and 5.6
Fig. 10 :
10The mean values of EROI µ of the runs performed during the sensitivity analysis (EROI [GSA], blue curve) with the 95% confidence interval (±2σ in gray). The EROI values of the three deterministic scenarios: (i) with the nominal value of the parameters corresponding to the complete phase-out of nuclear (EROI [deterministic] NUC-0, green curve); (ii) the two alternative scenarios with the extension of 2 [GWe] (EROI [deterministic] NUC-0, black curve) and 5.6 [GWe] (EROI [deterministic] NUC-5.6, red curve).of variation (CoV), defined as the ratio between σ and µ. It also provides the values of the system's EROI for the three deterministic scenarios:
Fig. 12 :
12The pillars of the energy transition to decrease the GHG emissions when maximizing the EROI of the system.6 Discussion and limitationsThis section first discusses the results of Sections 4 and 5. Then, it presents the limitations of the model and of the methodology used to perform the sensitivity analysis of the EROI.
12 depicts the key pillars of the energy transition when decreasing the GHG emissions. The system sequentially uses most of the options from the energy Mix scenario presented inLimpens et al (2020), which is a scenario accounting for an increased amount of renewable resources plus nuclear capacity and geothermal energy, but with a different priority.The model begins with low-energy intensive fossil (NG) and domestic renewable resources (wind) when there is no limit on GHG emissions. Then, it first improves its energy efficiency in the early stages by reducing the primary energy consumed to meet the demand. The electrification is progressively performed with the electricity imports at their full potential (27.57 [TWh/y]) to improve the electrification of the mobility (private electric vehicles) and heating sectors (heat pumps). Then, to enhance the electrification while reducing the overall global warming potential, the system uses , the model forces the system to import renewable fuels massively to achieve ambitious low GHG emissions targets. When maximizing the EROI, the system uses mainly renewable gas, and when minimizing the cost, it is a mix of H2, renewable gas, and renewable-liquid fuels (ammonia andmethanol). These pillars indicate the main levers to decrease GHG emissions while maximizing the EROI of the system and the research directions to decrease the uncertainties of the parameters of the related technologies and resources. Indeed, efforts should not be distributed equally to decrease the uncertainties of every model parameter. The sensitivity analysis provides the critical uncertain parameters responsible for the main contributions to the EROI variance. A similar conclusion to Rixhon et al (2021b); Limpens et al (2020) is drawn: policymakers, industries, and academia should spend time and energy improving the knowledge about renewable fuels by reducing the cost, the energy invested in the operation, and the related uncertainties. Concerning the second point, the sensitivity analysis reveals the impact of the maximum capacity of the nuclear power plants on the variance of the EROI. The contribution of this parameter reaches a maximum of 12.5% for the GHG we depict three main model limitations: (1) the snapshot approach (Codina Gironès et al, 2015) limits the concept of a trajectory between several GHG emissions targets. One way to overcome this issue is to consider a pathway (Limpens, 2021, Chapter 7) that could describe the different steps continuously in terms of technologies to implement and resources to exploit; (2) the unlimited availability of imported renewable fuels regardless of origin. For very ambitious GHG emissions targets, GWP tot ≤ 9.5 [MtCO 2eq./y], the domestic renewable energies such as solar and wind are replaced by imported renewable fuels and electric technologies by gas-based technologies. Thus, almost all the primary energy is composed of renewable fuels. This case is not realistic as it is improbable that Belgium would be able to import approximately 510 [TWh/y] of such renewable fuels. Estimating the maximum quantities of renewable fuels that could realistically be imported could be done with different costs and energy invested in operation concerning the origin. For instance, Colla et al (2022) propose in their study a framework to account for the different origins of biomass imports; (3) the linear optimization approach makes the results highly sensitive to the input parameters. A slight difference in technology efficiency or energy invested in construction or operation can make the system switch between two solutions which share a similar value for the objective function, but are very different in nature. The sensitivity analysis partially addresses this issue because it relies on the relevant definition of the list of uncertain parameters with their uncertainty range. Another approach could consist in investigating the feasible space near optimality. The study of Dubois and Ernst (2021) proposes a generic framework for addressing this issue. It allows looking for solutions that can accommodate different requirements, such as determining necessary conditions on the minimal energy that the system will invest in domestic renewable energies or imported renewable fuels. Finally, we outline four main limitations concerning the uncertainty characterization data have been obtained from the ecoinvent database (Wernet et al, 2016). However, new data and publications could help refine these values, especially for renewable fuels, around which research is booming; (2) the global warming potential data in the operation of renewable resources, particularly renewable fuels, is assumed to be 0. New data and publications could refine these values, similar to the data for energy invested. Indeed, these investigations are required to study low carbon energy system with GWP tot ≤ 10 [MtCO 2 -eq./y] to avoid having unrealistic results where imported synthetic fuels replace all the domestic renewable; (3) the choice of uncertain parameters. This study focuses mainly on energy invested related parameters and did not consider other parameters such as the technology efficiencies and lifetimes or the GWP of construction and operation. A complete investigation should be conducted to consolidate the results; (4) the uncertainty ranges considered are based on Moret et al (2017); Rixhon et al (2021b)
or 6 (
6Court, 2019); (ii) worldwide EROI, e.g., 8.5(Dupont et al, 2021) in 2018 and 12(Capellán-Pérez et al, 2019) in 2015. Second, the renewable fuels -mainly imported renewable gas -represent the largest share of the system primary energy mix when GHG emissions decrease due to the lack of endogenous renewable resources such as wind and solar. Third, the EROI trend is similar when decreasing GHG emissions when minimizing the cost or maximizing the EROI. In both cases, the EROI values decrease from 8.9 to 3.9 (EROI maximization) vs. 6.3 to 2.5 (cost minimization) for GHG emissions targets going from 100 to 19 [MtCO2-eq./y]. In addition, the strategy to decrease GHG emissions is similar when minimizing the cost of the system and maximizing the EROI. It consists of importing an increased share of renewable fuels to reduce GHG emissions. However, there is a difference; instead of using only large quantities of imported renewable gas in the case of EROI maximization, the renewable fuels are more diverse when minimizing the cost with renewable ammonia, methanol, and H2. Fourth, the sensitivity analysis reveals that the energy invested in the operation of renewable gas is responsible for 67.1% of the variation of the EROI for the GHG emissions target of 19 [MtCO 2 -eq./y]. Finally, the estimation of the EROI probability density functions exhibits that decreasing the GHG emissions makes the EROI of the system more variable to uncertain parameters. Indeed, the coefficient of variation, which is the ratio of the standard deviation over the mean, increases with GHG emissions reduction.Overall, the decrease in the EROI of the Belgian system with the GHG emissions raises questions about meeting the climate targets without adverse socio-economic impact. Indeed, most countries rely massively on fossil fuels, like Belgium, and they could probably experience such an EROI decline when shifting to carbon neutrality. As pointed out in the introduction, several attempts to determine a lower bound of the societal EROI below which a prosperous lifestyle would not be sustainable have been performed over the past few years. The estimation of this threshold differs from one study to the others.Thus, it is difficult to conclude what does mean an EROI value of 4 for Belgium in terms of lifestyle when reaching GHG emissions targets models assume at least a constant demand based on economic growth, if not an increase. Thus, the energy sector is likely to take a more significant share in the economy at the expense of other sectors to sustain such a demand with a decreasing EROI. A decreasing EROI implies a decreasing quantity of services and raises the question: which sectors and services should be favored? A challenging way to answer this question could be to extend the concept of the "Pyramid of Energetic Needs"
ited to a specific country or area; (ii) perform multi-criteria optimization in the vein of Muyldermans and Nève (2021) with indicators such as the system cost, global warming potential, and EROI; (iii) include a macroeconomic model following the approach of Dupont et al (2021) to estimate another indicator, introduced by Fagnart and Germain (2016), called the net energy ratio (NER) of the economy. The NER is more comprehensive than the EROI and allows assessing the energy embodied in the intermediate and capital consumptions of the entire economy.
Acknowledgments. The authors would like to acknowledge the authors and contributors of the EnergyScope TD model and the the collaboration of the teams and provided helpful insights and discussions about the present work. In addition, the authors would like to thank the editor and the reviewers for the comments that helped improve the paper. Declarations Conflict of interest. There is no conflict of interest to be reported. Availability of code and data. Code repository and data, and the latest documentation are available on Github: https: //github.com/energyscope/EnergyScope, https: //energyscope-td.readthedocs.io/en/master/. Authors' contributions. The first draft of the manuscript was written by Jonathan Dumas and all authors commented on previous versions of the manuscript. All authors helped improve the paper quality based on the reviewer's comments and approved the final manuscript. Jonathan Dumas did the validation of the results and conducted the formal analysis. Jonathan Dumas, Antoine Dubois, Paolo Thiran, Pierre Jacques, Francesco Contino, and Gauthier Limpens did the conceptualization of the approach and the methodology. Jonathan Dumas, Antoine Dubois,
Federal Planning Bureau discusses what role offshore wind can play in helping Belgium achieve climate neutrality by the middle of the century. The analysis is multi-sectors by considering the electricity, H2, and gas sectors. The model used is Artelys Crystal Super Grid (Artelys, 2022), which is not in open-access, and the data used for the study are not available. In particular, this report examines the development of joint hybrid offshore wind projects that both provide renewable energy capacity and can serve as interconnectors linking different countries. Two different scenarios are defined and studied; thus, this study is considered partially multi-scenarios. However, this study does not consider the EROI, and there is no sensitivity analysis. The study (Meinke-Hubeny et al, 2017) uses the TIMES/MARKAL model, a reference in scenario analysis. This model is open access (Fishbone and Abilock, 1981), but the different versions for each country are not open. This study has adapted the model to the Belgian case and is unavailable. The main assumptions are detailed in the report with some input parameters. However, there is no proper access to all the input data. The TIMES Belgium model includes different technology portfolios for different supply and demand sectors of the energy system and is consequently multi-sectors. The model generates a set of five scenarios where assumptions on three parameters, namely the import capacity for electricity, the fossil fuel prices, and the phase-out of nuclear energy, are being altered. Finally, the scenario analysis with the TIMES Belgium model is based on a system cost optimization approach; thus, it does not consider the EROI. The study Elia (2017) analyzes both shortterm and long-term policy options on the future energy mix for Belgium on the path towards 2050. It proposes the "base case scenario", "decentral scenario", and "large-scale RES scenario". On top of these scenarios, different sensitivities are assessed at the 2030 and 2040 time horizons, resulting in additional scenarios. The assumptions of each scenario are detailed, but the input data are not available, and there is no sensitivity analysis. The report focuses on the electricity sector with renewables (PV, onshore and offshore wind, biomass, hydro, and geothermal) and thermal (CCGT, nuclear, and CHP) generation plants, electric demand (heat pumps, electric vehicles), and considers interconnections with neighboring countries. However, it is not multi-sectors as it does not model the non-electric demand of the transportation, heating, and non-energy sectors. The electricity market simulator developed by RTE, Antares (Doquet et al, 2008; RTE, 2022) is used to perform the electricity market and adequacy simulations. Antares is open-source and calculates the most-economic unit commitment and generation dispatch. Finally, the scenario analysis with the Antares model is based on a system cost optimization approach; thus, it does not consider the EROI. The objective of the Energy Pathways to 2050 report (RTE, 2021a) is to construct and evaluate several possible options for the evolution of the French power system (generation, network, and consumption) to achieve carbon neutrality.To this end, several scenarios are proposed based on different assumptions, from 100% renewable generation technologies to a mix of renewable and nuclear capacities. Each scenario is detailed with the assumptions in the report, and the dataset used to conduct the study is open-access(RTE, 2021b). The open-source power system model, Antares(Doquet et al, 2008; RTE, 2022), describes the production capacities, the network, and the sources of consumption in all European countries, to simulate the production, consumption, and exchanges per country at hourly intervals in all the countries of the European Union.The study does not conduct a global sensitivity analysis of the input parameters. However, it performs several variations of some key parameters to assess the variation in the cost of the system. Finally, the Antares model uses a cost optimization approach.Springer Nature 2021 L A T E X template
Fig. 13 :
13Evolution of the electricity production, storage (electric, thermal, gas, ammonia, and methanol), and renewable fuels asset installed capacities breakdown by technology for several scenarios of GHG emissions in 2035. Abbreviations: combined cycle gas turbine (CCGT), photovoltaic (PV), electric (elec.), battery of electric vehicle (BEV), pumped hydro storage (PHS), decentralized electrical heat pump (DEC elec. HP), Decentralised fuel cell cogeneration gas (DEC FC CHP gas), Decentralised boiler gas (DEC gas boiler), centralized seasonal (DHN seasonal), high value chemicals (HVC).
Figure 17
17depicts the evolution of the FEC break-
GWP tot ≤ 19.0 [MtCO 2 -eq./y].
Fig. 20 :
20Sobol indices of the parameters using the second-order PCE. Parameters are sorted and critical ones (in blue) have an index above the threshold 1/d, with d the number of uncertain parameters considered in the second-order PCE. The y-axis is logarithmic.
bottom-up, optimization-based model;2. While many studies are devoted to planning a whole-energy system based on the cost indicator, those considering the EROI are rarer.MEDEAS-World(Capellán-Pérez et al, 2019), a global energy-economy-environment system dynamics model, is one of the few that consider the societal EROI evolution but is not a bottom-up, optimization-based model; 3. There currently exists no open-access consolidated EROI dataset for all technologies and resources of a whole-energy system; 4. There is no comparison of the EROI of a whole-energy system, accounting for parameters uncertainties, with the deterministic costoptimum situation.
, are fourfold: 1. Develop a novel and open-source approach by adding the EROI in a whole-energy system optimization model. This approach can be applied to an energy system to investigate the evolution of the societal EROI during the energy transition at the worldwide, country, or regional level; 2. Propose and implement a methodology to assess the impact of uncertain parameters on the EROI and compare the results with those of the deterministic analysis; 3. Use a real-world case study, the Belgian energy system, for several GHG emissions targets in 2035 to illustrate the novel approach by comparing the results when considering the cost as a leading indicator. In this case study, we emphasize the role of renewable fuels for decreasing the GHG emissions; 4. Provide a transparent and collaborative database of the EROI of all technologies and resources of a whole-energy system. In addition to these contributions, this study also provides open access to the code repository 5 and the latest documentation 6 to help the community reproduce the experiments. Table 1 presents a comparison of the present study with several state-of-the-art papers analyzing energy transition systems. Appendix A provides the justifications for the comparison. The present work provides decision-makers with insightful guidelines to answer the following questions: (i) What are the main changes in the planning of the transition of an energy system when using the EROI as a guiding indicator instead of the total system's cost ? (ii) To what extent should uncertainties be considered when EROI st u dy of a w h ole en er gy syst em Fig. 1: Paper skeleton with the main contributions.The energy system optimization model EnergyScope TD is used to assess the EROI of the Belgian energy system for several GHG emissions targets. Then, an EROI sensitivity analysis identifies the critical uncertain parameters X ∈ R N and estimates the EROI probability density functions using the surrogate modelf .lines the main findings and proposes ideas for further work. Appendix A presents the justifications for the comparison conducted inTable 1.Energy system
optimization model
Polynomial Chaos
Expansion
-critical uncertain parameters
-EROI mean & variance
EROI maximization
vs.
cost minimization
Methodology
Case study
EROI of the system
Surrogate model
Sen sit ivit y an alysis of t h e EROI of t h e syst em
EROI pdf
sample i of
planning a low-carbon energy system based on the
maximization of EROI? Furthermore, which are
the key parameters that drive the uncertainty in
the system's EROI ? (iii) Given the limited avail-
ability of local renewables in Belgium, what solu-
tions of the Mix scenario presented by Limpens
et al (2020), such as electrification, nuclear energy,
and import of synthetic fuels, would most affect
the variation of the system's EROI?
1.3 Organization
Figure 1 depicts the paper skeleton, which is orga-
nized as follows. Section 2 presents the EROI
definition used in this study and provides the suc-
cinct formulation of the EnergyScope TD model
with the main assumptions. Section 3 presents the
real-world case study of the Belgian energy system
in 2035, and Section 4 investigates its EROI evolu-
tion for several GHG emissions targets. Section 5
presents the results of the EROI sensitivity anal-
ysis, and Section 6 points out the model and
methodology limitations. Finally, Section 7 out-
Appendix B provides the methodology to derive
the final energy consumption from the simulation
results in EnergyScope TD. Finally, Appendices C
and D give additional results for the EROI study
of the Belgian energy system in 2035 and for the
sensitivity analysis, respectively.
2 Methodology
This section presents the EROI definition used
in this study and details the main assumptions
of the model, including the EROI-based objective
function. The EnergyScope TD complete formu-
lation, the documentation of the model, and the
input data are described in Limpens et al (2019,
Criteria
[1]
[2]
[3]
[4]
[5]
[6]
This study
Authors
EU
FPB
EV
ELIA RTE UCL UCL-ULG
Multi-sectors
×
×
×
Multi-scenario
×
∼
Model
PRIMES CSG TIMES
Antares
EnergyScope TD
EROI
×
×
×
×
×
×
Sensitivity analysis
×
×
×
×
∼
Open dataset
×
×
∼
∼
Open-access code
×
×
×
Table 1: The contributions of the present study are compared to several state-of-the-art studies about
the transition of the energy system. Justifications are provided in Appendix A.
References: [1] (European Commission et al, 2021); [2] (Devogelaer and Gusbin, 2021); [3] (Meinke-
Hubeny et al, 2017); [4] (Elia, 2017); [5] (RTE, 2021a); [6]
This study considers the EROI defined at the finalenergy stage
EROI fin =
Gross energy produced
Energy invested
=
E out
E in
. (1)
E out is computed at the final stage, i.e., the quan-
tity of gasoline or electricity required by cars
and trains, the heat produced for warming build-
ings, or the electricity delivered to households
and companies. E in is also measured in terms of
final energy. It is composed of: (1) the energy
required for building and operating all the infras-
tructure of the energy system, from the cradle to
the grave; (2) the energy used for operating the
energy system.
).EnergyScope TD represents the heating,
mobility, and electricity sectors with the same
level of detail. The main characteristics are: (i)
satisfying the system end-use demand (EUD)
instead of final energy consumption (FEC). The
system EUD is composed of electricity, heat,
transport, and non-energy demands. For instance,
passenger mobility is defined in passenger kilome-
ters per year rather than in a certain amount of
gasoline to fuel cars or electricity to power trains;
(ii) optimizing the system design and operation by
minimizing its overall cost; (iii) using an hourly
resolution which makes the model suitable for ana-
lyzing the integration of intermittent renewable
energy resources and storage; (iv) modelling the
Energy used to
produce machines to
store and convert.
Production of primary
energy
Transport to
energy system
Primary
energy
available for
system
Conversion
& storage
Final energy
consumption
Energy used for
transport.
Energy used to
extract energy.
Energy used to
produce machines
to extract energy.
Energy used to produce
machines for transport.
Dir ect energy
invested.
En er gy
con ver st ion
st age
EROI of the system:
In dir ect + dir ect
energy invested
In dir ect energy
invested.
Final energy
consumption
Energy lost
Energy lost
Table 2
2sum-
Table 2 :
2The specific value of operational energy inputs e op [GWh/GWh fuel ] and GHG emissions gwp op [MtCO 2 -eq./GWh fuel ] for each resource in 2035 used in the case study. The methodology of the data collection of gwp op and e op relies onMuyldermans and Nève (2021) where the data
have been collected from the ecoinvent database
(Wernet et al, 2016).
online documentation for the data related to the
construction of technologies.
Finally, EnergyScope TD has an hourly res-
olution and a tractable formulation with a few
minutes of computational time thanks to a for-
mulation with twelve typical days (Limpens et al,
2019). This number allows to reach a good trade-
off with: (i) a limited impact on the resulting
energy system strategy, i.e., the installed capacity
of the technologies and the use of resources remain
in the same order of magnitude as without the use
Table 3 :
3Comparisonof installed capacity [GWe]
or [GWth] of technologies using renewable energy
in 2015, 2020 and their maximal potential
expected in the model for 2035. † PV and solar
thermal technologies compete with the land avail-
ability constraint of 250km 2 which is equivalent
to 59.2 GWe of PV or 70 GWth of solar thermal
(centralized or decentralized). 2015 and 2020 data
are based on European Commission et al (2021)
and the 2035 projection on Limpens et al (2020).
Abbreviations: centralized (cen.), decentralized
(dec.), thermal (th.).
Resources
2015 2020
2035
Imported
fuels
bio-ethanol
0.48
? †
no limit
bio-diesel
2.89
? †
no limit
gas-RE
0
0 no limit
H2-RE
0
0 no limit
ammonia-RE
0
0 no limit
methanol-RE
0
0 no limit
Biomass
woody
13.9
? †
23.4
wet
11.6
? †
38.9
Waste
7.87
? †
17.8
Elec. import
24.54
-0.6
27.57
Table 4 :
4Comparisonof renewable resources
Table 5 :
5Comparison TWh).Table 6details the major technologies used to supply the demands ofTable 5in terms of share of production and installed capacity. The electricity generation relies TWh). A large part of the electricity production (42.3 TWh) is used to supply heat pumps which supply mainly decentralized and centralized lowtemperature heat demands. The gas cogeneration is the most prominent player in supplying the industrial high-temperature heat demand, besides a small share from gas boilers. Overall, mobility is also dominated by NG import:(1)passenger mobility is equally divided between private Finally, methanol and ammonia are imported to satisfy the non-energy demand, where a large part of the methanol is used to synthesize high-value chemicals (HVC). The result of an EROI-optimum for the 2035 Belgian energy system of 8.9 is close to the estimation of the 2018 societal worldwide EROI (Dupont et al, 2021). However, this comparison suffers from two limitations. First, in their model, the current global energy system was mainly based on fossil fuels in 2018. Second, the scope of their study differs as it considers the entire world. EnergyScope TD with the reference scenario indicates that renewable synthetic fuels are too energy-expensive to compete against the fossil equivalent when there is no constraint on GHG emissions. However,it is essential to remind that such a system results from linear optimization. A slight difference, e.g., efficiency, energy invested in construction or operation, can make the system switch between two completely different solutions but with similarof EUD for 2015, 2020,
and the 2035 projection. The 2015 and 2020 heat
low/high T. EUD are derived from the FEC of
the corresponding sector (residential, service and
industry for heat low T. and energy intensive
industries for heat high T.) by removing the corre-
sponding electricity FEC. 83.1% of the electricity
FEC of Belgium is allocated to the residential
and services sectors, and the remaining is the
energy-intensive industrial sector. This ratio is
estimated based on European Commission and
Eurostat (2018). 2015 and 2020 data are based
on European Commission et al (2021) and the
2035 projection on Limpens (2021). Abbrevia-
tions: end-use demand (EUD), temperature (T.),
passenger (pass.), tons (t).
between the EUD in 2015, 2020 and 2035. It
is possible to notice the COVID-19 impact in
2020. The 2035 passenger transport demand, 194
[Mpass.-km/y], is divided between public and pri-
vate transport. The lower and upper bounds for
the use of public transport are 19.9% and 50% of
the annual passenger transport demand, respec-
tively. The freight demand, 98 [Mt-km/y], can be
supplied by trucks, trains, or inland boats with
corresponding lower and upper bounds: 0% and
100%, 10.9% and 25% 15.6% and 30%, respec-
tively.
4 EROI analysis with fixed
parameters
This section presents the model's results in the
real-world case study of the Belgian energy sys-
tem in 2035. First, Section 4.1 presents the results
of the EROI maximization of the system without
imposing a GHG emissions target. Then, Section
4.2 investigates the evolution of the EROI of
the system for several GHG emissions targets. It
studies how this impacts the energy and tech-
nology mix of the system, the breakdown of the
GHG emissions, and the evolution of the primary
energy mix. Finally, Section 4.3 compares a solu-
tion maximizing the system's EROI to a solution
minimizing the system's cost for the same GHG
emissions targets.
4.1 Reference case study results
EnergyScope TD reaches an EROI-optimum Bel-
gian energy system in 2035 at around 8.9 and a
GWP tot of 100.3 [MtCO 2 -eq./y] without limiting
the GHG emissions. This case is called "reference
scenario-100%", where the constraint Eq. (6) is
not activated, and the parameters are at nominal
values. In comparison, the EU reference scenario
2020 (European Commission et al, 2021) provides
the actual 2015 and 2020 values and the 2035
forecast value for the total GHG emissions 8 of
Springer Nature 2021 L A T E X templateDemand
Technology Production Capacity
Electricity
CCGT
33.4
6.5
wind
43.0
16.0
PV
4.0
3.9
Heat HT
gas CHP
59.7
8.0
gas boiler
4.2
4.8
DHN heat LT
HP
45.2
12.9
gas CHP
7.0
4.3
DEC heat LT
HP
92.9
31.3
Private mobility gas car
97.0
-
Public mobility
train
48.5
-
tramway
29.1
-
gas bus
19.4
-
Freight
gas truck
44.1
-
gas boat
29.4
-
train
24.5
-
-gwp limit = 61.7 [MtCO 2 -eq./y]: PV technology and waste resource achieve the maximal available capacity with 59.2 [GWe] and 17.8 [GWh], representing 17% and 5% of the primary energy mix, respectively. Waste boilers and direct electricity heating replace the industrial gas boilers. The trucks shift from NG to electricity.
-gwp limit = 4.7 [MtCO 2 -eq./y]: there is an extreme shift from electric-based to gas-based technologies. Indeed, the wood, wet biomass, wind, and solar energies have almost completely vanished from the primary energy mix. The gas-RE, ammonia-RE, and methanol-RE imports amount to 86%, 2%, and 10% of the primary energy mix, respectively. The cars and trucks shift from electric to gas technologies using the gas-RE. The CCGT produces electricity with gas-RE.Finally, boilers and co-generation using gas-RE satisfy the heat demand. Note that the value of energy invested in the operation of renewable fuels is difficult to estimate. Thus, when the share of these fuels represents a large amount of the primary energy mix, the value of the EROI of the system becomes more uncertain than when using conventional fossil fuels.Figure 4 depicts the GWP constr and GWP op of the system, broken down by technologies and resources for the different yearly GHG emissions targets in 2035. The GHG construction emissions are mainly driven by electricity and mobility technologies. The PV installation amounts to a significant part of the electricity construction GHG emissions increase between GHG emissions targets of 80.6 and 61.7 [MtCO 2 -eq./y]. Private passenger mobility composes the prominent part of the mobility construction GHG emissions with battery-electric cars for GHG emissions targets between 90.1 and 9.5 [MtCO 2 -eq./y], and NG cars for the reference case and the GHG emissions target of 4.7 [MtCO 2 -eq./y]. The GHG operation emissions mainly comprise non-renewable resources: NG, electricity import, methanol, and ammonia. They decrease with the progressive shift from non-renewable to renewable resources. GWP constr .4.2.2 Breakdown of the system GHG
emissions
RE-fuels
Storage
Heat
Electricity
Mobility
(a) Natural gas
Ammonia
Electricity import
Wet biomass
Wood
Waste
Methanol
(b) GWPop.
Table 7
7presents the top-5 critical parameters and their total-order Sobol values [%] for each GHG emissions target considered. The total-order Sobol value of a parameter indicates its contribution to the variance of the EROI of the system.
Table 7 :
7TopMtCO 2 -eq./y], where the energy invested in construction is mainly composed of mobility and electricity technologies, and more particularly of PV and electric cars. The maximum capacity of nuclear power plants f NUC max is the third critical parameter. It has-5 critical parameters and their total-order Sobol values [%] for several GHG emissions
targets [MtCO 2 -eq./y]. Abbreviations: operating energy required to use resource i (e i
op ), energy invested
in the construction of a technology j (e j
constr ), maximal installed capacity of a technology j (f j
max ),
maximal availability of a resource i (avail i ), maximal share of public mobility (% public mob
max
), electric (elec.)
photovoltaic (PV), nuclear (NUC), renewable gas (Gas-RE), natural gas (NG).
and 9.5 [lower energy invested in construction than PV,
2600 vs. 4400 [GWh/GW], which is similar to
wind on/offshore, and a negligible related global
warming potential of construction. Thus, the sys-
tem consistently relies on the maximum capacity
of the nuclear power plants. f NUC
max is the second
most-impacting parameter with 12.5% for GHG
emissions target of 56.9 [MtCO 2 -eq./y], and the
third one with 4.8% and 3.4% for targets of 28.5
and 19.0 [MtCO 2 -eq./y].
The wet biomass avail Wet biomass and wood
avail Wood availabilities with 4.7% and 2.5%,
respectively, are the fourth critical parameters
for low GHG emissions targets of 28.5 and 19.0
[MtCO 2 -eq./y]. The operating energy required to
use the wood resource is lower than biomass,
0.049 vs. 0.056 [GWh/GWh] for an equivalent
global warming potential. The wood is used by
the model to produce methanol for satisfying the
non-energy demand. Thus, it allows for limiting
the methanol importations, which require higher
operating energy with 0.08 [GWh/GWh].
Finally, for GHG emissions targets of 28.5 and
19.0 [MtCO 2 -eq./y], [MtCO 2 -eq./y], the fifth crit-
ical parameters are the offshore wind maximal
installed capacity f Offshore wind
max
and the maximal
share of public mobility % public mob
max
with 4.2% and
2.3%, respectively. Private car is the most signif-
icant partaker in the passenger mobility in Bel-
gium. According to the Federal Planning Bureau
Phasing out of low energy-intensive fossil fuels, particularly NG, by relying on more renewables and importing renewable fuels naturally drives down the EROI of the system. This decrease in EROI raises concerns about a minimal societal EROI value below which a prosperous lifestyle would not be sustainable. The estimation of such value is complex and out of the scope of thisFig. 11: Probability density function (plain lines) of the EROI for several GHG emissions targets. The dashed vertical lines provide the EROI mean of the runs performed during the sensitivity anal-GWPtot [MtCO 2 -eq./y] 85.4 56.9 28.5 19.019.0
56.9
28.5
85.4
ysis: 8.4, 6.9, 4.7, and 4.2 for 85.4, 56.9, 28.5, and
19.0 [MtCO 2 -eq./y], respectively.
Deterministic NUC-0
7.9
6.2
4.4
3.9
Deterministic NUC-2
8.1
6.5
4.5
4.0
Deterministic NUC-5.6
8.6
6.9
4.6
4.2
Mean µ
8.4
6.9
4.7
4.2
Standard deviation σ
0.76 0.67 0.55 0.45
CoV σ/µ [%]
Table 8 :
8Deterministic value for the three deterministic scenarios, mean and standard deviation of the EROI resulting from the sensitivity analysis, and the ratio between σ and µ, the coefficient of variation (CoV).study. However, it is not impossible that con-
sidering the actual values of energy invested in
the construction of renewable technologies and
the required operational energy for renewable
resources, the EROI of the system could reach this
limit before achieving carbon neutrality. The esti-
mated EROI probability density functions indi-
cate that decreasing the GHG emissions makes
the EROI more sensitive to uncertain parameters.
the system uses an increased capacity of seasonal centralized thermal and daily decentralized thermal storage technologies to cope with seasonal and intraday intermittent electricity production. GWh]. The seasonal gas storage is filled with NG in the "reference scenario-100%".Its capacity decreases when GHG emissions are ≈ 85.4 [MtCO 2 -eq./y] with the electrification of the private mobility. Then, its capacity increases when GHG emissions are ≈ 71.1 [MtCO 2 -eq./y] and reaches a constant value with GHG emissions from 61.7 to 33.2 [MtCO 2 -eq./y]. Finally, its capacity increases progressively when GHG emissions decrease below 33.2 [MtCO 2 -eq./y] to satisfy the seasonality of the heating, mobility, and electricity demands that rely heavily on renewable gas. The HVC end-use demand, which amounts to most non-energy demand, is satisfied with technology that converts methanol into HVC. such as solar, wind, and waste, to satisfy the heat high-temperature end-use demand. When the GHG emissions are below 14.2 [MtCO 2 -eq./y], the waste boilers are replaced by gas boilers that use renewable fuels, including imported renewable gas. Finally, when the GHG emissions are below 9.5 [MtCO 2 -eq./y], the gas boiler technology is exclusively used with imported renewable gas. The decentralized low heat temperature end-use demand is always satisfied with heat pumps, except when GHG emissions decrease below 9.5 [MtCO 2 -eq./y]. In this case, decentralized gas boilers are used with imported renewable gas. Overall, the centralized heat low-temperature demand is mainly satisfied with centralized electricity heat pumps when GHG emissions are > 14.2 [MtCO 2 -eq./y]. The decrease of centralized gas CHP is first balanced by centralized electricity heat pumps and then by centralized biomass CHP. eq./y], centralized gas CHP, and gas boiler technologies use imported renewable gas to satisfy the demand. Private mobility relies on electric cars from GHG emissions of 85.4 to 9.5 [MtCO 2 -eq./y] and gas cars using imported renewable gas when GHG emissions decrease below 9.5 [MtCO 2 -eq./y]. The trend is similar for freight trucks. The freight boat first uses NG and then renewable gas when GHG emissions decrease. The freight trains rely only on electricity in EnergyScope TD; thus, there is no technology change for this mobility type.C.2 Energy invested evolutionFigures 15 and 16 depict the operation (E op )and construction (E constr ) system energy investedThe total system energy invested(E in,tot ) increases with the limitation of GHG emissions due to the increase of E constr and E op , and is driven by the increase of renewable fuels. The E op increase is mainly due to the shift from NG to renewable gas, and it exceeds the construction system energy invested when GHG emissions are below 47.4 [MtCO 2 -eq./y]. The main drivers of the E constr increase are the PV technology and the shift from NG cars and trucks to electric cars and trucks. Yearly emissions limit [MtCO2-eq./y] (e) Renewable fuels.byp j (eud) defined in Eq. (13).
Appendix C Reference
scenario
additional
results
This appendix presents the results of the simula-
tion with the reference scenario (see Section 4.2)
in terms of installed capacities for several GHG
emissions targets, energy invested, and FEC.
C.1 Assets installed capacity
evolution
Figure 13 depicts the installed capacities of elec-
tricity production, storage (electric, thermal, gas,
ammonia, and methanol), and renewable fuels
technologies. The PV technology drives the evo-
lution of electricity production assets by replacing
the CCGTs and reaching the maximal available
capacity of 59.2 [GWe]. Notice that the onshore
and offshore wind technologies are already at their
maximal capacities in the "reference scenario-
100%". When the GHG emissions are below 9.5
[MtCO 2 -eq./y], the PV and wind capacities are
replaced mainly by CCGT, which uses renewable
gas (gas-RE). The electric storage is composed
of daily storage: pumped hydro storage 12 (PHS)
and batteries of electric vehicle (BEV). The PHS
is already at its maximal available capacity in
the "reference scenario-100%", and the batteries
of electric vehicles are used when GHG emissions
are below 66.4 [MtCO 2 -eq./y] to cope with uncer-
tainty related to the increasing share of PV and
wind power in the primary energy mix. With the
shift from thermal to electric cars, batteries (BEV)
can interact with the electricity layer (vehicle-to-
grid) when GHG emissions decrease. They pro-
vide additional flexibility to cope with a primary
energy mix that relies on an increasing share of
intermittent renewable energy as the GHG emis-
sions decrease. Then, when the GHG emissions are
below 9.5 [MtCO 2 -eq./y], electric cars are replaced
by thermal cars, which use renewable fuels (gas-
RE). When the GHG emissions target is below
66.4 [MtCO 2 -eq./y], the PV installed capacity is
maximal (59.2 [GWe]), and the system relies on a
high share of intermittent renewable energy: solar
and wind to produce electricity. The centralized
and decentralized low heat temperature demands
are mainly satisfied by heat pumps. Therefore,
12 In Belgium, it is mainly the Coo-Trois-Ponts hydroelectric
power station.
When the GHG emissions target is below 9.5
[MtCO 2 -eq./y], the primary energy mix comprises
renewable fuels, including renewable gas. Thus,
the gas boiler technology mainly satisfies the cen-
tralized and decentralized low heat temperature
demands, and the capacities of centralized and
daily decentralized thermal storage technologies
are close to 0 [The methanol is imported and synthesized from
biomass when the GHG emissions are between
100.3 -33.2 [MtCO 2 -eq./y]. When the GHG emis-
sions are between 33.2 and 9.5 [MtCO 2 -eq./y], the
methanol imports are replaced by technologies to
synthesize methanol from imported renewable gas.
Finally, when the GHG emissions are below 9.5
[MtCO 2 -eq./y], there are only renewable methanol
imports.
Figure 14 depicts the installed capacities of
heating and mobility technologies. The indus-
trial gas boilers are replaced by waste boilers
and electrical resistors (I elec.) when GHG emis-
sions reach 66.4 [MtCO 2 -eq./y]. It corresponds to
the shift from a primary energy mix composed
mainly of NG to less intensive carbon energies,
When GHG emissions target is below 9.5 [MtCO 2 -
breakdown by resources, between renewable and
non-renewable, and technologies (all technologies,
and between electricity and mobility technolo-
gies).
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
20
40
60
80
100
120
Capacity [GWe]
CCGT
Hydro
PV
Wind offshore
Wind onshore
(a) Electricity production.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
20
40
60
80
100
120
140
160
Capacity [GWh]
BEV
Elec. battery
PHS
(b) Electric storage.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
200
400
600
800
1000
1200
1400
1600
Capacity [GWh]
DEC FC CHP gas
DEC elec. HP
DEC gas boiler
DHN seasonal
(c) Thermal storage.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
10000
20000
30000
40000
50000
Capacity [GWh]
Ammonia
Gas
Methanol
(d) Other storage.
100
80
66
52
37
23
9
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
Capacity [GW]
Biomass to methanol
H2 to ammonia
Methane to methanol
Methanol to HVC
Steam methane reforming
down by end-use demand: heat, mobility, nonenergy, and electricity. First, the FEC decreases Yearly emissions limit [MtCO2-eq./y] DHN HP DHN gas CHP DHN gas boiler DHN solar thermal DHN wet biomass CHP (e) Heat low T DHN. Yearly emissions limit [MtCO2-eq./y]Fig. 14: Evolution of the heat and mobility asset installed capacities breakdown by technology for several scenarios of GHG emissions in 2035. Abbreviations: industry (I), combined heat and power (CHP), centralized heat low temperature (Heat low T DHN), decentralized heat low temperature (Heat low T DEC), electric (elec.), heat pump (HP), fuel cell (FC).with the shift from NG cars to better efficient electric cars. Then, it increases slightly due to the shift from centralized gas co-generation to centralized bio hydrolysis CHP technology that uses more primary energy to produce the same amount of heat low-temperature end-use demand. Finally, it decreases with the shift from NG trucks to(b) Non-RE resources.Fig. 15: System energy invested in operation (E op ) evolution in 2035 for several GHG emissions targets breakdown between renewable (RE) (left) and non-renewable resources (right). Abbreviations: RE-fuels: gas-RE, methanol-RE, and ammonia-RE; electricity (Elec.). Yearly emissions limit [MtCO2-eq./y] (a) All technologies.Fig. 16: System energy invested in construction (E constr ) evolution in 2035 for several GHG emissions targets (upper), and breakdown between electricity (lower left) and mobility (lower right) technologies. Abbreviations: RE-fuels: gas-RE, methanol-RE, and ammonia-RE; natural gas (NG); electric (Elec.). more efficient electric trucks. When GHG emissions achieve 4.7 [MtCO 2 -eq./y], the heat lowtemperature decentralized FEC increases with the shift from electric technologies such as heat pumps Heat high T. Heat low T. DEC Heat low T. DHN (a) FEC heat. Mob. freight boat Mob. freight rail Mob. freight road Mob. private Mob. public (b) FEC mobility. Fig. 17: Final energy consumption (FEC) evolution for several GHG emissions targets in 2035 breakdown by end use demand: heat (upper left), mobility (upper right), non-energy and electricity (lower). Abbreviations: heat high temperature (Heat high T.); decentralized heat low temperature (Heat low T. DEC); centralized heat low temperature (Heat low T. DHN); mobility (Mob.); high value chemicals (HVC). to gas boilers that use renewable gas. Then, the FEC of mobility, public and freight road, increases due to the shift from electric vehicles to renewable fuel vehicles. This appendix details the sensitivity analysis methodology and provides additional results. Figure 18 depicts the framework of the EROI system sensitivity analysis and how the PCE method is implemented. First, uncertain parameters are Fig. 18: Framework of the EROI system sensitivity analysis. The steps 2 and 3 are conducted for each GHG emissions target considered. defined with their respective uncertainty ranges. Then, the PCE framework is applied to generate a surrogate model and retrieve the critical uncertain parameters. Finally, the mean and variance of the system's EROI are estimated, and the surrogate model is used to perform Monte Carlo sampling to estimate the EROI pdf for several GHG emissions targets. This appendix is organized as follows. First, D.1 details the framework used to perform the sensitivity analysis of the system's EROI. Then, D.2 presents the set of uncertain parameters considered with their respective uncertainty ranges.Finally, D.3 illustrates the selection process using the first-order PCE to build a shortlist of uncertain parameters for the second-order PCE. D.1 Sensitivity analysis methodology The PCE approach provides a computationally efficient alternative to the Monte Carlo simulation for uncertainty quantification to address the "curse of dimensionality" pointed out by Rixhon et al (2021b). Indeed, given limited information about the uncertainty of the parameters for longterm energy planning models, the PCE method constructs a series of multivariate orthonormal polynomials used as a surrogate modelf . It is a closed-form function that takes as input a vector composed of the values of the realization i of the N uncertain parameters considered X i = [X i 1 , · · · , X i n ] and outputs the EROI of the sys-Depending on the number of uncertain parameters, the polynomial order can be increased and is, therefore, more accurate. A few hundred evaluations are required for tens of uncertain parameters to have a first-order polynomial. However, thousands of evaluations are required to obtain a thirdorder polynomial. Then, the surrogate model Eq. (14) allows: (1) to extract statistical moments such as the mean and variance using the coefficients and the total-order Sobol indices. They illustrate the contribution of each uncertain input parameter to the variance of the quantity of interest, in our case, the EROI of the system, including the mutual interactions; (2) to conduct a Monte-Carlo evaluation where millions of samples are generated, and the associated results are calculated instantaneously. It provides the accurate estimation of the EROI pdf for several GHG emissions targets. The first step, depicted in Figure 18, is the uncertainty characterization which consists of defining a set of uncertain parameters and their uncertainty ranges. In this study, we use the extension to the Belgian energy system uncertainty characterization performed by Limpens(2021)based on the work ofMoret et al (2017). A preliminary screening was performed to determine which parameters had no impact and resulted in a set of 138 uncertain parameters X 0 = [X 1 , · · · , X 138 ] .The second step consists of conducting a firstorder PCE on these 138 uncertain parameters to build a shortlist of n critical parameters X n used for a second-order PCE. This step is performed five times to increase the confidence of the result.A parameter is considered negligible if its totalorder Sobol index is close to 0 for all five cases.The last step consists of conducting a second-order PCE to identify the m critical uncertain parameters X m based on X n and estimating an accurate total-order Sobol index for each of them. Then, a Monte-Carlo evaluation is performed using the surrogate modelf to estimate the pdf of the EROI for several GHG emissions targets. Steps 2 and 3 are conducted for each several GHG emissions targets.100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
5
10
15
20
25
Capacity [GW]
I elec.
I gas CHP
I gas boiler
I waste boiler
(a) Heat high T.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
50
100
150
200
250
Capacity [GW]
Elec. car
Gas car
(b) Private mobility.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
5
10
15
20
25
30
35
40
Capacity [GW]
DEC HP
DEC gas FC
DEC gas boiler
(c) Heat low T DEC.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
10
20
30
40
50
Capacity [GW]
Gas bus
Train
Tram or metro
(d) Public mobility.
100
80
66
52
37
23
9
0
5
10
15
20
25
30
35
40
Capacity [GW]
100
80
66
52
37
23
9
0
20
40
60
80
100
120
Capacity [GW]
Boat (gas)
Train
Truck (elec.)
Truck (gas)
(f) Freight mobility.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
20
40
60
80
100
120
140
160
Operation energy [TWh]
Ammonia-RE
Gas-RE
Methanol-RE
Wet biomass
Wood
(a) RE resources.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
5
10
15
20
25
Operation energy [TWh]
Ammonia
Elec. import
NG
Methanol
Waste
100
80
66
52
37
23
9
0
10
20
30
40
50
Construction energy [TWh]
Electricity
Heat
Mobility
RE-fuels
Storage
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
2
4
6
8
10
12
14
16
Construction energy [TWh]
CCGT
PV
Wind onshore
Wind offshore
(b) Electricity.
100
80
66
52
37
23
9
Yearly emissions limit [MtCO2-eq./y]
0
5
10
15
20
25
Construction energy [TWh]
Elec. car
Elec. truck
Gas car
Gas truck
(c) Mobility.
100
80
66
52
37
23
9
Yearly emissions [MtC02/y]
0
50
100
150
200
250
FEC [TWh]
100
80
66
52
37
23
9
Yearly emissions [MtC02/y]
0
20
40
60
80
100
FEC [TWh]
100
80
66
52
37
23
9
Yearly emissions [MtC02/y]
0
50
100
150
200
FEC [TWh]
Ammonia
Electricity
HVC
Methanol
(c) FEC electricity and non-
energy.
Appendix D Sensitivity
analysis
Parameters uncertainty
characterization
1st-PCE
Preliminary screening
Define the uncertainty range
Select uncertain parameters
STEP 1
STEP 2:
f ir st -or der
PCE
conducted 5
times
ES-TD
N1 samples
EROI values
n critical parameters "short-listed"
Monte Carlo
EROI pdf
2nd-PCE
ES-TD
N2 samples
EROI values
-m critical parameters
-EROI mean & variance
-surrogate model
STEP 3:
secon d-or der
PCE
temf
(X i ) = EROI i .
(14)
Table 9
9summarizes the uncertainty ranges for the different groups of technologies and resources considered in the sensitivity analysis. Following the approach developed by Moret et al (2017) and capitalizing on the works of Limpens (2021); Rixhon et al (2021b) the uncertainty intervals are defined. A preliminary screening, including all the parameters of the model, allowed to obtain an Springer Nature 2021 L A T E X template initial list of 138 parameters to be used for the first-order PCE. There are four categories of uncertain parameters: end-use demands, technologies, resources, and others. The uncertainty in the yearly end-use demands is split by energy sectors. The electricity demand, space heating demand, and industrial demand are related to the yearly industrial demand uncertainty endUses I year , which has the most extensive range. The freight and passenger mobility are related to the uncertainty of transport endUses T R year . Technologies are defined through different parameters: the energy conversion efficiency η, the investment cost c inv , the construction energy investment e constr , the yearly c p and hourly c p,t load factors, the potential f max , the maintenance cost c maint , and the lifetime.This study does not consider the energy conversion efficiency, investment and maintenance costs, yearly capacity factors, and lifetime as uncertain parameters. In addition, the energy invested in the construction of storage technologies is not taken into account. Intermittent renewable energy is limited in its potential (f max of PV, onshore and offshore wind) and the hourly capacity factor (c p,t of PV, solar, onshore and offshore wind, and hydroelectricity). The electricity % elec loss and heat % heat loss network losses are considered uncertain parameters. Resources are characterized by an operating cost c op , not considered uncertain in this study, energy invested in operation e op , and availability avail. Most resources have unlimited availability except biomass, waste, and electricity imported. The availability of local resources (wood, waste, and biomass) are uncertain parameters. Finally, there is a limited installed capacity f max imposed arbitrarily for nuclear f NUC max [GWe], electricity f GEO elec max [GWe] and heat f GEO DHN max [GWth] production from geothermal. This work also accounts for uncertainties on the upper bounds of mobility % public mob max [%], % train freight max [%] and % boat freight max [%], the upper bound of heat that can be covered by district heating network % DHN heat max , and the capacity of electrical interconnection with neighbours elec import max [GWe].
Table 9 :
9Application of the uncertainty characterization method to Ener-gyScope TD when maximizing the EROI of the system. Uncertainty is characterized for one representative parameter (rep. param.) per category.Due to the lack of data in the literature for 2035, the uncertainty intervals of e op and e constr are by default absolute uniform interval U[−25%, +25%]. Abbreviations: photovoltaic (PV), district heating network (DHN), industry (I), transport (TR), nuclear (NUC), geothermal (GEO), electricity (elec). parameters short-listed are named critical parameters and considered for the rest of the study in the second-order PCE.Figure 19 illustrates this selection process using the first-order PCE for the GHG emissions target of 28.5 [MtCO 2 -eq./y]. In this scenario, 42 parameters are identified (blue marks) as critical to be used in the second-order PCE. The red marks are the minimum values of the Sobol index for each parameter over the five runs, and the black marks are the mean of their five Sobol index values.Fig.19: Illustration of the selection process using first-order PCE for GWP tot ≤ 28.5 [MtCO 2eq./y]. The y-axis is logarithmic. For each parameter, the blue mark indicates the parameter is critical, and the grey mark that it is negligible. It corresponds to the maximal value of the Sobol index over the five runs. A parameter is critical if its maximal value of the Sobol index over the five runs is above threshold = 1/d. The red (black) mark is the minimum (mean) value of the Sobol index over the five runs.0 20 40 60 80 100 120 140
Parameters
0.10
0.72
10.00
80.00
%
min
max critical
max negligible
mean
negligible: 1/138
GHG target [MtCO 2 -eq./y] 85.4 56.9 28.5 19.0
# parameters short-listed
64
55
42
45
# critical parameters
9
27
17
5
Table 10 :
10Number (#) of short-listed and critical parameters using the first-order and second-order PCE.
//doi.org/10.1039/C9EE02627D, URL http:// dx.doi.org/10.1039/C9EE02627D Cleveland CJ, Costanza R, Hall CAS, et al (1984) Energy and the u.s. economy: A biophysical perspective. Science 225(4665):890-897. https://doi.org/10.1126/science.225.4665. 890, URL https://www.science.org/doi/abs/10. 1126/science.225.4665.890 Codina Gironès V, Moret S, Maréchal F, et al (2015) Strategic energy planning for large-scale energy systems: A modelling framework to aid decision-making. Energy 90:173-186. https://doi.org/https: //doi.org/10.1016/j.energy.2015.06.008, URL https://www.sciencedirect.com/science/ article/pii/S0360544215007136 Springer Nature 2021 L A T E X templateRanking
85.4
56.9
28.5
19.0
1
e NG cars
constr
39.2
e Elec. cars
constr
18.0
e Gas-RE
op
43.6
e Gas-RE
op
67.1
2
e NG
op 25.5
f NUC
max 12.5
e Elec. cars
constr
4.8
e Elec. cars
constr
6.1
3
e Elec. cars
constr
6.3
% public mob
max
7.7
f NUC
max 4.8
f NUC
max 3.4
4
% public mob
max
5.4
e PV
constr 5.0 avail Wet biomass 4.7 avail Wood 2.5
5
e Wet biomass
op
4.3
e NG
op 5.0
f Offshore wind
max
4.2
e NG cars
constr
2.3
6
e DHN wet biomass CHP
constr
2.2
avail Wood 4.2
endUses I
year 3.8
-
7
e Elec. trucks
constr
1.9
e NG cars
constr
3.6
f GEO DHN
max
3.3
-
8
e Methanol
op
1.8
c P V
p,t 3.0
e PV
constr 3.3
-
9
e Diesel trucks
constr
1.8
endUses I
year 3.9
e Offshore wind
constr
3.1
-
10
-
e Uranium
op
2.9
% public mob
max
3.1
-
11
-avail Wet biomass 2.9
f Onshore wind
max
3.0
-
12
-
f GEO DHN
max
2.9
e NG cars
constr
3.0
-
13
-
e Wet biomass
op
2.9
e Elec.
op
2.8
-
14
-
e Gas-RE
op
2.8
avail Wood 2.6
-
15
-
c Offshore wind
p,t
2.5
e Wet biomass
op
2.5
-
16
-
f Offshore wind
max
2.5 e Elec. wet biomass
constr
2.5
-
17
-
e Methanol
op
2.5
c Offshore wind
p,t
2.5
-
18
-
f Onshore wind
max
2.5
-
-
19
-
endUses T R
year 2.4
-
-
20
-
e H2
constr 2.4
-
-
21
-
% freight train
max
2.2
-
-
22
-
c Onshore wind
p,t
2.1
-
-
23
-
% freight boat
max
2.1
-
-
24
-
e I waste boilers
constr
2.0
-
-
25
-e DHN waste CHP
constr
1.9
-
-
26
-
e Wood
op
1.8
-
-
27
-
e CCGT ammonia
constr
1.8
-
-
Table 11 :
11Critical parameters and Sobol indices values [%] for several GHG emissions targets [MtCO 2eq./y]. Abbreviations: electric (elec.), mobility (mob), photovoltaic (PV), nuclear (NUC), renewable gas (Gas-RE), natural gas (NG), geothermal (GEO), transport (TR), industry (I), district heating networks (DHN), combined heat and power (CHP), combined cycle gas turbine (CCGT). Colla M, Blondeau J, Jeanmart H (2022) Optimal use of lignocellulosic biomass for the energy transition, including the non-energy demand: The case of the belgian energy system. Frontiers in Energy Research 10. https://doi.org/10.3389/fenrg.2022.802327, URL https://www.frontiersin.org/article/10. 3389/fenrg.2022.802327 Contino F, Moret S, Limpens G, et al (2020) Whole-energy system models: The advisors for the energy transition. Progress in
https://github.com/energyscope/EnergyScope 6 https://energyscope-td.readthedocs.io/en/master/
https://energyscope.readthedocs.io/en/master/sections/ Releases.html#case-studies
These GHG emissions values do not consider the international intra-EU and international extra-EU and Use, Land-Use Change and Forestry (LULUCF).
The use of imported electricity is highly dependent on its indirect emissions. In this study, electricity imports emit about half of the electricity production of a CCGT. Therefore, imported electricity replaces the production of CCGTs.
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Short note on the Sirenia disappearance from the Euro-North African realm during the Cenozoic: a link between climate and Supernovae?
F Cabral
University of Lisbon
1749-016Campo Grande, Lisboa, SupernovaeCenozoic, ClimatePortugal Keywords: Sirenia
M Cachão
University of Lisbon
1749-016Campo Grande, Lisboa, SupernovaeCenozoic, ClimatePortugal Keywords: Sirenia
Jorge Agostinho
University of Lisbon
1749-016Campo Grande, Lisboa, SupernovaeCenozoic, ClimatePortugal Keywords: Sirenia
R
University of Lisbon
1749-016Campo Grande, Lisboa, SupernovaeCenozoic, ClimatePortugal Keywords: Sirenia
G Prista
University of Lisbon
1749-016Campo Grande, Lisboa, SupernovaeCenozoic, ClimatePortugal Keywords: Sirenia
Short note on the Sirenia disappearance from the Euro-North African realm during the Cenozoic: a link between climate and Supernovae?
Sirenia are marine mammals that colonized the European shores up to 2.7 Ma. Their biodiversity evolution follows the climate evolution of the Cenozoic. However, several climate events, as well as the global climate trend of this Era are still struggling to be understood. When considering only Earth processes, the climate evolution of the Cenozoic is hard to understand. If the galactic environment is taken into account, some of these climate events, as well as the global climate trend, became more easily understood. The Milky Way, through Supernovae, may bring some answers to why Cenozoic climate had this evolution. With the assumption that SN can induced changes in Earth climate in long time scales, Sirenia disappearance from Europe would be a side effect of this process.
Introduction
Sirenia, an Order (Sirenia Illiger, 1811) of placental mammals that, along with cetaceans, represent the only mammals that evolved for a fully aquatic life (Clementz et al., 2009), and have the particularity of being the only herbivorous marine mammals (Domning, 2002), commonly named Seacow. They feed mainly on seagrass, although there are some differences between the two extant families, the trichechids and the dugongids. The Trichechidae family is not highly specialized when it comes to food and habitat. They live in fresh and sea-water, feeding on more than 60 species of marine plants, and can be considered, as suggested by Anderson (2002), opportunistic feeders on seagrass. The Dugongidae family is more specialized, feeding mainly on seagrass and is almost exclusively found in salt water. These characteristics are not exclusive of the four actual species, as shown by MacFadden et al. (2004), and can be traced back to the extinct species of both families. They first appeared after the Early Eocene Climatic Optimum (53-49 Ma (Höntzsch et al., 2011)), with the oldest record of Pezosiren portelli from Jamaica (Domning, 2001a). The coastal shores of Europe and North Africa have records dating from the Lutetian (Caria, 1957;Crusafont-Pairó, 1973;Savage, 1976;Zalmout and Gingerich, 2012), showing that the Tethys Sea was colonized by these marine mammals in both its north and south margins. Sirenians were abundant in Tethyan coastal waters, and also in the Paratethys and the Mediterranean, which evolved from it. The Sirenia that inhabited the European/North African shores are almost exclusively of the Dugongidae family (more than 95% of the European and North African fossil record belong to dugongids), meaning that they fed mainly on seagrass. Seagrasses are marine phanerogams that colonized the coastal waters around 100 Ma ago (Hemminga and Duarte, 2000). They show few changes in their evolutionary process and many of the genera found today can be traced back to the Eocene (like Cymodocea nodosa and Posidonia sp. from the Eocene of Paris) (Domning, 2001b;Bianucci et al., 2008).
After the Miocene Climatic Optimum (MCO) around 14 Ma ago (Böhme, 2003;Domingo et al., 2012), European and North African Sirenia declined in biodiversity (Prista et al., 2013;2014a). Only one genus is known from the Late Miocene and Pliocene, the Metaxytherium, and only three species have been classified for this time interval, M. medium, M. serresii and M. subapenninum. The Tortonian is the last age with Sirenia fossil records in the Northeast Atlantic shores, north of Portugal. In the Faluns Sea, northeastern France, the record is abundant until the Tortonian (Cottreau, 1928;Lécuyer et al., 1996). For the Messinian age, Portugal appears to be the only place with a fossil record on this side of the Atlantic, with two records from Santa Margarida do Sado (Ferreira do Alentejo, Beja) and Vale de Zebro (Alvalade, Setúbal) (Estevens, 2000). The Mediterranean has a slightly richer fossil record, with fossils from Libya (Zalmout and Gingerich, 2012) and probably Italy (Moncharmont Zei and Moncharmont, 1987) and Spain (Sendra Saez et al., 1998). This scenario is not totally understood, because it was during the Messinian that the Messinian Salinity Crises (MSC) occurred, a period of closure of the Mediterranean and great ecological disturbance (Prista et al., 2013). The Pliocene shows an increase in the fossil record for the Mediterranean Sea, and only one occurrence in the Atlantic, belonging to the Gulf of Cadiz on the Morocco shore (Ennouchi, 1954). The Zanclean age has records of M. serresii, which first appeared during the Late Miocene of Libya (Zalmout and Gingerich, 2012), from Montpellier, France (Domning and Thomas, 1987;Pilleri, 1987), Sahabi Formation, Libya (Domning and Thomas, 1987) and Alicante, Spain (Sendra et al., 1999;Bianucci et al., 2008). During this age appeared the last European/North African sirenian species, the M. subapenninum, with the oldest records from the Early Zanclean of Italy (Sorbi and Vaiani, 2007;Tinelli et al., 2012) and the last known records dated to the Early Piacenzian (Bianucci et al., 2008). M. serresii ceases its appearance in the fossil record during the Zanclean age. This decline in biodiversity, which culminated with Sirenia disappearance from European chores, has been explained by Prista et al. (2013;2014a), and is strongly related to climate changes. In fact, the taxonomic palaeobiodiversity of the European and North African sirenians shows a close relation with the palaeoclimatic evolution of the Cenozoic (Prista et al., 2014a). The authors also found that Sirenia biodiversity seems to be strongly affected by variations in seasonality, coupled with other geological processes, such as sea level changes, and responded rapidly during the Oligocene, the Early-Middle Miocene and the Late Miocene-Pliocene (Prista et al., 2014a). The climate system is a unique and open system with a multitude of interacting components and processes (Müller, 2010). However one question remains: which forces drive optimum climates and ice ages? Although several mechanisms must play a role in this Earth climate process, the galactic environment should not be neglected. During the last decade of the 20th century evidences liking galactic cosmic rays (GCR) to cloud cover were found through satellite observations (Marsh and Svensmark 2000b). This opened a great scientific debate, and today this direct relation is practically discarded. However that doesn't mean that GCR don't play a role in the Earth's climate. Their influence on the atmospheric electric current has been demonstrated by several studies (e.g. Tinsley and Yu, 2004;Serrano et al., 2006;Tinsley, 2012), and the CLOUD project at CERN has been conducting experiences that have lead us to better understand this process (Kirkby, 2008;Duplissy et al., 2010;Kirkby et al., 2012). Could the Milky Way affected Sirenia evolution?
Cenozoic climate over the past 65 Ma
During the Palaeogene several optimum climates took place: the Palaeocene-Eocene Thermal Maximum (PETM) (Sexton et al., 2011), the Early Eocene Optimum Climate (EEOC) (Höntzsch et al., 2011) and the Mid-Eocene Optimum Climate (MEOC) (Witkowski et al., 2012). These are all periods of less temperature gradient between high latitude regions and the tropics. During the Oligocene, the last epoch of the Palaeogene, the Antarctic continental glaciations (ACG) started (Zachos et al., 2001;Pollard and DeConto, 2005;Zachos et al., 2008;Cotton and Pearson, 2011;Diester-Haass et al., 2011). Although today we attribute the ACG to the strong influence of the Antarctic Circumpolar Current (ACC), when the ACG started, (around 34 Ma), the ACC was not formed yet (Lawver and Gahagan, 2003;Pfuhl and McCave, 2005). This means that a mechanism, other then the ACC, should have forced the beginning of the glaciations. The ACG were accompanied by a major global cooling. Oceans global temperature dropped ~2.5ºC (Héran et al., 2010); in Central Asia and Europe is observed a drop in temperatures and an increase in aridity (Abels et al., 2011;Costa et al., 2011); the Earth temperature gradient increased. After the Oligocene, started the Neogene period. It's first epoch, the Miocene, was warmer then the Oligocene, and the Earth temperature gradient got smaller again. During the Early and Middle Miocene an optimum climate took place, the Miocene Climatic Optimum (MCO) (Böhme, 2003;Kroh, 2007;You et al., 2009;Böhme et al., 2011). This climate event lasted for approximately 4 million years. Around 14 Ma Earth plunged into another cooling trend, and at 10 Ma the Arctic glaciations started. This cooling trend was almost continuous, with just a small warming interval during the mid Piacenzian, around 3 Ma (read Prista et al., 2014b). At 2.7 Ma the Northern Hemisphere continental glaciations begun, and Earth plunged into the present Ice Age (Naafs et al., 2010).
Galactic environment and Cenozoic climate
Earth processes haven't been able to completely explain Cenozoic climate evolution. However, if we look at the galactic environment throughout this Era, some coincidences are found. Optimum climates tend to occur outside the arms, while when crossing an arm region climate tend to globally cool. This would be expected from the cosmic rays link to the atmospheric current. Stronger CRF, stronger atmospheric current, increase in cloud formation. This sequence would lead to a global cooling. Looking at figure 1, this relation between the energy flux from Supernovae (SN) (main source of GCR) and Earth climate appears has something to be considered. Other studies suggest that this mechanism can't be ignored for long-term climate studies (geological time) (Shaviv, 2005;Medvedev and Melott, 2007;Kataoka et al., 2013).
Conclusions
Regarding the galactic environment: 1) optimum climates tend to occur outside the spiral arms (PETM, EEOC, MEOC and MCO); 2) the onset of the Antarctic glaciations is coincident with the passage through Sagittarius arm (the Antarctic Circumpolar Current was not formed yet and this suggests that the major increase in energy flux from SN may have played a role); 3) the beginning of ice formation in the Arctic region is coincident with the approximation to the Orion arm and the first occurrences of the 19 SN that occurred in the Gould region in the past 14 Ma; 4) climate degradation and the onset of the Northern Hemisphere continental glaciations is coincident with entering into the Orion arm and the occurrence of more SN in the Gould region. Regarding Sirenia: its biodiversity was higher during the Eocene, got very low during the Oligocene, had a small peak during the MCO and dropped again with the subsequent global cooling (data from Prista el., 2014a). Regarding climate: seasonality latitudinal gradient follows the energy flux variations. However it can been seen in figure 2 that other forces play a major role in this process, since seasonality is must higher with the lowest energy flux of the Orion Arm when compared to the highest flux of the Sagittarius Arm. Despite not being the only mechanism present, an influence of the galactic environment can be seen in long-term climate studies and should be taken into account. Indirectly, the Milky Way contributed to the disappearance of Sirenia from European shores.
Figure 1 -
1Energy flux from the occurrences of SN in the Milky Way over the past 100 Ma. In red is the δ 18 O curve from Zachos et al. (2008). 1-PETM; 2-EEOC; 3-MEOC; 4-ACG; 5-MCO; 6-Arctic glaciations; Black Barperiod in which 19 Supernovae occurred inside the Gould Region (Breitschwerdt and Avillez 2006).
Figure 2 -
2Energy flux from SN in the Milky Way. Red dots -SNIa; Blue dots -SNIbc; Green dots -SNII. Green line -Sirenia biodiversity variation; Blue line -latitudinal temperature/seasonality variation.
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A spatial-temporal graph deep learning model for urban flood nowcasting leveraging heterogeneous community features
0123456789
Hamed Farahmand
Yuanchang Xu
Ali Mostafavi
A spatial-temporal graph deep learning model for urban flood nowcasting leveraging heterogeneous community features
012345678910.1038/s41598-023-32548-x1 Scientific Reports | (2023) 13:6768 | https:// www.nature.com/scientificreports
Flood nowcasting refers to near-future prediction of flood status as an extreme weather event unfolds to enhance situational awareness. The objective of this study was to adopt and test a novel structured deep-learning model for urban flood nowcasting by integrating physics-based and human-sensed features. We present a new computational modeling framework including an attention-based spatialtemporal graph convolution network (ASTGCN) model and different streams of data that are collected in real-time, preprocessed, and fed into the model to consider spatial and temporal information and dependencies that improve flood nowcasting. The novelty of the computational modeling framework is threefold: first, the model is capable of considering spatial and temporal dependencies in inundation propagation thanks to the spatial and temporal graph convolutional modules; second, it enables capturing the influence of heterogeneous temporal data streams that can signal flooding status, including physics-based features (e.g., rainfall intensity and water elevation) and humansensed data (e.g., residents' flood reports and fluctuations of human activity) on flood nowcasting. Third, its attention mechanism enables the model to direct its focus to the most influential features that vary dynamically and influence the flood nowcasting. We show the application of the modeling framework in the context of Harris County, Texas, as the study area and 2017 Hurricane Harvey as the flood event. Three categories of features are used for nowcasting the extent of flood inundation in different census tracts: (i) static features that capture spatial characteristics of various locations and influence their flood status similarity, (ii) physics-based dynamic features that capture changes in hydrodynamic variables, and (iii) heterogeneous human-sensed dynamic features that capture various aspects of residents' activities that can provide information regarding flood status. Results indicate that the ASTGCN model provides superior performance for nowcasting of urban flood inundation at the census-tract level, with precision 0.808 and recall 0.891, which shows the model performs better compared with other state-of-the-art models. Moreover, ASTGCN model performance improves when heterogeneous dynamic features are added into the model that solely relies on physics-based features, which demonstrates the promise of using heterogenous human-sensed data for flood nowcasting. Given the results of the comparisons of the models, the proposed modeling framework has the potential to be more investigated when more data of historical events are available in order to develop a predictive tool to provide community responders with an enhanced prediction of the flood inundation during urban flood.Background. Flood nowcasting is a process by which areas at imminent risk of inundation can be identified using the spatial and temporal features that convey information regarding current flooding status. As extreme weather events accompanied by heavy precipitation occur more frequently, causing catastrophic flood events,OPEN
Scientific Reports
| (2023) 13:6768 | https://doi.org/10.1038/s41598-023-32548-x www.nature.com/scientificreports/ flood nowcasting has become an essential capability for communities to better respond to the impacts of these events 1 . Flood nowcasting enables predictive flood monitoring, the ability to anticipate imminent flood risks and impacts and situational awareness as an extreme weather event unfolds 2 . Departing from the standard flood monitoring approaches using hydraulic and hydrological (H&H) models that predict flood inundation levels for hazard mitigation and infrastructure improvements prior to flood events 3,4 , flood nowcasting focuses on nearfuture prediction (e.g., next few hours) of spatial and temporal flood status based on the current status of flooding. The traditional approaches for flood monitoring 5 do not provide certain essential information (e.g., what areas will be inundated within the next few hours). Nowcasting will enable public officials, emergency managers, responders, and residents to better tailor decisions and actions by enhancing situational awareness during response and recovery 6 . Hence, urban flood nowcasting facilitates identifying areas that will require emergency aid in hours immediately ahead and areas that need issuance of evacuation notices due to the high risk of flood inundation. This forewarning is critical for reducing the adverse impacts of flood events. It also facilitates taking proper managerial actions to control flood inundation using hydrological infrastructures, such as flood gates and pumps [7][8][9] . The main approach for sensing flood status is the use of rainfall and stream gauges; however, due to cost and maintenance limitations, the number of these physical sensors is limited, which affects proper observability of flood status 10 , and hence, flood nowcasting. New techniques for enhancing situation awareness and emergency response actions leverage heterogeneous community-scale datasets (including both physical sensors and crowdsourced data) in advance to provide the predictive capability to infer the flooding status for the near future in spatial units (e.g., zip code, census tract, and neighborhood), information [11][12][13] . Multiple studies have been conducted to develop predictive tools using a wide range of physics-based features and quantitative techniques. Conventionally, H&H simulation models are used for predicting the extent of flooding in urban areas using geomorphological hydrodynamic features to estimate water depth in urban areas 14,15 . These models often rely on the data collected from rainfall and flood gauges to provide an estimate of the spatial extent of flood propagation 6,16 . Despite their satisfactory accuracy and predictive performance, extensive computational cost and the sparsity of the reliable hydrological data in urban areas limit the existing physics-based H&H models [17][18][19] for providing near-future estimation for spatial-temporal propagation 20 . To complement the standard models, recent studies tested data-driven models based on harnessing data sources, such as satellite images, crowdsourced data, and remote-sensing data, that can help estimate flood status in near future timeframes 3,[21][22][23][24] . Also, a growing number of researchers have used the predictive capability of various machine learning (ML) models for flood predictive monitoring [25][26][27][28][29][30] . These models can include more community features than tradition models to forecast flood status, which facilitates capturing the large number of heterogeneous community features needed for flood nowcasting 31,32 .
In the following sections, we review the state-of-the-art in application of deep-learning models for flood nowcasting to identify gaps in the existing literature. We focus particularly on two major gaps: (1) the absence of a model architecture that enables capturing spatial and temporal dependencies in flood propagation and dynamically identifying influential features, and (2) limited efforts for integrating human sensing as an approach for collecting and extracting valuable temporal and spatial data. We also review the use of heterogenous humansensed data as a supplement for flood nowcasting to show the gap in the knowledge regarding the proper use of such data for improving the urban flood nowcasting models. Accordingly, we adopt a model proposed by Guo et al. 33 and test a novel graph-based deep-learning models that enable capturing spatial dependencies, as well as heterogeneous human-sensed features in flood propagation. We demonstrate the application of the proposed model in the context of the 2017 Hurricane Harvey flooding in Harris County, Texas.
Related works
Deep learning for flood nowcasting. Advances in machine learning techniques are responsible for the emergence of deep learning (DL), a sub-domain of ML that employs deep artificial neural network architectures and gradient descent algorithms for yielding more robust and computationally efficient predictive models [34][35][36][37][38] . Deep neural networks have been increasingly used for tasks that support flood predictive monitoring, such as flood depth mapping and flood detection. Multiple studies have applied DL techniques to improve the predictive performance of physics-based flood nowcasting models. For example, a convolutional neural networks (CNN) have been used in combination with conditional generative adversarial networks (cGAN) to improve the performance of physics-based flood forecast models 39 . In addition, a combined empirical mode decomposition (EMD) algorithm and encoder-decoder long short-term memory (En-De-LSTM) architecture have proved to yield a better prediction of peak flow values of streams during floods 40 . Recent data-driven models rely purely on the capability of DL models for flood prediction. For example, streamflow prediction using an integration of stacked autoencoders (SAE) and back propagation neural networks (BPNN) show higher accuracy compared with other tested ML models 41 . Also, Gated Recurrent Units (GRU)-based network architecture has been utilized for predicting the time series of stream sensors used for flood monitoring 42 . In a recent work by Dong et al. 39 , a Fast GRNN-FCN (fast, accurate, stable, and tiny gated recurrent neural network-fully convolutional network) was proposed for forecasting the water level in channel network sensors to provide flood signals in flood control network 43 . While the use of DL models for flood prediction is becoming prevalent in the literature and practice, the current research trends lack a computational data-driven modeling framework that enables a near-future prediction of flood status in spatial blocks (e.g., census tracts or zip codes). This gap is due mainly to: (1) inability of the existing models to capture the spatial interdependencies; (2) limitations in extracting features that provide indication of flood status in spatial blocks (due mainly to a limited number of physical sensors). The inability to predict near-future flood status in spatial blocks is a major hindrance to flood nowcasting. To address this gap, in this study, we propose a spatial-temporal graph deep-learning model.
Incorporating attention mechanisms into spatial-temporal deep-learning models for flood prediction elicits superior results compared to other state-of-the-art model architecture, and also improves interpretability of the model results 44 . These studies often leverage the ability of different DL models for time-series forecasting and early warning detection utilizing sensors that collect rainfall and streamflow data. Nevertheless, most recent studies have: (1) employed DL architectures that enable incorporating spatial correlation, and (2) created DL architectures that enable more feature incorporation. For spatial correlation, graph neural networks can capture the spatial similarity of model units 45 while an attention mechanism that enables the model to focus on the characteristic data when processing large numbers of features 46 and enable use of heterogeneous data to provide reliable prediction in urban units. In the next sections, we discuss the application of graph neural networks for spatial and temporal prediction as well as using heterogeneous data in flood predictive monitoring, which form the points of departure for this study.
Other than the deep learning models for flood nowcasting, coupled hydatic and hydrologic models that use multiple GPUs for forecasting urban flooding in real time r near real time have gain attention in the literature. The advantage of these models is that they can provide accurate flood maps using various surface and social properties as well as hydraulic and hydrologic properties. For example, coupled hydrologic-hydraulic model (HiResFlood-UCI) 47 for flash flood modeling has been developed to increase the efficacy of the hydraulic modeling to produce high-resolution flood maps. A fully coupled hydrologic-hydraulic modeling framework was also developed for flood prediction and modeling for both riverbank and overland inundation, which shows superior performance 48 . To enhance the performance of these models and reducing uncertainty, different approaches such as assimilation of satellite-based synthetic aperture radar (SAR) observations into the coupled mode have been proposed 49 . Besides, techniques such as remote-sensing have also been used for calibrating these models to improve their precision for flood detection 50 .
Graph neural networks for spatial-temporal prediction. Graph neural networks generalize convolution to data in a graph structure 51 . With their superior capability to characterize spatial and temporal dependencies for time-series predictions, Graph Convolutional Networks (GCNs) characterize networked data with spatial and temporal dependencies for time-series prediction using spatial and temporal convolutions. These models (referred to as spatio-temporal graph convolutional network (STGCN) models) are used for prediction problems such as traffic flow prediction 52,53 , disease diagnosis 54 , bike-demand prediction 55 , point-of-interest (POI) recommendation 53 , pedestrian flow prediction 56 , trajectory prediction 57 , and road network flood inundation prediction 2 . STGCN model architectures have been developed based on the problem characteristics. For example, dual-channel based graph convolutional networks (DC-STGCN) consider both daily and weekly correlation of the traffic data 58 . Discriminative spatio-temporal graph convolutional network (DSTGCN) were used for action recognition in to inner-class action distribution 59 . Wang et al. 5 developed an auto-STGCN algorithm that facilitates the detection of the optimal STGCNs models automatically using a reinforcement learning technique 60 . An attention mechanism allows DL models to focus more on the useful parts of features 46 . In graph neural networks, the attention mechanism allows the model to learn a dynamic and adaptive combination of the adjacency matrices and select the most relevant information 61 . Attention-based GCNs adaptively capture dynamic spatial and temporal correlation of heterogeneous data and its interpretability power 33 . The combination of attention mechanism and STGCN structure, therefore, could provide a powerful testbed for problems in which heterogeneous features with complex spatial and temporal correlation exist. The application of attentionbased STGCNs in the literature, however, is limited to traffic flow prediction 33 . Because of the characteristics of the urban flood nowcasting problem, attention-based STGCNs may provide models that could account for spatial interdependencies, as well as for the temporal correlations among features related to flood inundation status.
Heterogeneous human-sensed data for flood nowcasting. To complement the information sensed by physical sensors, other sources of data with distinct levels of reliability, aggregation, and the need for preprocessing have been tested in recent studies 31 . Satellite images, drone-recorded videos and images, and images captured by other cameras provide reliable information; however, limitations of data acquisition and challenges in data processing restrict extensive use of such data for flood predictive monitoring and vulnerability assessment 62-65 . Blumberg et al. 1 employed hurricane-related photos provided by volunteers to simulate flood inundation during 2012nHurricane Sandy in Hoboken and Jersey City, New Jersey. On the other hand, human-sensed crowdsourced data have become more available in different formats that can provide geo-located information regarding the flood status in a timely manner. For example, studies have analyzed anonymized social media content using ML and DL techniques and employed the extracted information for enhancing flood situational awareness 32,66-68 . In another study example, Huang et al. 69 integrated tweet data gathered by remote sensing and river water gauges to improve near real-time flood inundation maps. Nevertheless, the tweet activity data has also proven to expedite the detection of flood inundation and flood-related events when combined with satellite flood signals 70 . However, there are limitations in terms of content analysis and ensuring the credibility of the extracted information from social media 71 . Furthermore, social media data might be biased by factors such as distance to impacted areas, the popularity of the user, and demographic characteristics of users 72 . Recently, the digital trace of human activities (such as cellphone and location-based data) has also been deployed for flood prediction. The rationale is that the changes in the level of human activity and the concentration of human activity can indicate signals regarding flood status 73 . The combined use of different sources of data-physical flood sensors data, crowdsourced social media data, and telemetry-based human activity data provides opportunities to gather a more extensive set of indicators related to flood status for use in flood predictive monitoring 74 . Integrating such heterogeneous data requires a modeling framework that is able to recognize and focus on key data Point of departure. The review of the current state of the art shows two gaps in the knowledge for urban flood nowcasting: (1) the absence of a deep-learning structure that combines attention mechanism and graphbased convolutional network structure for extracting information from heterogeneous features with complex spatial and temporal correlation; and (2) the lack of a proper flood nowcasting modeling framework for integrating heterogeneous human-sensed features that can carry valuable flood-related information along with the physical sensor data. Recognizing these gaps, this study presents a deep-learning modeling framework including an adopted attention-based spatial-temporal graph convolution network (ASTGCN) model and streams of data that could be collected as a flood event unfolds, preprocessed, and fed into the prediction model to consider spatial and temporal features as well as dependencies in order to enable reliable urban flood nowcasting. The proposed model was tested in the context of flooding caused by the 2017 Hurricane Harvey in Harris County, Texas. The model performance and its implications for flood nowcasting, as well as enhancing situation awareness, are discussed. The novelty of this study is the creation a framework that addresses major limitations in the application of data-driven techniques for flood nowcasting by (1) focusing on graph-based architectures that enable co-location dependency between urban units for considering the spatial aspect of flood propagation, (2) identifying and processing various heterogeneous physics-based and human-sensed data that carry information for inferring flood status in spatial units, and (3) utilizing an attention-based time-series forecasting architecture for considering the temporal aspect of flood prediction and focusing on information with higher importance when processing large amounts of heterogeneous features.
Methods
Problem definition and abstraction. In this study, we model the study area as a network of census tracts to capture the spatial interdependence in urban flood propagation and recession. We used the census tract as the spatial unit for various reasons: its scale is neither so coarse as to lose the resolution nor so fine as to lose observability of flood status due to missing data. This makes the census tract a suitable spatial scale for aggregating and interpolating both human-sensed data and physics-based data while maintaining data accuracy and keeping it informative for flood nowcasting. Next, the purpose of any urban prediction model is to provide emergency managers and people with actionable data. Therefore, the alignment of spatial units of the outputs with the administrative boundaries make the results more insightful and valuable for decision makers. In addition, one issue that is associated with the use of human-sensed data is that these data are biased toward highly populated areas. Therefore, if the spatial unit is smaller in the locations with higher population, the bias is alleviated to some extent. Finally, demographic data is available for administrative boundaries with proper accuracy. Therefore, future research can focus on the issues related to the associated between model performance in areas with different demographic characteristics to investigate crucial aspects of the model such as fairness and demographic biases. We created an undirected graph G = (V , E, A) , where V is the set of N nodes, each representing a census tract in the study area; set E includes edges in graph G that represent the connection between different nodes; and matrix A N×N is the adjacency matrix of graph G . Entries of matrix A are determined based on the proximity and the extent to which two census tracts have similar features that potentially influence their flooding status. Therefore, matrix A is built upon the distance between census tracts and a set of static features, such as elevation, land use, and distance to stream, that impact the flooding status of particular areas 75 . At each timestep, each node in the graph G holds a vector of temporal features (more discussion about the features are provided in the next section) that contain information that is used as the model input for nowcasting flood in the model. These temporal features capture various physics-based and human-sensed data inputs that are aggregated and preprocessed into the same sampling frequency. Figure 1 shows a schematic representation of the graph model, as well as static and dynamic features that are used for feeding the model for flood nowcasting. Figure 2 shows the overview of the steps for the development and evaluation of the model. Overall, the design plan for the study involves four steps 76,77 : data collection, data preprocessing, model development, and model evaluation. First, we present the data used for the development of the model. The data includes ground truth data: static features, which represent the dependency between flooding status of different areas in the adjacency matrix; and dynamic features that provide indications of temporal propagation and recession of urban flooding in each census tract. We also elaborate on the data preprocessing needed for the preparation of static features and the construction of time series of the dynamic features. Then we present the model architecture and mechanisms used in the DL model for urban flood nowcasting. Finally, we discuss the performance evaluation metrics of the model, parameter tuning for optimizing the model performance, and comparison of the model performance with other state-of-the-art models.
Overview of the model development and evaluation.
Data collection and preprocessing. Ground truth. We used traffic condition data for 19,712 road segments in Harris County provided by the private company INRIX as proxies to determine if a certain road section was flooded. INRIX collects location-based data from both sensors and vehicles. The INRIX traffic data contains the average traffic speed of each road segment at 5-min intervals and their corresponding historical average traffic speed. Each road segment's identification information, such as name, geographic locations defining its head and end coordinates, and length, is also available from the INRIX data set. Previous research shows that road segments flooded due to Hurricane Harvey can be indicated by detecting the road segments with NULL values for their average traffic speed 20 www.nature.com/scientificreports/ main roads in inundation estimation. We found that this data division helps to reduce the data imbalance problem by capturing more flooded segments. The filtered data is used to determine the percentage of roads flooded as the indicator of the flood extent in census tracts. To do so, we characterized the flood status of each census tract as the ratio of flooded roads to the total number of roads. www.nature.com/scientificreports/ Static features. Static features were used to develop the adjacency matrix and assign weights of connection between nodes in the graph model. We developed the adjacency matrix primarily based on the distance between the centroids of census tracts. In addition, we incorporated the impact of six static features (five features in the Table 1 and physical distance) that characterize flood propagation in an area in the adjacency matrix. The rationale is that nodes that have similar static features would have similar flood propagation behavior. Table 1 shows static features including floodplain, land use, watershed, distance to coast and distance to stream and the description of how they are calculated. These features were collected for each census tract. For the features available for each point, the value of the centroid of the census tract is considered. Elevation from the sea level was calculated using the digital elevation model (DEM) of the study area. Distance to Galveston coast and distance to closest main streamflow were calculated by mapping the study area and the streams that discharge stormwater from the area into Galveston Bay. Moreover, we coded 22 watersheds within the study area, and each census tract was associated with the watershed within which its centroid falls. Similarly, we mapped the 100-year floodplain and determined whether the centroid of the census tract falls inside the floodplain. The resulting binary variable was then used as a static feature. Finally, we used the land-use map of Harris County and determined the ratio of residential area to total land area as a feature that is a determinant of the land properties. As a summary, ground truth is used as the dependent variable in the classification in the model. In addition, in case of static and dynamic features, the rationale for selecting static features is to capture similarities between spatial units of analysis to assign weights between them. The degree of influence was determined by testing different weights for the influence of static features versus physical distance. For dynamic features, the rationale for selecting features is (1) ability to provide temporal flood-related information and (2) availability of the temporal data with proper spatial resolution. The degree of influence of dynamic features were tested by developing different models that use different data inputs and investigating the performance of each model.
Dynamic features.
Dynamic features capture temporal changes that can indicate the flood propagation and can be used by the model for flood nowcasting. We considered both physics-based and human-sensed features. For physics-based features, we used the data recorded by the 175 flood gauge stations in Harris County. These flood gauge stations are located on the main channels and bayous to provide residents with timely information on rainfall accumulation and water elevation in the stream 78 . We collected the rainfall and stream elevation from the official website of Harris County Flood Control District 78 . We constructed three time series for each census tract based on the flood gauge data, including short-term rainfall intensity, long-term flood intensity, and water elevation. For short-term rainfall intensity, we used the accumulated rainfall in the past 2 h recorded by the flood gauge (Table 1). For long-term rainfall intensity, we used the accumulated rainfall in the past 24 h recorded by the flood gauges. Also, we used the ratio of recorded water elevation to the threshold elevation of flooding in each flood gauge as the water elevation indicator. It should be noted that the frequency of readings of rainfall and water elevation varies across time; in such cases, we performed interpolation and extrapolation to extract the value of the time series based on the available readings. The number of flood gauges is fewer than the number of census tracts; therefore, we used the weighted average of readings of the two closest flood gauges to determine measurements for each census tract. Weights are proportional to the inverse of the distance between the centroid of the census tract and the flood gauge. Figure 3 illustrates the process for determining physics-based features for each census tract based on the flood gauge data.
Physics-based features provide a reliable source for indicators needed for flood nowcasting; however, due to limitations such as sparsity of data points and lack of sufficient data (limited number of physical sensors) for inferring flood status in near future, we used a number of human-sensed data types to supplement the data www.nature.com/scientificreports/ needed for flood nowcasting. We used three different types of human-sensed data ( Table 1): records of 3-1-1 flood reports, Twitter activity, and the telemetry-based digital trace of human activity. We collected 4275 floodrelated 3-1-1 reports for the study period from the official website of the City of Houston 79 . Then, we filtered reports based on report type so that only reports that indicated flooding were included. More 3-1-1 flood reports during a certain timeframe in an area indicate a higher risk of flooding 75 ; thus, we spatially aggregated the number of reports in each timestep and created a time series showing the number of floods reported through the 3-1-1 platform for each census tract. Social media platforms are another means by which people disseminate information regarding flooding in near real-time. Hence, the relevant data collected from social media can improve flood nowcasting. We incorporated flood-related information posted by Twitter users as an input for our flood nowcasting model. The geotagging feature of Twitter links tweets with accurate longitude and latitude of the location from which tweets originate 80 . Although a small percentage of tweets have geotagged, this small percentage generates thousands of tweets that provide reliable insights into flood status, especially areas lacking physical sensors. To examine social media attention, we used collected tweets for the study time period (August 25, 2017, to September 2, 2017) in 84 super-neighborhoods in Houston. Twitter PowerTrack API (application programming interface) was used for collecting the 29,256 geotagged tweets during the study time period. Two filters were applied to ensure the relevance of the tweets. The first filter identifies the tweets, whose geotags like in our predefined bounding boxes, posted by the users whose profiles show their location Harris County. The second filter was the keywords (i.e., the names and abbreviations of the areas) that identify the tweets specifically related to the study area 71 . Regarding the use of Twitter data, it should be noted that multiple research studies show that crowdsourced data such as Twitter data are subject to various biases such as population bias, spatial bias, and sample bias 80,81 . Particularly, there are studies that investigate the biases in geotagged tweets for Hurricane Harvey 75 . However, one of the potential promises of the model developed in this study is to alleviate the biases in the use of different data sources for flood prediction by data integration. For example, studies show that the crowdsourced data is biased toward less vulnerable populations and the areas with higher population 80 , therefore, solely relying on these data poses great biases on the predictions while including flood sensor data that are somehow evenly distributed across the county chiefly based on the flood exposure and without consideration of population, reduces the bias in the model prediction.
In addition to flood reports and social media activities, recent studies show that telemetry-based human activity fluctuations, which is registered by the concentration of aggregated usage of cellphone users in specific areas can signal flood inundation or other disaster-related impacts 82,83 . To incorporate information regarding human activity in our flood nowcasting model, we obtained digital traces of human activities for the study timeframe from Mapbox. We chose Mapbox as the source of the telemetry data due to its ability to collect temporal and www.nature.com/scientificreports/ spatial telemetry-based human activity with a proper level of aggregation. Human activity is collected, aggregated, and normalized by Mapbox based on the geography information updates of locations of users' devices (such as cell phones) from applications that use Mapbox Software Development Kit (SDK). Human activity here is calculated as the density of the usage of cellphone users in specific areas that are recorded, aggregated, and anonymized by Mapbox SDK globally contributing to live location updates. (The data is gathered from app developers who access Mapbox data through the SDK. Mapbox records locations of users of the maps service.) Mapbox provided a 4-h temporal resolution as raw data. In terms of spatial resolution, tiles represent square geographic areas approximately 100 m per side, a size which varies depending on latitude. The more users located in a tile at time t , the greater the human activity index. Data might not exist for all spatial units, as data is derived from cell phone activity depending on the updates of the geography information of cell phone users. Moreover, to preserve privacy and the data aggregation process, traces are excluded from tiles with small numbers of users. The raw index of human activity is normalized. Normalization is compartmented separately by month and type of trace and yields a normalized activity index for each tile in each 4-h time period of human activity provided by Mapbox. The normalized values range between 0 and 1. We created time series of human activity by aggregating tiles into census tracts and averaging the activity indexes for all the tiles that fall into a census tract in a certain timestep. Thus, we used linear interpolation to aggregate indexes of human activity for each 30-min timestep as the time period considered for our model. Table 1 also provides a summary of dynamic features used for flood nowcasting in this study.
ASTGCN model. Graph adjacency matrix.
Considering that the graph represents an area, and each node represents a census tract, co-location of two census tracts can imply similarities between their state of flooding. Therefore, we considered the distance between census tracts as the major determinant of the weights in the adjacency matrix. In addition to physical distance, we considered static features that imply similarity in flooding status of two areas. In particular, we considered features that influence flooding status in a flood-prone urban area: (1) whether the area is inside the 100-year floodplain, (2) distance to the closest main streamflow, (3) distance to the outlet (Galveston Bay in our study area), (4) the watershed in which that the area is located, and (5) the land-use pattern. To include these static features in our adjacency matrix, we created a vector of size five for each census tract containing the static features and calculated the Euclidean distance similarity for each pair of census tracts. To combine the impact of static features and co-location dependency, we used the weighted average of the Euclidean distance similarity and the physical distance. Based on the early experiments on the model for tuning the weights for the adjacent matrix, we found that choosing 0.1 as the weight for Euclidean distance similarity and 0.9 as the weight for physical distance yields the best result.
Model architecture. We adopted the ASTGCN model architecture design from the model proposed by Guo et al. 33 that was developed primarily as an attention-based graph convolutional network for forecasting traffic flow. The original model framework includes three independent input components and employs information fusion to consider different temporal properties of the traffic flow and to deal with the seasonality of the traffic data. In the case of flood nowcasting, however, there is often no seasonality in the temporal changes of major features-such as rainfall, stream elevation, and human activity-during the hazard period. Hence, we used a single input component in our architecture that consists of time series of three physics-based and three human-sensed dynamic features recorded for each node of the graph. Thus, given the six dynamic features, and N nodes in the graph model of the area, all the features over the T timesteps form X = (x 1 , x 2 , . . . , x t , . . . , x T ) T as the input, where x t includes all the features for all the nodes at timestep t . Moreover, we used the percentage of inundated roads (determined based on INRIX traffic data) as the target variable and used y i t to represent the flooding status of census tract i at timestep t.
As shown in Fig. 4, the ASTGCN model consists of spatial-temporal (ST) blocks and a fully connected layer. Each ST block consists of a spatial attention module and a temporal attention module that is followed by a spatial-temporal convolution module on the graph model. The attention modules are included to capture the spatial and temporal correlation of the dynamic heterogeneous input features in the nowcasting flood status. These www.nature.com/scientificreports/ modules enable the network to adjust the weights of the features and determine the pieces of data upon which the model needs to rely more heavily to have generate predictions. The output is then fed into the spatial-temporal convolution module that captures the dependencies between different nodes based on the adjacency matrix and the time series of input features. The model includes L ST blocks, where the input for (l + 1) th block is:
where C l denotes features of the input data in the (l + 1) th layer, τ l denotes the length of the temporal dimension in the l th layer, which for l = 1 , equals T . The spatial attention is then determined as follows:
where P s and b s are N × N learnable parameters, and W 1C l , W 2C l ×τ l , and W 3C l are also learnable parameters that are fed into sigmoid function σ as the activation function. Similarly, the temporal attention module captures the strength of information between two timesteps i and j . After processing at the attention modules, the data becomes more valuable for the convolution layer as it extracts and captures both dynamic spatial and temporal dependencies. The data is then fed into the spatial-temporal convolution module, which also has spatial and temporal dimensions. For applying convolution of the network structure, Guo et al. 33 used the spectral graph theory, and for each timestep, graph convolutions operate on the graph to extract correlation in the spatial dimension based on the developed adjacency matrix. Given D as the degree matrix and A as the adjacency matrix, Laplacian matrix ( L ) is defined as follows:
The normalized form of the Laplacian matrix is used to apply convolution on the graph as follows:
where * G operates a convolution on the graph G given the signal x and U is Fourier basis. Guo et al. 33 adopt a Chbyshev polynomial to approximate the eigenvalue decomposition on the Laplacian matrix and get the neighborhood of 0 to k − 1-order of each node by g θ as follows:
where θ consist of K polynomial coefficients, T k (x) = 2xT k−1 (x) − T k−2 (x) and L is determined as follows:
and max is the maximum eigenvalue of the Laplacian matrix. The Hadamard product of T k L and SAtt ′ is used in the approximation to include the effect of the spatial attention. Doing so, we can perform required number of filters for each node at each timestep and ensure that the neighboring information has been captured in the spatial dimension. Next, we use the similar standard temporal convolution to update the information based on the past timesteps; for the l th layer, we have:
where * represents standard convolution, parameters of temporal kernel, and ReLU is the rectified linear unit activation function. The model in this study includes three appended ST blocks that are stacked to a fully connected layer that uses a softmax activation function for classifying the dependent variable, flood status.
Model evaluation. The original ASTGCN model that has been adopted by this study is a regression model. However, based on the nature of this study, we transformed the task to classification. The reason for transferring the model from regression to classification is mainly the imbalance in the predictor variable (i.e., the road data). As a common issue in flood prediction task, the data is often imbalance toward non-flooded values. Our experiments on both regression and classification tasks showed that splitting flood extent can reduce the imbalance in the data and better capture the flooding in the model prediction. In addition, interpretability of the performance of the model in classification task is the other reason. Although metrics such as MAE and RMSE can be compared for different models in the regression task, the comparison cannot provide proper insight on the model performance on failure to capture flooding (recall) and incorrect detection of flood (precision), which are very important to understand the performance of predictive models in rare event predictions. We employed various classification metrics which can capture the performance of the model on the imbalance data. Accuracy, precision, recall, and F1 score are used for the case that the target variable is a categorical variable capturing the status of flooding. Our target variable has three different classes, thus we employed macro precision, recall, F1 score, and accuracy as model evaluation parameters to highlight the performance of the model on the minority class.
(1) www.nature.com/scientificreports/ It should be noted that while this study adopted the ASTGCN model structure, it provides various modifications and adjustments to make the model suit for the problem in this study versus the traffic prediction task in the initial version of the ASTGCN model proposed by 33 . These adjustments have been performed to ensure that the model proposed by Guo et al. 33 is properly adopted for the purpose of this study 84 . These adjustments include (1) transforming the model structure to perform a classification task instead of the regression task in the original model. This has been done by modifying the activation function and using evaluation metrics fitted for classification task, (2) varying the number of layers to yield the optimal model performance by doing multiple experiments, (3) modifying the method for determining the weights for the formation of the graph adjacency matrix based on features other than the distance to capture similarity in flood-related features, and (4) stacking and feeding various curated data into the model (versus feeding the model by single feature aggregated in different time periods in the original model).
X l = x 1 , x 2 , x 3 , . . . , x T l ∈ R N×C l ×τ l (2) SAtt = P s · σ X l W 1 W 2 W 3 X l T + b s (3) L = D − A (4) g θ * G x = g θ (L)x = g θ U�U T x = Ug θ (�)U T x (5) g θ * G x = K−1 k=0 θ k T k L x
Results
Study context. As one of the most flood-prone areas in the United States, Harris County has experienced several devastating floods since the latter half of the twentieth century. Notably, Hurricane Harvey, as a Category 4 hurricane, made landfall in Texas on August 25, 2017. Hurricane Harvey led to a catastrophic flood that necessitated 100,000 rescue requests in the week following its landfall in Harris County, as well as damage to 80,000 structures 75 . Contained within Harris County's 1777 square miles are 22 primary watersheds. Detailed information regarding individual watersheds can be found at the Harris County Flood Control District website 85 . Each watershed has independent flooding management issues. Some of them merge and drain into one of the major creeks or bayous, but ultimately, all stormwater drains into Galveston Bay. We defined our study timeline from August 25, 2017, to September 3, 2017, and we collected the sets of data required for the flood nowcasting model for 787 census tracts in Harris County.
Implementation details. In this study, we used data from August 25 to August 30, 2017, as our training set, and data from August 31, 2017, to September 3, 2017, as our test dataset. We used 30-min intervals to give us 288 timesteps for training the data and 192 timesteps for testing the model. We split the data in a way that both training and testing sets capture portions of flood propagation and recession due to Hurricane Harvey. There were two main factors that governed the decision for data split. First, to perform proper prediction, both training and testing datasets need to include sufficient (and ideally close) ratio between the number of observations in each classes of the response variable. However, the fact is that the flooding mainly occurs in the specific timeframe and it is challenging to split the data in a way that both datasets include a reasonable case of flooding. To deal with this issue, we plotted the flood status time series to understand what threshold would best divide the data into train and test set that capture sufficient flood cases. It leads to selecting the existing train/test datasets in which the ratio of the test dataset is slightly larger than the convention. Besides, the other consideration is that the model needs to see sufficient number of data points to perform proper prediction based on the time series of the observed data. therefore, the test set cannot be as small as the conventional models employ (e.g., 10% of the entire dataset). Accordingly, all the dynamic features were extracted and underwent data preprocessing required for feeding into the model. In cases that the dynamic features were not available in the time units of the study, linear interpolation and extrapolation were used to extract the required values for the missing timesteps. We categorized flooding statuses into three classes: in each timestep, census tracts with fewer than 1% of roads flooded are considered as "no flood, " census tracts with 1%-10% of roads flooded are considered as "moderate flood, and census tracts with more than 10% roads flooded are considered as "severe flood. " The selection of the ratio for determining classes of flood extent was primarily done by a combination of testing different ratios and authors' judgement. In fact, we plotted the different ratios to see which ratio can better reflect the flood extent in the area in accordance with other ground truths such as flood maps during Hurricane Harvey. In should be noted that since the ground truth in this study captures road/street flooding, it does not perfectly match with flood maps since not all flood inundations cause street flooding. however, the overall comparison can be made using the flood maps and the historical information regarding the flood impact during 2017 Hurricane Harvey in Harris County.
In this case, the model solves a classification problem in which the objective is to minimize the misclassified samples. We performed hyperparameter tuning by focusing on the learning rate and dropout rate to select the model with the best performance.
Model performance and comparison. Along with model implementation and to better evaluate the model performance, we used different state-of-the-art models against which ton compare the performance of the ASTGCN model. Moreover, we examined the extent to which the integration of human-sensed data can improve the performance of a model that relies solely on physics-based data for flood nowcasting. To this end, we ran four different experiments. First, we ran the model on the attention-based spatial-temporal graph convolution network model fed by physics-based data (model 1). Next, we employed the same ASTGCN model and employed both physics-based and human-sensed features as input (model 2). To assess the impact of the attention mechanism on the model performance, we used a relatively similar spatial-temporal graph convolutional network (STGCN) model (model 3) adopted from Yu et al. 86 . Finally, we used a long-short term memory (LSTM) model (model 4) as the baseline for model performance comparison. Table 2 shows the performance of the models in terms of precision, recall, F1 score, and model accuracy. Comparing the performance of graph-based models (models 1, 2, and 3) with the LSTM model, we can see that the graph-based models show significantly better performance in terms of precision, recall, and F1 score, while all the models have proper accuracy. The poor performance of the LSTM model in macro precision, recall, and www.nature.com/scientificreports/ F1 score shows that the model is unable to classify minority classes (i.e., flooded areas), which indicates that the model cannot provide insight for flood nowcasting. Comparing the performance of graph-based models, the STGCN model demonstrates highest recall and accuracy. However, the precision is 9.28% lower than the model with the highest precision, model 2, which uses physics-based and human-sensed input. This considerable difference is also reflected in the F1 score. The implication is that model 3 properly captures flooded cases (high recall), which is particularly valuable for flood nowcasting since it ensures the majority of the flooded areas are captured; however, the downside is that it erroneously captures many non-flooded cases. Finally, the comparison of model 1 and model 2 reveals valuable insights for flood nowcasting and risk prediction. As shown in Table 2, model 2 over-perform model 1 in major evaluation metrics, including precision, recall, and F1 score. Particularly, model 2 yields 2.92% higher precision, 8.13% higher recall, and a 4.99% higher F1 score. Therefore, it can be seen that the use of human-sensed features as the supplement to physics-based input for flood nowcasting in the graph-based model significantly improves the predictive performance of the model. This finding shows the benefit of using heterogeneous community data and integrating different dynamic features for flood nowcasting. It reinforces the need for developing pipelines for collecting, preprocessing and integrating human-sensed data that becomes available during a flood event to improve awareness. Figure 5 shows an instance of the prediction performance for model 2. As can be seen in boxes (I), (II), and (III), the model performed well in the case of the clusters of flooded areas, although in some cases (box (II)), there are misclassified regions. These region errors might indicate the impact of capturing the spatial dependency on the predictive performance that enables the model to identify the inundation hot spots and aid decision-makers to detect regions that need to be prioritized for emergency response in near future. On the other hand, as we can see in the red circles in Fig. 5b, particular areas that are not in the flooded clusters have been classified incorrectly. This result might indicate the need for more data, particularly human-sensed data, which can signal inundation of areas where flooding is difficult to detect by the co-location dependency. Figure 6 also shows two cases of flood nowcasting performance by model 2, which shows significant differences in predictive performance. As shown in Fig. 6a, the model has performed properly in identifying the majority of the flooded area; however, in considerable misclassified areas are evident in Fig. 6b. Considering that Fig. 6a shows a timestep close to the start time of the test set (timestep 2), while Fig. 6b is a timestep that captures the third day in the test set (timestep 136), it might be inferred that the model performance decays as the time passes, which can be addressed by updating the model during the flood event.
Conclusions
A crucial step for effective and timely disaster response and recovery is situational awareness, how the situation is evolving, and how community actors and residents respond to the evolving situation 87 . In this regard, flood nowcasting plays a pivotal role in enhancing situational awareness by providing a realistic prediction of the areas at risk of flood inundation in near future. In this study, we adopted an attention-based spatial-temporal graph convolution network (ASTGCN) model for urban flood forecasting. The model employs both physics-based and human-sensed features, as well as static features that capture spatial dependency in terms of flood propagation. In the ASTGCN model, the attention mechanism enables automatically updating the importance of spatial and temporal dependencies for flood nowcasting, and the spatial and temporal convolutions extract the local dependencies in the model. We demonstrated the application of the model and compared its performance in the context of flooding following Hurricane Harvey in Harris County, Texas, in August 2017. The results indicate that, in general, the graph-based structure significantly improves prediction of flooded areas. For example, the model performs significantly better than the conventional long-term short-term memory models in terms of precision and recall, which are metrics of interest in prediction tasks using an imbalanced data set. Moreover, the attention mechanism improves the model precision and helps to capture the majority of flooded areas. The results also indicate that the ASTGCN model performs significantly better if it employs heterogeneous human-sensed data as a supplement of the physics-based data that traditionally used by hydraulic and hydrologic models. This finding is particularly significant since it demonstrates the promise of developing data pipelines for data fusion using physics-based data collected by flood gauges and sensors and data that is either generated by residents or captures the digital trace of residents' activity.
The main contributions of this study are twofold: first, we adopted and tested a novel graph deep-learning model for urban flood nowcasting. Second, the study showed the value of leveraging human-sensed data to complement physical flood sensor data for observing flood status across a region to improve flood nowcasting. Through these contributions, this study advances the body of knowledge related smart flood resilience. The advances in a structured deep-learning model provide opportunities for employing model architectures that extract information from spatial and temporal dependencies 2 and modules that extract information by putting more attention on the varying spatial and temporal features 44 . Moreover, the increasing availability of heterogeneous human activity data in near real-time calls for pipelines that leverage the information embedded in such data that can provide signals for urban flooding. The novel deep learning-modeling approaches and the availability of human-sensed data advance smart flood resilience by providing tools and pipelines that help people better respond and react to floods through enhanced predictive flood exposure and risk mapping before and during floods. This study, in particular, demonstrates the promise of integrating physics-based and human-sensed data into a graph-based deep-learning model that captures spatial and temporal dependencies for flood nowcasting. Also, this study showed the promise of data-driven models to complement physics-based H&H models for predictive flood monitoring and situational awareness.
It should be noted that the one of the main challenges in urban flood prediction studies is the scarcity of the required data in urban scale and limited data availability. The ideal case is to have data of various flood events to train model on specific events and test it on the other events to evaluate the model performance. However, this is only possible for various flood prediction studies that solely rely on sensor data 43 . When it comes to leverage emerging datasets such as human activity and crowdsourced data, some of the datasets (i.e., Mapbox and Twitter data) are currently available only for limited number of events (e.g., Hurricane Harvey in this study). Nevertheless, the availability of these datasets is increasing, and therefore, it is valuable to test the applicability of these data for future employment in larger scale. In fact, we aimed at using the existing datasets, acknowledging the www.nature.com/scientificreports/ abovementioned limitation in data scarcity, and aiming at limiting the impact of the data scarcity on the model performance by different techniques. While the model performance cannot guarantee the same model performance in the future events due to the data limitations, the comparison made by using various model structures shows the potential for the superior performance of the proposed framework (i.e., employing graph-based models and data integration to capture different flood signals). Future studies can focus on developing techniques to reduce the computational demand of the existing models to make the use of these models more feasible for flood nowcasting once more data streams are fed into the model. Moreover, further studies can generalize the approach demonstrated in this paper by testing the model on other flood cases and utilizing other types of physics-based and human-sensed features as inputs. As mentioned earlier, one limitation of this study is that the model was tested in a single event and region, as the data used in this study was not available for historical events. As various physical sensor and human-sensed data become more available in future events, however, the model could be employed and tested in other events and contexts.
Data availability
All data were collected through a CCPA-and GDPR-compliant framework and utilized for research purposes. The data that support the findings of this study are available from Mapbox and INRIX, but restrictions apply to the availability of these data, which were used under license for the current study. The data can be accessed upon request by the data providers. Other data we use in this study are all publicly available.
Figure 1 .
1Schematic representation of the problem abstraction; the study area is modeled as a graph; static features and distance are used to determine weights, and physics-based and human-sensed dynamic features are used for predicting the extent of flooding.
Figure 2 .
2Overview of the model framework, including steps for collecting and preprocessing ground truth and features, developing the ASTGCN model architecture, and evaluating the performance of the model.
Figure 3 .
3Schematic illustration of calculating census tracts' distances and weights of two closest flood gauges as inputs to the census tract physic-based features. Scientific Reports | (2023) 13:6768 | https://doi.org/10.1038/s41598-023-32548-x
Figure 4 .
4Model architecture, including model input, spatial-temporal blocks, attention layers, and the fully connected layer at the end.Scientific Reports | (2023) 13:6768 | https://doi.org/10.1038/s41598-023-32548-x
Figure 6 .
6An example of model flood nowcasting performance; (a) a proper prediction (August 31, 00:30 a.m.-01:00 a.m.) versus (b) model prediction with more misclassification (September 2, 8:30 p.m.-9:00 p.m.). Scientific Reports | (2023) 13:6768 | https://doi.org/10.1038/s41598-023-32548-x
. We filtered the road segments with speedlimit ≥ 30 mph to only account for theScientific Reports
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Table 1 .
1Static and dynamic features used for urban flood nowcasting.Influencing factor
Feature
Static feature
Floodplain
Whether or not the area is inside the 100-year floodplain
Land use
Percentage of the residential area
Watershed
The watershed that the area falls inside it
Distance to coast
Distance to Galveston coast
Distance to stream
Distance to the closest main stream flow
Dynamic feature
Physics-based features
Short-term rainfall intensity
Estimated accumulated rainfall in past 2 h
Long-term rainfall intensity
Estimated accumulated rainfall in past 24 h
Water elevation
Estimated ratio of water level to the flooding threshold, based on
average readings of two closest channels
Human-sensed features
Flood reports
Number of reported flooding in the neighborhood through 3-1-1 platform
Social media activity
Number of flood-related filtered tweets
Human activity
Activity index of telemetry-based digital trace of human activity
Table 2 .
2Evaluation metrics for performance comparison of different models. Significant values are in [bold]. *ASTGCN with physic-based features. **ASTGCN with physic-based and human-sensed features.Figure 5. An example of model overall predictive performance (August 31, 6:00 a.m.-6:30 a.m.); (a) ground truth versus (b) model prediction.Criteria/Model
ASTGCN-I* (model 1) ASTGCN-II** (model 2) STGCN (model 3) LSTM (model 4)
Precision
0.785
0.808
0.733
0.416
Recall
0.824
0.891
0.906
0.413
F1 score
0.802
0.842
0.819
0.414
Accuracy
0.975
0.979
0.999
0.981
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© The Author(s) 2023
AcknowledgementsThe authors would like to acknowledge funding support from the National Science Foundation project CRISP 2.0 Type 2 #1832662: Anatomy of Coupled Human-Infrastructure Systems Resilience to Urban Flooding: Integrated Assessment of Social, Institutional, and Physical Networks and the funding support from the X-Grant program (Presidential Excellence Fund) from Texas A&M University. Any opinions, findings, and conclusion or recommendations expressed in this research are those of the authors and do not necessarily reflect the view of the funding agencies.Code availabilityThe code that supports the findings of this study is available from the corresponding author upon request.Competing interestsThe authors declare no competing interests.Additional informationCorrespondence and requests for materials should be addressed to H.F.Reprints and permissions information is available at www.nature.com/reprints.Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative Commons Attribution 4.0 InternationalLicense, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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| sample_239 | 0.8464 | arxiv | |
Robust Relationship Between Mid-latitudes CAPE and Moist Static Energy in Present and Future Simulations Submitted for publication in Geophysical Research Letters
13 Dec 2022
Ziwei Wang
Department of the Geophysical Sciences
University of Chicago
ChicagoIllinois
Center for Robust Decision-making on Climate and Energy Policy (RDCEP)
University of Chicago
ChicagoIllinois
Elisabeth J Moyer
Department of the Geophysical Sciences
University of Chicago
ChicagoIllinois
Center for Robust Decision-making on Climate and Energy Policy (RDCEP)
University of Chicago
ChicagoIllinois
Robust Relationship Between Mid-latitudes CAPE and Moist Static Energy in Present and Future Simulations Submitted for publication in Geophysical Research Letters
13 Dec 2022manuscript submitted to Geophysical Research Letters manuscript submitted to Geophysical Research LettersCorresponding author: Elisabeth Moyer, moyer@uchicago.edu -1-
Convective available potential energy (CAPE), a metric associated with severe weather, is expected to increase with warming. Under the most widely-accepted theory, developed for strongly convective regimes, mean CAPE should rise following the Clausius-Clapeyron (C-C) relationship at 6-7%/K. We show here that although the magnitude of CAPE change in high-resolution model output is only slightly underestimated with simple theories, it is insufficient to describe the distributional changes, which has a down-sloping structure and is crucial for impact assessment. A more appropriate framework for understanding CAPE changes uses the tight correlation between CAPE and moist static energy (MSE) surplus. Atmospheric profiles develop appreciable CAPE only when MSE surplus becomes positive; beyond this point, CAPE increases as ∼25% of the rise in MSE surplus. Because this relationship is robust across climate states, changes in future CAPE distributions can be well-captured by a simple scaling of present-day data using only three parameters.
Introduction
Convective Available Potential Energy (CAPE), loosely defined as the vertically integrated buoyancy of a near-surface air parcel, is a metric closely associated with the extreme convective weather events that can cause substantial socioeconomic damages (e.g., Johns & Doswell, 1992). CAPE is derived from the difference between the temperature profile of a parcel rising pseudo-adiabatically from the surface and that of the background environment (Moncrieff & Miller, 1976), which determines the maximum possible updraft velocity during undiluted ascent. In meteorology, CAPE is used to predict thunderstorm events and in particular hail (Groenemeijer & van Delden, 2007;Kunz, 2007;Kaltenböck et al., 2009). Studies have also used the covariate of CAPE and wind shear to explain differences in thunderstorm frequency across locations (Brooks et al., 2003(Brooks et al., , 2007 or across climate states (Trapp et al., 2009;Diffenbaugh et al., 2013).
Studies of CAPE in observations have tended to focus on decadal-scale trends, often finding large increases. For example, Gettelman et al. (2002) found trends equivalent to ∼50%/K in 15 tropical radiosonde stations. (See SI Section S1 for a wider review.) Model studies of CAPE under climate change have tended to produce smaller effects. Several recent studies that simulate the tropics using convection-permitting models (0.2-4 km resolution) without advection, i.e. approximating radiative-convective equilibrium, find CAPE increases of 8%/K (Muller et al., 2011), 8%/K (Romps, 2011), 12%/K (Singh & O'Gorman, 2013), 7%/K (Seeley & Romps, 2015), and 6-7%/K from theory (Romps, 2016). Analyses of coarser-resolution global models have found even smaller changes in the tropical W. Pacific, of ∼4.5%/K (Ye et al., 1998, at 4 • x 5 • ) and ∼5%/K (Chen et al., 2019, at 1 • ). In the mid-latitudes, changes may be larger: Chen et al. (2019) show ∼10%/K over a selected region of the continental United States.
Theoretical frameworks to explain climatological CAPE fall into two groups. One approach assumes that environmental profiles are fully determined by surface temperature, and predicts the background environmental temperature profile by considering the effects of convective entrainment. Singh and O'Gorman (2013) proposed a "zero-buoyancy model" based on the assumption that entrainment makes actual in-cloud buoyancy in an ascending convective plume small relative to CAPE, and Singh and O'Gorman (2015) evaluated its applicability in radiative-convective equilibrium simulations. Zhou and Xie (2019) extended the model to use an ensemble of plumes. The zero-buoyancy concept is intended to represent convective regions such as the tropics, where environmental temperature profiles are largely set by convection, with horizontal advection playing a negligible role. It would not be expected to explain variations in CAPE across space or on short timescales over mid-latitudes land.
A second approach, which may be more generally applicable, treats surface and midtropospheric conditions as independent variables. Early efforts sought to characterize empirical relationships in CAPE as a function of near-surface temperature and moisture (Williams & Renno, 1993;Ye et al., 1998). Emanuel and Bister (1996) (henceforth EB96) considered the moist static energy h instead and described the relationship as
CAP E = A · (h s − h m )(1)
where h s and h m are moist static energy (MSE) at near-surface (boundary layer) and mid-troposphere, respectively. The dimensionless constant A in EB96 reduces to (1− T /T s ), analogous to a Carnot efficiency, where T s is the near-surface temperature and T relates to the temperature of those levels emitting radiation to space. In this perspective, CAPE represents the maximum possible kinetic energy that could be generated given a heat transfer of (h s − h m ).
Recent work has further extended on EB96 and tested applicability to mid-latitudes CAPE. Agard and Emanuel (2017) (henceforth AE17) and Li and Chavas (2021) use a similar functional form but slightly different formulations for the slope A and for the 'threshold' term. Li and Chavas (2021) confirm that their model broadly captures both the spatial pattern and diurnal variation of CAPE in renalysis data over the continental United States. These theories do not fully predict future CAPE, since they provide no guidance on future changes in the threshold term relative to h s , i.e. on changes in the shape of the environmental temperature profile. However, because all are grounded in simple mathematical definitions -for moderately convective conditions, a linear CAPE dependence on surface MSE is a necessary consequence in any dataset where mid-tropospheric conditions are decoupled from the surface -they should provide a useful framework for understanding model-projected changes.
In this work we use a modified formulation with a different threshold term. Mathematically, CAPE is proportional to the vertically integrated difference between h s and the local "saturation MSE" h * z , neglecting the virtual temperature effect and difference in q * between parcel and environment (Emanuel, 1994;Randall, 2012). If we assume the shape of the environmental temperature profile does not vary strongly with h s , the definition of CAPE can be reduced to:
CAP E = A · (h s − h * m )(2)
where h * m is the minimum value of mid-tropospheric saturation MSE, and we term the difference h s −h * m the 'MSE surplus'. The value of A must be determined empirically, and because its value depends on the shape of environmental profiles, it does not necessarily remain constant between climate states.
Despite the interest in understanding potential future CAPE increases, few studies have systematically evaluated these frameworks, especially in the continental midlatitudes where severe thunderstorm impacts are greatest. In this work, we diagnose CAPE relationship to surface and mid-tropospheric conditions in both observation and highresolution convection-permitting model simulations of continental North America, to determine what aspects of the relationship are robust under climate change. Our goal is to quantify projected CAPE changes in the mid-latitudes and to provide a simple framework that explains them.
Data Description and Methodology
Data Description
The convection-permitting model output used here is a paired set of present and future dynamically downscaled simulations over continental North America from the Weather Research and Forecasting model (WRF, version 3.4.1) run at 4 km resolution. Both runs are described in , and model output is available from NCAR Research Data Archive ds612.0 . The present-day simulation (CTRL) is forced by ERA-Interim reanalysis for initial and boundary conditions; the future simulation is a pseudo-global-warming (PGW) scenario that applies a spatially varying offset to ERA-Interim based on the CMIP5 multi-model mean projection under RCP8.5. In both runs, spectral nudging is applied to levels above the planetary boundary layer. Note that hot and dry biases over the Central U.S. lead to a small underestimation of CAPE in the high tail by 6-10% Wang et al., 2021), but this bias does not necessarily affect fractional future changes.
In this work, we use the years 2001-2012 and equivalent future period. For 'paired' comparisons we match each profile in CTRL with its equivalent in PGW. We calculate surfaced-based CAPE and subset to 80 grid points that match the International Global Radiosonde Archive (IGRA) weather stations as in Wang et al. (2021). See SI Section S2 for spatial distribution of stations and further model validation. Most analyses here use observations in summertime (MJJA) only, when convection is most active, following Sun et al. (2016) and K. L. Rasmussen et al. (2017).
Methodology
To maintain the focus on highly convective conditions, many comparisons here involve values for profiles above the 73rd quantile in CAPE, which corresponds to CAPE >1000 J/kg in CTRL (e.g. Figure 3 and Figure 4, left). When computing linear fits, we use orthogonal distance regression (ODR) because it is most appropriate in conditions where errors in both dependent and independent variables matter. When computing fractional changes between CTRL and PGW climate states, we define them as ln(PGW/CTRL)/∆T. See SI Section S3 for details on subsetting and averaging, and Schwarzwald et al. (2021) for discussion of ODR.
Synthetic profiles
We construct five synthetic CAPE distributions to help understand the minimal information needed to realistically reproduce future distributional changes. All are constructed based an assumed 3.92 K surface temperature increase, the mean change for profiles above the 73rd CAPE quantile. (Note that this change is smaller than the 4.65 K average for the entire dataset; see SI Section S3.) All cases but #4 take the CTRL profiles and CAPE values as the baseline. One case (#1) is a simple transformation of the CTRL CAPE distribution, and three (#2-4) require re-calculating CAPE for a set of synthetic atmospheric profiles. See SI Section S4 for further details.
1. For Clausius-Clapeyron scaling, shown for illustrative purposes only, we simply multiply each CTRL CAPE value by 1.27 (e 0.061·3.92 ), where 6.1%/K is the C-C change for the mean temperature of high-CAPE profiles, 301.8 K. We omit several systematic changes that largely cancel: C-C would be changed by -0.4%/K by including the projected reduction in surface RH, by -0.1%/K by treating profiles separately, and by +0.6%/K by incorporating the rise in the Level of Neutral Buoyancy (LNB). 2. For the constant offset case, we add 3.92 K to each CTRL profile at each level from surface to 200 hPa, near the level of neutral buoyancy in the mean CTRL profile. From 200 hPa we linearly interpolate to zero change at 75 hPa. We also adjust surface RH by -0.9%, the mean change above the 73rd CAPE percentile. 3. For the lapse rate adjustment synthetic case, we modify the constant offset procedure to also include a change in lapse rate. That is, we linearly interpolate between the 3.92 K surface warming and a similarly derived 200 hPa warming of 4.94 K. We apply the same surface RH adjustment as in constant offset.
4. For the SO13 case, we add 3.92 K to surface temperatures and calculate a climatological mean profile using the zero-buoyancy model of Singh and O'Gorman (2013). We use an entrainment rate of 0.62 and column RH of 0.44. We construct profiles in both CTRL and PGW environments, so that the theory provides a selfconsistent prediction of changes.
3 Results
Changes in CAPE distributions
We begin our analysis by asking: in mid-latitudes model projections, how much and how does CAPE change with warming? Over the entire dataset, mean CAPE rises 61% between CTRL and PGW, from 684 to 1103 J/kg, yielding a 10%/K increase given the mean surface temperature rise of 4.65 K (assuming incremental changes). The mean change may not be the most relevant metric, however, since mid-latitude CAPE distributions are zero-inflated even in the convective summertime, and the strongest temperature changes occur in conditions where CAPE is small or zero. An alternate approach that emphasizes changes in higher-CAPE conditions is to take an orthogonal regression to the density distribution of paired profiles in present and future runs (Figure 1, left, solid line). This distribution shows a clear shift upwards, even though weather systems are not identical in the two runs and the scatter is therefore large. The regression slope gives a CAPE increase of 45% or 8.0%/K, slightly larger than Clausius Clapeyron (6.1%/K). By contrast, the constant offset synthetic overpredicts CAPE increases (11.7%/K) and the SO13 theory underpredicts them (5.8%/K); see SI Section S5.1.
The orthogonal regression implicitly assumes that the change in CAPE distributions is a simple multiplicative shift. To test this assumption, we also show in Figure 1 a quantile regression, which compares individual quantiles of CTRL and PGW distributions. The future CAPE distribution is in fact narrower than in the simple multiplicative case. Comparing to the orthogonal regression, the lower quantiles lie above the 45% line and the most extreme quantiles (>∼3000 J/kg) below it (left panel, dots). This narrowing effect is even more clear in a plot of the quantile ratio of future vs. present-day CAPE (right, black); it manifests as a downward slope. Both the constant offset (green) and SO13 (purple) cases also show similar narrowing, despite their different mean predicted changes. Distributional changes in model CAPE therefore resemble an offset with a small lapse rate adjustment that lowers CAPE.
Because the SO13 theory was developed to represent the mean profile in highly convective conditions, we also test whether it can capture the present-future CAPE change of the averaged late-afternoon (00 UTC) profile in our simulations, but the underprediction remains substantial. (See SI Section 5.1.) Changes in mid-latitudes lapse rates require a new explanatory framework.
Changes in environmental profiles
To quantify the effect of changing environmental lapse rates on future CAPE, we examine mean CAPE in surface temperature and humidity (T-H) space following Wang et al. (2021). Since surface T and H uniquely define the moist adiabat on which a parcel rises, a change in CAPE for a given T,H is due only to an altered environmental profile. This approach allows decomposing CAPE changes into two governing factors: f samp is the fractional change that would result from only changed surface T,H sampling (Figure 2, top row) and f env is that resulting from only changes in environmental profiles (Figure 2, bottom row). Both factors are defined for CTRL CAPE >1000 J/kg conditions. In these model runs, increased sampling of warmer surface conditions in PGW would more than double CAPE from its CTRL value (f samp ∼ 2.2) if lapse rates did not change. However, CAPE contours shift strongly in the PGW run, so that warmer or wetter sur- 98.9%, respectively). We begin the x-axis at 40% to omit quantiles where CTRL CAPE is zero.
Model future CAPE changes resemble a constant offset with a small lapse rate adjustment.
face conditions are required to achieve the same CAPE. If T,H sampling remained the same, CAPE would fall by a third due to environmental effects alone (f env ∼ 0.64). The combined effect is f samp ·f env = 1.40, close to the 1.45 derived from orthogonal regression in Figure 1. (See SI Section S5.2 for details on calculations.)
The effects seen in Figure 2 do not necessarily mean there is substantial excess warming at altitude. Most of the environmental damping of potential CAPE increases occurs even in the constant offset case of uniform warming, because present-day environmental profiles are correlated with surface temperature. Since upper tropospheric temperature is relatively homogeneous, extreme local surface temperature necessarily implies a steep lapse rate. Under climatological warming, surface temperatures that were previously extreme become associated with more normal lapse rates instead. For this reason even the constant offset case shows an f env of 0.77, i.e. apparent potential CAPE increases are damped by 23% by this covariance effect alone. (The total derived CAPE change in constant offset is 1.71, close to its orthogonal regression slope of 1.72.) Excess warming at altitude is therefore required only to explain the residual difference between effects in PGW (f env = 0.64) and in constant offset (f env = 0.77). Changes in temperature profiles between present and future runs are in fact very subtle. If the entire dataset is averaged, warming is actually greater at surface than at altitude (∆T s = 4.65 K and ∆T 200 = 4.05 K), an effect that would tend to amplify CAPE. However, as discussed in Methods, when data is subdivided to include only conditions that can produce substantial CAPE, lapse rate changes are weakly positive (∆T s = 3.92 K and ∆T 200 = 4.94). That is, in conditions favorable for convection, future environmental changes should slightly dampen the CAPE increase expected from surface warming alone.
CAPE-MSE framework
It is clear that CAPE in our dataset must exhibit a strong relationship with surface MSE, since the contours of CAPE in T-H space in Figure 2 are closely aligned with those of MSE. (See SI Section S5.2; this effect was also shown by previous paper, e.g. Donner et al. (1999).) The relationship is in fact reasonably linear in each climate state (Figure 3, left, which shows all CAPE values >1000 J/kg), but shifts as the climate warms. In both CTRL and PGW model runs, the x-intercept to the fitted regression matches the mean mid-tropospheric saturation MSE to < 0.3%: on average, CAPE does not develop unless surface MSE (h s ) exceeds saturation MSE (h * m ) in the mid-troposphere. These results suggest that the more fundamental relationship is between CAPE and MSE surplus (h s − h * m ), as in Equation 2. When CAPE is plotted against MSE surplus (Figure 3, right), residual variance does indeed become smaller (24% vs. 31% for CTRL and 8% vs. 26% for PGW) and intercepts become almost zero (0.67 and 1.07 kJ/kg for CTRL and PGW, respectively). The relationship between CAPE and MSE surplus is in fact sufficiently fundamental that it holds across climate states. Fitted slopes are nearly identical in CTRL and PGW runs, at 0.27 (Figure 3, right). In this perspective, the effects of climate change reduce to only a greater sampling of conditions with high MSE surplus. Furthermore, the relationship between CAPE and MSE surplus is robust across other temporal and spatial comparisons as well. Fitted slopes and variance explained remain similar when the dataset is divided by latitude (northern vs. southern stations), by daytime vs. nighttime profiles, by anomalously warm vs. cold years, or even by winter vs. summers (SI Section S5.3). Using an alternative fitting method (all samples above 1000 J/kg CAPE instead of binned median values) produces smaller slopes (0.17 and 0.16 for CTRL and PGW), but they remain consistent across all comparisons.
The fact that WRF output and observations are well-described by Eq. 2 -CAP E = A × (h s − h * m ) -will naturally follow if the mid-troposphere is reasonably decoupled from the surface. If variation in h * m is uncorrelated with that in h s , a linear relationship between CAPE and MSE surplus is a straightforward mathematical consequence. As a partial test of this condition, we plot saturation MSE profiles for data subset by a variety of CAPE thresholds (SI Section S5.4). In all conditions with any appreciable CAPE (>100 J/kg), the minimum of saturation MSE in the mid-troposphere remains nearly constant across subsets, suggesting that mid-tropospheric temperature and h * m are not strongly coupled to surface conditions in these mid-latitudes simulations.
A simple lapse rate adjustment framework
While theories of future CAPE based only on surface conditions do not work well in the mid-latitudes, we consider whether adding a single parameter to describe mid-tropospheric effects can yield accurate predictions of future CAPE distributions. As described in Section 2.3, we construct a transformation of present-day atmospheric profiles based on only 3 parameters: mean changes in surface temperature and humidity, and a separate value for warming at 200 hPa (∆T s , ∆ RH, ∆T 200 ). To evaluate how well this lapse rate adjustment captures CAPE changes in actual model output, we show also results for a twoparameter transformation -the constant offset shift with RH adjustment, which uses only mean surface ∆T s and ∆ RH -and for reference, a simple C-C scaling applied to each individual profile. See Section 2.3 and SI Section S5.5 for details.
The three-parameter lapse rate adjustment transformation does indeed capture the characteristics of future CAPE changes (in high-CAPE conditions). In the CAPE-MSE perspective (Figure 4, left), it realistically captures the future relationship, both in its slope and x-intercept. In the quantile ratio perspective (Figure 4, right), it reproduces both the downsloping structure and the magnitude of fractional change in the high CAPE quantiles. On a T-H diagram, lapse rate adjustment reproduces the future CAPE contours well while other transformations produce clear discrepancies (SI Section S5.5). Note that in the highest CAPE conditions, future changes in model output and in lapse rate adjustment begin to approach Clausius-Clapeyron, but remain above it. Changes in the 99th quantile are 6.9%/K in WRF and 7.1%/K in lapse rate adjustment, while the C-C line in Figure 4 is shown as a constant 6.1%/K, and would be similar even if treated more realistically. (See Methodology, and SI Section 5.5 for more extensive comparisons.) While mid-latitudes CAPE is too complex to be treated with simple scalings, a relatively straightforward 3-parameter transformation appears to reproduce its full distributional change in a future warmer climate. Future changes in CAPE as quantile ratio plots, with dots marking quantiles at 1% increments.
As in Figure 1, four x-axis ticks mark 1000-4000 J/kg, and PGW/CTRL CAPE values are on the numerator/denominator. All the synthetic future (scatters) fractional changes are referenced to CTRL. CAPE-MSE instead of the CAPE-MSE surplus framework is shown because the latter requires further assumptions about how the mid-tropospheric MSE would change. The lapse rate adjustment synthetics best reproduce future CAPE.
Discussion
Increases in severe weather events, which are associated with high CAPE, are a substantial societal concern under global warming. We show here that the projected increase in mean mid-latitudes CAPE in high-resolution model output is substantially higher than in theories developed under assumptions appropriate for the tropics, which are close to Clausius-Clapeyron (C-C). The discrepancy is smaller for the most extreme conditions, but even in the highest quantiles in this analysis, model CAPE changes are over 20% above C-C. This difference translates to large changes in the projected occurrence of CAPE exceeding a given threshold. For example, incidences of summertime CAPE >2000 J/kg, a commonly-used threshold for severe weather, rise twice as much in model projections as in Clausius-Clapeyron scaling: from 13% in CTRL to over 24% in the future PGW projection, vs. to only 19% under C-C scaling.
The midlatitudes apparently require a different framework for understanding CAPE changes than the convective tropics. Both the influence of advection and the strong surface diurnal variation means that mid-tropospheric values cannot be predicted from surface conditions. Furthermore, the wide range of surface conditions in the mid-latitudes continental U.S. mean that lapse rate effects vary spatially across the domain, with upper tropospheric warming strongest in the subtropics and lapse rates changes actually negative north of 33N (SI Section S7). Nevertheless, we find that future CAPE distributional changes can be well-captured by a simple synthetic transformation based only on three changes averaged over the entire domain (∆T s , ∆RH s , and either ∆T 200 or ∆T 650 ). These three parameters can be folded into a single metric of "MSE surplus", the difference between surface MSE and mid-tropospheric saturation MSE. In the model output described here, CAPE does exhibit a strong dependence on MSE surplus, as expected: in each climate state the relationship is a straightforward mathematical consequence. We show here that the relationship is robust even across climate states (empirical slopes of 0.27 and 0.26 in Figure 3) implying that atmospheric structure does not change dramatically.
These results can be compared to prior theories based on analogies to heat engines. The slope A can be thought of as the maximum conversion rate of MSE surplus to mechanical work. Similarly, theories such as EB96 treated CAPE as the maximum work possible given a flow of energy between hot and cold reservoirs, and therefore predicted a Carnot-like slope of (1 − T /T s ). This theoretical value can be derived by constructing a mean atmospheric profile (using all incidences of CAPE > 1000 J/kg); our dataset yield theoretical slopes of 0.18 for both radiosonde observations and CTRL model output, similar to the 0.14 in Emanuel and Bister (1996). This value is lower than the empirical slopes of Figure 3 (right), but is nearly identical to slopes derived without fitting the binned median values: 0.18 for observations and 0.17 for CTRL. It appears that the heat engine framework does capture some physical constraint on CAPE, though MSE surplus (h s −h * m ) is the more fundamental regressor. Note that CAPE represents only the potential production of kinetic energy, not the true conversion rate, which is affected by factors that reduced efficiency below Carnot (e.g. Romps, 2008).
Understanding how CAPE responds to CO 2 -induced warming is a key scientific question with significant societal consequences. This work suggests that in the mid-latitudes, the decoupling of surface and mid-troposphere means that changes in CAPE can be larger than predicted by theories developed for the convective tropics. We find that a simple 3-parameter transformation captures not only future mean increases in midlatitudes CAPE but their full distributional shifts. It does remain an outstanding question how the presentday mapping of CAPE to convective updraft velocities and extreme convective events may alter under climate change. However, the strong and consistent dependence of CAPE on MSE surplus provides a simple but robust framework for predicting and understanding changes in CAPE distributions.
Figure 1 .
1(Left) Comparison of CAPE in present (CTRL) and future (PGW) model runs as a density plot of paired profiles (see Methodology), using all pairs where both have nonzero CAPE. Dashed line is the one-to-one line; solid line is the orthogonal regression; and dots are quantiles of the distribution (large dots, ∆ = 1% increments from 0-0.99; small dots ∆=0.1% above 0.99). (Right) Quantile ratio plot, constructed by taking the ratio of future CAPE quantiles over those of present climate from actual model output (black, dots as in L. panel), and three synthetic datasets: C-C scaling (light blue), constant offset (limegreen), and SO13 (purple). All data are used and zeroes are included. For internal consistency, SO13 changes are computed relative to its own CTRL distribution; see methods for details. Gray horizontal line marks the mean CAPE fractional change from the orthogonal distance regression line in left panel. Four vertical tick bars mark the percentiles matching 1000, 2000, 3000, and 4000 J/kg (73.2%, 86.5%, 95.1%, and
Figure 2 .
2(Top) Density heatmap of T-H bins sampled and (bottom) of mean CAPE in eachT-H bin, in CTRL (left) and PGW (right) runs during summer (MJJA). Bins shown are all those with 3 or more observations. Solid and dashed lines mark RH of 100 and 50%. In bottom row, dashed/dotted lines mark CAPE contours at 2000 and 4000 J/kg (with contours cut off at RH=100% to avoid artifacts). Both future distributions move up and to the right. The PGW run samples higher maximum temperatures (top), which in fixed environmental conditions would lead to higher CAPE by fsamp = 2.2, but CAPE contours also shift (bottom), reducing CAPE changes by fsamp = 0.62. Note that CAPE contours resemble those of moist static energy (SI Section S5.2); their future shift means that higher MSE on average is required for a given CAPE value.
Figure 3 .
3Relationships between CAPE in N. America summertime and MSE (left) and MSE surplus (right), for CTRL (blue, dotted) and PGW (red, solid) runs. Here we use all cases where CAPE is larger than 1000 J/kg. Lines are fitted orthogonal regressions. MSE surplus is calculated as hs-h * m , where h * m is the minimum saturation MSE in each profile. Color shading increments are 1.5% for the left panel and 0.75% for the right panel. Median in CAPE bins are used for the orthogonal regression to remove the role of uneven sampling across low to high CAPE conditions. Slopes of CAPE-MSE (left) are 0.249 and 0.239 for CTRL and PGW, respectively, and of CAPE-MSE surplus (right) are 0.271 and 0.270.
Figure 4 .
4Comparison of present and future CAPE in model output (black) and synthetics, with those built from existing theories (C-C scaling, light blue; and from this work in the bottom row (constant offset, dark orange; lapse rate adjustment, green). (Left): Fitted regression lines of the future CAPE-MSE relationship as in Figure 3. Model CTRL is shown for reference (dashed black). See SI Section S5.5 for more details, including table of slopes and x-intercepts. (Right)
Acknowledgements The authors thank Dan Chavas, Tiffany Shaw, Funing Li, Zhihong Tan, and Osamu Miyawaki for constructive comments, and the National Center for Atmospheric Research (NCAR) for providing the WRF dataset. This work is supported by the Center for Robust Decision-making on Climate and Energy Policy (RD-CEP), funded by the NSF Decision Making Under Uncertainty program, Award SES-1463644, and was completed in part with resources provided by the University of Chicago Research Computing Center.Data Availability StatementThe 4-km WRF Convection-permitting model output is downloaded from NCAR RDA https://rda.ucar.edu/datasets/ds612.0/ (http:// doi.org/10.5065/D6V40SXP). The IGRA radiosonde data is downloaded from https:// www.ncei.noaa.gov/products/weather-balloon/integrated-global-radiosonde-archive (http://doi.org/10.7289/V5X63K0Q).
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| sample_249 | 0.9954 | arxiv | |
Attractors and bifurcation diagrams in complex climate models
Maura Brunetti
Group of Applied Physics
Institute for Environmental Sciences
University of Geneva
Bd. Carl-Vogt 66CH-1205GenevaSwitzerland
Charline Ragon
Group of Applied Physics
Institute for Environmental Sciences
University of Geneva
Bd. Carl-Vogt 66CH-1205GenevaSwitzerland
Attractors and bifurcation diagrams in complex climate models
(Dated: March 30, 2023)APS/EA12173
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, that reveals the regions of multi-stability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, whose relaxation time is of the order of thousand years, or other feedback mechanisms that act on even longer time scales, like continental ice or carbon cycle. Using a coupled setup of the MIT general circulation model, we test two techniques for the construction of bifurcation diagrams with complementary advantages and reduced execution time. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches using estimates of the internal variability and of the surface energy imbalance on each attractor, and is more precise in finding the position of tipping points.
INTRODUCTION
The climate is a dynamical complex system that is fuelled by the incoming solar radiation and reaches a steady state under the effect of dissipation over a multitude of temporal and spatial scales [1]. Under a given forcing (such as astronomical Milankovitch cycles, or the increasing atmospheric CO 2 content due to volcanism or present-day anthropogenic emissions) the system can be driven out of the steady state. In such conditions, the system can reach critical thresholds (or tipping points) where its properties abruptly change, often in an irreversible way. Such behaviour can be illustrated by the so-called bifurcation diagram (BD), where a state variable (for example, the mean surface air temperature) is plotted as a function of the driving force, as schematically shown in Fig. 1 (second row), together with the corresponding potential curve (first row) for the different types of tipping mechanism [2,3]: 1) Bifurcationinduced tipping (B-tipping), that occurs when the deterministic system dynamics reach a bifurcation [4][5][6][7][8][9][10][11][12]; 2) Noise-induced tipping (N-tipping), when the internal variability or 'climate noise', that occurs in the absence of evolving external forcing and includes processes intrinsic to the system (in the case of climate, to the atmosphere, ocean, land, and cryosphere and their interactions [13]), increases up to exceed the height of a critical barrier separating two basins of attraction, so that the system can access another dynamical solution [14][15][16]; 3) Shock-induced tipping (S-tipping), related to sudden shocks that induce the passage from one state to another, as happened when a huge asteroid presumably caused the Cretaceous-Tertiary extinction 66 million years ago [17], or when volcanic emissions initiated glaciation episodes [18]; 4) Rate-induced tipping * maura.brunetti@unige.ch (R-tipping), when the rate of change of the forcing or some internal parameter exceed a critical value [19][20][21], allowing the system to cross, for example, a moving basin boundary (note, however, that R-tipping can be induced by different mechanisms and does not necessarily requires multistability [3]). In climate physics, these mechanisms are extensively studied to illustrate the stability of tipping elements in the present-day climate [22,23] (two examples among many others are the Arctic sea ice [24][25][26][27][28] and the ocean overturning circulation [29][30][31][32][33][34]), bifurcations at the global scale occurring in the geological past of our planet leading to the snowball state [35][36][37][38][39][40] or to a state with an ice-free equatorial waterbelt [41][42][43][44], and also to explore the habitability of exoplanets [45][46][47].
BDs are easily obtained using energy balance models [4][5][6], the simplest in the hierarchy of climate models [48]. In intermediate complexity models [49] or low resolution general circulation models [9,12], BDs can be still constructed with a reasonable computational cost. As the complexity of the model increases, the amount of CPU time needed to perform series of simulations that explore a huge range of driving force and initial conditions toward steady states becomes prohibitive. Indeed, the standard method requires convergence toward the steady state (or attractor) to obtain the BD, that means to perform simulations over time scales of the order of several times the relaxation time of the included climatic components [48], which can be 10 3 years for the deep ocean, 10 4 years for the carbon equilibration between atmosphere and ocean [12], and even higher for dynamical ice sheets.
Using a general circulation model (thus, at the top of the hierarchy in model complexity) in coupledaquaplanet configuration (i. e. a planet entirely covered by the ocean where fully nonlinear interactions are taken into account between atmosphere, ocean and sea ice), Ragon et al. [50] obtained the bifurcation diagram using the standard method over time scales of thousand years, [51,52] (MITgcm) is used here in the same configuration, with coupled atmosphereocean-sea ice at 2.8 • horizontal resolution, 15 levels in an ocean depth of 3 km, and 5 pressure layers in the atmospheric column. The atmospheric module is based on SPEEDY [53] that provides a rather realistic representation of the radiative scheme despite the coarse vertical resolution, with the advantage of requiring less computer resources than state-of-the-art atmospheric modules. On the other hand, the ocean dynamics is as accurate as in state-of-the-art Earth system models and this is crucial to include nonlinear feedbacks on millennial time scales. Using this setup, it is possible to run nearly 200 years in 1 day using 13 cores on clusters like those at the University of Geneva. The same MITgcm setup, with an additional land module, has been succesfully applied to investigate the ocean dynamics during the Jurassic [54], the present-day climate [55], and the climatic oscillations in the Early Triassic.
Here we compare the standard technique to construct the BD with two additional methods which require lower computational costs. We will describe such techniques in Section 2, the resulting BDs in Section 3 and we draw our conclusions on pros and cons for each method, and future developments in Section 4.
II. CONSTRUCTION OF BIFURCATION DIAGRAMS
We first describe the standard technique and the corresponding BD. Since, in this case, convergence to the dynamical attractors is required over time scales comparable to the longest feedback process in the setup (in our case, until deep ocean equilibrium is reached), this BD is used for comparisons with those obtained with less computationally expensive techniques that will be described in the following subsections.
A. Standard technique
The standard method for BD construction is based on the theory of dynamical systems. The phase space can be divided in basins of attraction, i. e the minimal invariant closed sets attracting an open set of initial conditions as time goes to infinity [56] for given values of the internal parameters (such as viscosity, diffusion coefficients, albedo of different surfaces, . . . ) and external forcing. Note that under a constant forcing, the system is ergodic [57], i. e sufficiently long temporal averages from a single simulation correspond to large ensemble averages.
The first step is to consider a huge number of initial conditions spanning a large part of phase space. Starting from these initial conditions, the system then evolves in time until the attractors are reached. Statistically steady-state conditions are realised within each attractor in the climate system when its global mean annual surface energy balance F s , i. e. the sum of sensible, latent, net solar and longwave radiation fluxes at the surface, becomes nearly zero (< 0.2 W m −2 in absolute value in [58]). In general, simulation runs over n ∼ 5-10 times the relaxation time t relax are needed to guarantee convergence on the attractor [59], where t relax depends on the nonlinear feedbacks implemented in the numerical simulation. In an aquaplanet, there are no ice sheets (characterised by a time scale of the order of 10 5 yr), and no vegetation (10 2 -10 3 yr). An active carbon cycle between ocean and atmosphere (10 4 yr) is also excluded, thus the deep-ocean dynamics is the process with the largest relaxation time of the order of 10 3 yr. In our setup, it turns out to be between 500 and 2000 yr, depending on the attractor (see Fig. 2b in [58]).
Five steady climates have been found in Brunetti et al. [58] under the same forcing, represented by the same amount of incoming solar radiation (S 0 = 342 W m −2 ) and atmospheric CO 2 content (fixed at 326 ppm): snowball (where ice covers the entire surface), waterbelt (where an ocean belt survives near the equator), cold state (with an ice cap extending to 43 degree latitude), warm state (with an ice cap comparable to the present one, up to 60 degree) and hot state (a planet without ice). Simulations are stopped when the surface energy imbalance F s becomes lower than 0.2 W m −2 in absolute value in [58], corresponding to an ocean temperature drift dT o /dt = F s /(c p ρh) (Marshall and Plumb 2008, p. 229) lower than 0.05 • C per century, with c p = 4000 J K −1 kg −1 being the specific heat capacity, ρ = 1023 kg m −3 the seawater density, and h = 3000 m the ocean depth. Indeed, under such conditions, there is essentially no drift in the annual averages of the climatic observables.
The second step is to slightly vary the forcing, starting from each attractor, and let the system relax again [59]. In this way, stable branches of the BD can be constructed. In practise, in the aquaplanet simulations, Ragon et al. [50] performed the following: the simulations are initialized from the five attractors, found in Brunetti et al. [58] at S 0 = 342 W m −2 , with slightly different values of the incoming solar radiation until convergence. The CO 2 content is kept constant. This procedure is repeated until a B-tipping point is reached, that is where a shift of the state variable to a different attractor is observed on a timescale of the order of hundred years.
Since the attractors are complex dynamical objects living in a high dimensional manifold [58,60], the projection of their invariant (or natural) measure [61] on a given state variable, as the surface air temperature T , is arbitrary [57,62]. It turns out that different quantities are maximised in each attractor, as found in [50], i. e. total precipitation and surface temperature in hot state, intensity of the Lorenz energy cycle in warm state, heat transport in cold state, available potential and kinetic energies in waterbelt, while snowball minimises all the above quantities. Thus, each climatic state would be better represented by a different projection. However, in the present study, the projection is performed, as commonly done in the literature, in terms of the surface air temperature which spans an interval of more than 70 • C from the snowball to the hot state, thus differentiating well all the attractors.
The BD obtained in such a way is shown in Fig. 2, where it can be seen that the range of stability of the warm state is very small in comparison to the others, while the snowball is stable over all the range of forcing that has been explored, from 334 to 350 W m −2 . The positions of B-tipping are also evident, bracketing either end of the stable ranges for warm and cold states, and the cold end of waterbelt and hot state. Note that the warm state may become unstable when carbon exchanges between atmosphere and ocean are included, as shown in [12] using a setup with horizontal resolution of 3.75 • .
Such BD has been obtained using a very computationally expensive technique. The total simulation time t tot can be estimated as t tot ∼ n(N + M ) t relax , where n ∼ 10 to reach convergence, N ∼ 40 is the number of initial conditions in the first step, M ∼ 40 is the number of points on the stable branches of the bifurcation diagram (see Fig. 2), giving approximately t tot ∼ 800 t relax ∼ 8·10 5 yr. Of course, the effective time can be optimized by launching N simulations in parallel with different initial conditions, and by considering separately each stable branch. Note, however, that the term nM t relax cannot be reduced further, since the initial conditions at one forcing value are the final state of the previous one.
B. Method I: random fluctuations in the forcing
The method is based on the idea described in [63,64] of studying noise-induced transitions (N-tipping) between basins of attraction. In order to explore the entire phase space of the system, and not only the single basin of attraction allowed in nonlinear deterministic dynamics, random fluctuations of the incoming solar radiation are introduced around a given value (S 0 = 342 W/m 2 in our setup) at discrete times. Even if noise directly affects only a small fraction of degrees of freedom, it propagates to all, since scales are interconnected in the coupled climate model [63].
If η is a random number taken from a normal distribution with zero mean and standard deviation σ, a new value of the incoming solar radiation S is prescribed as S = S 0 (1+η) at regular temporal intervals ∆t 1 . We have tested several values of the standard deviation, ranging from σ = 0.01 to 0.1, and of the temporal interval, from ∆t 1 = 1 yr to 100 yr. The smaller ∆t 1 , the more uniformly the phase space is filled, since the system cannot relax toward the attractor, and thus the reconstruction of the position of the attractors in phase space becomes unfeasible. On the contrary, too large values of ∆t 1 are computationally expensive. On the other hand, the standard deviation σ regulates the range of forcing values being explored and the portion of phase space than can be accessed, a weaker noise corresponding to rarer transitions between the basins of attraction [64]. Note that the time step used in our simulations is half an hour (for the ocean dynamics), much smaller than ∆t 1 , thus even if the forcing has Gaussian fluctuations, the resulting time series of the state variable does not correspond to white noise.
In our MITgcm setup, the values σ = 0.025 and ∆t 1 = 10 yr correctly reproduce the attractors found in the BD with the standard method (Fig. 2) [65], the relaxation time is governed by upper ocean processes and is of the order of several decades for 5.6 • of horizontal resolution and 10 atmospheric levels [64]. In this case, the reconstruction of the invariant measure is obtained using σ = 0.18 and ∆t 1 = 1 yr [64]. We find that a good reconstruction occurs after a total simulation time of the order of t tot ∼ 10 4 yr. Using different seeds for the random variable and/or changing the initial conditions (S 0 or any state variable, possibly using Monte Carlo methods), such total time can be easily partitioned over different set of runs.
C. Method II: reconstruction of stable branches
The first step coincides with that in the standard technique: the attractors at a given forcing are needed as starting points and are obtained by scanning a large ensemble of initial conditions [58]. However, the second step differs. We require the change in forcing to be small enough so that the invariant measure on the attractor remains nearly the same [57], in particular its mean and standard deviation. In other words, while the forcing is changed by ∆S, the corresponding variation on the attractor is small enough that the surface energy imbalance remains nearly zero. This excludes for the presence of Rtipping and guarantees quasi-ergodicity of the system. In practise, starting from each attractor found during the first step, the forcing is changed by +∆S (−∆S) each ∆t 2 = N 2 yr in order to determine the upper (lower) stable branch in the bifurcation diagram, until a tipping point is reached.
The tipping point is attained when one of the three following criteria is satisfied: (i) the standard deviation within the N 2 points for each forcing value becomes larger than the internal variability on the attractor (an early warning of critical slowing down of the dynamics [66]); (ii) the N 2 points turn out to be ordered in time, pointing from the original attractor toward a new one; (iii) the surface energy imbalance F s becomes much larger than zero (in our setup, larger than 0.5 W m −2 in absolute value, which is slightly larger than the threshold 0.2 W m −2 used to characterise the convergence to an attractor). When one of these criteria is satisfied, the system is no longer on the initial dynamical attractor and is approaching the unstable branch where a shift toward a new basin of attraction takes place.
We have tested different values of ∆S from 0.1 to 0.5 W m −2 and N 2 from 10 to 100. Like in the previous case, the choice is model dependent. We have checked that in our setup good agreement with the bifurcation diagram from the standard technique (that is very accurate albeit highly time consuming) is obtained when ∆S ≤ 0.25 W m −2 and N 2 ≥ 20. With less points, the criterium based on the standard deviation is not applicable (low statistics). With larger ∆S the position of Btipping is less accurate and the requirement of remaining on the same original attractor cannot be satisfied, while too small values require large CPU time. The total simulation time can be estimated as t tot = nN t relax +M 2 ∆t 2 , where M 2 is the number of points in the forcing along all the branches. The second term M 2 ∆t 2 is smaller than the analogous in the standard model, nM t relax , since ∆t 2 t relax . Note that a small ∆S corresponds to a large value of M 2 , thus implying that ∆t 2 can be set to a small value since the system is near the attractor, and Method II can still save time.
III. RESULTS
We take advantage of the BD obtained with the standard (computationally expensive) technique to test the other two methods described in Sections II B and II C, and understand under which conditions they can be applied.
FIG. 3. Normalised 2-dimensional histogram obtained with
Method I by adding random fluctuations with standard deviation σ = 0.025 to the incoming solar radiation S0 at regular temporal intervals ∆t1 = 10 yr. The diverging colormap goes from low (blue) to high density of points (red).
A. Method I
We construct the bifurcation diagram by plotting the normalised 2-dimensional histogram (projection of the invariant measure) in terms of the global annual surface air temperature and the forcing, as shown in Fig. 3 using a standard deviation of the normal distribution equal to σ = 0.025 and time interval ∆t 1 = 10 yr. Other BDs obtained for different values of σ and ∆t 1 are provided in the Supplemental Material (Fig. S1) 1 . As can be seen, the overall structure of the phase plane corresponds quite well to that in the standard BD (see Fig. 2). The main attractors (hot, cold, waterbelt and snowball) can be easily recognised and correspond to regions of high density of points. However, the uncertainty in the exact position of the attractors is large, so that, for example, the warm state, with a short stable branch, cannot be distinguished from the hot climate and, in general, it is not possible to precisely infer the edges of the stable branches.
Moreover, a region with increased density different from the ones that correspond to the five attractors appears at T ∼ −20 • C that may correspond to an additional steady state. This can be checked by performing simulations without noise starting from initial conditions 1 See Supplemental Material for additional figures obtained with different parameters in Methods I and II (Figs. S1, S3), a description of the transient feature observed around T ∼ −20 • C in Fig. 3 (Fig. S2), BD in terms of the atmospheric CO 2 content at fixed incoming solar radiation (Fig. S4).
in such region of high density, and let the system relax towards a steady state under fixed forcing, i. e. until the surface energy imbalance becomes negligible. It turns out that the feature at T ∼ −20 • C is only transient, as shown in the Supplemental Material (Fig. S2) 1 : the system remains near such value of temperature for nearly 100 yr with a small surface imbalance but eventually is attracted to the waterbelt.
B. Method II
Starting from the five attractors found in [58] at S 0 = 342 W/m 2 , the stable branches are derived by changing the forcing by ∆S each N 2 years. The resulting BD is shown in Fig. 4 using ∆S = 0.1 W m −2 and N 2 = 100 (20 for waterbelt upper branch). As can be seen, the five stable branches can be recovered. If ∆S is too large, the edges of the stable branches are not correctly reproduced, as shown in the Supplemental Material (Fig. S3) 1 . Moreover, by applying the criteria listed in Section II C to determine the position of B-tipping, we check that they correspond well to those found with the standard technique (see Fig. 4a and its enlargements (panels b, c, d, e, f), where the red arrows correspond to B-tipping and colorbar corresponds to the time ordering of the N 2 points). In Fig. 5, two examples of evolution (hot to colder climates and cold to snowball) show when the system abandons the attractor at the point where the standard deviation of the temperature becomes larger than the internal variability on the attractor and/or |F s | > 0.5 W m −2 (following the criteria (i) and (iii) in Section II C, respectively).
Another interesting feature in Figs. 4a,c is the transition from the cold state to colder climates. When the system looses stability on the cold branch, it is attracted first by transient structures, like the one at T = −20 • C. Then, instead of relaxing to the waterbelt, it is directly attracted to the snowball. This can be understood by remembering that the climate state lives on a high dimensional space that we are arbitrarily projecting to a single state variable (the surface air temperature). In a higher dimensional space, the two climatic trajectories (the transition from cold to snowball and the waterbelt stable branch) would not cross each other. This behavior and the fact that an analogous crossing occurs in the transition from hot to snowball (see Fig. 4a) show that the waterbelt climate is not well described by a single state variable.
Finally, the dependence of the invariant measure can be investigated, as done here, in terms of the incoming solar radiation S for a fixed atmospheric CO 2 content. The opposite can also be considered: different CO 2 for fixed S [12]. An example is shown in the Supplemental Material (Fig. S4) 1 where, however, the MITgcm setup does not include the feedback of the atmospheric carbon with the ocean.
IV. SUMMARY AND CONCLUSIONS
We have tested two methods for the construction of BDs in general circulation models (GCM), where the number and timescale of nonlinear feedback mechanisms make the computational costs of the standard method prohibitive. Such diagrams store crucial information about the nonlinear structure of the climate system, like the regions of multistability, the kind of tipping, the amplitude of climatic oscillations or the intensity of forcing necessary to give rise to a climatic shift.
In the first method, random fluctuations of the forcing allow to explore the entire phase space of the climate system [64]. The choice of the parameters for such method, i. e. the standard deviation of the Gaussian fluctuations and the temporal interval after which the forcing randomly changes its value, is model dependent. However, once the parameters are fixed, such method gives an overall picture of the phase space projected on a given state variable, revealing the number of attractors and their position. The disadvantage is that the attractors with small stable branches may be blurred and the position of B-tippings is not precise.
The second method reconstructs the stable branches of the attractors [30] by changing the forcing by a small amount that guarantees the system to remain on the same attractor until a B-tipping is reached. The signature of a shift is given by increased variance of the internal variability, non-null surface energy imbalance or an ordered temporal sequence of points toward another climatic state. The advantage of such a method is that the reconstruction of B-tipping is quite accurate with much lower computational costs with respect to the standard method.
The two methods can be used in sequence when no previous information on the attractors is available: a first guess on the position of tipping points and the extension of stable branches can be obtained using Method I. Then, simulations with the standard method or Method II can be performed to fill in the details of the bifurcation diagram, depending on the desired level of precision.
The proposed methods have been described by projecting the high dimensional space of the attractors to a single state variable (global annual mean of surface air temperature). Of course, they can be applied using other projections, and averages over different temporal and spatial scales. This is particularly useful in order to develop early warning indicators that are based not only on temporal series but also on spatial information [67,68]. From the BD one can infer the forcing that induces a tipping and perform a detailed analysis in space to identify where the main changes take place, since gridded data in general circulation models permit such kind of spatial studies. The advantage is that spatial early warning indicators do not need a long temporal record to get a meaningful signal, thus they play a crucial role in identifying tipping mechanisms from datasets with irregular or infrequent temporal resolution [69].
BDs can also be applied to estimate the climate sensitivity [57,70,71], in particular to analyse how this metric depends on the attractor, on the nonlinear feedback mechanisms included in the simulations within a given integration time, on the phase space region explored by the considered initial conditions, and on the perturbation amplitude, all aspects recently discussed in [72].
Apart from the fundamental and practical interest of obtaining the BD for our present-day climate, there are many aspects that are worth to be analysed. An open question is, for example, whether the attractors and the BD are model dependent. The robustness of the results presented here should be tested against other climatic models and other BD reconstruction methods [63,73].
For the comparison, analogous numerical setups should be chosen at the level of horizontal/vertical resolutions and included nonlinear feedback mechanisms. Important information on the description of the nonlinear processes and their interplay can be gained from such comparison of BDs produced by different models, that can be used to improve algorithms and to correct biases. This is why we suggest including the comparison of BDs in coarseresolution GCMs with simplified configurations in the Tipping Point Model Intercomparison Project (TipMIP) beside that of Earth System Models in the present-day configuration.
ACKNOWLEDGMENTS
We are grateful to Sacha Medaer and Enzo Samy Ferrao for running some of the MITgcm simulations with noise. We thank Alexis Gomel and Jérôme Kasparian for useful discussions. The computations were performed on the Baobab and Yggdrasil clusters at University of Geneva. The data that support the findings of this study were generated by the MIT general circulation model that is openly available on GitHub (http: //mitgcm.org/, https://github.com/MITgcm/MITgcm, version c67f). We acknowledge the financial support from the Swiss National Science Foundation (Sinergia Project CRSII5 180253).
Supplemental Material for 'Attractors and bifurcation diagrams in complex climate models'
Maura Brunetti * and Charline Ragon
Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Bd. Carl-Vogt 66, CH-1205 Geneva, Switzerland
CONTENT OF THIS DOCUMENT
We provide additional figures obtained by using different parameters in the methods described in the main article (see Figures S1 and S3). We also show in Figure S2 that the high density region around T ∼ −20 • C in Fig. 3 does not correspond to a new attractor but to a transient feature. Finally, the bifurcation diagram obtained in terms of the atmospheric CO 2 content at fixed incoming solar radiation is shown in Figure S4.
obtained with the standard method, adapted from[50]. Solid lines corresponds to stable branches. Dashed lines are a sketch of theoretical unstable branches.
FIG. 4 .
4(a) Bifurcation diagram obtained with Method II; red arrows show the positions of B-tipping obtained with this method and panels b-e their enlargements, with colors corresponding to the location of tipping from: (b) cold to hot; (c) cold to snowball; (d) warm to cold, warm to hot, hot to colder climates; (e) waterbelt to hot. Colorbar refers to the time (in years) since the last change in the forcing.
FIG. 5 .
5Temporal evolution of mean global surface energy imbalance Fs (a,c) and surface air temperature T (b,d), with superposed incoming solar radiation (right axes) for (top) hot to colder climates; (bottom) cold to snowball. The strip in panels (a,c) corresponds to an imbalance of ±0.5 W m −2 . Shadow areas in (b,d) correspond to the standard deviation in temperature within N2 = 100 points.
FIG. S1 .
S1Normalised 2-dimensional histograms obtained using Method I in the main text. Random fluctuations with standard deviation σ are added to the incoming solar radiation at regular temporal intervals ∆t1: σ = 0.025, ∆t1 = 1 yr (up left) ; σ = 0.1, ∆t1 = 1 yr (up right); σ = 0.1, ∆t1 = 10 yr (bottom). The diverging color map goes from low (blue) to high density (red). * maura.brunetti@unige.ch arXiv:2211.01929v2 [physics.ao-ph] . S2. Temporal evolution of global mean surface temperature T (left) and surface energy imbalance Fs (right) starting from initial conditions in the high density region near T = −20 • C in Fig. 3 in the main article under constant incoming solar radiation S (see legend). This region does not represent a new attractor since the system remains near T = −20 • C with Fs ∼ 0 for only 100 years in each case to finally relax to the waterbelt climate. FIG. S3. Portion of the bifurcation diagram obtained with Method II in the main text using ∆t2 = 100 yr and ∆S = 0.25 W m −2 (blue); ∆S = 0.1 W m −2 (red). The position of B-tipping is better defined with lower ∆S. FIG. S4. Bifurcation diagram obtained with Method II in the main text by varying the atmospheric CO2 content at fixed incoming solar radiation S0 = 342 W m −2 using ∆t2 = 10 yr and ∆CO2 = 0.5 ppm.
FIG. 1. Tipping mechanisms in terms of potential landscape (first row) and corresponding bifurcation diagram (second row). Blue circles: state of the system; red/black arrows: evolution of landscape/state. thus excluding nonlinear feedbacks on longer time scales such as those induced by ice sheets and vegetation. The MIT general circulation modelPotential
R-tipping
S-tipping
N-tipping
B-tipping
State variable
State variable
State variable
State variable
Forcing
State variable
Forcing
N-tipping
Forcing
S-tipping
Forcing
R-tipping
B-tipping
B-tipping
in a reasonable amount of time. Such values are model-and setup-dependent. For example, in the Planet Simulator (PlaSim), an open-source intermediate complexity climate model with slab ocean
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| sample_275 | 0.8034 | arxiv | |
Sea Ice Extraction via Remote Sensed Imagery: Algorithms, Datasets, Applications and Challenges
Anzhu Yu
Wenjun Huang
Qing Xu
Qun Sun
Wenyue Guo
Song Ji
Bowei Wen
Chunping Qiu
Sea Ice Extraction via Remote Sensed Imagery: Algorithms, Datasets, Applications and Challenges
1Index Terms-Sea iceextractionsemantic segmentationSARinfraredmapping
The deep learning, which is a dominating technique in artificial intelligence, has completely changed the image understanding over the past decade. As a consequence, the sea ice extraction (SIE) problem has reached a new era. We present a comprehensive review of four important aspects of SIE, including algorithms, datasets, applications, and the future trends. Our review focuses on researches published from 2016 to the present, with a specific focus on deep learning-based approaches in the last five years. We divided all relegated algorithms into 3 categories, including classical image segmentation approach, machine learning-based approach and deep learningbased methods. We reviewed the accessible ice datasets including SAR-based datasets, the optical-based datasets and others. The applications are presented in 4 aspects including climate research, navigation, geographic information systems (GIS) production and others. It also provides insightful observations and inspiring future research directions.
I. INTRODUCTION
T HE sea ice extraction (SIE) has been a crucial problem in many application aspects, such as the polar navigation [1], terrain analysis [2], polar cartography [3] and polar expedition [4]. With the rapid development of machine learning technique, computational capability and data acquisition, the SIE problem has reached the deep learning era. Machine learning-based approaches are being increasingly introduced to detect, segment or map the sea ice.
As a branch of the machine learning, Deep Learning technique attracts more attention to solve the SIE problem in last five years, based on which the mapping or cartography problem could also be solve subsequently. Most literature convert the SIE problem to another common topic, namely the semantic segmentation problem, which determines the category of each pixel via a post-classification procedure after the category probability is regressed by the deep convolutional neural networks. In recent years, there has been a growing body of research focusing on SIE. To gain insights into this field, we conducted a literature search using the keywords "sea ice extraction" and applied the Citespace [5] statistical algorithm to visualize the co-citation network of relevant publications from the past five years (Fig. 1). The visualization highlights key themes and research areas associated with SIE, with a particular emphasis on remote sensing and SAR. * Authors share equal contribution. Currently, SIE primarily relies on remote sensing techniques such as visible/infrared remote sensing, passive microwave remote sensing, and active microwave remote sensing [6]. Visible/infrared remote sensing can provide texture information of sea ice, which is helpful for SIE tasks. However, it has certain limitations. Firstly, it is restricted in polar regions due to the occurrence of polar day and polar night phenomena. Additionally, the orbital inclination (typically 97 • -98 • ) and altitude of conventional remote sensing satellites affect observations in polar regions, leading to polar data gaps where effective observations are not possible. Consequently, polar orbit satellites are relied upon for conducting observations. On the other hand, passive microwave remote sensing, as an active remote sensing approach, offers global coverage capabilities and therefore holds certain advantages. Nevertheless, its drawback lies in relatively low spatial resolution. Typical instruments for passive microwave remote sensing, such as AMSR-E and AMSR2, generally provide spatial resolutions at the kilometer level. Such lower resolution may not fulfill the requirements for detailed SIE and further mapping. In contrast, active microwave remote sensing techniques, such as SAR, offer higher resolution capabilities. SAR technology can achieve resolutions at the meter level, making it highly suitable for fine-scale sea ice mapping [7] [8]. As a consequence, current research on SIE predominantly focuses on the application of active microwave remote sensing technologies, notably SAR. Besides, significant achievements have been made in SIE tasks through the utilization of optical remote sensing [9] [10] and the integration of SAR with optical approaches [11] [12] [13]. In addition to the aforementioned remote sensing satellite observations, some literatures have utilized real-time ice monitoring using aerial images captured by cameras onboard icebreakers [14] [15] and unmanned aerial vehicles (UAVs) [16] [17]. These methods serve as valuable supplementary approaches for SIE tasks.
Machine learning methods have made significant applications in the field of SIE. Recently, several reviews have provided summaries of sea ice remote sensing. In [18], the focus was on analyzing the advantages and disadvantages of sea ice classification methods based on SAR data. In [19], the advancements of Global Navigation Satellite System-Reflectometry (GNSS-R) data in SIE, ice concentration estimation, ice type classification, ice thickness inversion, and ice elevation were reviewed. In [8], a comprehensive analysis of sea ice sensing using polarimetric SAR data was conducted. Key geophysical parameters for SIE, including ice type, concentration, thickness, and motion, as well as SAR scattering characteristics analysis, were summarized. However, these papers primarily focused on providing overviews of sea ice monitoring methods using SAR technology, lacking comprehensive summaries of specific technical approaches. Moreover, they predominantly concentrated on summarizing sea ice remote sensing methods and lacked a comprehensive overview of downstream tasks related to SIE, specifically applications. Therefore, this review aims to provide a comprehensive summary of the latest SIE methods developed in the past five years. It aims to systematically categorize and analyze these methods, taking into account the associated datasets and subsequent mapping applications. Additionally, this review incorporates the latest advancements in technology to assess the challenges and future developments in SIE through the utilization of large-scale models.
The overall structure of this review is presented in Fig. 2. Section II of this review will provide detailed insights into recent methods for SIE. Section III will summarize the currently available open-source datasets related to ice. Section IV aims to outline downstream tasks and enumerate the generated geospatial information products resulting from ice extraction. Lastly, Section V will highlight areas where future developments are needed.
II. METHOD OF SEA ICE EXTRACTION
A. Classical image segmentation methods
In the early stages, research on SIC primarily relied on statistical algorithms. These algorithms generally combined probabilistic models and classical classification methods with texture or polarization features to generate sea ice type maps. There is a rich body of literature on classical image segmentation methods, and this section will focus on including only some recent publications.
1) Bayesian: A new Bayesian risk function is proposed in [20] to minimize the likelihood ratio (LR) for polarimetric SAR data supervised classification. A novel spatial criterion is also introduced to incorporate spatial contextual information into the classification method, achieving a sea ice classification accuracy of 99.9%. Bayesian theorem, as described in [21], is utilized to compute the posterior probabilities of each class at each observed location based on the texture features extracted from the gray-level co-occurrence matrix (GLCM) of the image. In [22], labels each pixel in the SAR imagery as ice or water using the MAp-Guided Ice Classification (MAGIC) [23] and models the labeled pixels as a Bernoulli distribution. The estimated ice concentration is then obtained by incorporating the labeled data into the Bayesian framework along with AMSR-E ice concentration data. The work [24] introduces a Gaussian Incidence Angle (GIA) classifier for sea ice classification, which replaces the constant mean vector in the multivariate Gaussian probability density function (PDF) of the Bayesian classifier with a linearly varying mean vector. The simplicity and fast processing time of the GIA classifier enable near real-time ice charting. The work [25] utilizes this GIA classifier to generate classified winter time series of sea ice in the regions covered during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) campaign, providing reliable support for navigation.
2) Maximum Likelihood Estimation: In [26], Maximum Likelihood Estimation is used to compute the probabilities of ice and water in the observed SAR images. An unsupervised mixture Gaussian segmentation algorithm is proposed in [27], which provides reasonable sea ice classification results under similar incidence angle conditions. The work [28] applies logistic regression (LR) statistical techniques to demonstrate that the average and variance of texture features, specifically the GLCM, are most suitable for maximum likelihood supervised classification, thus extracting the sea ice density map of the western Antarctic Peninsula region.
3) Thresholding Method: Zhu et al. [29] utilized the Delay-Doppler Map (DDM) of the Global Navigation Satellite System (GNSS) signals reflected by sea ice and seawater, which exhibit distinct scattering characteristics. The differential DDM, observed as the difference between two adjacent normalized DDMs, provides information about the differences between the two DDMs. By employing a thresholding method, the type of the reflecting surface can be determined, thus extracting the sea ice. Building upon this, Alexander et al. [30] proposed an adaptive probability threshold for automatic detection of ice and open water areas. Qiu et al. [9] discussed the textural and edge features of different sea ice types in various turbid regions, using the Yellow River Delta as an example, laying the foundation for the classification of sea ice types. Automatic extraction of sea ice can be achieved by employing the OTSU algorithm to determine the threshold automatically.
4) Other Methods: Additionally, Zhang et al. [31] proposed an automatic classification method for SAR sea ice images combining Retinex and the Gaussian Mixture Model algorithm (R-gmm). Experimental results demonstrated that this algorithm effectively enhances the clarity of SAR imagery compared to the Single Scale Retinex Algorithm, GMM, and Markov Random Field (MRF)-based methods, thereby improving segmentation accuracy. Liu et al. [32] introduced a method based on curvelet transform and active contour to automatically detect the marginal ice zone (MIZ) in SAR imagery. In [33], a multi-scale strategy of the curvelet transform was further utilized to extract curve-like features from SAR images, distinguishing the MIZ from open water and consolidated ice areas. Xie et al. [34] employed the polarization ratio (PR) between VV and HH in SAR images calculated based on the roughness characteristics of the sea surface scattering and the X-Bragg backscatter model. This measurement comparison can differentiate between open water and sea ice, achieving an overall accuracy of approximately 96%. Mary et al. [35] utilized the coefficient of variation (COV) from co-pol/crosspol SAR data to detect thin ice during the Arctic freezing period using a synergistic algorithm. 5) Limitations: Generally, classical image segmentation methods exhibit high efficiency for simple segmentation tasks. However, as the complexity of the input image scenes increases, it becomes challenging to determine the appropriate thresholds for multiple-class objects. Moreover, the choice of thresholds is sensitive to image brightness and noise, which limits the generalization ability when applied to different scenes.
While classical methods have their strengths, these limitations pave the way for exploring alternative approaches to address the aforementioned challenges. By leveraging advanced techniques such as machine learning, probabilistic models, and adaptive algorithms, researchers have sought to overcome the issues associated with threshold-based segmentation. These alternative methods offer promising avenues to enhance segmentation accuracy, handle complex scenes, and mitigate the sensitivity to brightness and noise.
B. Machine learning-based methods
Machine learning methods primarily leverage the polarimetric characteristics of sea ice images (HH, HV, HH/HV) and selected features such as GLCM texture features. These features are then subjected to rule-based machine learning methods for classification, enabling the differentiation between sea ice and open water areas. Furthermore, in the literature, there are approaches that further refine the classification of sea ice, distinguishing between multi-year ice (MYI) and first-year ice (FYI), among other categories. Expanding on the various methodological approaches, let's delve into each method and its specific contributions in sea ice classification.
1) Iterative region growing using semantics (IRGS): Yu et al. [24] proposed an image segmentation method called IRGS. IRGS [36] models the backscatter characteristics using Gaussian statistics and incorporates a Markov random field (MRF) model to capture spatial relationships. It is an unsupervised classification algorithm that assigns arbitrary class labels to identified regions, with the mapping of class labels left for manual intervention by human operators. Building upon IRGS, several researches have been conducted for sea icewater classification. In [23], a binary ice-water classification system called MAGIC was developed. Subsequently, in [37], the authors used glocal IRGS to capture the spatial contextual information of RADARSAT-2 SAR images and identified homogeneous regions using a hierarchical approach. Pretrained SVM models were then used to assign ice-water labels. The IRGS method, combined with modified energy functions and the contributions of glocal and SVM classification results, balanced the contextual and texture-based information. This method was tested in [38] with four different SAR data types: dual-polarization (DP) HH and HV channel intensity images, compact polarimetric (CP) RH and RV channel intensity images, all derived CP features, and quad-polarimetric (QP) images. The experimental results demonstrated that utilizing CP data achieved the best classification results, which were further supported by similar findings in [39] and [40]. The self-training IRGS (ST-IRGS) was introduced in [41], which integrated hierarchical region merging with conditional random fields (CRF) to iteratively reduce the number of nodes while utilizing edge strength for classification and region merging. The key feature of ST-IRGS is the embedded selftraining procedure. Wang et al. The work [42] extensively tested IRGS on dual-polarization images for lake ice mapping, minimizing the impact of incidence angle. The experimental results demonstrated that the IRGS algorithm provides reliable ice-water classification with high overall accuracy.
As emerging image classification methods advance, IRGS has been seamlessly integrated with various classification techniques to enhance sea ice classification. In [43], IRGS segmentation was integrated with supervised labeling using RF. The IRGS segmentation algorithm incorporated spatial context and texture features from the ResNet, utilizing region pooling for ice-water classification [44] . In [45], a comparison was made between two benchmark pixel classifiers, SVM and RF, and two models, IRGS-SVM and IRGS-RF. The experimental results indicated that IRGS-RF achieved better performance and demonstrated stronger robustness. In [46], the IRGS algorithm was utilized to oversegment the input HH/HV scene into superpixels. A graph was constructed on the superpixels, and node features were extracted from the HH/HV images. With limited labeled data, a two-layer graph convolution was employed to learn the spatial relationships between nodes. In [47], the segmentation results from the IRGS algorithm were combined with pixel-based predictions from the Bayesian CNN, and by analyzing the uncertainty of SAR images, sea ice and water were distinguished.
These researches demonstrate the versatility of IRGS and its integration with different classification methodologies, leading to improved performance and enhanced classification accuracy in sea ice analysis.
2) Random Forest (RF): Han et al. [48] utilized texture features from backscatter intensity and GLCM as input variables for sea ice mapping and developed a high spatial resolution summer sea ice mapping model for KOMPSAT-5 EW SAR images using a RF model. Mohammed Dabboor et al. [49], [50] employed the RF classification algorithm to identify effective compact polarimetric (CP) parameters and analyzed the discriminatory role of CP parameters for distinguishing between FYI and MYI. Alexandru Gegiuc et al. [51] applied RF for estimating the ridge density of sea ice in C-band dual-polarization SAR images. Han et al. [52] evaluated four representative sea ice algorithms using binary classification with RF based on PM-measured sea ice concentration (SIC) data. Tan et al. [53] employed a RF feature selection method to determine optimal features for sea ice interpretation and implemented a semi-automated sea ice segmentation workflow. Dmitrii MURASHKIN et al. [54] utilized a RF classifier to investigate the importance of polarimetric and texture features derived from GLCM for the detection of leads. James V. Marcaccio et al. [55] employed image object segmentation and an RF classifier for automated mapping of coastal ice, indicating Laurentian Great Lakes winter fish ecology. Yang et al. [56] developed an RF model to extract lake ice conditions from land satellite imagery. Jeong-Won Park et al. [57] performed noise correction on dual-polarization images, supervised texturebased image classification using the RF classifier, and achieved semi-automated SIE. Meanwhile, in [58], the first approach directly utilizing operational ice charts for training classifiers without any manual work was proposed based on RF.
These studies demonstrate the diverse applications of RF in sea ice analysis, including sea ice mapping, classification of different ice types, feature selection, noise correction, and automated ice detection. The RF model has shown its effectiveness in leveraging various image features for accurate and efficient sea ice analysis and has contributed to advancements in sea ice research and monitoring.
3) Multilayer Perceptron (MLP): Ressel et al. [59], [60] compared the polarimetric backscattering behavior of sea ice in X-band and C-band SAR images. Extracted features from the images were inputted into a trained Artificial Neural Network (ANN) for SIE. The experiments found that the most useful classification features were matrix-invariant features such as geometric strength, scattering diversity, and surface scattering fraction. In [61], further evidence was presented for the high reliability of neural network classifiers based on polarimetric features, demonstrating their suitability for near real-time operations in terms of performance, speed, and accuracy. [62] used neural networks to describe the mapping between image features and ice-water classification, with texture features extracted from co-polarized and cross-polarized backscatter intensities and autocorrelation. It was tested for ice-water classification in the Fram Strait, showing that the C-band reliably reproduced the contours of ice edges, while the L-band had advantages in areas with thin ice/calm water. Suman Singha et al. [63] inputted the extracted feature vectors into a neural network classifier for pixel-wise supervised classification. The classification process highlighted matrixinvariant features like geometric strength, scattering diversity, and surface scattering fraction as the most informative. The findings were consistent for both X-band and C-band frequencies, with minor variations observed for L-band. Furthermore, the work [64] explored the influence of seasonal changes and incidence angle on sea ice classification using an ANN classifier. The study concluded that in dry and cold winters, the classifier could adapt to moderate differences associated with the incidence angle. Additionally, it was found that the incidence angle dependency of backscatter remained consistent across various Arctic regions and ice types.
Juha Karvonen et al. [65] estimated ice concentration based on SAR image segmentation and MLP, combining highresolution SAR images with lower-resolution radiometer data. In [66], they further demonstrated that MLP can estimate SIC from SAR alone, but the results were more reliable and accurate when SAR was combined with microwave radiometer data. Furthermore, in [67], they estimated the SIC and thickness in the Bohai Sea using dual-polarization SAR images from the 2012-2013 winter, AMRS 2 radiometer data, and sea ice thickness data based on the High-resolution Ice Thickness and Surface Properties (HIGHTSI) model. Additionally, Yan et al. [68] demonstrated the feasibility of using the TDS-1 satellite data for neural network-based sea ice remote sensing using a satellite-based GNSS-R digital data acquisition system. It relied on a MLP neural network with backpropagation learning using an LM algorithm (800 inputs, 1 hidden layer with 3 neurons, and 1 output). In a recent study [69], it was shown that MLP outperformed LR in capturing the nonlinear decision boundaries, thus reducing misclassifications in certain cases. Additionally, MLP combined cognitive uncertainty prediction methods with arbitrary heteroscedastic uncertainty to allow estimation of uncertainty at each pixel location.
Overall, MLP has proven to be a valuable tool in sea ice remote sensing, providing accurate classification results and enabling the estimation of sea ice parameters. As research in this field continues, further advancements in MLP models and their integration with other data sources will contribute to a better understanding of sea ice dynamics, improved sea ice monitoring, and enhanced decision-making for various applications related to sea ice. 4) Support Vector Machine (SVM): Prior to the surge in popularity of deep learning, SVM was the most favored models due to their solid mathematical foundation and the ability to achieve global optimum solutions (unlike linear models trained with gradient descent that may only converge to local optima). SVMs are commonly employed for binary classification tasks and are defined as linear classifiers that maximize the margin in the feature space.
The work [70] utilized backscattering coefficients, GLCM texture features, and SIC as the basis for SVM-based sea ice classification. Experimental results demonstrated that SVMs exhibit stronger robustness against normalization effects compared to Maximum Likelihood (ML) results.Some cases [71]- [74] showcased the effectiveness of SVMs in distinguishing open water areas from sea ice tasks. In a study [75], combining Kalman filtering, GLCM, and SVM yielded better sea ice accuracy compared to simple CNN models at that time. Yan et al. [76], [77] proposed a simple yet effective feature selection (FS) approach and employed SVM classification, resulting in improved accuracy and robustness compared to NN, CNN, and NN-FS approaches. Furthermore, experiments indicated that SVMs require less data storage and fewer tuning parameters.
Additionally, researchers have explored combining SVM with other methods to enhance classification accuracy. For example, the work [78] integrated statistical distribution, region connection, multiple features, and SVM into the CRF model. Experimental comparisons revealed that SVM-CRF achieved the best performance. Moreover, by utilizing Transductive Support Vector Machines (TSVM) as the classifier had good performance on two hyperspectral images obtained from EO-1 [79].
In summary, SVMs were highly popular models in the field of sea ice classification before the rise of deep learning. They offer robustness, suitability for binary classification tasks, and the potential for integration with other techniques, contributing to their effectiveness in accurately distinguishing sea ice from other classes. Furthermore, SVMs have advantages such as lower data storage requirements and fewer tuning parameters.
5) Others:
In addition to the commonly used machine learning methods mentioned above, decision tree (DT), LR, and k-means have also been used in ice classification tasks. DT is commonly used to solve binary classification problems. For example, the work [80] employed a supervised classification model based on DT to differentiate ice lakes from water ice using the radiometric and textural properties of Landsat 8 OLI multispectral data. Furthermore, Johannes Lohse et al. [81] utilized DT for multi-class problems by decomposing them into a series of binary questions. Each branch of the tree separates one class from all other classes using a selected feature set specific to that class. In the Fram Strait region, ice was accurately classified into categories such as grey ice, lead ice, deformed ice, level ice, grey-white ice, and open water. Komarov et al. [82] modeled the probability of ice presence in the study area using LR. They automatically detected ice and open water from RADARSAT dualpolarized imagery. Additionally, based on the aforementioned modeling approach, they developed a multi-scale SAR icewater inversion technique [83]. In [84], a multi-stage model was proposed for sea ice segmentation using superpixels. The preprocessing involved enhancing contrast and suppressing noise in high-resolution optical images. The segmentation results were refined through superpixel generation, K-means classification, and post-processing.
Furthermore, various machine learning algorithms have been combined to better extract sea ice. Wang et al. [85] proposed a two-round weight voting strategy in ensemble learning. In the first round of voting, six base classifiers, namely naive Bayes, DT, K-Nearest Neighbors (KNN), LR, ANN, and SVM, were employed. Misclassified pixels were further refined through fine classification. Kim et al. [86] combined image segmentation, image correlation analysis, and machine learning techniques, specifically RF, extremely randomized trees, and LR, to develop a fast ice classification model. Liu et al. [87] selected KNN and SVM classifiers for single-featurebased sea ice classification, while the classification of sea ice based on multiple feature combinations was performed using the selected KNN classifier. In [88], a Gaussian Markov Random Field model for automatic classification was introduced. The initial model parameters and the number of categories were determined by fitting the histogram of the imagery using a finite Gaussian mixture distribution. Experimental results show that it can achieve good classification effect. 6) Limitations: In summary, researchers have integrated different machine learning algorithms to improve SIE. The two-round weight voting strategy and LR have demonstrated favorable classification performance. Combining image segmentation, correlation analysis, and machine learning techniques has facilitated the development of fast ice classification models. Additionally, the Gaussian Markov Random Field technique and self-supervised learning approaches have shown promise in SAR sea ice image classification. However, these approaches often involve manual feature extraction prior to network training, which can be a labor-intensive and timeconsuming process. Additionally, when dealing with complex image scenes, the training process can become intricate and challenging.
C. Deep learning-based methods
Traditional approaches to sea ice classification rely heavily on manual feature extraction from remote sensing images and the construction of classifiers. However, this methodology entails significant human and time costs, and often yields less accurate results in complex scenarios. In contrast, deep learning offers the ability to automatically learn and extract features, enabling more effective handling of sea ice classification tasks. Deep learning methods, such as classification networks and semantic segmentation networks, have been widely applied in sea ice classification, showcasing remarkable performance in feature extraction and classification, thus significantly improving the accuracy of sea ice classification. In this section, we will discuss the applications of deep learning methods in sea ice classification and explore the performance of different models in this domain, as shown in Fig. 3.
1) Supervised Learning: Early on, researches generally used some simple CNN structures for sea ice classification. Wang et al. [89] were the first to employ CNN for SIC estimation from SAR images. Their work utilized a two-layer architecture consisting of convolutional and pooling layers, followed by a fully connected operation, eliminating the need for separate feature extraction or post-segmentation processing. The generated SIC maps exhibited an absolute average error of less than 10% compared to manually interpreted ice analysis charts. In [90], a fully convolutional neural network (FCNN) was proposed for estimating SIC from polarimetric SAR images. Experimental results showed slightly higher accuracy in SIC estimation using FCNN compared to CNN, along with additional computational efficiency. In [91], a three-layer CNN with convolutional and pooling operations, as well as non-linear transformations, was constructed. This CNN demonstrated reduced differences and biases between ice concentration and labels compared to MLP or ASI algorithms, highlighting the superiority of CNN. In [92], the CIFAR-10 CNN model was adapted to construct a CNN architecture, and experimental results demonstrated that CNN-based SIE achieved higher accuracy compared to traditional SVM methods. Yan et al. [93], [94] designed a classification-oriented CNN for SIE and a regression-based CNN for SIC estimation. The CNN comprised five 7x7 convolutional and pooling layers, followed by two fully connected layers. This was the first application of CNN technology to TDS-1 DDM data for SIE and SIC estimation. Compared to NN, this approach exhibited improved overall accuracy and required fewer parameters and less data preprocessing. Han et al. [95] utilized GLCM to extract spectral and spatial joint features from hyperspectral sea ice images and constructed a 3D-CNN for sea ice type classification. In [96], CNN was employed for sea ice type classification based on Sentinel-1 SAR data, distinguishing between four categories: ice-free, young ice, FYI, and old ice. Experimental comparisons with existing machine learning algorithms based on texture features and RF demonstrated improved accuracy and efficiency. CNN-based SIC estimation was shown to outperform earlier estimation algorithms in [97]. Additionally, Malmgren-Hansen et al. [98] tested CNN under the scenario of disparate resolutions between Sentinel-1 SAR and AMSR 2 sensors and found that CNN was suitable for multi-sensor fusion with high robustness. Additionally, the integration of SE-Block into a 3D-CNN deep network was proposed in [99] to enhance the contribution of different spectra for sea ice classification. By optimizing the weights of various spectral features through the fusion of SE-Block, based on their respective contributions, the quality of samples was further improved. This approach enables superior accuracy classification of small-sample remote sensing sea ice images.
Given the significant progress in deep learning, a wide range of mature classification and segmentation networks have been developed. Researchers have successfully applied these existing networks to achieve accurate SIE. By building upon these established networks, they have been able to effectively [101] employed transfer learning to extract features from patches using AlexNet and applied a softmax classifier, achieving an overall classification accuracy of 92.36% on test data. They also improved SIC estimation by augmenting the training dataset with more independent samples of undersampled classes [102]. The impact of transfer learning, data augmentation, and input size on deep learning methods for binary classification of sea ice and open water, as well as multi-classification of different types of sea ice, was further investigated in [103]. Subsequently, DenseNet [104] was introduced and demonstrated excellent performance on the challenging ImageNet database. In [105], DenseNet was employed to extract SIC from SAR images, achieving errors of 5.24% and 7.87% on the training and testing sets, respectively. DenseNet161 was used in [106], where multiscale techniques were employed for automatic detection of the MIZ in SAR images. Analysis of the DenseNet prediction results by Kruk et al. [107] revealed that neural networks faced greater challenges in distinguishing different types of ice samples compared to differentiating between water and ice samples. Lyu et al. [108] obtained SIE and classification results for the first time from real polarimetric SAR data using the Normalizer-Free ResNet (NFNet) [109]. The Sea Ice Residual Convolutional Network (AS-SI-Resnet) was proposed in [110], and experimental results demonstrated its superiority over MLP, AlexNet, and traditional SVM methods. The authors further considered spatial characteristics and temporal variations of sea ice and introduced long short-term memory (LSTM) networks to improve the accuracy of sea ice classification [111].
Building upon the outstanding performance of CNN in SIE tasks, researchers have further explored its application in larger datasets and research areas. Kortum et al. [112] combined convolutional neural networks with dense conditional random fields (DCRF) and incorporated additional spatio-temporal background data to enhance model robustness and achieve multi-seasonal ice classification. Zhang et al. [113] developed a deep learning framework called Multiscale MobileNet (MSMN), and experimental tests demonstrated an average improvement of 4.86% and 1.84% in classification accuracy compared to the SCNN and ResNet18 models, respectively. Singh Tamber et al. [114] trained a CNN using the binary cross-entropy (BCE) loss function to predict the probability of ice, and for the first time, explored the concept of augmented labels to enhance information acquisition in sea ice data.
In various domains, deep learning has made remarkable advancements in semantic segmentation in recent years. In particular, the U-Net network has been widely applied in various semantic segmentation tasks and has shown good segmentation performance. Researchers have also explored the application of the U-Net architecture in SIE. Ren et al. [115] proposed a U-Net-based model for sea ice and open water SAR image classification. This model can classify sea ice at the pixel level. Subsequently, the authors introduced a dual-attention mechanism, forming a dual-attention U-Net model (DAU-Net), which improved the segmentation accuracy compared to the U-Net model [116], [117]. Kang et al. [10] improved the decoding network and loss function, achieving excellent results in the 2021 High-Resolution Challenge. Baumhoer [118] used a modified U-Net for automatic extraction of Antarctic glacier and ice shelf fronts. Ji et al. [119] constructed the BAU-NET by adding a batch normalization layer and an adaptive moment estimation optimizer to the U-Net. In addition, An FCN inspired by the U-Net architecture was applied to SIC prediction [120]. Radhakrishnan et al. [121] proposed a novel training scheme using curriculum learning based on U-Net to make the model training more stable. Wang et al. [122] stacked U-Net models to generate aggregated sea ice classifiers. Stokholm et al. [123] studied the effect of increasing the number of layers and receptive field size in the U-Net model on extracting SIC from SAR data. RES-UNET-CRF (RUF) was proposed in [124], which leverages the advantages of residual blocks and Convolutional Conditional Random Fields (Conv-CRFs), as well as a dual-loss function. Experimental results show that the proposed RUF model is more effective compared to U-Net, DeepLabV 3, and FCN-8. Song et al. [125] proposed a network called E-MPSPNet, which combines multi-scale features with scale-wise attention. Compared to mainstream segmentation networks such as U-Net, PSPNet, DeepLabV 3, and HED-UNet, the proposed E-MPSPNet performs well and is relatively efficient. UNET++ was proposed in [126], and it performs well in medical image segmentation tasks.
Murashkin et al. [127] applied UNET++ to the task of mapping Arctic sea ice in Sentinel-1 SAR scenes. Feng et al. [128] proposed a joint super-resolution (SR) method to enhance the spatial resolution of original AMSR2 images. They used a DeepLabv3+ network to estimate SIC, which demonstrated good robustness in different regions of the Arctic at different times. In addition, Zhang et al. [129] combined semantic segmentation frameworks with histogram modification strategy to depict the disintegration frontier of Greenland's glaciers. It was found that the combination of histogram normalization and DRN-DeepLabv3+ was the most suitable. A hierarchical deep learning-based pipeline was designed [130], which significantly improved the classification performance in numerical analysis and visual evaluation compared to previous flat N-way classification methods.
In addition, Colin et al. [131] conducted segmentation research on ten marine meteorological processes using the fully supervised framework U-Net, demonstrating the superiority of supervised learning over weakly supervised learning in both qualitative and quantitative aspects. Hoffman et al. [132] employed U-Net with satellite thermal infrared window data for Sea Ice Lead detection. An improved U-Net was used for glacier ice segmentation [133]. It introduced a new self-learning boundary-aware loss, which improved the segmentation performance of glacier fragments covering ice. CNN has not only been well-applied in SIE tasks but also used for extracting river and lake ice to achieve continuous monitoring of glacial lake evolution on Earth [134]- [136]. These researches will provide references based deep learning for SIE tasks.
With the popularity and cost reduction of UAV technology, and considering its high spatiotemporal resolution, it has been widely applied in ice monitoring. It could fill the gap in satellite imagery data to some extent. Zhang et al. [14], [17] proposed ICENET and ICENETv2 networks for finegrained semantic segmentation of river ice from UAV images captured in the Yellow River. ICENET achieved good results in distinguishing open water, surface ice, and background. In addition to UAV imagery, a few researches have utilized in-situ digital sea ice images captured by airborne cameras. Compared to large-scale satellite images, information recorded by airborne cameras has lower spatial scales, providing more detailed information about the formation of surrounding sea ice at higher resolutions. Dowden et al. [137] constructed semantic segmentation datasets based on photographs taken by the Nathaniel B. Palmer icebreaker in the Ross Sea of Antarctica. SegNet and PSPNet architectures were used to establish detailed baseline experiments for the datasets. In [138], an automated SIE algorithm was integrated into a mobile device. In [139], considering the impact of raindrops on the segmentation results of captured images, raindrop removal techniques were developed to improve the classification performance. In [140], a semantic segmentation model based on conditional generative adversarial network (cGAN) was proposed. This model has good robustness and makes the effect of raindrops on the segmentation results smaller. In addition, a fast online shipborne system was developed and validated in [15] for ice detection and estimation of their locations to provide "ground truth" information supporting satellite observations. Ice-Deeplab [141] was developed to segment airborne images into three classes: Ocean, Ice, and Sky. Zhao et al. [142] improved the U-Net network by introducing Vgg-16 and ResNet-50 for encoding, constructing the new networks VU-Net and RU-Net, and achieved good results in testing with mid-high-latitude winter sea ice images captured by airborne cameras. Furthermore, a multi-label sea ice classification model embedded with SE modules was used for airborne images [143], showing significant improvement in accuracy compared to machine learning methods such as RF and gradient boosting decision tree [144].
Deep learning techniques have also found application in predicting SIC from daily observations of passive microwave sensors such as SMMR, SSM/I, and SSMI/S [145]- [147]. Chen et al. [148] have utilized passive microwave and reanalysis data to quantitatively predict SIC, thereby providing not only navigational assurance for human activities in the Arctic but also valuable insights for studying Arctic climate change. Additionally, Gao et al. [149], [150] have made significant contributions by employing collaborative representation and a transferred multilevel fusion network (MLFN) to detect and track sea ice variations from SAR images, which holds crucial importance for ensuring maritime safety and facilitating the extraction of natural resources.
2) Semi-supervised Learning: The current research on SIE is often limited by the scarcity of available datasets. To extract accurate information from large-scale datasets when only a limited number of labeled data is available, researchers have introduced SSL [151]. SSL is a technique that leverages unlabeled data to improve model performance. In the context of sea ice classification tasks, SSL can better utilize unlabeled sea ice images to enhance the model's classification accuracy. Staccone et al. [152] presented a SSL method based on generative adversarial networks (GANs) for sea ice classification. The approach leverages labeled and unlabeled data from two different sources to acquire knowledge and achieve more accurate results. Khaleghian [153] proposed a Teacher-Student label propagation method based on SSL (TSLB-SSL) to deal with a small number of labeled samples. Experimental results demonstrated its superior generalization capability compared to state-of-the-art fully supervised and three other semi-supervised methods, namely semi-GANs, MixMatch, and LP-SSL. Jiang et al. [46] proposed a semi-supervised sea ice classification model (IRGS-GCN) that combines graph convolution to address this challenge. Furthermore, a weakly supervised CNN approach was proposed in [154] for ice floe extraction. This research leveraged a limited number of manually annotated ice masks as well as a larger dataset with weak annotations generated through a watershed segmentation model, requiring minimal effort. By effectively leveraging unlabeled or weakly labeled data, this method was able to build more accurate extraction models on limited labeled datasets.
3) Unsupervised Learning: Due to ongoing technological advancements, unsupervised learning has emerged as a promising approach for sea ice classification tasks. Taking advantage of the principle that SAR imagery can depict the electromagnetic properties of sea ice, Huang et al. employ a guided learning approach based on physical characteristics, designing the structure and constraints of the models to better capture the scattering characteristics and information of sea ice in SAR imagery. By combining physical models, prior knowledge can be introduced into deep learning models, enhancing their interpretability and generalization capability. In their work [155], the scattering mechanism was encoded as topic compositions for each SAR image, serving as physical attributes to guide CNN in autonomously learning meaningful features. A novel objective function was designed to demonstrate the learning process of physical guidance. The unsupervised method achieved sea ice classification results comparable to supervised CNN learning methods. In another work [156], a novel physics-guided and injected learning (PGIL) unsupervised approach for SAR image classification was proposed. Compared to data-driven CNN and other pretraining methods, PGIL significantly improved classification performance with limited labeled data. Furthermore, in [157], uncertainty was embedded into transfer learning to estimate feature uncertainty during the learning process. Experimental results demonstrated that this method achieved better sea ice classification performance.
These researches all demonstrate that physics-guided learning can help address the issue of scarce sea ice data. Manual annotation of SAR imagery data is time-consuming and expensive, making it challenging to obtain large-scale annotated data. However, physical characteristics can provide additional information to assist models in achieving more accurate classification and segmentation with limited labeled data. By leveraging physical models and prior knowledge, synthetic SAR imagery data can be generated for model training and optimization, thereby alleviating the problem of data scarcity. Therefore, future research can focus on achieving a more comprehensive and accurate understanding and classification of SAR imagery by combining physical characteristics with deep learning methods.
4) Limitations:
The application of deep learning in sea ice classification has certain limitations. One of these limitations is its dependence on labeled sea ice data for training, yet currently, there is a lack of large-scale and representative benchmark datasets. Additionally, the absence of large-scale models like SAM poses a challenge in determining whether it is feasible to conduct large-scale training across different regions and latitudes to adapt to varying SIC tasks. Furthermore, research on multi-source data fusion in SIC is relatively limited. The challenge lies in leveraging the complementary characteristics of different data sources to improve the accuracy of SIC. Multi-source data fusion can encompass remote sensing images acquired from different sensors, meteorological data, and oceanic observation data, among others. By integrating and analyzing these diverse datasets, more comprehensive and accurate sea ice information can be obtained.
III. ACCESSIBLE ICE DATASETS
According to the guidelines established by the World Meteorological Organization (WMO), sea ice can be classified in multiple ways, taking into account factors such as the stages of its growth process, its movement patterns, and the horizontal dimensions of its surface. The predominant classification method found in the literature is based on the developmental stages of sea ice, which encompass frazil ice, nilas ice, FYI, and MYI. Additionally, some studies focus on specific tasks, such as the binary classification of open water and sea ice, as well as the multi-classification of different types of sea ice.
Currently, as researchers' interest in sea ice continues to grow, there is a rising availability of relevant datasets that are openly accessible. In order to meet the demands for further experimental evaluations and establish a standardized framework for future researches, we have meticulously compiled a comprehensive database. This database encompasses all currently available open-source SAR-based, optical-based, airborne camera-based and drone-based datasets. A total of 12 datasets have been collected, accompanied by detailed descriptions of their sources. The emphasis is placed on key attributes such as sensor types, study areas, data sizes, and partitioning methods, ensuring a comprehensive and structured resource for the research community.
A. SAR-based datasets 1) Radiation characteristics of sea ice: SAR is the most commonly used active microwave data type and has been employed in 80% of SIC publications. The radar wavelength, polarization mode, and incidence angle of SAR have significant impacts on the extraction performance. The specific parameters can be referred to the work [7].
• Radar wavelength Many literatures on sea ice classification have discussed the effectiveness of different radar wavelengths, including the X-band, L-band, and C-band SAR. In summary, X-band and Ku-band are suitable for winter sea ice monitoring, while L-band offers advantages for summer sea ice monitoring. The C-band, which lies between Ku-band and L-band, provides a balanced choice for sea ice monitoring across different seasons. Currently, many sea ice monitoring tasks opt for SAR in the C-band for research purposes. The study [158] demonstrates that, compared to the C-band, the L-band is more accurate in detecting newly formed ice. • Polarization mode Polarimetric techniques offer valuable insights for sea ice identification by capturing more detailed surface information using polarimetric SAR. This leads to improved classification of different sea ice types. For instance, the distinctive rough or deformed surfaces of FYI result in higher backscattering coefficients in crosspolarization. Conversely, MYI, known for its stronger volume scattering, exhibits higher backscattering coefficients in both co-polarization and cross-polarization.
Notably, Nilas ice, characterized by its smooth surface and high salinity content, demonstrates consistently low backscattering coefficients across both polarizations in radar observations. • Incidence angle In many scattering experiments, the statistical characteristics of sea ice backscattering coefficients with respect to varying incidence angles can be observed distinctly. When a radar emits microwaves towards a calm open water surface, the echo signal becomes prominent when the incidence angle is close to vertical or extremely small. However, as the incidence angle increases, the backscattering from the sea surface weakens, resulting in a gradual reduction in surface roughness. Researches have shown that at higher frequency bands, increasing the incidence angle improves the classification accuracy between sea ice and open water. Additionally, the backscattering coefficients during the melting period of sea ice are also influenced by the incidence angle. For instance, in HH-polarized data, the backscattering coefficients obtained at small incidence angles are significantly higher, and they exhibit a linear relationship with increasing incidence angles.
2) Datasets:
• SI-STSAR-7 [159] The dataset is a spatiotemporal collection of SAR imagery specifically designed for sea ice classification. It encompasses 80 Sentinel-1 A/B SAR scenes captured over two freeze-up periods in Hudson Bay, spanning from October 2019 to May 2020 and from October 2020 to April 2021. The dataset includes a diverse range of ice categories. The labels for the sea ice classes are derived from weekly regional ice charts provided by the Canadian Ice Service. Each data sample represents a 32x32 pixel patch of SAR imagery with dualpolarization (HH and HV) SAR data. These patches are derived from a sequence of six consecutive SAR scenes, providing a temporal dimension to the dataset.
• The TenGeoP-SARwv dataset [16] The dataset is built upon the acquisition of Sentinel-1A wave mode (WV) data in VV polarization. It comprises over 37,000 SAR image patches, which are categorized into ten defined geophysical classes.
• SAR WV Semantic Segmentation The dataset is a subset of The TenGeoP-SARwv dataset. It consists of three parts: training, validation, and testing. The images comprise 1200 samples and are stored as PNG format files with dimensions of 512x512x1 uint8. The label data is stored as npy files, represented by arrays of size 64x64x10, where each channel represents one of the ten meteorological classes.
• KoVMrMl The dataset utilizes Sentinel-1 Interferometric Wide (IW) SAR data, including Single-Look Complex (SLC) and Ground Range Detected High-Resolution (GRDH) products in the HH channel. The GRDH images are annotated with seven types of sea ice in patches of size 256×256. The H/α labeling is obtained by processing the dual-polarization SLC data using SNAP software.
• SAR based Ice types/lce edge dataset for deep learning analysis The dataset is specifically compiled for sea ice analysis in the northern region of the Svalbard archipelago, utilizing annotated polygons as references.
It encompasses a total of 31 scenes and contains six distinct classes. The dataset is organized into data records, referred to as patches, which are extracted from the interior of each polygon using a stride of 10 pixels.
Each class is represented by patches of different sizes, including 10x10, 20x20, 32x32, 36x36, and 46x46 pixels.
• AI4SeaIce [123] The dataset consists of 461 Sentinel-1 SAR scenes matched with ice charts produced by the Danish Meteorological Institute during the period of 2018-2019. The ice charts provide information on SIC, development stage, and ice form in the form of manually drawn polygons. The dataset also includes measurements from the AMSR2 microwave radiomete sensor to supplement the learning of SIC, although the resolution is much lower than the Sentinel-1 data. Building upon the AI4SeaIce dataset, Song et al. [125] constructed a icewater semantic segmentation dataset.
• Arctic sea ice cover product based on SAR [122] The dataset is based on Sentinel-1 SAR and provides Arctic sea ice coverage data. Approximately 2500 SAR scenes per month are available for the Arctic region. Each S1 SAR image acquired in the Arctic has been processed to generate NetCDF sea ice coverage data. Each S1 image corresponds to an NC file. The spatial resolution of the SAR-derived sea ice cover is 400 m. The website has released the processing of S1 data obtained in the Arctic from 2019 to 2021 and has uploaded the corresponding sea ice coverage data.
B. Optical-based datasets 1) Common optical sensors: There are several types of optical sensors commonly used for ice classification:
• MODIS MODIS is an optical sensor widely used for ice classification. It is carried on the Terra and Aqua satellites. By observing the reflectance and emitted radiation of the Earth's surface, MODIS can provide valuable information about ice characteristics such as color, texture, and spectral properties.
• VIIRS VIIRS is an optical sensor with multispectral observation capabilities, used for monitoring and classifying the Earth's surface. It provides high-resolution imagery and has applications in ice classification.
• Landsat series The Landsat satellites carry sensors that provide multispectral imagery for land cover classification and monitoring, including ice classification. Sensors such as OLI (Operational Land Imager) and TIRS (Thermal Infrared Sensor) on Landsat 8, as well as previous sensors like ETM+ (Enhanced Thematic Mapper Plus), have been extensively used in ice classification tasks.
• Sentinel series The European Space Agency's Sentinel satellite series includes a range of sensors for Earth observation, including multispectral and thermal infrared sensors. The multispectral sensor on Sentinel-2 is utilized for ice classification and monitoring, while the sensors on Sentinel-3 provide information such as ice surface temperature and color.
• HY-1 (Haiyang-1) HY-1 also contribute to ice classification and monitoring. The HY-1 satellite is a Chinese satellite mission dedicated to oceanographic observations, including the monitoring of sea ice. The HY-1 satellite carries the SCA (Scanning Multichannel Microwave Radiometer) sensor, which operates in the microwave frequency range. This sensor can provide measurements of SIC, sea surface temperature, and other related parameters. By detecting the microwave emissions from the Earth's surface, the SCA sensor can differentiate between open water and ice. These optical sensors capture spectral information or radiation characteristics in different bands, enabling the acquisition of valuable data on ice morphology, types, and distribution. They play a crucial role in ice classification and monitoring. These sensors are widely employed in remote sensing and Earth observation, providing valuable data for ice monitoring and research purposes.
C. Datasets based on alternative acquisition methods
Ice classification datasets based on alternative acquisition methods include imagery captured by icebreakers and drones.
• Airborne camera-based datasets The dataset is constructed from GoPro images captured during a two-month expedition conducted by the Nathaniel B. Palmer icebreaker in the Ross Sea, Antarctica [137]. The video clips captured can be found at https://youtu.be/BNZu1uxNvlo. These images were manually annotated using the opensource annotation tool PixelAnnotationTool into four categories: ice, ship, ocean, and sky. The dataset was divided into three sets, namely training, validation, and testing, in an 8:1:1 ratio. Data augmentation was performed by horizontally flipping the images, resulting in a training dataset of 382 images.
• River ice segmentation [160] The dataset collects digital images and videos captured by drones during the winter seasons of 2016-2017 from two rivers in Alberta province: the North Saskatchewan River and the Peace River. The images in the dataset are segmented into three categories: ice, anchor ice, and water. The training set consists of 50 pairs, while the validation set includes 104 images; however, there are no labels available for the validation set.
• NWPU YRCC2 dataset A total of 305 representative images were selected from videos and images captured by drones during aerial surveys of the Yellow River's Ningxia-Inner Mongolia section. These images contain four target classes and were cropped to a size of 1600 × 640 pixels. The majority of these images were collected during the freezing period. Each pixel of the images was labeled into one of four categories: coastal ice, drifting ice, water, and other, using Photoshop software. The dataset was split into training, validation, and testing sets in a ratio of 6:2:2, comprising 183, 61, and 61 images, respectively. These datasets provide valuable resources for training and evaluating ice classification algorithms using imagery from icebreakers and drones. They contribute to the development of accurate and robust models for ice classification, utilizing alternative data sources.
IV. APPLICATIONS
Given the progress in SIE and classification technologies, obtaining accurate spatial distribution and dynamic changes of sea ice has become increasingly vital. Through careful analysis and evaluation, a multitude of valuable geographic information products have been developed. These products play a pivotal role in various domains, including weather forecasting [161], maritime safety [162], resource development [149], and ecological conservation [163]. In this section, we will delve into the specific applications derived from and classification, as shown in Fig. 4. Fig. 4. The extracted sea ice information finds significant applications in various domains, including meteorological forecasting and climate research, navigation and maritime navigation, and geospatial information products.
A. Meteorological Forecasting and Climate Research
The results of have significant applications in meteorological forecasting and climate prediction. By utilizing remote sensing techniques to extract and classify sea ice data, it becomes possible to improve the models that depict the interactions between the ocean and the atmosphere, further enhancing our understanding of sea ice response to climate change [164]. Analysis from research [161] reveals the potential value of sea ice observation data. The authors emphasize the regional variations in sea ice trends and highlight the lack of comprehensive records regarding marine connections. They utilize observation data to establish extensive Arctic and regional sea ice trends, enabling the identification and selection of climate models with optimal predictive capabilities on a global scale. These models subsequently provide more accurate predictions of future sea ice changes, which are closely linked to vital marine pathways in the Arctic region.
Furthermore, the extraction and classification of sea ice hold significant implications for monitoring climate change. This is due to the high albedo [165] of sea ice, which greatly alters the energy balance of the ocean. Additionally, sea ice exhibits low thermal conductivity, exerting a significant influence on the heat exchange between the ocean and the atmosphere. Thus, sea ice serves as a crucial indicator of climate change. Through regular extraction and classification of sea ice, we can monitor its temporal and spatial variations, analyze the trends of sea ice retreat and formation, and provide data support for climate change research. Research outlined in [163] evaluates Arctic amplification and sea surface changes by observing the anomalies in Arctic sea ice extent, thickness, snow depth, and ice concentration in comparison to the mean state during different periods (2011-2018).
Hence, the application of and classification is crucial for meteorological forecasting, climate prediction, and climate change monitoring. By utilizing remote sensing techniques to extract and classify sea ice data, we can enhance the predictive capabilities of climate models, delve deeper into the interactions between sea ice and the climate system, and assess and monitor the trends and impacts of climate change.
B. Maritime and Ocean Navigation
Accurate extraction and classification of sea ice data play a vital role in maritime and ocean navigation. By utilizing remote sensing techniques to extract and classify sea ice information, it becomes possible to efficiently generate valuable products such as sea ice distribution maps, ice edge charts, and route planning tools. These products serve as crucial aids for ships, enabling them to navigate safely and avoid ice-prone areas.
the Arctic Northeast Passage (NEP) has undergone remarkable changes in sea ice conditions, significantly impacting both the environment and navigational capabilities [166]. Research indicates a continued reduction in Arctic sea ice, leading to the shortening of trade routes in the Arctic Ocean and potentially affecting the global economy [167]. The work [168] focusing on the Arctic NEP have examined the influence of sea ice variations on the future accessibility of the route. While reduced sea ice has made it relatively easier for vessels to traverse the Arctic NEP, challenges and risks still persist. Another work [169] analyzed changes in sea ice volume and age, assessing the accessibility and navigable regions of the Arctic route.
Furthermore, the extent and thickness of sea ice hold significant importance for navigation, as emphasized in [170]. MYI, known for its thickness and hardness, poses substantial risks to ships. In contrast, younger and thinner ice enables icebreakers and regular cargo vessels to navigate more freely along ice-free coastal areas during the summer [171]. A recent study [172] investigated the impact of sea ice conditions. Similarly, research [173] revealed that sea ice thickness has a greater impact on vessel speed than ice concentration, underscoring its pivotal role in successful transit through the Arctic route. Therefore, future research endeavors should focus on enhancing the spatial and temporal resolution of sea ice monitoring to accurately evaluate the navigational capabilities of critical straits and regions.
Recent achievements have been made in this domain. A study [174] utilized high-quality, co-located satellite data and observation-calibrated reanalysis data to analyze sea ice changes along Arctic shipping routes. This research investigated the spatiotemporal distribution characteristics, melt/freeze timing, and variations across trans-Arctic routes using datasets such as NSIDC SIC and daily PIOMAS SIT products. Additionally, by incorporating optimal interpolation sea surface temperature (SST) and SIC data, another study [175] examined the spatiotemporal distribution characteristics of SST and SIC above 60°N in the Arctic, along with their interrelationships. These findings hold crucial implications for Arctic shipping and sea ice forecasting, contributing to enhanced navigation and decision-making in the region.
C. Geographic Information Products
In recent years, significant advancements have been made in utilizing remote sensing techniques to generate geographic information products related to ice and polar regions. These applications encompass various aspects, including mapping, GIS, and algorithmic approaches. Reference [176] highlights the positive impact of Interferometric Synthetic Aperture Radar (InSAR) technology on Antarctic topographic mapping, not only at scales as small as 1:25,000 but also in thematic analysis and monitoring. By employing multiple radar images and D-InSAR techniques, it becomes possible to monitor subtle centimeter-level changes, offering tremendous potential for studying Antarctic glacier movement, mass balance, and global environmental changes. In a similar vein, the work [177] demonstrates the production of polar remote sensing products using very high-resolution satellite (VHRS) imagery, which proves to be an effective alternative to costlier aerial photographs or ground surveys. Moreover, the work [178] utilizes high-resolution ICESat laser altimetry to observe the dynamic changes in the grounding line of Greenland and Antarctic ice sheets, revealing a widespread thinning phenomenon across Greenland's latitudes and intensified thinning along critical Antarctic grounding lines.
Furthermore, the work [179] introduces the Ship Navigation Information Service System (SNISS), an advanced ship navigation information system based on geospatial data. SNISS offers a macroscopic perspective to develop optimal navigation routes for the Arctic NEP and provides ice image retrieval and automated data processing for key straits. Similarly, the work [180] develops RouteView, an interactive ship navigation system for Arctic navigation based on geospatial big data. By incorporating reinforcement learning and deep learning technologies, RouteView calculates the optimal routes for the next 60 days and extracts sea ice distribution. These studies have the potential to enhance the safety of vessels navigating the NEP and drive the development of augmented reality (AR) information extraction methods. Arctic sea ice distribution maps serve as valuable aids for route planning, enabling vessels to avoid ice-covered areas and ensure sufficient water depth for safe passage. In addition, PolarView is a ship navigation and monitoring system specifically designed for polar regions. It offers real-time vessel positioning and navigation information, including sea ice coverage, ship route planning, and hazard zone alerts. In the realm of path planning optimization, a sophisticated maze path planning algorithm with weighted regions has been proposed in research [162].
As remote sensing techniques continue to advance and polar observation data becomes increasingly accessible, a variety of geographic information integration and visualization platforms have emerged. One notable platform is Quantarctica [181], which has been specifically designed as a comprehensive visualization platform for mapping Antarctica, the Southern Ocean, and the islands surrounding Antarctica. It encompasses scientific data from nine disciplines, including sea ice, providing a wealth of information for researchers. Another significant resource is the International Bathymetric Chart of the Southern Ocean (IBCSO) [182], which offers detailed information about the bathymetry of the Southern Ocean. This dataset serves as a valuable resource for marine science research and the exploration of marine resources in the region. For terrain data in polar regions, ArcticDEM is a prominent system that enables terrain analysis, glacier research, hydrological modeling, and more. Its comprehensive dataset contributes to a better understanding of the physical characteristics of the polar regions. To access a wide range of information about the polar regions, the ArcticWeb platform serves as a comprehensive polar information hub. It offers various resources including maps, satellite imagery, weather data, and sea ice information. This integrated platform facilitates access to vital information for researchers, scientists, and policymakers working in the polar regions. Additionally, there are online systems dedicated to sea ice monitoring and prediction. IceMap utilizes satellite data and numerical models to provide real-time sea ice coverage maps, thickness estimates, and predictive simulations. It assists users in monitoring the state and trends of sea ice, providing valuable insights for various applications. For studying Arctic sea ice changes, the PIOMAS system offers simulation and analysis capabilities. It provides information on Arctic sea ice thickness, volume, and distribution, which are crucial for climate research and analysis of ice conditions. In terms of monitoring snow and ice cover thickness in polar regions, the SnowSAT remote sensing system employs radar and laser altimetry data to deliver high-resolution measurements. This data is valuable for understanding snow depth and ice cover thickness, aiding in researches related to climate change and polar ecosystems. Lastly, the Sea Ice Index, an online system provided by the U.S. National Snow and Ice Data Center, offers monitoring capabilities for global sea ice coverage and changes. It provides satellite-based sea ice indices and spatiotemporal distribution maps, enabling effective climate monitoring, environmental conservation, and management of marine resources in polar regions. These systems collectively contribute to a comprehensive understanding of the polar regions and their dynamic characteristics. Moving forward, it is crucial to enhance the analytical capabilities of these systems by incorporating structured modeling of sea ice, enabling more sophisticated geographical analysis and providing better support for various applications in polar environments.
From glacier change observations to information system integration, and from ship navigation to route planning, these applications provide valuable data and tools for scientists, governments, policymakers, and related industries, helping them better understand and manage sea ice resources. Additionally, scholars have conducted research on polar mapping and achieved significant results. Wang et al. [183] identified three commonly used map projection methods for the Antarctic region: Polar Stereographic Projection, Transverse Mercator Projection, and Lambert Conformal Conic Projection, all of which are equal-angle projections. Fig. 5 lists several commonly used projection visualizations of the Arctic region. The Quantarctica system utilizes the Antarctic Polar Stereographic projection EPSG:3031. Due to the unique geographical position of polar regions, commonly used map projections have their limitations, and specific research is needed to address specific issues.
D. Others
Sea ice information is critical for the development of natural resources in coastal areas. Extracting and classifying sea ice can help assess its impact on activities such as fishing [184], oil and gas extraction [185], and submarine cable laying [186], providing important references for decision-makers.
Sea ice is an essential component of the polar ecosystem. Its freezing and melting not only has a certain balancing effect on temperature changes in polar regions, but also affects the stability of ocean temperature, salinity, and stratification, thereby impacting global ocean circulation [187]. Extracting and classifying sea ice can generate information such as sea ice boundaries, ice-water interfaces, and cracks, which are useful for ecological research and conservation efforts.
The results of and classification can be used in various fields of marine science [188] [189], including ocean physics, marine biology, and marine geology. By analyzing the characteristics and distribution of sea ice, changes and evolutionary processes of the marine environment can be inferred.
V. CHALLENGES IN ICE DETECTION
There are several issues and challenges in SIE tasks. Firstly, a major problem is the limited availability of data sources, which restricts the accuracy and spatiotemporal resolution of SIC. The scarcity and discontinuity of existing data sources make it difficult to comprehensively capture and analyze sea ice features. Secondly, current SIC techniques have limited accuracy in complex sea ice conditions. Sea ice exhibits diverse variations in morphology, density, thickness, and other characteristics, making it challenging for traditional algorithms to cope with. Moreover, complex sea ice features such as cracks, ridges, and leads undergo intricate changes, which are difficult to capture and represent using conventional methods. Additionally, there are limitations in the ability to detect underwater ice, making it challenging to obtain parameters such as its morphology and thickness. To address these issues, further exploration is needed in terms of detection methods, modeling approaches, and mapping applications.
A. Exploration Methods Aspect 1) Multi-sensor integration: Current research in primarily relies on optical imagery, SAR imagery, or aerial photography captured by airborne cameras. Different sensors have their own characteristics and limitations in observing sea ice. A single sensor may not provide comprehensive information about sea ice. By introducing multi-sensor integration, the advantages of various sensors can be fully utilized to compensate for the limitations of a single sensor and obtain more comprehensive and accurate sea ice data. Multi-sensor integration can combine different technological approaches, such as microwave radar, optical sensors, acoustic techniques, etc., to acquire more comprehensive information about sea ice. For example, combining radar and optical sensor data enables simultaneous extraction of sea ice geometry and surface features, facilitating more precise and monitoring. Moreover, multi-sensor integration can also fuse data obtained from ground-based observations, satellite remote sensing, UAVs, and other platforms, providing multi-scale and multi-angle sea ice observations, thereby gaining a more comprehensive understanding of the spatiotemporal variations of sea ice.
Furthermore, establishing a continuous monitoring system using multiple sensors allows for dynamic monitoring and analysis of sea ice through long time series of remote sensing observations. By utilizing satellite remote sensing and other data sources, long-term monitoring of sea ice changes can be achieved to reveal its seasonal and interannual variations. This enhances the reliability and consistency of data, enables multi-scale and all-weather sea ice observations, and improves the capability of sea ice monitoring and prediction. These advancements provide more comprehensive and accurate data support for sea ice research and related applications.
2) Underwater ice detection: Currently, remote sensing techniques are primarily used for, employing remote sensing sensors such as satellites, aircraft, and UAVs to obtain image data of sea ice. Common remote sensing techniques include optical remote sensing, SAR, and multispectral remote sensing, which provide information on the spatial distribution, morphological features, cracks, and ice floes of sea ice. In addition, close-range images of sea ice can be acquired by mounting imaging devices on ships. Shipborne observations provide higher accuracy and local-scale sea ice information. Furthermore, UAVs equipped with sensors such as cameras and thermal infrared cameras enable high-resolution observations and measurements of sea ice. UAV technology offers high maneuverability and flexibility, allowing for more detailed information about sea ice.
However, remote sensing methods are primarily suitable for surface detection and observation of sea ice, while direct remote sensing detection of underwater ice, such as subsea ice caps, is relatively challenging. Due to the absorption and scattering properties of water, remote sensing techniques are limited in their penetration and detection capabilities underwater. However, the detection of underwater ice is crucial for navigation and hydrographic surveying, as it can have significant implications for ship and navigation safety. The presence of underwater ice can lead to collisions, obstruction of navigation, or structural damage to vessels. Therefore, accurate detection and localization of underwater ice are essential for safe navigation planning and guidance.
Some remote sensing techniques and sensors can still provide some information about underwater ice under specific conditions. Sonar remote sensing is a technique that uses sound waves for detection and imaging in underwater environments. It can provide relevant information about underwater ice, such as the morphology of the ice bottom surface and ice thickness, by measuring the time and intensity of sound waves propagating in water. Sonar remote sensing finds widespread applications in the study of subsea ice caps and marine surveying. Additionally, technologies such as lasers and radars can also be used to some extent for underwater ice detection. Laser depth sounders can measure the distance and shape of underwater objects, providing information about ice thickness. Radar systems can penetrate to a certain depth underwater and detect the presence of underwater ice layers when operating at appropriate frequency bands.
B. Model Approaches Aspect 1) Multi-source data fusion model: The monitoring of sea ice primarily relies on SAR remote sensing technology, which can penetrate meteorological conditions such as clouds, snowfall, and polar night to obtain high-resolution sea ice information. SAR also has the advantage of being sensitive to the structure and morphological changes of sea ice, enabling the identification and differentiation of different types of sea ice and providing more accurate monitoring and prediction of sea ice. There are also a few researches that utilize optical remote sensing technologies, such as visible light and infrared satellite imagery. However, optical remote sensing is limited under conditions of cloud cover, polar night, and other factors, making it difficult to obtain clear sea ice information. Furthermore, due to the complexity and variability of sea ice, the limitations of a single optical remote sensing technology can lead to misclassification and omission errors.
Therefore, some studies have fully considered the complementarity of optical and SAR data in sea ice classification and have fused the two to extract sea ice information in the study area. Li et al. [11] analyzed the imaging characteristics of sea ice in detail and achieved fusion by solving the Poisson equation based on Sentinel-1 and S2 images to derive the optimal pixel values. Compared to the original optical images, the fused images exhibit richer spatial details, clearer textures, and more diverse material textures and colors. The constructed OceanTDL 5 model is then employed for SIE.
In addition to directly fusing heterogeneous images, Han et al. [12] proposed a fusion of the features extracted from both sources. They first utilized an improved Spatial Pyramid Pooling (SPP) network to extract different-scale sea ice texture information from SAR images based on depth. The Path Aggregation Network (PANet) was employed to extract multilevel features, including spatial and spectral information, of different types of sea ice from the optical images. Finally, these extracted low-level features were fused to achieve sea ice classification. In their work [13], they further introduced a Gate Fusion Network (GFN) to adaptively adjust the feature contributions from the two heterogeneous data sources, thereby improving the overall classification accuracy.
Han's work primarily focuses on feature-level fusion of SAR and optical images. In addition, input-level fusion and decision-level fusion have been demonstrated as effective methods [190]- [192], yielding favorable results in land use classification tasks. However, in the context of sea ice classification, it is crucial to consider the influence of different spectral bands on the radiation properties of sea ice. For instance, a simple approach involves replacing one of the R, G, or B channels in the RGB image with a single SAR band. Through experimentation, it was found that replacing the B band yielded superior results, as the B band exhibits weaker texture characteristics while SAR better reflects the radiation properties of sea ice. Furthermore, another approach involves concatenating a single SAR band with the RGB threechannel image to form a four-channel image. However, during the model's pretraining process, there may be difficulties in loading certain weights, resulting in suboptimal outcomes.
2) Unsupervised Deep Learning: However, deep learning methods currently face challenges in the classification of remote sensing images, and one major challenge is the extensive manual annotation required. Additionally, accurate labeling of sea ice categories relies on expert knowledge, resulting in a scarcity of large-scale sea ice datasets for research purposes. The emergence of unsupervised deep learning presents a promising solution to this problem. By leveraging pre-training techniques such as transfer learning and self-supervised learning, unsupervised approaches can learn informative features for different sea ice types, enabling effective sea ice classification tasks.
Researches generally focus on specific regions of interest, such as the Greenland area. However, imagery exhibits variations across different regions, and sea ice distribution patterns differ as well. Consequently, testing the same model in different regions yields substantial discrepancies in the results. To tackle this challenge, the work [74] proposed the integration of texture features derived from gray-level cooccurrence matrices into the extraction and classification of training samples. Unsupervised generation of training samples replaced the costly and labor-intensive process of manual annotation. Moreover, the method produced adaptable training samples that better accommodate the pronounced fluctuations in sea ice conditions within the Arctic MIZ. This concept has undergone initial testing using a subset of Gaofen-3 images. In response to the scarcity of labeled pixels in remote sensing images, the work [193] presents an effective approach for sea ice classification from two perspectives. Firstly, a feature extraction method is developed that extracts contextual features from the classification map. Secondly, an iterative learning paradigm is established. Experimental results demonstrate that with limited training data available, the training and classification of sea ice image representations with comprehensive exemplar representation under mutual guidance provide insights for addressing the scarcity of labeled sea ice data.
Therefore, in response to the limitations of annotated datasets in sea ice research, unsupervised deep learning emerges as a highly promising avenue. By directly extracting insights from unlabeled data itself, it serves as a powerful tool for automatic feature learning, representation learning, and clustering. Unsupervised deep learning methods exploit the intrinsic structures and patterns within sea ice imagery, enabling the automatic extraction of informative features without the reliance on external labels or manual feature engineering. Within the realm of sea ice classification tasks, unsupervised deep learning techniques, such as autoencoders, GANs, and variational autoencoders (VAEs), excel at acquiring meaningful representations from unlabeled sea ice data. These approaches discover similarities, textures, shapes, and other discernible patterns inherent in sea ice images, thereby transforming them into valuable feature representations. Moreover, the utilization of extensive unlabeled sea ice data for training purposes expands the available dataset, consequently enhancing the generalizability and robustness of sea ice classification models across varying timeframes, locations, and sensor conditions. However, the application of unsupervised deep learning methods to SIC tasks introduces certain challenges. Primarily, the absence of external labels as supervision signals may yield inaccurate or ambiguous feature representations. Therefore, it is imperative to design suitable objective functions and loss functions to guide the unsupervised learning process, ensuring the acquired features effectively facilitate the classification and analysis of sea ice images. Additionally, training unsupervised learning models may necessitate increased computational resources and time due to the involvement of complex network architectures and larger-scale datasets. Furthermore, evaluating the performance of unsupervised learning methods and conducting comparative analyses to discern the strengths and weaknesses of different approaches represent inherently challenging tasks in this domain.
3) Construct ICE-SAM large model: The Segment anything model (SAM) [194], originally designed for segmenting natural images, is capable of segmenting various objects. We applied this model to the task of sea ice classification, and the segmentation results are shown in Fig. 6.
SAM demonstrates high precision in the task of sea ice image segmentation, effectively distinguishing different types of sea ice. However, the model itself cannot directly determine the specific category names of the sea ice, i.e., it cannot associate the segmentation results with predefined sea ice categories. To address this issue, we try to introduce the CLIP model [195] as an auxiliary classifier, as it possesses the capability of joint understanding of images and text. We use the segmented sea ice image patches as inputs and compare them with a range of predefined sea ice category names. Through this comparative analysis, the CLIP model comprehends the connection between image content and category names, identifying the most matching category. Consequently, we can accurately classify the sea ice image patches into their respective sea ice categories, obtaining specific category names for each sea ice region. Thus, the role of the CLIP model in sea ice image segmentation is to provide inference capability for sea ice category names. By leveraging its understanding of both images and text, the CLIP model establishes the association between segmentation results and category names, enabling us to acquire more comprehensive and detailed sea ice classification information. This approach allows for a more comprehensive understanding of sea ice features and attributes, providing more accurate data support for sea ice monitoring and research.
C. Cartographic Applications Aspect 1) Polar Geographic Information Systems (GIS): Researchers have developed various GIS and tools specifically tailored for polar regions to support the processing, analysis, and visualization of polar environments and related data. In the early stages, a web-based GIS system [196] was developed, providing online access, exploration, visualization, and analysis of archived sea ice data. Subsequently, systems such as PolarView, SNISS [179], and RouteView [180] were designed for polar navigation planning and ship navigation. These systems offer functionalities such as voyage planning, vessel position monitoring, and channel information retrieval, utilizing real-time data and model analysis to facilitate safe and efficient navigation in polar waters. However, these systems have limited integration of information, and the analysis paths considered are relatively narrow, resulting in somewhat idealized outcomes that have only limited reference value. Furthermore, with the increasing availability of polar observation data, several geographic information integration and visualization platforms have emerged. For example, Quantarctica [181], (IBCSO) [182], ArcticDEM, and ArcticWeb provide functionalities for visualizing polar geographic data, scientific data querying, map generation, and analysis. Online systems dedicated to sea ice monitoring and prediction, such as IceMap, PIOMAS, SnowSAT, and Sea Ice Index, offer realtime sea ice coverage data, thickness estimation, and predictive simulations.
The aforementioned systems primarily encompass ship navigation and monitoring, sea ice monitoring and prediction, polar mapping and geospatial information display, ice thickness measurement, climate research, and environmental protection. These GISs generally employ a layered architectural framework consisting of a data layer, an application layer, and a user interface layer. The data layer is responsible for storing and managing various polar-related geographic data, generally organized and stored in databases or file systems. These data can originate from multiple sources such as satellite observations, remote sensing imagery, marine surveys, meteorological stations, and vessels. The application layer is dedicated to processing and analyzing polar geospatial data, providing various functionalities and services. Within these polar systems, the application layer includes functions such as sea ice monitoring and prediction, navigation planning and guidance, map creation and visualization, and geospatial analysis and modeling. The functionalities within the application layer are typically implemented through algorithms, models, and tools, enabling data processing, analysis, and generating corresponding results and products. The user interface layer is responsible for presenting and displaying geospatial data, functionalities, and results to users, facilitating interaction and visualization of the system's capabilities.
However, most existing systems primarily focus on data integration and visualization, lacking comprehensive geospatial analysis capabilities. In order to achieve geospatial analysis functions for polar regions (taking sea ice as an example), the architectural design and expansion of polar systems can be further improved. Here are some suggested feature enhancements and architectural directions:
• Data Integration and Management. Polar systems should integrate sea ice data from multiple sources and manage them in a unified and standardized manner. This includes satellite observations, remote sensing imagery, marine measurements, and more. To enable structured modeling and geospatial analysis, the data integration and management module should incorporate functionalities such as data cleansing, format conversion, quality control, and metadata management. • Structured Modeling. The system needs to develop algorithms and models for structured modeling of sea ice, transforming raw sea ice data into structured representations with geospatial information. This involves modeling sea ice morphology, density, thickness, distribution, and the relationships between sea ice and other geographical features. The sea ice structured modeling module should consider the spatiotemporal characteristics of sea ice and establish associations with the geographic coordinate system. • Geospatial Analysis Capabilities. The system should provide a wide range of geospatial analysis functions to extract useful geospatial information from the sea ice structured model. This may include spatiotemporal analysis of sea ice changes, thermodynamic property analysis, analysis of sea ice interactions with the marine environment, and more. The geospatial analysis module should support various analysis methods and algorithms, along with interactive visualization and result presentation. It can be observed that: the first column accurately segments the image, the second and fifth columns can easily differentiate sea ice, the third and sixth columns do not perform segmentation, and the segmentation result in the fourth column is excessively detailed.
• Real-time Data and Updates. To ensure timeliness, the system should support real-time acquisition and updates of sea ice data. This can be achieved through realtime connections with data sources such as satellite observations, buoys, UAVs, and more. Additionally, the system should possess efficient and scalable data storage and processing capabilities to handle large-scale data processing requirements.
Future systems can further expand their architectural framework by incorporating technologies such as distributed computing, cloud computing, and artificial intelligence to enhance system performance and scalability. Furthermore, strengthening data sharing, standardization, and interoperability can facilitate data integration and functional consolidation among different systems, enabling a higher level of integration and collaborative work. These extended functionalities will enhance the overall performance and practicality of polar systems, providing comprehensive support for scientific research, navigation safety, and environmental protection, among other domains.
2) Polar Map Projections : The unique shape and geographical attributes of the Earth's surface in polar regions make mapping challenging, hence research on polar cartographic projections has always been an important topic.
Specifically, Bian et al. [197] introduced the concept of complex variable isometric latitude based on the Gauss projection complex variable function. They overcame the limitations of traditional Gauss projections and established a unified and comprehensive "integrated representation" of Gauss projection in polar regions. Building upon this foundation, through rigorous mathematical derivations, they provided theoretically rigorous direct and inverse expressions for Gauss projection that can be used to fully represent polar regions, as well as corresponding scale factors and meridian convergence formulas. This approach addresses the problem of the impracticality of traditional Gauss projection formulas in polar regions and is of significant importance in improving the mathematical system of Gauss projection. It can be applied to the entire polar region and has important reference value for compiling polar maps and polar navigation [198]. Furthermore, research [199] demonstrates that the non-singular Gauss projection formula for polar regions meets the requirements of continuous projection within the polar region, providing a theoretical basis for the production of polar charts. Due to its conformal property, Gauss projection can better determine directional relationships and is of significant reference value for the production of topographic maps along the central meridian in polar regions, and can be combined with the current need for polar navigation charts for the Arctic route. Gauss projection has advantages over sundial projection when applied to polar regions. Currently, most globally released Antarctic sea ice distribution maps are presented in a spherical projection, which cannot be directly used for mainstream tiled map publication. The work [200] converts polar azimuthal stereographic projection sea ice charts to the mainstream web Mercator projection map, and utilizes appropriate image resampling methods to generate tiles and store them with numbered tiles according to different scale levels, ultimately achieving the publication and sharing of sea ice image maps.
In recent years, there has been a relative lack of research on the latest developments in polar cartographic projections. The current major challenges include severe distortion of commonly used projection methods in polar regions and the difficulty of finding a suitable balance between equal area and equal angle properties. Additionally, polar regions generally possess highly complex data, such as sea ice distribution and ice sheet changes. Therefore, another challenge in polar projection is how to effectively visualize and present the geographical information of polar regions. To more effectively visualize and present geographic information of the polar regions to meet the needs of different users, there are several potential research prospects and directions for future development, including:
• Novel polar projection methods. Researchers can continue to explore and develop new polar projection methods to address the existing issues in current projection methods. This may involve introducing more complex mathematical models or adopting new technologies such as machine learning and artificial intelligence to achieve more accurate and geographically realistic polar projec-tions. • Multiscale and multi-resolution polar projections. Polar regions encompass a wide range of scales, from local glaciers to the entire polar region, requiring map projections at different scales. Therefore, researchers can focus on how to perform effective polar projections at various scales and resolutions to meet diverse application requirements and data accuracy needs. • Dynamic polar projections. The geographical environment in polar regions undergoes frequent changes, such as the melting of sea ice and glacier movements. Researchers can investigate how to address this dynamism by developing dynamic polar projection methods that can adapt to changes in the geographical environment, as well as techniques for real-time updating and presentation of geographic information. • Multidimensional polar projections. In addition to spatial dimensions, data in polar regions also involve multiple dimensions such as time, temperature, and thickness. Researchers can explore how to effectively process and present multidimensional data within polar projections, enhancing the understanding of polar region changes and features.
VI. CONCLUSION
This review provides a summary and overview of the methods used for SIE in the past five years, including classical image segmentation methods, machine learning-based methods, and deep learning-based methods. In addition, we have compiled a list of currently available open-source datasets for ice classification and segmentation, and explored the application aspects of from multiple perspectives. Finally, we have identified potential research directions based on the challenges encountered in detection methods, model approaches, and cartographic applications.
A.Yu, W. Huang, Q. Xu, Q. Sun, W. Guo, S. Ji, B. Wen and C. Qiu are with the PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China. Corresponding author: Wenjun Huang (huangwj geo@126.com).
Fig. 1 .
1The co-citation network for SIE research. The frequency of the keywords was visually represented by the size of the nodes, while the strength of their relationships was indicated by the width of the linking lines. Additionally, the publication year was visually depicted through the color variation of the nodes.
Fig. 2 .
2Structure of this review.
Fig. 3 .
3Chronological overview of the most relevant deep learning-based SIE methods. extract sea ice from various data sources and achieve accurate results. In [100], a hyperspectral sea ice image classification method based on principal component analysis (PCA) was proposed. A comparison was made among SVM, 1D-CNN, 2D-CNN, and 3D-CNN, showing promising results in sea ice classification with fewer training samples and shorter training time. Xu et al.
2 )
2Datasets: Compared to SAR-based datasets, there are fewer datasets based on optical imagery. To the best of our knowledge, there are currently two open-source optical imagery datasets available: • 2021Gaofen The dataset is based on HY-1 visible light images with a resolution of 50m. The scenes cover the surrounding region of the Bohai Sea in China. The provided images have varying sizes ranging from 512 to 2048 pixels and consist of over 2500 images. Each image has been manually annotated at the pixel level for sea ice, resulting in two classes: sea ice and background. The remote sensing images are stored in TIFF format and contain the R-G-B channels, while the annotation files are in PNG format with a single channel. In the annotation files, sea ice pixels are assigned a value of 255, and background pixels have a value of 0. • Arctic Sea Ice Image Masking The dataset consists of 3392 satellite images of the Hudson Bay sea ice in the Canadian Arctic region, captured between January 1, 2016, and July 31, 2018. The images are acquired from the Sentinel-2 satellite and composed of bands 3, 4, and 8 (false color). Each image is accompanied by a corresponding mask that indicates the SIC across the entire image.
Fig. 5 .
5Several Projection Visualizations in the Arctic Region: (a) The projection center is at the North Pole, characterized by a circular boundary. The map is symmetrically and uniformly distorted in all directions from the North Pole as the center. (b) The projection center is shifted away from the North Pole. The map still has a circular boundary, but the center is no longer the North Pole, and the distortion of the projection is not symmetric. (c) Rectangular maps are commonly used to display the entire polar region. (d) Vertical map. The Universal Transverse Mercator projection is used to simultaneously depict the North and South Poles. (e) The projection center is shifted, resulting in a non-global polar effect, with the coordinate range forming a sector-shaped area.
Fig. 6 .
6SAM segmentation results applied to Sentinel-2 imagery. (a) Sentinel-2 imagery and (b) SAM segmentation results.
TABLE I THE
IOVERVIEW OF THE DETAILED DESCRIPTION OF THE 12 DATASETS WE COLLECTED.Type
Dataset
Data Source
Research Area
Task
Ref.
Download Link
SAR-based
SI-STSAR-7
Sentinel-1 A/B dual-
polarization (HH and HV)
in EW scan mode
cover the entire
open ocean
Classified by: OW, NI, GI, GWI, ThinFI, MedFI
and ThickFI
[159] Download link
The TenGeoP-SARwv dataset
the WV in VV polariza-
tion from Sentinel-1A
over the open ocean Classified by: Atmospheric Fronts, Biologi-
cal Slicks, Icebergs, Low Wind Area, Micro
Convective Cells, Oceanic Fronts, Pure Ocean
Waves, Rain Cells, Sea Ice, Wind Streaks
[16]
Download link
SAR WV Semantic Segmen-
tation
Same as above
Same as above
Same as above
[131] Download link
KoVMrMl
Sentinel-1 IW SAR data,
including SLC and GRDH
products with HH channel
Belgica Bank, an
ice-covered
area
along the north-east
coast of Greenland
Classified by: Water, Young ice, FYI, Old ice,
Mountains, Iceberg, Glaciers and Floating Ice
[155] Download link
SAR based Ice types/lce edge
dataset for deep learning anal-
ysis
Sentinel-1A EW GRDM
north of svalbard
Classified by: Open Water, Leads with Water,
Brash/Pancake Ice, Thin Ice, Thick Ice-Flat and
Thick Ice-Ridged
-
Download link
AI4SeaIce
The Sentinel-1 dual-
polarization HH and HV,
along with the PMR
measurements from the
AMSR2 instrument on the
JAXA GCOM-W satellite
the waters surround-
ing Greenland
Sea ice concentration, developmental stages, and
forms of sea ice
[123] Download link
Arctic sea ice cover product
based on spaceborne SAR
Sentinel-1
dual-
polarization
HH/HV
data in EW mode
the Arctic
Arctic sea ice coverage data
[122] Download link
Optical-based
2021Gaofen
HY-1 visible light imagery
with a resolution of 50
meters
near the Bering
Strait,China
Segmentation into sea ice and background
[10]
Download link
Arctic Sea Ice Image Masking The Sentinel-2 satellite,
composed of bands 3, 4,
and 8 (false-color)
Hudson Bay sea
ice in the Canadian
Arctic
Segmented into different SIC categories
Download link
Airborne
camera-
based
Sea Ice Detection Dataset and
Sea Ice Classification Dataset
GoPro images captured by
the Nathaniel B. Palmer
icebreaker
Ross Sea, Antarc-
tica
automated detection of sea ice (ice, ocean,
vessel, and sky) and classifying sea ice types
(ocean, vessel, sky, lens artifacts, FYI, new ice,
grey ice, and MYI)
[14]
Download link
Drone-based
River ice segmentation
The Reconyx PC800 Hy-
perfire professional game
camera, and the Blade
Chroma drone equipped
with the CGO3 4K camera
at the Genesee dock
two
Alberta
rivers:
North
Saskatchewan River
and Peace River
Segmented into ice, anchor ice, and water
[160] Download link
NWPU YRCC2 dataset
a fixed wing UAV
ASN216 with a Canon
5DS visible light camera
and a DJI Inspire 1
the Ningxia-Inner
Mongolia reach of
the Yellow River
Segmented into: coastal ice, pack ice, water, and
other
[17]
Download link
Influence of propeller on brash ice loads and pressure fluctuation for a reversing polar ship. L Zhou, S Zheng, S Ding, C Xie, R Liu, Ocean Engineering. 280114624L. Zhou, S. Zheng, S. Ding, C. Xie, and R. Liu, "Influence of propeller on brash ice loads and pressure fluctuation for a reversing polar ship," Ocean Engineering, vol. 280, p. 114624, 2023.
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Mapping of polar areas based on high-resolution satellite images: the example of the henryk arctowski polish antarctic station. Z Kurczyński, S Różycki, P Bylina, Reports on Geodesy and Geoinformatics. 1041Z. Kurczyński, S. Różycki, and P. Bylina, "Mapping of polar areas based on high-resolution satellite images: the example of the henryk arctowski polish antarctic station," Reports on Geodesy and Geoinfor- matics, vol. 104, no. 1, pp. 65-78, 2017.
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Irgs: Image segmentation using edge penalties and region growing. Q Yu, D A Clausi, IEEE transactions on pattern analysis and machine intelligence. 30Q. Yu and D. A. Clausi, "Irgs: Image segmentation using edge penalties and region growing," IEEE transactions on pattern analysis and machine intelligence, vol. 30, no. 12, pp. 2126-2139, 2008.
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Contextual classification of sea-ice types using compact polarimetric sar data. M Ghanbari, D A Clausi, L Xu, M Jiang, IEEE Transactions on Geoscience and Remote Sensing. 5710M. Ghanbari, D. A. Clausi, L. Xu, and M. Jiang, "Contextual classi- fication of sea-ice types using compact polarimetric sar data," IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 10, pp. 7476-7491, 2019.
Unsupervised segmentation of multilook compact polarimetric sar data based on complex wishart distribution. Mohsen Ghanbari, David A Clausi, Linlin Xu, Mingzhe Jiang, IGARSS 2020 -2020 IEEE International Geoscience and Remote Sensing Symposium. Ghanbari, Mohsen and Clausi, David A and Xu, Linlin and Jiang, Mingzhe, "Unsupervised segmentation of multilook compact polari- metric sar data based on complex wishart distribution," in IGARSS 2020 -2020 IEEE International Geoscience and Remote Sensing Symposium, 2020, pp. 1456-1459.
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A semi-supervised approach for ice-water classification using dual-polarization sar satellite imagery. F Li, D A Clausi, L Wang, L Xu, Proceedings of the IEEE conference on computer vision and pattern recognition workshops. the IEEE conference on computer vision and pattern recognition workshopsF. Li, D. A. Clausi, L. Wang, and L. Xu, "A semi-supervised ap- proach for ice-water classification using dual-polarization sar satellite imagery," in Proceedings of the IEEE conference on computer vision and pattern recognition workshops, 2015, pp. 28-35.
Semi-automated classification of lake ice cover using dual polarization radarsat-2 imagery. J Wang, C R Duguay, D A Clausi, V Pinard, S E Howell, Remote Sensing. 10111727J. Wang, C. R. Duguay, D. A. Clausi, V. Pinard, and S. E. Howell, "Semi-automated classification of lake ice cover using dual polarization radarsat-2 imagery," Remote Sensing, vol. 10, no. 11, p. 1727, 2018.
Lake ice-water classification of radarsat-2 images by integrating irgs segmentation with pixel-based random forest labeling. M Hoekstra, M Jiang, D A Clausi, C Duguay, Remote Sensing. 1291425M. Hoekstra, M. Jiang, D. A. Clausi, and C. Duguay, "Lake ice-water classification of radarsat-2 images by integrating irgs segmentation with pixel-based random forest labeling," Remote Sensing, vol. 12, no. 9, p. 1425, 2020.
Sea ice-water classification of radarsat-2 imagery based on residual neural networks (resnet) with regional pooling. M Jiang, L Xu, D A Clausi, Remote Sensing. 14133025M. Jiang, L. Xu, and D. A. Clausi, "Sea ice-water classification of radarsat-2 imagery based on residual neural networks (resnet) with regional pooling," Remote Sensing, vol. 14, no. 13, p. 3025, 2022.
Sea-ice mapping of radarsat-2 imagery by integrating spatial contexture with textural features. M Jiang, D A Clausi, L Xu, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 15M. Jiang, D. A. Clausi, and L. Xu, "Sea-ice mapping of radarsat-2 imagery by integrating spatial contexture with textural features," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 15, pp. 7964-7977, 2022.
Semi-supervised sea ice classification of sar imagery based on graph convolutional network. M Jiang, X Chen, L Xu, D A Clausi, IGARSS 2022-2022 IEEE International Geoscience and Remote Sensing Symposium. IEEEM. Jiang, X. Chen, L. Xu, and D. A. Clausi, "Semi-supervised sea ice classification of sar imagery based on graph convolutional network," in IGARSS 2022-2022 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2022, pp. 1031-1034.
Uncertainty-incorporated ice and open water detection on dualpolarized sar sea ice imagery. X Chen, K A Scott, L Xu, M Jiang, Y Fang, D A Clausi, IEEE Transactions on Geoscience and Remote Sensing. X. Chen, K. A. Scott, L. Xu, M. Jiang, Y. Fang, and D. A. Clausi, "Uncertainty-incorporated ice and open water detection on dual- polarized sar sea ice imagery," IEEE Transactions on Geoscience and Remote Sensing, 2023.
A study of the feasibility of using kompsat-5 sar data to map sea ice in the chukchi sea in late summer. H Han, S.-H Hong, H Kim, T.-B Chae, H.-J Choi, Remote Sensing Letters. 85H. Han, S.-H. Hong, H.-c. Kim, T.-B. Chae, and H.-J. Choi, "A study of the feasibility of using kompsat-5 sar data to map sea ice in the chukchi sea in late summer," Remote Sensing Letters, vol. 8, no. 5, pp. 468-477, 2017.
Assessment of the high resolution sar mode of the radarsat constellation mission for first year ice and multiyear ice characterization. M Dabboor, B Montpetit, S Howell, Remote Sensing. 104594M. Dabboor, B. Montpetit, and S. Howell, "Assessment of the high resolution sar mode of the radarsat constellation mission for first year ice and multiyear ice characterization," Remote Sensing, vol. 10, no. 4, p. 594, 2018.
Assessment of simulated compact polarimetry of the high resolution radarsat constellation mission sar mode for multiyear and first year sea ice characterization. Mohammed Dabboor, Montpetit, Benoit, Stephen Howell, IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium. IEEEDabboor, Mohammed and Montpetit, Benoit and Howell, Stephen, "Assessment of simulated compact polarimetry of the high resolution radarsat constellation mission sar mode for multiyear and first year sea ice characterization," in IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2018, pp. 2420- 2423.
Estimation of degree of sea ice ridging based on dualpolarized c-band sar data. A Gegiuc, M Similä, J Karvonen, M Lensu, M Mäkynen, J Vainio, The Cryosphere. 121A. Gegiuc, M. Similä, J. Karvonen, M. Lensu, M. Mäkynen, and J. Vainio, "Estimation of degree of sea ice ridging based on dual- polarized c-band sar data," The Cryosphere, vol. 12, no. 1, pp. 343-364, 2018.
Evaluation of summer passive microwave sea ice concentrations in the chukchi sea based on kompsat-5 sar and numerical weather prediction data. H Han, H.-C Kim, Remote Sensing of Environment. 209H. Han and H.-c. Kim, "Evaluation of summer passive microwave sea ice concentrations in the chukchi sea based on kompsat-5 sar and numerical weather prediction data," Remote Sensing of Environment, vol. 209, pp. 343-362, 2018.
Semiautomated segmentation of sentinel-1 sar imagery for mapping sea ice in labrador coast. W Tan, J Li, L Xu, M A Chapman, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 115W. Tan, J. Li, L. Xu, and M. A. Chapman, "Semiautomated segmenta- tion of sentinel-1 sar imagery for mapping sea ice in labrador coast," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 11, no. 5, pp. 1419-1432, 2018.
Method for detection of leads from sentinel-1 sar images. D Murashkin, G Spreen, M Huntemann, W Dierking, Annals of Glaciology. 5976pt2D. Murashkin, G. Spreen, M. Huntemann, and W. Dierking, "Method for detection of leads from sentinel-1 sar images," Annals of Glaciol- ogy, vol. 59, no. 76pt2, pp. 124-136, 2018.
Automated coastal ice mapping with sar can inform winter fish ecology in the laurentian great lakes. J V Marcaccio, J Gardner Costa, J L Brooks, C M Boston, S J Cooke, J D Midwood, Canadian Journal of Remote Sensing. 481J. V. Marcaccio, J. Gardner Costa, J. L. Brooks, C. M. Boston, S. J. Cooke, and J. D. Midwood, "Automated coastal ice mapping with sar can inform winter fish ecology in the laurentian great lakes," Canadian Journal of Remote Sensing, vol. 48, no. 1, pp. 19-36, 2022.
Simple method to extract lake ice condition from landsat images. X Yang, T M Pavelsky, L P Bendezu, S Zhang, IEEE Transactions on Geoscience and Remote Sensing. 60X. Yang, T. M. Pavelsky, L. P. Bendezu, and S. Zhang, "Simple method to extract lake ice condition from landsat images," IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1-10, 2021.
Classification of sea ice types in sentinel-1 synthetic aperture radar images. J.-W Park, A A Korosov, M Babiker, J.-S Won, M W Hansen, H.-C Kim, The Cryosphere. 148J.-W. Park, A. A. Korosov, M. Babiker, J.-S. Won, M. W. Hansen, and H.-C. Kim, "Classification of sea ice types in sentinel-1 synthetic aperture radar images," The Cryosphere, vol. 14, no. 8, pp. 2629-2645, 2020.
Automated sea ice classification using sentinel-1 imagery. J.-W Park, A Korosov, M Babiker, H.-C Kim, IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing Symposium. IEEEJ.-W. Park, A. Korosov, M. Babiker, and H.-C. Kim, "Automated sea ice classification using sentinel-1 imagery," in IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2019, pp. 4008-4011.
Comparing near coincident space borne c and x band fully polarimetric sar data for arctic sea ice classification. R Ressel, S Singha, Remote Sensing. 83198R. Ressel and S. Singha, "Comparing near coincident space borne c and x band fully polarimetric sar data for arctic sea ice classification," Remote Sensing, vol. 8, no. 3, p. 198, 2016.
Evaluating suitability of pol-sar (terrasar-x, radarsat-2) for automated sea ice classification. R Ressel, S Singha, S Lehner, Land Surface and Cryosphere Remote Sensing III. SPIE9877R. Ressel, S. Singha, and S. Lehner, "Evaluating suitability of pol-sar (terrasar-x, radarsat-2) for automated sea ice classification," in Land Surface and Cryosphere Remote Sensing III, vol. 9877. SPIE, 2016, pp. 137-150.
Investigation into different polarimetric features for sea ice classification using xband synthetic aperture radar. R Ressel, S Singha, S Lehner, A Rösel, G Spreen, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 97R. Ressel, S. Singha, S. Lehner, A. Rösel, and G. Spreen, "Investigation into different polarimetric features for sea ice classification using x- band synthetic aperture radar," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 9, no. 7, pp. 3131-3143, 2016.
Comparison of ice/water classification in fram strait from c-and l-band sar imagery. W Aldenhoff, C Heuzé, L E Eriksson, Annals of Glaciology. 5976pt2W. Aldenhoff, C. Heuzé, and L. E. Eriksson, "Comparison of ice/water classification in fram strait from c-and l-band sar imagery," Annals of Glaciology, vol. 59, no. 76pt2, pp. 112-123, 2018.
Arctic sea ice characterization using spaceborne fully polarimetric l-, c-, and x-band sar with validation by airborne measurements. S Singha, M Johansson, N Hughes, S M Hvidegaard, H Skourup, IEEE Transactions on Geoscience and Remote Sensing. 56S. Singha, M. Johansson, N. Hughes, S. M. Hvidegaard, and H. Skou- rup, "Arctic sea ice characterization using spaceborne fully polarimetric l-, c-, and x-band sar with validation by airborne measurements," IEEE Transactions on Geoscience and Remote Sensing, vol. 56, pp. 3715- 3734, 2018.
Robustness of sar sea ice type classification across incidence angles and seasons at l-band. S Singha, A M Johansson, A P Doulgeris, IEEE Transactions on Geoscience and Remote Sensing. 5912S. Singha, A. M. Johansson, and A. P. Doulgeris, "Robustness of sar sea ice type classification across incidence angles and seasons at l-band," IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 12, pp. 9941-9952, 2020.
A sea ice concentration estimation algorithm utilizing radiometer and sar data. J Karvonen, The Cryosphere. 85J. Karvonen, "A sea ice concentration estimation algorithm utilizing radiometer and sar data," The Cryosphere, vol. 8, no. 5, pp. 1639- 1650, 2014.
Baltic sea ice concentration estimation using sentinel-1 sar and amsr2 microwave radiometer data. Juha Karvonen, IEEE Transactions on Geoscience and Remote Sensing. 555Karvonen, Juha, "Baltic sea ice concentration estimation using sentinel- 1 sar and amsr2 microwave radiometer data," IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 5, pp. 2871-2883, 2017.
Bohai sea ice parameter estimation based on thermodynamic ice model and earth observation data. J Karvonen, L Shi, B Cheng, M Similä, M Mäkynen, T Vihma, Remote Sensing. 93234J. Karvonen, L. Shi, B. Cheng, M. Similä, M. Mäkynen, and T. Vihma, "Bohai sea ice parameter estimation based on thermodynamic ice model and earth observation data," Remote Sensing, vol. 9, no. 3, p. 234, 2017.
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Application of sea ice map projection transformation and tile cutting over the antarctic ocean. T Lu, A Songtao, E Dongchen, G Hongqing, S Quan, X Ning, Z Hongyang, Chinese Journal of Polar Research. 243284T. Lu, A. Songtao, E. Dongchen, G. Hongqing, S. Quan, X. Ning, and Z. Hongyang, "Application of sea ice map projection transformation and tile cutting over the antarctic ocean," Chinese Journal of Polar Research, vol. 24, no. 3, p. 284, 2012.
| sample_329 | 0.9432 | arxiv | |
IMPACT: INTEGRATED BOTTOM-UP GREENHOUSE GAS EMISSION PATHWAYS FOR CITIES
The Engineering
University
Texas
T X Austin
The Of Architecture
University
Texas
Austin
IMPACT: INTEGRATED BOTTOM-UP GREENHOUSE GAS EMISSION PATHWAYS FOR CITIES
1 9 5 SCHOOL OF PUBLIC POLICY, GEORGIA INSTITUTE OF TECHNOLOGY, GA, USA 6 DNV, NORWAY 15
18Increasing urbanization puts ever-increasing pressure on cities to prioritize sustainable growth and avoid carbon lock-in, yet available modeling frameworks and tools fall acutely short of robustly guiding such pivotal decision-making at the local level. Financial incentives, behavioral interventions, and mandates 21
drive sustainable technology adoption, while land-use zoning plays a critical role in carbon emissions from the built environment. Researchers typically evaluate impacts of policies top down, on a national scale, or else post-hoc on developments vis-à-vis different polices in the past. Such high-level analyses 24
and post-hoc evaluations cannot forecast emission pathways for specific cities, and hence cannot serve as input to local policymakers. Here, we present IMPACT pathways, from a bottom-up model with residence level granularity, that integrate technology adoption policies with zoning policies, climate 27 change, and grid decarbonization scenarios. With the city at the heart of our analysis, we show that for our site rapid grid decarbonization is the largest single mitigation measure. We identify an emission premium for sprawling development and show that adverse policy combinations exist that can exhibit 30 rebounding emissions over time.
POLICY RELEVANCE
33
Cities are at the forefront of implementation of climate impact mitigation strategies. Yet, there are no tools available for them to project expected emissions for given policies into the future. As there are no one-size-fit all mitigation measures, they have to be compared to each other. It is also important to 36 compare impacts over longer periods of time to analyze compounding effects. This paper makes the case that cities should generate projections of their building stock development and anlyze their impact on emissions on residence resolution. This allows to integrate measures such as incentives and adoption for 39
technologies, e.g., heat pumps as well as longer term effects such as spatial planning and grid decarbonization. The paper also makes the case that it should become common practice to investigate energy demand of buildings using climate change scenarios. 42
INTRODUCTION
Buildings account for ~40% of the global energy consumption and ~30% of the associated greenhouse 45 gas emissions, while also offering a 50-90% CO2 mitigation potential Lucon & Ürge-Vorsatz, 2014;Wang et al., 2018a). Growing urbanization puts pressure on cities in order to absorb increasing populations, requiring decisions on land-use (IEA, 2021;Kennedy, Ibrahim, & Hoornweg, 48 2014). While it is generally acknowledged that urban infill development is beneficial compared to outward expansion in terms of economics and carbon emissions (Asfour & Alshawaf, 2015;Conticelli, Proli, & Tondelli, 2017;Lima, Scalco, & Lamberts, 2019;McConnell & Wiley, 2012), quantifying these 51 benefits under various external factors, e.g., climate change, is challenging (Teller, 2021). Integration of urban strategies for mitigation and adaptation to climate change is needed to avoid carbon lock-in effects (Seto et al., 2016;Ürge-Vorsatz et al., 2018) and to identify potential synergies and reduce suboptimal 54
trade-offs between mitigation responses. As such, if policies put in place to drive these improvements are to be effective, they should be designed by anticipating the integrated landscape of infrastructure, climate, and behavioral conditions and responses. 57
End-use electrification in combination with electric grid decarbonization and higher energy efficiency is considered to be the major pathway toward decarbonization of the built environment (Leibowicz et al., 2018). Since energy demand in buildings is mostly dominated by HVAC equipment, one promising 60 policy lever is the provision of financial incentives for higher-efficiency system upgrades or solar photovoltaic (PV) installations (Khanna et al., 2021). Mandates are used in building codes to require that certain minimum efficiency standards or technologies (e.g., solar PV) are met in buildings at the time of 63 building or after major renovations.
It is debated whether individual (bottom-up) action or system-level (top-down) action is more important and should receive greater focus in decarbonization efforts (Goldstein, Gounaridis, & Newell, 2020;66 Hultman et al., 2020;Khanna et al., 2021). According to the United Nations Environment Programme, however, this is a false dichotomy as both perspectives must be used in conjunction to effect necessary change(United Nations Environment Programme, 2020). The challenges with developing a federal-level 69 coordinated climate policy in the US has no doubt increased focus on state, local, and individual action, but it is unclear how those lower-level actions aggregate to measurable differences in energy use in the urban built environment. Modeling and integrating individual decision-making within the context of 72 changing land-use has become critical to understanding what outcomes we can expect based on undirected individual choice versus those that will require incentives or even mandates to generate the aggregated benefits needed for rapid decarbonization. 75
Often policies and their impact are evaluated top down, on a national scale, or post-hoc on developments vis-à-vis different policies in the past (Berrill & Hertwich, 2021;Creutzig et al., 2016;Goldstein et al., 2020;Kennedy et al., 2014). Global-scale emission pathway studies typically focus on target warming 78 temperatures and backcast how they can be achieved (Rogelj et al., 2016). Forward projection of emissions and mitigation efforts have been only been explored recently in a few studies, considering carbon pricing as a policy mechanism for relatively short target years, e.g., 2030 (Sognnaes et al., 2021) 81 or integration with economic models (Lu et al., 2021). Exploratory forward projections are useful because they can provide realistic estimates of emission reductions under certain given conditions. As a consequence, forward projection can inform what range of emission reductions can be achieved 84 realistically, which in turn could be linked to target warming temperatures.
Here we emphasize that despite cities' position at the forefront for implementation of climate impact mitigation strategies (IEA, 2021; Intergovernmental Panel on Climate Change, 2022), there are no tools 87 available for them to project expected emissions for given policies into the future. Put differently, if citylevel forward projections could be done systematically and robustly, would the aggregate of those projections match top-down national/global emissions and warming projections under the same policy 90 scenarios? Unfortunately, we do not know if that will actually be the case and how wide the resulting differences will be.
To address this gap, we introduce IMPACT: Integrated bottoM-up greenhouse gas emission PAthways 93
for CiTies, a spatio-temporal model for the evolution and composition of neighborhoods (see Figure 1a). Our model starts at the parcel level. Each parcel can contain one or more buildings with multiple individual residence units whose type for each decade is governed by zoning policy and redevelopment 96 schedule in the specific neighborhood (see Figure 1b, Figure 2 and Methods: Future Land-use and Transformation Scenarios), and whose energy demand is calculated according to its type, decade, and climate change scenario (see Figure 1c and Methods: Architectural and Energetic Modeling of Building 99
Archetypes and Methods: Climate Change Pathways). Each residence unit also contains a "decisionmaker" who decides whether to adopt certain technologies based on the incentives and information available to them (see Methods: Technology Adoption), which in turn are governed by policy and 102 economic scenarios (see Figure 1d and Methods: Policy Instruments for Technology Adoption). In the supportive scenario, financial incentives are available for everyone and mandates require each new building to adopt high efficiency technologies. In the neutral scenario, adoption may happen, but typically 105 at a lower rate due to the economics involved for the decision maker. In buildings whose occupants decide to adopt high-efficiency/green technologies (in our case HVAC, smart thermostats, solar photovoltaics and storage) the annual energy demand is reduced accordingly (see Methods: Efficiency 108
Improvements of Adopted Technologies). Finally, as a simplification, the energy demand is assumed to be met using fully electrified buildings. This simplification allows us to estimate the resulting CO2 equivalent emissions based on grid carbon content (see Figure 1e and Methods: Grid Decarbonization 111
Pathways).
Our objective is to create an exploratory model, which for each decade can provide the composition of a neighborhood (types of buildings), the adopted technologies within it, its energy demand under different 114 climate change assumptions, and the resulting annual equivalent CO2 emissions. Comparing different scenarios allows us then to explore how different assumptions play out over longer periods of time, how policies interact and what combinations of strategies provide pathways to reduced operational emissions 117 of neighborhoods. Other metrics and inputs can be easily integrated at the individual parcel and residence level, which makes this a very versatile tool to explore potential pathways and mitigation strategies and policies. Notice that here we do not consider emissions linked to transportation and embodied emissions 120 for construction.
METHODS
123
Here, we review the inner workings and assumptions of each component of our model.
Future Land-use and Transformation Scenarios 126
We apply scenario planning to explore to the range of potential energetic impacts associated with changing urban morphology (Schüler, Cajot, Peter, Page, & Maréchal, 2018). We use Envision Tomorrow (ET), an open-access scenario modeling tool, to generate the scenarios (Gabbe & Fregonese,129 2013). ET utilizes a set of linked MS Excel spreadsheets with an ArcGIS extension to enable parcel-level land development to be mapped over existing neighborhood geographies, generating demographic, economic, transportation, and energy outputs. ET allows the user to control a range of building and urban 132 design variables, yielding highly differentiated development types necessary for neighborhood scenario development.
We use a parcel-level dataset of the City of Austin, Texas including address, current zoning and land-use 135
class, year of structure construction, and assessed property value. The dataset includes an improvementto-land ratio (ILR), which, as a measure of the economic potential of a property, is the appraised value of the structure divided by the value of its land (City of Austin, 2009). We use the ILR to create a parcel 138 rank of re-development likelihood used to schedule parcel redevelopment through 2100, where we assume that a parcel is more likely to redevelop the smaller its ILR is.
We selected study neighborhoods within Austin, Texas, USA, guided by the likelihood of a neighborhood 141 experiencing major changes to building morphology due to (re)development. Given Austin's high rates of population growth, housing demand, and resulting increasing residential property values, neighborhoods currently composed largely of older single-family homes were seen as the most likely candidates to 144 experience major redevelopment. Further narrowing criteria for identifying neighborhoods included homes constructed before 1970 (as an indicator of opportunity for upgrades or replacement), the relationship between lot size and existing building footprint (as an indicator of under-utilization), and the 147 existence of households below the median income of Austin (as an indicator of gentrification pressure). Finally, we included geographic variation as a factor to account for property value differentials that might impact redevelopment. The three selected neighborhoods are Brentwood, South Menchaca, and 150
Montopolis, and provide a diverse geographic, income, construction age, infill and redevelopment potential based on the above criteria. Specifically, Brentwood, South Menchaca, and Montopolis represent a progression from most-to-least utilized and, conversely, least-to-most vulnerable to 153 gentrification. Table 1 shows the characteristics of the three neighborhoods at the beginning of our modeling period in 2020. We envision two development pathways: a) a low-density, sprawling, future with redevelopment indicative of auto dependent urban patterns, consisting primarily of larger single-family homes, and higher floor area per capita (Pincetl et al., 2014) and b) a high-density future supported by greater 159 pedestrian activity and transit (Appleyard, Ferrell, & Taecker, 2017;Cervero & Landis, 1997) with high intensity, multi-story residential and commercial buildings along major streets, and greater reliance on intermediate density multi-family ("missing middle"). The future land-use scenarios for each of the three 162 neighborhoods were developed starting in 2020 for the target year 2100 in steps of 10 years with the following assumptions: First, we assume that all buildings will be redeveloped by 2100 and, second, that each parcel will only go through a single redevelopment. These assumptions serve to simplify the 165 scenario process for the purposes of assessing the impacts of morphology on future energy use, in our exploratory scenarios. We also create a reference scenario that reflects the current land-use, i.e., no redevelopment. 168
Nr of Lots
To account for the uneven nature of land redevelopment pressure, the future land-use scenarios contain internal differentiations by land-use class and location. Specifically, we initially classified the parcels based on their current land-use and location. We combine the current land-use into three classes, 171
representing similar building morphologies: small residential, large residential, commercial/mixed-use. Similarly, we identify three categories to account for location: along a major traffic corridor, within an identified transit-oriented development (TOD) area, or within the interior of the neighborhood. Major 174 corridors and TOD areas were determined by the Image Austin Comprehensive Plan, which specially identified the locations as preferred "activity corridors" and "centers" for future growth. (Wallace, Roberts, & Todd, 2012) 177
We build a redevelopment schedule into the dataset to explore the process of land-use changes by decade. The redevelopment schedule is the percentage of parcels in the neighborhood considered to redevelop over the course of each decade from 2020 to the target year of 2100 (see Table 2). Montopolis has large, 180 undeveloped portions, and therefore a great percentage of parcel redevelopment occurs quickly. The redevelopment schedule is implemented through a redevelopment rank determined by the ILR and broken out by the three locations (interior, corridor, TOD). The lowest ILR in each location is assigned the 183 highest rank for each use class. Redevelopment is implemented using the percentage of all parcel land-use ordered by max rank by decade. The specific type of redevelopment was assigned using parcel size and location as the factors limiting potential land-use intensity. The major differences in the development of 186 the different neighborhoods can be summarized as
• Montopolis (Mont) -the only neighborhood with significant greenfield potential. We chose to subdivide the larger lots inside the neighborhood since these are likely to become small 189 residential in the near term. But there remain many large lots suitable for mid-rise development.
Existing single-family lots are the biggest of the three. So: greatest potential variability neighborhood. 192
• Brentwood (Brent) -the smallest lot sizes, both for larger and smaller parcels. But has significant acreage of larger parcels suitable for mid-rise development (especially compared to SM). So: scenario leaning toward concentrated (and therefore greater) density 195
• South Menchaca (SM) -larger lots than Brent, but a greater share of small residential parcels. The least potential for mid-rise development. So: more decentralized density (
Architectural and Energetic Modeling of Building Archetypes 201
Envision Tomorrow (ET) has precomputed constant annual energy demand for each of its various building archetypes, which is not suitable for our purposes because it does not reflect impact of climate change or efficiency upgrades. Thus, we develop building energy models for the 25 different residential 204 and commercial building archetypes from ET ( Figure 3), which are then subsequently used in the land-use and transformation scenarios described above. Detached homes are assumed to have rectangular floor plans 7.6m width and the length adjusted to the area assumed in Envision Tomorrow. Ceiling heights are 207 3m. For multi-family and multi-use building types, we assume double loaded 2.4m corridor down the middle, and the different units are studio, one-, two-, three-and four-bedroom apartments with a standard depth of 7.6m and the length again adjusted according to the overall area. Mixed-use buildings have 210 storefronts at the bottom floor. All buildings assume a wood frame construction, and double pane windows. We assume 2.5 people per residential dwelling unit. The buildings are designed in Rhinoceros 3D (McNeel, 2010) and simulated with EnergyPlus (Crawley et al., 2001) using the DIVA plugin (Jakubiec 213 & Reinhart, 2011) and the weather files corresponding to the three studied climate change pathways.
Policy Instruments for Technology Adoption
Currently in Austin, TX the following policy incentives are available for the technologies being 231 considered in this model. For Solar PV, homeowners can avail a Federal Investment Tax Credit (FITC) of 26%, which was stepped down from 30% in 2020. Since 2019, a flat rebate of $2,500 is also available for systems over 2.5kW. For upgrading to efficient HVAC, a rebate of up to $2550 is available since 2020, 234
whereas installing a smart thermostat can earn a $110 rebate. From these existing baselines, we model two bounded policy scenarios for technology adoption. In the best-case scenario: 1) the FITC for solar PV steps down to 22 percent in 2023 and expires in 2024 as defined by the current federal policies; and 2) the 237 rebates for all the three technologies continue to exist until 2100, with the rebate for solar PV available for systems above 1.2kW from 2022 onwards. In the worst-case scenario, the FITC, as well as all the local rebates, expire by 2020 and no economic incentives are available for any of the three technologies 240 under consideration. Modeling these two scenarios provides upper and lower bounds for adoptions, which allows the integrated model to explore the full range of impact from individual adoption decisions.
Agent-based model of technology adoption in households 243
We model the diffusion of energy technologies at the household level using an agent-based model (ABM) as demonstrated previously (Rai & Robinson, 2013;Robinson & Rai, 2015). The ABM approach allows us to simulate realistic social drivers of home energy technology adoption decision-making. At the core of 246 the model is a dual-threshold model of gateway technology adoption mated to a novel sequential model of technology co-adoption. The gateway model identifies the first technology adopted by a household as a function of their access to financial and informational resources and the conditions at the time of their 249 financial and informational activation. The sequential model specifies the order and timing of subsequent co-adoptions conditioned on prior adoptions -including gateway technology -and dwelling type. Note that single family homes can adopt all possible technologies (high efficiency HVAC, solar, storage and 252 smart thermostats), while multi-family homes can only adopt smart thermostats. The available roof space for PV is estimated from building footprint, tree cover and elevation; orientation of the roof is not explicitly estimated. 255
The ABM initializes with more than 181,000 buildings, including single-family homes in Austin, Texas, as well as single-and multi-family homes within focal neighborhoods, dependent on the development scenario. Agent state data at initialization includes indices for access to financial and informational 258 resources, geospatial location, and type of dwelling. Agents' social networks are estimated at initialization in three steps: 1) all alter agents within a geographic radius φ of an ego agent are geographic candidates for connection, 2) a homophily constraint -the top ρ percent of similar agents according to financial 261 resource access -is applied to the geographic candidates and the remaining agents are connected, and 3) an additional λ proportion of the total connected neighbors are randomly selected from the entire agent pool and connected. The resulting social network is empirically informed and has small-world 264 characteristics.
The economic and policy context are also established at initialization. The economic context consists of future sale prices of home energy technologies estimated by combining historical data with simple trend 267
assumptions, e.g., stable decreases in prices over time with constant variability. The policy context comprises the primary set of decision variables in the model and includes many aspects that shape agent decision-making. For example, the rebate available for any home energy technology at any point in time 270 reflects a policy interest in offsetting a portion of the financial burden (captured in the economic context) associated with technology acquisition. Similarly, a mandate requiring that all new units have a particular technology -regardless of rebate availability -reflects policy interest in that technology. 273
The informational context captures the social drivers of technology adoption: during the simulation, agents exchange information with their social neighbors altering the level and distribution of information in the system. As the simulation progresses, agents make adoption decisions that diffuse the target 276
technologies. Agents are sparked to adopt a gateway technology when they acquire sufficient informational resources: i.e., when they are convinced that adopting the technology is a good idea through the dynamic and emergent informational context. The gateway technology and subsequent technologies 279 that compose the agents' home energy plans are randomly selected from the empirical distribution of gateway technologies and subject to constraints imposed by agent status as renter or owner. Once activated with a gateway technology, agents solicit bids to install each technology in the home energy 282 plan. Successful adoption occurs when agents solicit bids that they can afford: i.e., the agent has access to sufficient financial resources as indicated through their financial index. When weighing the prospective benefits of a bid, the benefit of each technology is calculated with respect to the suite of previously 285 installed technologies. For example, the benefit of installing a smart thermostat differs for agents who do versus do not already have solar PV installed; in the first case, it would reduce their overall energy use, which is valued at the rate of the feed-in-tariff, while in the second, its reduction in energy use would be 288 valued at the retail electric rate.
Also, as the simulation progresses, development scenarios determine agent exit from, and entry to, the population. When a scenario includes changes in a parcel's use (e.g., density changes such as shifting 291 from a lone single-family home to two single-family homes on the same parcel), the ABM creates and removes agents as appropriate. New agent states are initialized following the procedure described above.
Efficiency improvements of adopted technologies 294
We estimate the effect of energy efficiency measures as follows. If a building is adopting High-efficiency HVAC, it's annual energy demand is reduced by the highest efficiencly available for that year based on the technology adoption model; if a building is not adopting high-efficiency technologies, it follows a 297 regular lifetime update, i.e., every 20 years, the HVAC system is updated with one that is slightly more efficient, with the general efficiency improvements assumed to be 2% per year for 20 years until a theroretical limit is reached (Wang et al., 2018b). 300
The effect of solar PV and storage on the energy demand is estimated in two steps. First, we determine the annual energy generated ! in (kWh) based on the panel size that has been selected by the technology adoption module using on the solar sun hours method as 303
! = 356 × !"# ×
Where !"# (in hr) is the average daily sun hours in a location, and in (kW) is the nominal power output of the solar array. For Austin, !"# ≈ 5 hr. The impact of the added battery is modeled by 306
assuming an average annual self-sufficiency of 40%. Using these numbers for energy improvements, each building's pre-simulated energy demand is updated and reduced to reflect technology adoption.
Grid Decarbonization Pathways 309
We include three grid mix evolution pathways in our study. The first maintains the 2020 level of carbon content at ~430 gCO2eq/kWh (no grid decarbonization) and serves as a reference. This number is the 312 average for the grid mix from 2010-2019 (City of Austin, 2022). As an indication, the 2019 grid mix was approximately 47% natural gas, 20% coal, 20% wind, 11% nuclear, and 1% wind (ERCOT, 2019) . A rapid grid decarbonization scenario is used for the TX grid (Rhodes & Deetjen, 2021), at a rate of about -315 100 gCO2eq/kWh/decade reaching a constant value of ~50 gCO2eq/kWh by 2060. This is a "net-zero by 2050" scenario as the final value of 48 gCO2eq/kWh by 2100 represents the embodied emissions of the renewable generation in the grid(Intergovernmental Panel on Climate Change, 2014). The third, 318 moderate, pathway is defined as the arithmetic average between the previous two, resulting in a decarbonization rate of -50 gCO2eq/kWh/decade until its plateau at about 240 gCO2eq in 2060, after which grid decarbonization efforts stall at a non-zero operational emission grid mix. These three 321 pathways cover a large variety of overall carbon content in the TX grid, regardless of the generation composition, which is sufficient for our case. The grid carbon content factor is used to convert annual operational electricity demand to annual greenhouse gas emissions. 324
Comparing high and low-density development: Premium for Sprawl
We are generally interested to assess the emissions in the buildings belonging to the study neighborhood, i.e., limited by their geographical area. However, keeping the area fix, means that densification allows 327 more people to be accommodated, who otherwise would move to another area and whose emissions in absolute terms would not be counted. Thus, to allow a fair comparison in absolute emission values between different urban developments, we extrapolate the results for the low-density developments to 330 match the number of units of the high-density development. We then define as the Premium for Sprawl as the difference in emissions (in tCO2eq/yr) of low-density developments compared to the high-density development. In other words, the Premium for Sprawl describes the surplus in emissions due to sprawling 333 for a fixed number of residences (or persons). The Premium for Sprawl is inspired by the Premium for Height for tall buildings, resulting from the increase of cost for the required material to withstand wind loading (Ali & Moon, 2007). 336
Model Limitations
To convert energy demand to emissions in the buildings, we assume that all energy used is electric, i.e., all buildings are electrified. For our case study in Texas, where cooling is the dominant energy use and 339
typically met with electric air conditioning systems, this is a reasonable assumption, especially to compare pathways amongst each other. For other climates, where heating is dominant, one must include fuel switching scenarios that also consider transitioning from fossil fuel heating systems to electric 342 heating systems, e.g., heat pumps.
Urban energy systems, such as district heating and cooling are not investigated. Also, our models are not capturing extreme weather situations like heat waves or cold snaps. As indicated above, our model also 345
does not include emissions from transporations or embodied construction emissions. However, the parcel, level formulation of the model allows the integration of these with reasonable assumptions in the future. Similarly, if a realistic initial condition of the neighborhood in terms of construction material can be 348 created, then building retrofitting, e.g. envelope and window improvement would be another scenario dimension that could be explored (Felkner & Brown, 2020).
As with any long-term forecasting models, we assume that general behaviors, e.g., on technology 351 adoption or urban transformation drivers do not change significantly over time. While these are strong assumptions, they also let us investigate their relative importance, such that one can decide which of the models should be further improved to better assess their overall impact. 354
We are not explicitly including population numbers in the neighborhoods. Instead, we couple population numbers to the building units by assuming 2.5 occupants per residence, which is consistent with the US average household size according to the 2018 census. As a consequence, per unit indicators are 357 equivalent, in our case, to per capita indicators.
RESULTS: IMPACT PATHWAYS
360
We explore the IMPACT pathways for the three neighborhoods in Austin, TX with the scenarios shown in Figures 1 and 2 not refer to the same scenario in both figures, but is rather used to support our narrative starting at A. Figure 4 and Figure 5 and show the relative (per residence unit) and absolute IMPACT pathways, 369 respectively, for the A1B climate scenario and all other considered scenarios, aggregated for all three studied neighborhoods (shown in Figure 2).
Policy Interactions: Synergies, Trade-offs and Rebounds
The relative pathways offer an apples-to-apples comparison between the urban development scenarios 372 (Figure 4). Clearly, fast grid decarbonization has the largest overall effect on emission reductions (Figure 4 (A)). In addition, both low-and high-density development further amplify the emissions reductions in the beginning (Figure 4 (B)). However, after 2070 the emissions of the low-density development begin to 375 slightly increase again, while they remain flat for the high-density development.
In the moderate grid decarbonization scenario, the low-density development rebounds its emissions after 2050 (Figure 4 (C)), while for densification the annual emissions remain flat after 2050 (Figure 4 (D)). In 378 fact, densification without grid decarbonization (Figure 4 (E)), reduces the relative emissions of the neighborhoods by about 25% between 2020 and 2100. By contrast, low-density development without grid decarbonization first reduces the annual emissions by 20% in 2050, but ultimately rebounds by 2100 to 381 about the same levels as 2020 (Figure 4 (F)). While this is about 20% lower than the reference case that only considers climate change and no urban development or grid decarbonization (Figure 4 (G)), it is also 30% higher than the corresponding high-density development (Figure 4 (E)). 384
Comparing Figure 4 (E) and (H), we observe that several scenario combinations can lead temporarily to similar outcomes: no grid decarbonization with high density development (Figure 4 (E)) and moderate grid decarbonization alone (Figure 4 (H)) have about the same annual emission until about 2050, after 387 which they diverge. Thus, the same relative emission pathways can be achieved with different policy combinations.
Our results clearly demonstrate that in the absence of a zoning policy that is favorable for densification, 390 the major driver for the decarbonization of the neighborhoods is grid decarbonization. This is a rather important realization as the drivers behind the two are not necessarily related or combined and subject to different socio-techno-economic and political boundary conditions. We demonstrate here that their 393 interaction has substantial effect on emissions outcomes and pathways.
Our results show that technology adoption has a comparatively small impact, e.g., the three curves for Figure 4 (C) representing the neutral, no tech adoption and supportive policies, and have almost identical 396
pathways. Therefore, all technology adoption scenarios are implicitly assumed in the corresponding grid decarbonization and urban development scenarios. We discuss the implications of this further below when comparing individual action vs systemic change. 399
402
In terms of absolute emissions (Figure 5), again rapid grid decarbonization of the grid leads to the fastest emission reductions by far, regardless of other policies. Because there are fewer buildings in the lowdensity neighborhood, its annual emissions in this case (Figure 5 (A)) are somewhat lower than the 405 corresponding high-density neighborhood (Figure 5 (B)). At the other grid decarbonization extremewhen the grid carbon content remains unchanged-densification and climate change substantially increase the overall emissions (Figure 5 (C)) due to the increased number of units in the neighborhoods. 408
This somewhat counter intuitive result stems of course from the fact that the high-dentisty neighborhood absorbs many more people, which are not considered in the low-density scenario. We further discuss and compare high and low density developments below in Premium for Sprawl. 411
For moderate grid decarbonization and low-density urban development (Figure 5 (D)), grid decarbonization mainly drives the initial emission decrease. After 2050, however, emissions begin to rebound and by 2100 the annual emissions return to their level of about 2040. The high-density 414 development even rebounds to annual emissions higher than their 2020 level (Figure 5 (E)).
If only climate change is considered (no grid decarbonization, and no urban redevelopment), the annual emissions increase slightly (Figure 5 (F)). Adding low-density urban development (Figure 5 (G)) shows 417 that it can reduce emissions until about 2050, due to efficiency increases in newly built buildings. However, here also the emissions eventually rebound, due to energy demand increase driven by climate change, and by 2100, the annual emissions return to their values at about 2020. 420
Comparing Figure 5 (E) and (G), we again see that different scenario combinations can temporarily achieve the same emission outcomes: Both set of curves (E: moderate grid decarbonization and highdensity development) and (G: no grid decarbonization and low-density development) follow a similar 423 reduction until about 2050, and a similar rebound until about 2070. After 2070 their pathways separate.
Notice that this is contrary as for the relative pathways, where the two scenario combinations are clearly separated (Figure 4 (F) and (D), respectively). 426 High density development can rebound to annual emission higher than 2020. F. Without any decarbonization measures, annual emissions increase due to climate change. G. Low-density development without grid decarbonization can initially reduce emissions but increase in energy demand due to climate change leads to a rebound after 2050. E and G show similar decrease until 2050 and rebound until 2070, after which their pathways separate.
Individual action (technology adoption) vs Systemic change (zoning policy) 429
Figure 4 also demonstrates that urban redevelopment has a substantially larger effect on emission reductions compared to technology adoption. Since the fast grid decarbonization dominates both, we highlight this on the moderate grid decarbonization scenario (Figure 4 (C) and (D)). Clearly, technology 432 adoption reduces emissions in all cases, the falling price scenario being the most favorable for adoption. The effect is larger for the low-density development, where sustained reductions can be achieved during the rebound phase (Figure 4 (C)). Under high-density development, single-family dwellings give way to 435 multi-family dwellings -for which the full menu of technology adoption adoptions is typically not available -effectively eliminating the impact of technology adoption over time (Figure 4 (D)). Of course, because overall accumulated emissions matter more for slowing climate change, every bit helps. 438
This has clear implication in the ongoing policy discourse of individual/market-driven solution vs systemic solutions. Clearly, technology adoption incentivization alone cannot be the central cornerstone of any serious climate policy. We conjecture that the same conclusion could be drawn for other types of 441 technology adoptions. For example, we do not explicitly model fuel-switching adoption, i.e., a home switching from a gas-furnace for heating to an electric heat pump. However, given that that is also typically a high price upgrade, the adoption rate would be similar to what is presented here. 444
Climate change and Premium for sprawl
For the moderate grid decarbonization scenario, Figure 6a shows the impact of climate change on the 447 relative emissions (tCO2eq/unit) for each urban redevelopment scenario. As the first part (until 2050) is driven by grid decarbonization and the different climate scenarios are still relatively similar, there is virtually no difference within the land-use scenarios, low-density redevelopment having higher relative 450 emissions than high-density, and both being higher than their emissions without climate change. After 2050, grid decarbonization stalls, urban redevelopment increases and the effects of climate change intensify, resulting in different pathways. 453
As one would expect, the A2 climate scenario has the highest emissions, while B1 the lowest. We can see that an amplifying high emission combination pathway (A2 & low-density development) can be up to 65% higher than an amplifying low emissions combination pathway (B1 & high-density development) in 456 2100. Further, a favorable climate scenario (B1) coupled with low-density development is still about 30% higher in 2100 than the worst-case climate scenario (A2) with high-density development. In other words, an unfavorable zoning policy, will be amplified by climate change. 459 Figure 6b) and c) shows the premium for sprawl for two neighborhoods for grid decarbonization scenarios and A1B climate scenario (without technology adoption). For Brentwood (Figure 6b)) we show the values in 2100 as an example. Note there is no scenario in which the premium is negative, i.e., high-densitity 465 development is always more favorable in terms of reducing emissions (for a given population size). Even for rapid grid decarbonization and without considering climate change (Figure 6b) bottom), in 2100 the low-density development still emits on the order of 2,500 tCO2eq more annually than the high-density 468 equivalent. For moderate grid decarbonization, the premium for sprawl is about five times higher, ~12,800 tCO2eq, and it is about nine-fold if the grid is not decarbonized (23,000 tCO2eq). These ratios are relatively consistent across the decades and neighborhoods. The A1B climate scenario amplifies the 471 premium for sprawl by about +10%, for example, for the moderate case 14,300 tCO2eq (A1B) compared to 12,800 tCO2eq (no climate change). For B1 and A2 climate scenarios, we find this amplification to be +5% and +15%, respectively. 474
Comparing ( Figure 6b) and (Figure 6c), we can also identify the interaction between urban redevelopment and grid decarbonization. The Brentwood neighborhood (Figure 6b) develops more slowly in the first part of the century, while Montopolis (Figure 6c) develops more quickly. Consequently, there are relatively 477 fewer new buildings in Brentwood compared to Montopolis, and the difference between the low-and high-density developments is small, reflected in the similar evolution of the premium for sprawl until about 2050. As Montopolis develops more quickly earlier, the premium for sprawl increases in the 480 beginning until about 2040. Eventually, the decarbonization of the grid progresses sufficiently to reduce the premium again. From 2050 onwards both neighborhoods undergo significant redevelopment, highlighting the premium for sprawl for moderate and no decarbonization scenarios, while maintaining 483 comparatively low constant values for the rapidly decarbonizing grid.
Importance of Baseline 486
One important aspect of policy development and interpretation is the choice of the appropriate baseline against which potential decarbonization interventions are compared. Recently, it has been argued that policies to address climate change should be analyzed by considering only the outcome when climate 489 change is accounted for (Hausfather & Peters, 2020;Jafino, Hallegatte, & Rozenberg, 2021). This helps capture potential interactions and avoids overestimating the impacts of the policy. We illustrate this in Figure 7a), where we show the annual energy demand of the neighborhoods for the climate change 492
forecasts compared to their current state (2010) and excluding urban redevelopment and technology adoption (grid carbon content is irrelevant for energy demand).
Energy demand is increasing by +10% by 2050 in any climate scenario and increases to above 20% by 495 2100 for A1B and A2, while plateauing at about +15% for B1 after 2080. Therefore, any energy efficiency policy that fails to include climate change, will overestimate its expected impact by at least 10% by 2050. IMPACT pathways reduce this bias by incorporating climate change scenarios. While this 498 may seem rather obvious, surprisingly few, if any, building energy and decarbonization scenarios are presented with climate changed modified weather scenarios.
Absolute vs relative emission pathways
For comparison between scenarios, relative values are convenient by normalizing, e.g., for the built area (tCO2eq/m 2 ), which, in analogy to the energy use intensity index, could also be referred to as emission 504 intensity of a building or neighborhood. Since we are also considering urban development, we put forward that the comparison of emissions per built residence unit (tCO2eq/unit) is more use-and insightful than per built area, since the same built area could potentially serve multiple units. By residence 507 units, we understand the subdivisions of a building, i.e., a multi-family house is one building with several housing units.
Relative emission values must be used and interpreted with care as they can obfuscate real pathways. This 510 is shown in Figure 7b- However, comparisons between different urban redevelopment scenarios should use (tCO2eq/unit) to account for the fact that there exists a cap on the total number of people that a neighborhood can 519
accommodate. This cap is smaller for lower density developments, and so in a generally growing city, additional people must move elsewhere, and their emissions are not captured in absolute pathways comparisons. The premium for sprawl indicator resolves the issue of the correct but harder to interpret 522 relative emission pathways using (tCO2eq/unit) and offers a true comparison between different pathways for a neighborhood or municipality.
DISCUSSION
525
It is tempting to consider our results of different decarbonization measures independently and rank them based on their ability to reduce emissions. However, this would disregard several long term temporal effects and potential interactions between the measures, which can be discovered in bottom-up 528 exploratory models. Our results clearly show that researcher must include climate change forecasts in energy modeling to ensure that potential shifts in heating and cooling loads are adequately captured. Policy makers must plan with long term scenarios to avoid rebound effects as short term gains can be 531 cancelled out by long term developments.
The IMPACT pathways demonstrate that comparatively short-term emission reductions driven by one mechanism, e.g., grid decarbonization, can be effectively overturned in the longer term by a potentially 534 adverse set of events, e.g., unguided urban development. This highlights the necessity to decarbonize the electric grid as fast as possible to avoid adverse effects: if the initially dominant mechanism stalls at some point, e.g., for the moderate grid decarbonization scenario, urban development can eventually counteract 537 all the gains. Furthermore, the IMPACT pathways have shown that in the short-term several combinations of scenarios can potentially produce the same emission reductions, while their impact differs in the longer term. Of course, given the obvious uncertainties associated with making long-term predictions of coupled 540 systems, rigorous monitoring and accounting of emissions is necessary to keep track of model predictions, and develop better models and forecasts as more data is collected.
IMPACT pathways are exploratory and allow us to compare both top-down (policy) and bottom-up 543 (individual) processes to understand the degree and type of interventions necessary to rapidly curb residential emissions. What's more, they also clearly show where the impactful decision-makers are located. For example, in our case study, the individual decision makers, i.e., the technology adopters in 546 the residences, do not emerge sufficiently powerful to have an impact on emissions. Consequently, policy incentivizing or mandating certain technology adoptions, typically at the national level, has equally little impact. Whether this is due to the low number of adopters or low impact of the adopted technoly is not 549 clear. By contrast, grid decarbonization and zoning policy have the largest individual impact. The two must be coordinated to effectively deliver an effective net-zero emissions agenda, doing which will likely heavily involve the municipality level (IEA, 2021). 552
Densification has long been theorized as central to decarbonization (Teller, 2021), and it has been well established that per capita transportation emissions decline as density rises (Gately, Hutyra, & Wing, 2015). However, there had remained a gap in understanding "the magnitude of the emissions reduction 555 from altering urban form, and the emissions savings from integrated infrastructure and land-use planning" (Intergovernmental Panel on Climate Change, 2015). The IMPACT pathways presented here contribute to uniting "measurement and meaning" in integrated land-use and infrastructure studies (Richter, 2021). We 558 clearly demonstrate that zoning policy and housing can have a substantial impact and must be considered as a viable decarbonization measure. We have introduced the Premium for Sprawl to quantify the fact that low density developments accrue emissions outside of their geographical limits due to people who cannot 561 be accommodated in the neighborhoods.
When evaluating our results, one must be aware of the limitations built into the assumptions. It is not clear how our results would be impacted if transportation emissions would be directly included. We can 564
hypothesize that lower density development will be more favorable for transportation emissions but quantifying them requires additional research. An interesting avenue for future work is to integrate the transition to electric vehicles as it would couple transportation emissions directly to the grid. Again, a 567 sprawling development will likely require more frequent EV charging, and therefore result in higher emissions compared to the denser development. Given that our model is at the building unit level, it is relatively straightforward to implement assumptions on EV charging (load and frequency). Similarly, to 570 obtain an even more integrated picture of the impact of the built environment on emissions, embodied emissions should be integrated in future research. This would help compare the impact of efficiency upgrades to new construction. 573 IMPACT pathways are complimentary to life-cycle assessment (LCA) research on net-zero energy neighborhoods, e.g., (Wiik et al., 2022) in that they provide a temporal exploration of possible scenarios and policy impacts ("what-if" questions), rather than holistic design guidelines, or normative pathways to 576 achieve a certain emission target.
Since we are working with annual average energy demand and grid carbon content, more research is needed to determine the potential of more fine grained temporal resolution for the operation of the 579 electrical grid. It is also not clear what the impact of other potential building efficiency upgrades, e.g. insulation, would be. However, we can hypothesize that since the impact of high efficiency is modeled by reduced annual energy demand, any equivalently impactful technology will have a similar effect, 582 especially considering the mandate scenario. In that case, the impact is limited by the fraction of buildings redeveloping, which in our model is already relatively large (>6%/yr) compared to the typical 2-3% retrofit rate. 585
CONCLUSION
IMPACT pathways generate results consistent with recent studies on the emission reduction potential of 588 buildings (Goldstein et al., 2020) and on the relatively low impact of technology adoption . They integrate decisions and processes at the individual residence level and can be easily further integrated with other policies and impacts of interest, e.g., fuel switching in heating systems, building 591 retrofit (Felkner & Brown, 2020), transportation emissions, adoption of electric vehicles, or embodied carbon in building construction (Berrill & Hertwich, 2021). Further, hourly energy simulation results not presented here, could be used for studies on demand response programs and on grid-interactive buildings 594
(Department of Energy, 2021; Vazquez-Canteli & Nagy, 2019). To unlock the tremendous potential that the built environment offers to address climate change, integrated multi-domain models spanning several spatiotemporal scales can inform decision makers on the effectiveness of policies. IMPACT pathways are 597 key in defining and analyzing policies, as well as in tracking their implementation progress.
DATA PROCESSING AND AVAILABILITY
The output of each model is organized into sets of spreadsheets in which a given parcel is associated with its own 600 unique ParcelID, allowing for linkage of the models. Data are joined and further processed in a set of Tableau workbooks. An interactive dashboard with all the data is available at https://public.tableau.com/app/profile/intelligent.environments.laboratory/viz/IMPACTPathways/IMPACTPathways 603
Figure 1 :
1a) Overview of the IMPACT model used to generate multi-domain emission pathways (ILR: Improvement-to-land ratio; Individual D-M: Decision Maker). b) Number of building types for high-and lowdensity urban development scenarios for the Brentwood neighborhood in Austin, TX c) Average annual temperature in Austin, TX, for different climate change scenarios, d) Policy and economic inputs for technology adoption scenarios e) Grid decarbonization scenarios.
Figure 2 :
2Residential zoning policy scenarios in each of the three studied neighborhoods
. Each individual pathway is a combination of the urban development scenarios (no 363 change, high density, low density), grid decarbonization (no, moderate or rapid decarbonization), and technology adoption (no adoption, neutral, and supportive policy). The combinations are labeled with uppercase letters (A-I/J) in Figures 4/5 and shown in the Figure legend. Notice that the same letter does 366
Figure 4 :
4IMPACT Pathways for relative annual emissions aggregated for all three neighborhoods. A. Rapid grid decarbonization results in the fastest emission reductions. B. Emission reductions are amplified by densification. C. For moderate grid decarbonization, low-density development shows rebound of emissions after 2060, while D. the high-density development does not show rebound. E. Densification without grid decarbonization can reduce emissions without rebound and is similar in reduction potential until 2050 than moderate grid decarbonization alone (H). F. Low-density development without grid decarbonization reduce emissions until 2050, but rebounds by 2100 to higher emissions than 2020. G.Without any decarbonization measures, annual emissions increase due to climate change.
Figure 5 :
5IMPACT Pathways for total annual emissions aggregated for all three neighborhoods. A. Rapid grid decarbonization results in greatest emission reductions. B. Densification can offset emission reductions. C. Densification without grid decarbonization leads to highest annual emissions. D. Moderate grid decarbonization drives emission reductions until 2050 when low-density development rebounds. E.
Figure 6 :
6a) Impact of climate change and urban redevelopment on relative emissions under moderate grid decarbonization aggregated for all three neighborhoods b) Premium for Sprawl in Brentwood and c) Montopolis 462
Figure 7 a
7) Energy demand under climate change. Energy efficiency policy that fails to include climate change, will overestimate its expected impact. b) Emission Pathways for Brentwood for climate change scenario A1B in absolute values (tCO2eq), c) per housing unit (tCO2eq/unit), and d) per built area (tCO2eq/m 2 ).
Characteristics of the studied neighborhoods 156Total Lot
Area (m 2 )
Housing
Units
Total Housing
Area (m 2 )
Average 2020
population
Brentwood
2,580
3,340,000
4,790
606,240
14,350
South Menchaca 2,378
2,831,000
3,099
441,520
9,100
Montopolis
2,143
4,744,000
3,619
494,530
11,600
Table 1
Redevelopment schedule (% of lots redeveloped) in each neighborhood8-plexes inside the
neighborhood)
198
2020 2030 2040 2050 2060 2070 2080 2090 2100
Montopolis
15% 15%
6%
6%
9%
9% 10% 15%
15%
Brentwood
6%
6%
6%
9%
9%
12% 12% 20%
20%
South Menchaca
6%
6%
6%
9%
9%
12% 12% 20%
20%
Table 2:
Figure 3Building archetypes. Detached homes are assumed to have rectangular floor plans 7.6m width and the length adjusted to the area assumed in Envision Tomorrow. Ceiling heights are 3m. For multi-family and multiuse building types, we assume double loaded 2.4m corridor down the middle, and the different units are studio, one-, two-, three-and four-bedroom apartments with a standard depth of 7.6m and the length again adjusted according to the overall area. Mixed-use buildings have storefronts at the bottom floor. All buildings assume a wood frame construction, and double pane windows. We assume 2.5 people per residential dwelling unit.For the energy simulation we use weather files for Austin, TX based on the IPCC 2000 Special Report on Emission Scenarios (SRES) A1B, A2 and B1 provided by Meteonorm (Meteonorm, 2019) for each 219 decade between 2020 and 2100, in addition to the typical mean year (TMY) weather data for current weather reference. For our purposes, these SRES scenarios are similar to the Representative Concentration Pathways (RCP), e.g., SRES A1B is similar to RCP 6.0 and SRES B1 is similar to RCP 4.5(Riahi et al., 2017). Similarly, the most recent Shared Socioeconomic Pathways scenarios (SSPs) have close matches in the SRES scenarios, e.g., SSP1 and B1 scenarios are close, both assuming a better case scenario for global sustainability, and SSP3 and A2 scenarios are similar in their outlook on 225 global cooperation(van Vuuren & Carter, 2014). As a point of reference, the three climate scenarios (B1, A1B and A2) result in an average annual temperature increase in 2100 in Austin of +1.5C, +2.5C and +3C, respectively. 228216
2.3. Climate Change Pathways
222
d for Brentwood's low-density redevelopment for the moderate grid decarbonization scenarios. All pathways show decreasing emissions until about 2050. After 2050, the annual emissions increase for both (tCO2eq) and (tCO2eq/unit), while the continue to decline for 513 (tCO2eq/m 2 ). Any indicator can be useful and appropriate depending on the purpose. For example, the absolute emissions indicate the carbon footprint of the neighborhood, while comparisons of interventions for the same urban development scenario can be compared using the built area (tCO2eq/m 2 ) because the 516 same buildings and residence units are compared to each other.
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| sample_391 | 0.9998 | arxiv | |
A framework for model-assisted T × E × M exploration in maize
June 9, 2022
Jennifer Hsiao
Department of Biology
University of Washington
SeattleWAUnited States
Soo-Hyung Kim
School of Environmental and Forest Sciences
University of Washington
SeattleWAUnited States
Dennis J Timlin
USDA-ARS Adaptive Cropping Systems Laboratory
BeltsvilleMDUnited States
Nathaniel D Mueller
Department of Ecosystem Science and Sustainability and Department of Soil and Crop Sciences
Colorado State University
Fort CollinsCOUnited States
Abigail L S Swann
Department of Biology
University of Washington
SeattleWAUnited States
Department of Biology
Department of Atmospheric Sciences
University of Washington
SeattleWAUnited States
A framework for model-assisted T × E × M exploration in maize
June 9, 2022
Breeding for new crop characteristics and adjusting management practices are critical avenues to mitigate yield loss and maintain yield stability under a changing climate. However, identifying high-performing plant traits and management options for different growing regions through traditional breeding practices and agronomic field trials is often time and resource-intensive. Mechanistic crop simulation models can serve as powerful tools to help synthesize cropping information, set breeding targets, and develop adaptation strategies to sustain food production. In this study, we develop a modeling framework for a mechanistic crop model (MAIZSIM) to run many simulations within a trait × environment × management landscape and demonstrate how such a modeling framework could be used to identify ideal trait-management combinations that maximize yield and yield stability for different agro-climate regions in the US.
Introduction
Food demand is increasing but our ability to sustain crop productivity will be impacted by a warming climate. Breeding has consistently played a critical role in the progress of continuous yield gain and was estimated to account for up to 50-60% of the total on-farm yield gain in the past several decades (Duvick, 2005). These gains through genetic improvements are complemented by changes in management practices, such as an increase in fertilizer use, chemical weed control, higher planting densities, and earlier planting dates (Cardwell, 1982;Kucharik, 2008). Recently, however, practices such as nitrogen application and weed control are nearly fully exploited in the US corn belt; simple adjustments in management strategies alone are likely insufficient to sustain an increasing yield trend. Additional yield gains would need to rely further on genetic improvements in new cultivars, as well as management changes that accompany climate-resilient characteristics to fully leverage the interactions among genetics, environment, and management (the G × E × M paradigm, Hatfield and Walthall, 2015).
Continued development of new cultivars better-suited for future climate is critical for sustaining current yield trends or to prevent yield loss (Burke et al., 2009;Challinor et al., 2017). Progress in breeding for climate adaptation has been demonstrated in several areas, including changes in morphological traits (e.g. improved root system architecture that improves soil water access; G. L. Hammer et al., 2009), increases in drought and salinity tolerance (Fita et al., 2015;, improvements in physiological traits (e.g. greater nitrogen use efficiency; Fischer and Edmeades, 2010), and shifts in copping duration (Zhu et al., 2018), to name a few. Our ability to utilize the genetic diversity preserved in wild relatives, landrace species, and undomesticated wild species to develop new climate-ready cultivars is increasingly important to achieve sustainable and intensified food production (Godfray et al., 2010;McCouch et al., 2013).
Maize trait changes in the past few decades have also been accompanied by shifts in crop management practices, such as more erect plant forms that facilitated notable increases in planting densities (Duvick, 2005), shifts towards earlier planting dates by about 3 days per decade (Butler et al., 2018;Zhu et al., 2018), increases in nutrient supply (Duvick, 2005), and increases in area irrigated (Mueller et al., 2016). In addition, the suitability of a cultivar often varies considerably across environmental gradients (e.g. Messina et al., 2015), thus optimal plant traits and management options are usually identified within defined target environments . This breeding strategy allows for designing different cultivars to perform favorably and withstand stresses in their target environments, and what is considered "ideal" may differ between locations and climate. We expect optimal management to shift under future climate conditions and in combination with different phenotypic traits, providing important means of adaptation in many systems (Deryng et al., 2011).
Mechanistic modeling tools that integrate physiological, morphological, and phenological properties of a crop (G), their performance under different management options (M ), and their interactions with the surrounding environment (E ) on a whole-plant level can serve as useful tools for breeding practices through the quantification of a yield-trait-performance landscape (Messina et al., 2011). The structure of such models allow for testing effects of traits (e.g. leaf elongation rate, total leaf number) on integrated outcomes such as yield. While mechanistic crop models may not specifically describe genetic-level properties, higher-level traits are often used as proxies to describe the underlying genotype. This makes models ideal tools to test and screen for potentially promising traits and management (T × M ) combinations under different climate and environmental conditions (E ) as a first step before carrying out actual breeding practices (Andrivon et al., 2012;Messina et al., 2011), and on large scales that are often not feasible under actual experimental settings B. Peng et al., 2020). Such information can further be used to synthesize cropping knowledge, set breeding targets, and develop climate-targeted adaptation strategies to sustain food production.
Despite broad recognition that mechanistic, process-based crop simulation models can be a powerful tool to synthesize cropping information, set breeding targets for developing climate-ready crops, and develop adaptation strategies for sustaining food production Muller & Martre, 2019), few comprehensive studies have been performed to produce climate-specific trait and management combinations for staple crops including maize in the US, a necessity given rapidly changing environmental conditions facing the US cropping systems. In this study, we construct a modeling framework to identify targeted plant traits and effective crop management to achieve maximum crop performance in both the current and future climates. Specifically, we addressed how an ensemble of plant traits (i.e. physiology, morphology, phenology) combined with realistic adjustments to management choices (i.e. shifting planting dates, planting density, and row spacing) can be used to build resilience and improve productivity under the stresses induced from a changing climate.
Material and methods
We set up a data-model framework to quantitatively identify high performing regions within a T × E × M landscape. The framework consists of three main components ( Fig. 1): 1) a process-based crop simulation model (section 2.1), 2) model inputs to drive the model, including present-day climate information (section 2.2), idealized future climate information (section 2.3), simulation site soil information (section 2.4), and sampled trait and management options (section 2.5), and 3) processed model outputs that identify performance within the T × E × M landscape (section 2.6 -2.7), and summarized in-season growth outputs (section 2.8).
Process-based crop simulation model -MAIZSIM
MAIZSIM is a deterministic and dynamic model developed and calibrated for maize plants to represent key physiological and physical processes such as gas exchange, canopy radiative transfer, carbon partitioning, water relations, nitrogen dynamics and phenology (Kim et al., 2012). MAIZSIM interfaces with a 2-dimensional finite element model (2DSOIL) that simulates a dynamic soil water and nutrient vertical 2D profile (Timlin et al., 1996). The coupled model responds to daily or hourly meteorological information throughout the growing season that includes temperature, relative humidity, solar radiation, and CO 2 concentrations.
At the leaf-level, MAIZSIM captures gas exchange processes through a C4 photosynthesis model (von Caemmerer, 2000) coupled with a stomatal conductance model (Ball et al., 1987) and an energy balance equation (Collatz et al., 1992); leaf-level gas exchange processes are scaled to canopy-levels using a sunlit/shaded leaf framework (de Pury & Farquhar, 1997). The model simulates crop development throughout the growing season following a nonlinear temperature response (Yin et al., 1995), and adopts a leaf area model developed by Lizaso et al., 2003 to describe the expansion and senescence of individual leaves. MAIZSIM dynamically simulates leaf water potential and uses it to trigger water stress responses such as reduced growth rate and hastened senescence when values drop below designated thresholds .
The model has been validated at different scales -including physiological aspects such as gas exchange , leaf development and biomass gain (Kim et al., 2012), leaf growth water stress responses , as well as field-level validations in AgMIP projects (Bassu et al., 2014;Kimball et al., 2019) and FACE site studies (Durand et al., 2018) that tested for yield responses to different temperature and CO 2 conditions. The model has also recently been used to test the independent impacts of temperature versus VPD on growth and yield in maize growing regions in the US (Hsiao et al., 2019).
Present-day climate data
We assembled hourly data of temperature, relative humidity, precipitation, and solar radiation over years 1961-2005 for our simulation sites as weather data input for our model simulations. Specifically, we accessed hourly air temperature (T air ), dew point temperature (T dew ), and precipitation data from the NOAA National Center for Environmental Information Integrated Surface Hourly database (https: //www.ncdc.noaa.gov/isd), and hourly solar radiation data from the National Solar Radiation Data Base (https://nsrdb.nrel.gov/data-sets/archives.html).
We followed the Clausius-Clapeyron equation (Eqn. 1-2) to back out atmospheric humidity information in the form of relative humidity (RH) from T air and T dew :
E s = E sref · e Lv Rv ·( 1 T ref − 1 T air ) (1) E = E sref · e Lv Rv ·( 1 T ref − 1 T dew )(2)
The equation uses the saturation vapor pressure (E sref , 6.11 mb) at a reference temperature (T ref , 273.15 K), the vaporization latent heat (L v , 2.5·10 6 J kg -1 ), and the gas constant (R v , 461 J K -1 kg -1 ) to calculate the saturated water vapor pressure (E s , mb) and the actual water vapor pressure (E, mb) at air temperature (T air , K). We then use E and E s to calculate RH (%) (Eqn. 3):
RH = E E s(3)
We selected overlapping sites and years that had data available from both the Integrated Surface Hourly Data Base and the National Solar Radiation Data Base over years 1961-2005 and filtered for site-years that had less than two consecutive hours of missing data throughout the growing season (broadly defined to be between February 1 st -November 30 th ) and retained at least two-thirds of the weather data (Fig. S1). We then gap-filled any missing data by linearly interpolating the missing information with weather data of the hours prior and post the missing data point. Next, we linked valid weather stations with maize planting area and irrigation level data accessed through the United States Department of Agriculture -National Agriculture Statistics Service (USDA-NASS, https://www.nass.usda.gov/Data and Statistics/index.php). Specifically, we calculated the average maize planting area across our simulation period in the continental US and accessed average irrigation level (%) for the same sites through four available census years (1997,2002,2007,2012) (Fig. S2). We used the planting area and irrigation level averaged across five USDA-NASS sites closest to each weather station (via Euclidean distance) to represent their cropping information, and to exclude sites that either had less than 10,000 acres of corn planted or had greater than 25 % of crop land irrigated. We excluded sites with less than 15 years of data to insure sufficient sampling to assess inter-annual climate variability (Soltani & Hoogenboom, 2003;Van Wart et al., 2013). Following this method, we were able to compile 1160 site-years of meteorology data for our simulations, which included a total of 60 sites, each site with available weather data ranging from 15-27 years (Fig. 2).
Idealized projected climate
We assembled idealized projected climate information at two future time points, 2050 and 2100, to analyze crop performance shifts under future climate (Table 1). Specifically, we created monthly temperature and relative humidity anomaly maps under a substantial but not extreme greenhouse gas emissions scenario (SSP3-7.0, Riahi et al., 2017) from the latest Coupled Model Intercomparison Project version 6 (CMIP6) outputs; we used these anomaly maps to calculate location-specific warming and associated changes in relative humidity levels throughout the growing season for each simulation site (Fig. 3). This method preserves correlations between climate variables (i.e., between temperature, relative humidity, and solar radiation) on short timescales and limits known biases in modeled variability (Donat et al., 2017;Vargas Zeppetello et al., 2019). Since both magnitude and pattern of future precipitation projections are highly uncertain, we applied a general trend of precipitation reduction in accordance to the SSP3-7.0 scenario, and increased atmospheric concentrations of CO 2 to 550 ppm and 850 ppm for years 2050 and 2100, respectively (O'Neill et al., 2016).
Soil data
We used soil information from USDA-NASS locations nearby our simulation sites to curate site-specific soil files for each location. Soil properties are highly Figure 3: Monthly pattern of warming derived from CMIP6 multimodel means for our simulation sites. Numbers in color bar indicate temperature scaling values to multiply with global average climate sensitivity to calculate projected warming for each simulation site. For example, under our assumption of 3.1°C global average warming by 2100, a scaling value of 2 for a specific simulation site will equal a total warming of 6.2°C for that location. Table 1: Description of idealized climate treatments with projected changes in temperature (T), relative humidity (RH), precipitation (precip.), and projected CO 2 concentrations by years 2050 and 2100 under the SSP3-7.0 emission scenario.
Year Climate Scenario 2050 + 1.4°C mean T, -RH, -15% precip, 550 ppm 2100 + 3.1°C mean T, -RH, -30% precip, 850 ppm heterogeneous, and since our simulation sites are based on weather station locations that do not directly come from agricultural land, we use this method to broadly represent soil makeup of agricultural sites within the region without skewing towards any particular site. We queried soil information from the National Resources of Conservation Services (NRCS) SSURGO soil database (Soil Survey Staff, n.d.) to identify soil properties for each NASS location with maize planting area greater than 10000 acres and irrigation levels less than 25%. For each site, we accessed soil information at five depth categories (surface, 50, 100, 150, and 200 cm), which included sand-silt-clay-organic matter composition, soil bulk density (the oven dry weight of less than 2 mm soil material per unit volume of soil at a water tension of 1/3 bar), and the volumetric content of soil water retained at a tension of 1/3 bar (33 kPa, field capacity) and 15 bar (1500 kPa, wilting point) expressed as a percentage of the whole soil. With the sand-silt-clay composition, we categorized the queried soil data into 12 texture groups following the USDA Textural Soil Classification (Staff, 1999) and excluded sites classified as Sandy or Clay due to their lack of representation in agricultural fields. Next, we determined the soil class within each depth category for all our simulation sites by assigning it the most prevalent soil class from it's 11 nearest NASS sites calculated through Euclidean distance, and assigned it the mean soil conditions of that texture-depth class averaged across all NASS sites within that category. Finally, we estimated soil hydraulic properties of each soil type through a water release curve predicted by the van Genuchten equation (van Genuchten, 1980).
Sampling within the trait and management space
We selected several key model parameters that represent a range of maize traits and management options to investigate combinations that lead to high performance under present and future climate conditions. Since we do not have robust observation-based data on the natural distribution and boundaries of most parameters, we assumed a uniform distribution and set biologically reasonable boundaries around literature-based default values (Table 2). We assumed all parameters to be non-correlated and used a Latin hypercube sampling method (McKay et al., 1979) to create 100 different trait-management (T × M) combinations within the parameter space.
Performance within the T × E × M landscape
We defined high crop performance as crops that achieve high yield (i.e. yield mean across years) and high yield stability (i.e. yield dispersion across years).
We developed a cost function (Eqn. 4) to quantify the performance of any T × M combination by calculating its distance to a theoretical best-performing combination within the yield and yield stability space (Eqn. 4):
D score = w yield * (y mean − y max ) 2 + w disp * (y disp − d min ) 2(4)
y mean and y disp represent mean yield and yield dispersion (variance/mean) across years for the target T × M combination at a specific simulation site, respectively. We standardized yield and dispersion to values between 0 and 1 to avoid skewed contribution due to difference in scale. y max and d min denote the standardized maximum mean yield (1) and minimum yield dispersion (i.e., maximum yield stability, 0) achieved within all T × M combinations at a specific simulation site. w yield and w disp are empirical coefficients between 0 and 1 that assign weighted importance to yield mean and yield dispersion, respectively. We used the calculated D score to rank the top 20 performing T × M combinations for each simulation site. We determined an overall ranking for each T × M combination based on their rankings across all simulation sites (Fig. 5a). With this method, T × M combinations with high rankings across a few sites versus combinations with medium ranking across several sites can all result in overall high performance. T × M combinations that do not rank within the top 20 performers at any site will not receive a ranking.
Regional difference in performance
We used a climate space approach to identify how the performance of T × M combinations differed with baseline climate conditions. We used a k-means clustering algorithm to cluster our sites based on mean growing season temperature and VPD, and total growing season precipitation, roughly dividing our simulation sites into four groups of climate spaces -cool and medium precip, mild, warm and wet, and warm and mild to dry (Fig. 6). We analyzed the performance of T × M combinations within each cluster of sites by calculating a standardized performance score (Eqn. 5):
P score = n i=1 R i R max * n(5)
R i denotes the performance ranking of a T × M combination at site i among a total of n sites within each climate space, and R max indicates the maximum performance ranking a T × M combination can achieve at a single site. In our workflow, we only considered the top 20 performing T × M combinations when ranking high performing combinations (see section 2.6), so R max equals 20. The resulting standardized performance score ranges between 0 and 1, in which a T × M combination that ranks with highest in performance across all locations within the climate space would receive a P score of 1.
In-season model outputs
MAIZSIM generates outputs of a number of plant growth outputs throughout the growing season on an hourly time step. We describe in Table 3 a select few outputs in more detail. We summarized these high time frequency outputs across four phenological stages (emerged, tassel initiation, tasseled and silked, and grain-filling) to facilitate analysis and interpretation. Specifically, we queried net photosynthetic rate (A n ), net carbon gain (P n ), and stomatal conductance (g s ) values from daylight hours, and averaged them within the designated phenological stages. We represented ear biomass, total biomass, and total leaf area (ear biomass, total biomass, LA) within each developmental stage with maximum values within each stage. Finally, we queried water supply, demand, and deficit (ET supply, ET demand, water def icit) values at noon and averaged all values within each phenological stage, and represented predawn leaf water potential (Ψ) with values queried at 5 am, and averaged the all values within each phenological stage.
Experiment setup and model simulation
We prescribed the sampled planting density (Table 2, pop) for each ensemble member and adjusted the planting date for each ensemble member and simulation site based on climate and growing degree days (GDD) requirements. We calculated GDD for each simulation site through accumulated heat units starting from February 1st with a base temperature of 8°C (Kim et al., 2012) and determined the planting date once GDD surpassed the sampled for each ensemble member (Table 2, gdd ). This led to earlier planting dates in warmer regions and vice versa (Fig. 7), and created diversity in cropping cycle start time among T × M combinations, mimicking early versus late-planting cultivars (Fig. 13). To simulate well-fertilized conditions, we prescribed a total of 200 kg ha -1 of nitrogen throughout the growing season, applying half as base fertilizer prior to planting and the rest top-dressed one month post planting. For each simulation site, we ran the MAIZSIM model with default parameters that represented a generic crop cultivar across all locations (see default values in Table 2). Next, we carried out a site-level ensemble of simulations in which we used past meteorology data (see section 2.2) to each of the 100 trait-management parameter combinations (see section 2.5) for each of our 1160 site-years (see section 2.6) and identified top performing (high yield and yield stability) traitmanagement combinations. Finally, we repeated the site-specific trait and management ensemble of simulations with idealized future climate (see section 2.3) to understand how high performing trait and management combinations under current climate conditions fared under future climate.
Model validation
We validated simulated yields with default parameter values (control T × M combination, see Table 2) with historic yield data from the United States Department of Agriculture -National Agriculture Statistics Service (USDA-NASS, https://www.nass.usda.gov/Data and Statistics/index.php). We compared yield data from observation sites closest to our simulation sites calculated through a Euclidean distance (Fig. 8). We scaled our whole-plant level simulation outputs to field level by applying a planting density of 10 plants per m 2 and compared our simulated yield with averaged yield observations in between years 2005-2012, since our default parameter and management options resemble modern-day plant traits, planting density, and planting dates. 3 Results and discussion
Model validation
In general, simulated yields showed less spatial difference compared to observations (Fig. 8). The model captured historic yield observations well in the higher latitude Corn Belt regions but overestimated yield in various warmer sites in southern locations (Fig. 9). Southern locations experience much warmer temperatures, especially during later parts of the growing season (Fig. S3, grain-fill). While MAIZSIM dynamically describes temperature and water stress throughout the growing season through impacts on gas exchange and leaf developmental processes, the model lacks direct depiction of climate stress responses on reproduction processes such as flowering, pollination, and grain-filling, which are likely reasons for the yield over-estimation in warmer regions.
Cultivar differences between crops planted in southern versus northern locations could also contribute to these discrepancies. Farmers in warmer southern locations choose cultivars that are both planted and harvested earlier in the growing season, leading to an overall shorter crop cycle duration compared to those planted in the north (USDA-NASS, Crop Progress and Conditions). While our simulation set up captures earlier planting in warmer regions (Fig. 7), it does not capture potential differences in cultivar and management choices that growers in the south have likely been opting for in order to avoid late season heat and water stress. Finally, we note that by applying a universal soil depth (200 cm), we may be overestimating soil water availability. This could disproportionately affect warmer locations in south, in which late-season water availability could partially alleviate water stress later in the growing season and contribute to yield overestimation in those locations (Fig. 9).
Performance difference across climate spaces
In Hsiao et al. (2022, submitted), we followed the framework described in this paper and identified several top-performing strategies among all T × M combinations under present-day and future climate conditions, categorized based on different combinations of phenological (grain-filling start time and duration) and morphological (total leaf area) features. Top-performing strategies under present-day climate conditions included T × M combinations that either reached reproductive stage early (Early Starting), were slow in aging (Slow Aging), stress averting (Stress Averting), or had large canopies and were high in yielding (High Yielding). More details are described in Hsiao et al. (2022) and briefly summarized below.
Early Starting, Slow Aging, and Stress Averting strategies all have a smaller canopy size and relatively earlier transition times from vegetative to reproductive stages, but differ in grain-filling duration. Slow Aging strategies have long grain-filling durations that prolong cropping duration, while Stress Averting strategies display the shortest longevity, allowing plants with this strategy to complete their cropping cycle early and avoid late season stressors such as dry and hot conditions. On the other hand, High Yielding strategies have larger canopy sizes accompanied by delayed transition from vegetative to reproductive stages. While all categorized as top-performing under present-day climate, these strategies showcase a range of trade-offs between yield and yield stability, with performance differing across simulation sites (Fig. 5, 10) and climate spaces (Fig. 11a). Under current climate conditions, T × M combinations with Slow Aging strategies tend to be generalists, showing high performance across all climate spaces. On the other hand, strategies such as Early Starting fared best in cool and wet regions, while High Yielding strategies perform best under warm and wet conditions (Fig. 11a). Under future climate conditions, we observed an overall yield loss for all T × M combinations in most simulation sites (Fig. 12), including strategies that improved in performance ranking with climate change (Fig. 12a), such as High Yielding and Large Canopy (Fig. 11c). In general, warmer regions with low precipitation levels exhibited the greatest yield sensitivity (% yield loss per degree C of warming, Fig. 12); high-performing strategies under future climate partially buffered, but did not prevent yield loss.
High-performing strategies under present-day climate conditions shifted with climate change (Fig. 11b, c). T × M combinations with early starting strategies experienced the greatest drop in performance ranking overall, showing declines in most climate spaces (Fig. 11c, Early Starting). Slow aging strategies still remained one of the higher performers by the end of the century (Fig. 11b, Slow Aging), but showed clear performance ranking declines in warm climate spaces (Fig. 11c, Slow Aging), allowing several other strategies to compete for top performance in those climate spaces (Fig. 11c); T × M combinations with high yielding and compensating strategies progressed further in performance ranking (Fig. 11c, High Yielding), and new high-performing strategies with larger canopies and delayed transition timings into reproductive stages emerged (Fig. 11c, Large Canopy, Compensating, Middle Ground ).
Mechanisms for high performance
We analyzed detailed in-season outputs of various phenological, physiological, and morphological outputs of the model (Table 3) and describe here some general trends observed in top-performing T × M combinations.
Phenology
Climatological differences between simulation sites and parameter differences among T × M combinations both lead to the range of phenology output we see in our simulation outputs (Fig. 7, 13). Phenology differs across simulation sites due to imposed planting date adjustments based on growing degree day requirements, allowing for an earlier planting date in warmer regions (Fig. 7). Climatological differences throughout the growing season further shape the difference, especially during the grain-filling stage in which simulation sites in the south become substantially warmer than those in the north (Fig. S3), leading to hastened development (Fig. S5). On the other hand, phenology differs among T × M combinations due to differences in perturbed traits linked to phenology (e.g. planting time, developmental rate, leaf number, Fig. 13). High performing T × M combinations under present-day climate conditions tend to show earlier starts in reproductive stages with a longer duration (Fig. 13). Higher ranking T × M combinations tend to show a greater fraction of grain-filling length over total growing season length (Fig. S4b) despite no clear trends in total growing season length (Fig. S4a).
Physiology
Net photosynthetic rates are generally higher in top-performing T × M combinations during transition from vegetative into reproductive stages (Fig. S6), but the differences in photosynthetic rates become dominated by climatological differences between simulation sites during the final grain-filling stage, with greater photosynthetic rates in warmer southern regions (Fig. S6). In general, we see a linear relationship between temperature and photosynthetic rate during vegetative stages (Fig. 14). This relationship eventually plateaus around 28-30°C later in the growing season, and starts to decline in a few warmest site-years (Fig. 14b). While warmer temperatures generally led to higher photosynthetic rates, hastened development and greater water deficit under warmer conditions also led to overall shorter grain-filing durations (Fig. S7, S5a), compensating one another, dampening the overall difference between northern versus southern sites in terms of net carbon gained throughout grain-filling (Fig. S8) and final yield (Fig. S9).
Morphology
Differences in simulated total leaf area was largely dominated by parameter make up within T × M combinations, showing much less difference in simulated yield across sites (Fig. S10). Simulated plants approached full canopy sizes around tassel initiation, and top-performing combinations showed mid to lower total leaf area under present-day climate conditions. This was consistent with most top-performers under present-day climate exhibiting early transitions into reproductive stage (e.g., Slow Aging, Early Starting, Stress Averting). These strategies partly achieved early reproductive start through short vegetative stages through fewer total number of leaves and hence smaller canopy size (i.e., lower
Discussion
Crop production is expected to suffer under future climate conditions as the climate warms. Adaptation of crop management practices, location of planting, as well as adaptation of the crops themselves all have the potential to limit expected yield loss and help to sustain agricultural productivity. However, we lack a systematic understanding of which adaptations are likely to have the biggest impact and why, both critical pieces of knowledge for agricultural planning. Mechanistic, process-based crop simulation models can be a powerful tool to synthesize cropping information, set breeding targets, and develop adaptation strategies for sustaining food production, yet have been underutilized for developing specific climate-adaptation options.
Breeding for and adopting new cultivars involve exploring and navigating the hills and valleys of the G × E × M landscape, in which optimal plant traits and management options are identified within defined target environments Messina et al., 2011). Requirements from breeding, delivering, and adopting a desirable cultivar depends on many factors, and the whole process can take from years to decades (Challinor et al., 2017). Recent developments in breeding practices have greatly expanded the efficiency in genotyping and phenotyping methods (Voss-Fels et al., 2019), yet the breeding pipeline is still time and resource intensive, limiting its ability to explore the full range of G × E × M combinations and interactions.
A typical breeding cycle starts out by exposing a large germplasm pool under extremely high selection pressure, filtering genotypes from the order of 10 6 individuals down to a few dozen promising candidates (Cooper et al., 2014;. In the early stages of a breeding program, trait selection is often limited to those that can easily be identified through automated processes, and commonly based on plants in early developmental stages. It is not until later in the breeding cycle that selection criteria shift from genotype to phenotype-based, and promising hybrids are evaluated on-farm at various locations with a range of background climate conditions (Gaffney et al., 2015). Management optimization also occurs around this time, in which field trials are set up to identify the best management practices for the final candidates prior to commercial release. Further, common breeding methods that either select for higher yield or eliminate defect traits do not allow for a clear understanding of the mechanisms in which favorable traits contribute to greater performance and yield, and effective combinations of plant traits, if not actively sought for based on a mechanistic understanding of crop growth and yield, could only occur by chance (Donald, 1968).
There is growing recognition that mechanistic crop simulation models can be a powerful tool to synthesize cropping information, set breeding targets, and develop adaptation strategies for sustaining food production. Such applications can complement current breeding efforts of developing new climate-resilient cultivars by facilitating broad exploration of the G × E × M landscape within a modeled setting as a first step Messina, Cooper, Reynolds, et al., 2020;Muller & Martre, 2019;Rötter et al., 2015). The process-based nature of such models allow for mechanistic insight through which these adaptations influence yield and their sensitivity to different climate factors, providing a more complete assessment of the uncertainty associated with different possible climate conditions, including those that do not currently exist yet.
Ramirez-Villegas et al. (2015) provided a few successful examples of modelaided breeding projects, such as the New Plant Type program developed by IRRI for rice crops, in which process-based models were used to help make informed decisions to target breeding directions and resulted in new plant types that out-yielded conventional cultivars within two breeding cycles (S. Peng et al., 2008). This success further inspired the super rice program in China that led to newly developed rice varieties with 15-25% higher yield than common hybrid cultivars planted in other regions in China (S. Peng et al., 2008). While model-aided breeding practices are less commonly targeted towards a changing climate (Ramirez-Villegas et al., 2015), demonstrated success under current climate suggest it as a promising pathway to guide breeding direction for climate adaptation moving forward, and expanded experiments evaluating a range of G × E × M conditions can enable production system responses to changing environmental conditions .
Regardless, thorough evaluation and application of crop models for developing specific climate-adaptation options (e.g., designing adaptive phenotypes for specific soil-climate combinations) for US agriculture remains scarce. We bridge this gap by constructing an integrated data-model framework set up to explore crop performance across a defined G × E × M landscape. With this framework, we identified high-performing plant trait and management combinations (G × M) best suited for current climate conditions, as well as targets and priorities to adapt to impending climate stressors (E). Heterogeneity in performance exists within the sampled climate space, which stemmed from underlying physiological, morphological, and phenological processes within the simulated crop. Model outputs on hourly time steps allowed us to compile detailed in-season outputs of various plant processes and summarize them according to associated phenological stages. This form of model output allows for more in-depth analysis that go beyond final yield and yield stability, and investigation of mechanisms that contribute to high crop performance and the differences across climate spaces and under future climate projections.
We demonstrate how such a framework can be used to identify adaptation options with an emphasis on climate-resilient plant traits and effective management that will mitigate yield loss and optimize productivity both across space and through time in US corn growing regions under future climate conditions. Our modeling results demonstrate that application of mechanistic modeling holds substantial promise to inform breeding within the US maize production system. Figure S1: Available weather data based on different gap-filling intervals. For example, if consecutive missing hours equals 0, then only site-years with complete hourly weather data records will be included for weather data. If consecutive missing hour equals 1, site-years with gaps no greater than one hour consecutively will be included and gap-filled linearly. Figure S2: Maize planting area (top) and irrigation levels (bottom) across continental U.S. Figure S3: Mean air temperature (°C) across phenological stages for top phenotypes across all sites, ranked by performance of T × M combinations, and averaged within phenological stages. Figure S4: a) Total growing season length (gray, days) and grain-filling length (pink, days) for all phenotypes, ranked by performance, starting with the highest performers towards the left, and b) the fraction of grain-filling over total growing season. Figure S5: Start time and duration of each phenological stage across T × M combinations, averaged across all simulation sites for a) southern sites versus b) northern sites, ranked by overall performance, with the highest performers listed towards the top. Figure S6: Net photosynthetic rate (µmol CO 2 m -2 sec -1 ) across phenotypes and sites, ranked by the performance of T × M combinations, and averaged within each developmental stage. Figure S7: Mean water deficit (g H 2 O) across phenotypes and sites, ranked by the performance of T × M combinations, and averaged within each developmental stage. Figure S8: Net carbon gain throughout phenological stage (g C) across phenotypes and sites, ranked by the performance of T × M combinations, and averaged within each developmental stage. Figure S9: Ear biomass (g/plant) across phenotypes and sites, ranked by the performance of T × M combinations, and averaged within each developmental stage. Figure S10: Total leaf area (cm 2 ) across phenotypes and sites, ranked by the performance of T × M combinations, and averaged within phenological stages..
Figure 1 :
1Diagram of the data-model framework.
Figure 2 :
2Simulation sites and number of years simulated (purple triangles), along with historic maize yield and planting area data (green circles). Colors indicate yield and circle size indicate planting area.
Figure 4 :
4Soil texture across simulation sites. Soil texture categories include clay loam (ClLo), loam (Lo), loamy sand (LoSa), sandy clay loam (SaLoLo), sandy loam (SaLo), silty clay (SiCl), silty clay loam (SiClLo), and silty loam (SiLo).
Figure 5 :
5Simulated a) yield, b) yield dispersion, and c) performance ranking of across T × M combinations and locations. T × M combinations are ordered from top to bottom starting from the highest performance ranking. Sites are order from left to right from sites located in the south to the north.
Figure 6 :
6a) Map of simulation sites clustered based on mean growing season temperature (°C), mean growing season VPD (kPa), and total growing season precipitation (mm). Mean growing season temperature (°C), mean growing season VPD (kPa), and total growing season precipitation (mm) levels for all simulated site-years (b, c).
Figure 7 :
7Start time and duration of each phenological stage across simulation sites, indicated by state abbreviations. Sites are roughly ranked by latitude, starting from southernmost sites towards the top.
Figure 8 :
8Observed (top) and simulated (bottom) yield (tons/ha) across simulated sites. Numbers indicate site numbers that correspond inFig. 9.
Figure 9 :
9Observed versus simulated yield (tons/ha) across simulated sites. Colors indicate latitude of simulation site. Numbers correspond to site numbers shown inFig. 8.
Figure 10 :
10Performance ranking across simulation sites for T × M combinations of different top-performing strategies under present-day climate conditions.
Figure 11 :
11Standardized performance rankings of different strategies across climate spaces (see section 2.7) under a) current, b) future climate conditions, and c) the difference between the two.
Figure 12 :
12Percent yield loss within mean growing season temperatureprecipitation climate space among T × M combinations that a) improved versus, b) declined in performance ranking under future climate conditions.
Figure 13 :
13Start time and duration of each phenological stage across T × M combinations, averaged across all simulation sites, ranked by overall performance, with the highest performers listed towards the top.
Figure 14 :
14Relationship between mean temperature (°C) and mean photosynthetic rate (µmol CO 2 m -2 sec -1 ) for all simulated site-years during a) vegetative versus b) reproductive stages for four representative T × M combinations within top-performing strategies. total leaf area).
Table 2 :
2MAIZSIM parameters tested for yield optimizationProcesses
Params
Description
Default (Range) Citation
Physiology
g
1
Ball-Berry g
s model slope
4 (2∼6)
Miner et al., 2017; Shekoofa et al.,
2016
V
cmax
Max RUBISCO capacity
65 (65∼80)
Kim et al., 2006; Wu et al., 2019
J
max
Max electron transport rate
350 (350∼420)
Kim et al., 2006; Wu et al., 2019
phyf
Reference leaf water potential
(MPa) used to describe stomata
sensitivity to leaf water potential
-1.9 (-3∼-1)
Shekoofa et al., 2016; Tuzet et al.,
2003; Yang, Kim, et al., 2009
Phenology
SG
Duration that leaves maintain ac-
tive function (stay-green) after
reaching maturity
3 (2∼6)
Gregersen et al., 2013; Timlin et
al., 2019; Zhang et al., 2019
gleaf
Total leaf number
19 (11∼25)
Padilla and Otegui, 2005; Parent
et al., 2018
LTAR
Max leaf tip appearance rate
(leaves/day)
0.5 (0.4∼0.8)
Kim et al., 2012; Padilla and
Otegui, 2005
Morphology
LM
Leaf length of the longest leaf
(cm)
115 (80∼120)
LAF
Leaf angle factor
1.37 (0.9∼1.4)
Campbell, 1986; Dzievit et al.,
2019
Management gdd
Growing degree days accumu-
lated by sowing
100 (80∼160)
Sacks and Kucharik, 2011; Timlin
et al., 2019
pop
Density (plants/m 2
Table 3 :
3Key model outputsOutput
Description
Unit
A n
Net photosynthetic rate
µmol CO 2 m -2 sec -1
P n
Net carbon gain
g /plant hour
g s
Stomatal conductance
g H 2 O m -2 sec -1
ear biomass
Total ear biomass
g/plant
total biomass Total plant biomass
g/plant
LA
Total leaf area
cm 2
phenostage
Phenological stage
-
ET supply
Evapotranspiration (ET) supply g H 2 O
ET demand
Evapotranspiration demand
g H 2 O
water def icit ET demand -ET supply
g H 2 O
Ψ
Leaf water potential
MPa
AcknowledgementsWe thank Lucas Vargas Zeppetello for providing CMIP6 temperature and relative humidity projection scaling patterns. JH acknowledges support from the AFRI NIFA Fellowships Grant Program: Predoctoral Fellowships [grant no. 2020-67034-31736] from the USDA National Institute of Food and Agriculture. ALSS acknowledges support from NSF AGS-1553715.
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| sample_513 | 0.9979 | arxiv | |
DISPERSION FORCES STABILISE ICE COATINGS AT CERTAIN GAS HYDRATE INTERFACES WHICH PREVENT WATER WETTING A PREPRINT
April 16, 2019 13 Apr 2019
M Boström
Centre for Materials Science and Nanotechnology
Department of Physics
University of Oslo
Blindern, NOP. O. Box 10480316OsloNorway
R Corkery corkery@kth.se
Applied Physical Chemistry
KTH Royal Institute of Technology
100 44StockholmSESweden
E R A Lima
O I Malyi
S Y Buhmann
Freiburg Institute for Advanced Studies
Albert-Ludwigs-Universität Freiburg
Albertstr. 1979104FreiburgGermany
C Persson
I Brevik
D F Parsons d.parsons@murdoch.edu.au
J Fiedler
Centre for Materials Science and Nanotechnology
Department of Physics
University of Oslo
Blindern, NOP. O. Box 10480316OsloNorway
Department of Energy and Process Engineering
Surface and Corrosion Science Department of Chemistry KTH Royal Institute of Technology SE
Centre for Materials Science and Nanotechnology Department of Physics
Programa de Pós-graduação em Engenharia Química Universidade do Estado do Rio de Janeiro CEP
Norwegian University of Science and Technology NO
100 44, 20550-0137491Trondheim, Stockholm, Rio de Janeiro RJNorway, Sweden, Brazil
Physikalisches Institut Albert-Ludwigs
University of Oslo
Blindern NOP. O. Box 10480316OsloNorway
Centre for Materials Science and Nanotechnology Department of Physics
Universität Freiburg
Hermann-Herder-Str. 379104FreiburgGermany
Department of Energy and Process Engineering
University of Oslo
Blindern NOP. O. Box 10480316OsloNorway
School of Engineering and IT
Norwegian University of Science and Technology NO
7491TrondheimNorway
Physikalisches Institut Albert-Ludwigs
Murdoch University
90 South St Murdoch6150WAAustralia
Universität Freiburg
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DISPERSION FORCES STABILISE ICE COATINGS AT CERTAIN GAS HYDRATE INTERFACES WHICH PREVENT WATER WETTING A PREPRINT
April 16, 2019 13 Apr 2019A PREPRINT -APRIL 16, 2019Gas hydrates · Interfacial ice formation · Buoyancy · Lifshitz interactions · Dispersion forces
Gas hydrates formed in oceans and permafrost occur in vast quantities on Earth representing both a massive potential fuel source and a large threat in climate forecasts. They have been predicted to be important on other bodies in our solar systems such as Enceladus, a moon of Saturn. CO 2 -hydrates likely drive the massive gas-rich water plumes seen and sampled by the spacecraft Cassini, and the source of these hydrates is thought to be due to buoyant gas hydrate particles. Dispersion forces cause gas hydrates to be coated in a 3-4 nm thick film of ice, or to contact water directly, depending on which gas they contain. These films are shown to significantly alter the properties of the gas hydrate clusters, for example, whether they float or sink. It is also expected to influence gas hydrate growth and gas leakage.
Introduction
Gas hydrates are systems consisting of water and gas molecules forming a solid ice structure. Such systems can naturally be found in ice-cold water [1]; in particular, they can occur in permafrost [2], sediments [3], and below the oceans in the seabed [4]. For the latter, there are particularly interesting examples where gas hydrates are considered important in connection with planetary processes and the implications for life. The aqueous ocean-bearing moons Europa and Enceladus are perhaps the best examples in our solar system beyond Earth where gas hydrates are formed in salty oceans that are favourable for life [5]. On Mars, methane distribution is associated with subterranean water, implying the presence of methane hydrates [6]. On Enceladus giant plumes of erupted gases are observed and the composition directly measured to be water, salts and volatile gases including CO 2 , CO, N 2 , H 2 S and methane [7,8]. Several hypotheses consider gas hydrates to be important for the creation of volatile enriched plumes and for the composition of ice layers beneath and/or entrained into, or sprayed onto the outer surface of Enceladus [9,10,11]. In particular, type II gas hydrates on Enceladus and Europa are calculated to be less dense than water and can float in their respective oceans. They are thereby available for incorporation into the overlying thick ice layer of each icy moon. Type I CO 2 hydrates are at a density where their positive or negative buoyancy is uncertain [12,13,14,15,9]. However, if a layer of water ice forms on these gas hydrates in the presence of ice cold liquid water, then the growth of such hydrate crystals may be limited by the capping effect. This may have an impact on their buoyancy, and thus on the hypothesized composition of the ice layers in Enceladus and Europa, with obvious implications for the composition of their plumes and their potential to sample the underlying oceans and any harboured life. water ice Hydrate ε 1 ε 2 ε 3 wet surface dry surface d Figure 1: (Color online). Schematic figure of the considered arrangement. A gas hydrate surface (ε 3 ) on the left, separated by an ice layer (ε 2 ) of thickness d from a water layer (ε 1 ). A dry surface feels a repulsive Casimir force at the ice-water interface which yields a stable ice interface. In contrast, an attractive force results in a wet surface due to the vanishing of the ice interface.
On Earth, methane hydrates occur naturally and in engineered situations. Large reservoirs of methane hydrates occur in sediments of deep oceans basins, at shallower depths in the sediments of arctic sea shelves, and in deep permafrost regions. In all these cases, the understanding of whether a layer of ice forms on the hydrate has implications for exploration and production of fossil fuels, and also for understanding the potential for methane contribution to greenhouse gases as the planet becomes warmer.
In all of the contexts above, hydrates are usually surrounded by ice cold water. Depending on the gas hydrate structure with respect to contributions and volume fractions, it turns out that some hydrates form an ice interface to water, whereas others do not. The latter have a wet surface. The ones with a gas hydrate-ice interface may be considered to have a dry surface. The prediction of the wet or dry surface cannot be made easily. In the present paper we address this issue by considering a planar three-layer system, as depicted in Fig. 1, namely a gas hydrate layer, an ice sheet, and a water layer. Thus, we assume that initially all hydrates are covered by an ice interface. We estimate the Casimir force acting on the outside at the ice-water interface, i.e., the pressure acting on the system. Depending on the sign of the Casimir force, it will work towards growth or melting of the thin ice sheet. We assume that the temperature is at the triple point of water. An attractive pressure acting on the ice layer thus results in a melting of the ice sheet [16,17,18]. It will simply vanish. This kind of consideration is not new. In the past, ice melting at the triple point with a nano-sized film of water was discussed [19]. It was found that a thin water film is energetically favourable up to a certain thickness where it has an energy minimum [19,20,21,22,23]. The inclusion of retardation resulted in incomplete melting while a non-retarded approximation predicted complete melting for an ice surface at the triple point of water [19].
Here we apply Lifshitz theory to estimate the energy of the hydrate-ice-system as a function of ice thickness, and show that for some gas hydrates the ice film is stabilised at a thickness of 3-4 nm, while for other gas hydrates the ice film is unstable, resulting in direct wetting.
Materials and Methods
Dispersion forces between solid bodies
The Casimir interaction energy F (d) (also known as Lifshitz free energy) per unit area between material 1 (water) with dielectric function ε 1 and material 3 (gas hydrate), ε 3 , separated by the distance d across medium 2 (ice), ε 2 as depicted in Fig. 1 can be written at temperature T as [24,25,26,27]
F (d) = ∞ n=0 g TM (ξ n ) + g TE (ξ n ) ,(1)
where g TX (ξ) (TX=TM, TE) denotes the trace over the scattering for transverse magnetic (TM) and transverse electric (TE) Green's function. This fundamental solution comes from the vector Helmholtz equation for the electric field. The primed sum denotes that the n = 0 term is weighted by a factor one half. At finite temperature these functions are evaluated at the discrete Matsubara frequencies ξ n = 2πnk B T / [28]. The systems in this study, as mentioned, are all studied at the triple point of water. For the considered three layer system, the traces over the scattering Green's functions, including multiple reflection in the center layer, can be written (in cgs units) as
g TX (ξ n ) = 1 β d 2 q (2π) 2 ln 1 − e −2γ2d r TX 12 r TX 32 ,(2)
with β = 1/(k B T ), and the Fresnel reflection coefficients are
r TM i2 = ε i γ 2 − ε 2 γ i ε i γ 2 + ε 2 γ i ,(3)
for TM waves and
r TE i2 = γ 2 − γ i γ 2 + γ i ,(4)
for TE waves. We have introduced the imaginary part of the transverse wave vector γ 2 i = q 2 + ξ 2 ε i /c 2 . We assume nonmagnetic media.
Material Modelling
Dielectric functions (at imaginary frequencies) were taken from Elbaum and Schick [19] using the data from Daniels [29] and labeled by ice JD and from Seki et al. [30] (ice SM ) for ice (ε 2 ) and from Elbaum and Schick [19] for water (ε 1 ). These dielectric functions are for a system at the triple point of water, close to zero degrees Celsius at low pressure. The final results for ice melting [19,20,21,22,23,31,32] and water freezing [33,34] are sensitive to the dielectric functions of ice and water since these are extremely similar when the water is in equilibrium with the ice. We show in Fig. 2 the dielectric functions for crystalline CO 2 , water and ice.
A model for the dielectric function of a gas hydrate (ε 3 ) is derived using the Lorentz-Lorenz model [35] with the mixing scheme specifically for gas hydrates taken from Bonnefoy et al. [36,37]
ε 3 = 1 + 2Γ 1 − Γ ,(5)
with
Γ = ε 2 − 1 ε 2 + 2 n wh n i + 4πα M n M 3 ,(6)
which means that the dominating factors for the dielectric function of gas hydrates are the ice polarisability weighted by density of water in the hydrate relative to pure ice, and the polarisabilities of different gas molecules weighted by their corresponding densities. The mass density of water in pure ice is 0.9167 g/cm 3 [38], giving the number density of water molecules in pure ice as n i = 3.06 × 10 −2 Å −3 . The number densities of gas molecules (n M ) and water molecules (n wh ) in different gas hydrate structures are tabled in Tab. 1 with the water/gas number density ratio
p = n wh n M .(7)
Quantum chemical calculations of dynamic polarisabilities at discrete frequencies were represented at arbitrary imaginary frequencies iξ by fitting to the oscillator model,
α M (iξ) = j α j 1 + (ξ/ω j ) 2(8)
A 5-mode fit has previously been found to describe the dynamic polarisability accurately to a 0.02% relative error [41]. The adjusted parameters for a 5-mode model for CO 2 , CH 4 , N 2 , and H 2 S are given in our recent work [42]. Quantum Table 1: Hydrate mass densities (ρ h ) and number densities of water (n wh ) and gas molecules (n M ) in different gas hydrates. The water/gas number density ratio is denoted p. Gas molecule Here we show these for the three CO 2 gas hydrates and the two CH 4 gas hydrates that we consider (the inset shows the same on a linear scale).
p ρ h (g/cm 3 ) n M (Å −3 ) n wh (Å −3 ) CO 2 ,
calculations on which the fits were based were taken at a coupled-cluster singles and doubles (CCSD) level of theory [43] using aug-cc-pVQZ basis sets [44].
Product of Reflection Coefficients
As can be observed in Eq. (2), the Casimir force is determined by the product of reflection coefficients at both interfaces, summed over all frequencies. Thus, the magnitude and sign is given by the balance of areas enclosed by these curves above and below the frequency axis. This behaviour is illustrated in Fig. 3, where the products of the non-retarded Fresnel coefficients (TM mode) are shown each given by
r i2 = ε i − ε 2 ε i + ε 2 .(9)
One can get insights from this quantity also in cases where retardation matter. Negative values for the product shown in Fig. 3 (larger in magnitude for CO 2 hydrates than for CH 4 hydrates) for high frequencies contribute to repulsion. The crossing point at 1.6 × 10 16 rad s −1 where r 12 r 32 = 0 corresponds to the frequency where the dielectric function of ice crosses that of pure water, seen in Figure 2. For nonretarded, small film thicknesses, the respective sum over all frequencies (with many more terms for high frequencies than for low frequencies) gives the net sign for the free energy of very thin ice films. Retardation favours the small-frequency contributions and hence screens out high frequency (repulsive) contributions for thicker ice films. It turns out that already for film thicknesses as thin as a few nanometers retardation is important for ice-water related systems [19]. The net sign in our case is not trivial, and we will demonstrate later that CO 2 and N 2 hydrates in water behave differently from CH 4 and H 2 S hydrates in water.
Results
Gas hydrate specific ice formation
While it is well known that water can start to freeze from its surface when the temperature goes to zero degrees Celsius, Elbaum and Schick [33] predicted that dispersion forces do not play a role in this mechanism. In fact, they found that a thin ice film on the surface would have its energy minimum for zero ice film thickness which would not result in surface freezing on open water surfaces. The underlying mechanism for why ice growth actually occurs at the surface is that large ice structures float with a certain fraction above a water surface due to the lower density of ice. In contrast to their results, we have found that buoyancy combined with dispersion and double layer forces establish an equilibrium where large ice particles float on the surface while small (micron-sized) ice particles are trapped at a distance below a water surface [45]. Further, it was shown that ice formation can be induced by dispersion forces near silica-water interfaces (where silica can be used as a model for rock material) [34]. Before presenting the gas hydrates, we first use the dielectric functions shown in Fig. 2 to perform calculations for the free energy for an ice film growing on an interface between crystalline CO 2 and ice cold water. We see in Fig. 4 that this three layer system has an energy minimum corresponding to an equilibrium ice film with thickness (d) between 3.3 nm and 3.9 nm, depending on the model for the dielectric function of ice. In the remainder of this letter, we use ice JD , the Daniels [29] model for ice, since both models give very similar results. The thicknesses correlate with the frequency where the dielectric functions of ice and water have a crossing [34]. Figure 5 shows the free energy as a function of ice film thickness for different gas hydrates in ice cold water. Ice films are predicted for CO 2 hydrates (d=44, 43 and 37 Å for volume fractions p = 5.75, 6 and 7.67, respectively) and for the N 2 hydrate (d = 32 Å) but not for any of the CH 4 or H 2 S hydrates. In the former cases, retardation plays a role at the nanometer scale as it is the reason for the change in the sign of the Lifshitz energy. This model is sensitive to the various dielectric functions which are involved in the system [46]. While the results are model dependent for the specific combination of materials used, the clear trend is that interfacial ice caps can exist at some gas hydrates in ice cold water, but not for others.
The stark difference in behaviour between CO 2 or N 2 hydrates and CH 4 or H 2 S hydrates can be understood from differences in gas polarisability in the optical/UV spectrum, combined with the difference in the dielectric spectra of water and ice. These are expressed in the maximum and minimum seen in the product of reflection coefficients in Figure 3. The positive value of the product r 12 r 32 at low frequencies contributes to stabilisation of the water interface towards the hydrate interface, i.e., wetting, with removal of the ice layer. Negative values at high frequencies destabilise the water interface, i.e., stabilise the ice layer. The overall behaviour is a balance between these two regimes. As discussed above, the positive and negative regimes ultimately derive from the reflection coefficient r 12 between liquid water and ice, that is from the crossing in the dielectric functions of ice and cold water at 1.6 × 10 16 rad s −1 seen in Figure 2. The effect of the hydrate (via reflection coefficient r 32 ) is to strengthen or attenuate r 12 . Figure 3 shows that the high frequency stabilisation of the ice layer is weaker for CH 4 and N 2 than for CO 2 at all hydrate ratios, while H 2 S is only weaker than CO 2 at higher water/gas ratios. At low frequencies, destabilisation of the ice layer is much stronger for H 2 S than CO 2 , while weaker for N 2 . In the balance between low frequency destabilisation and high frequency stabilisation of the ice layer, high frequencies dominate for CO 2 , but are insufficiently weak for CH 4 . In the case of N 2 , low frequency behaviour is weaker than for other gases, so again high frequency stabilisation of ice dominates. In the case of H 2 S, low frequency destabilisation of the ice layer is stronger than for CO 2 and dominates over high frequency stabilisation. These patterns follow the underlying polarisabilities of the gas molecules, see Figure 6: the polarisability of CH 4 is weaker than CO 2 at all frequencies. The polarisability of H 2 S is significantly stronger than CO 2 at low frequencies, but drops rapidly at high frequencies, crossing CO 2 to respond similarly to CH 4 in the UV spectrum. The polarisability of N 2 is much weaker than other gas molecules, in particular, is much closer to the polarisability of a water molecule. The polarisability per ice molecule is shown in Figure 6 for comparison. This results in an N 2 gas hydrate dielectric function closer to that of ice, leading to a smaller reflection coefficient. Stabilisation of the ice layer at a hydrate surface is determined predominantly from the polarisability of the gas molecule relative to a water molecule in the optical spectrum around 3 × 10 15 rad s −1 (stabilising water wetting) and in the UV spectrum around 3 × 10 16 rad s −1 (stabilising the ice layer).
Size dependence for floating of gas hydrate clusters
Buoyancy of gas hydrate particles is of considerable importance for understanding the distribution and composition of ices, water and gases in subglacial water bodies in Antarctica and on ocean bearing moons of our solar systems and extra solar planets. Buoyancy of gas hydrates on these water bodies depends on hydrate density and assumed ocean densities.
Lake Vostok, located 4 km below the Antarctic surface, is an analogue of deeper subglacial oceans the Jovian and Saturnian moons and is a notable target for astrobiological studies. McKay et al. [12] suggest the observed lack of gas hydrates accreted at the top of Lake Vostok in Antarctica (density 1.016 g cm −3 ) is consistent with formation of relatively dense CO 2 clathrate hydrates that sink to the lake floor. Mousis et al. (2013) later estimated the densities of type I and II clathrate CO 2 hydrates in Lake Vostok, concluding that CO 2 -containing type I clathrates sink above a critical CO 2 composition in the lake. et al. [15] discuss the buoyancy of CO 2 hydrates using two further density estimates of the oceans of Europa (density 1.016 g cm −3 ) and Enceladus (1.003 g cm −3 ) and used measured gas hydrate densities. Bouquet et al. [9] consider the buoyancy of multiple guest clathrates on Enceladus using a calculated high pressure sea water density of 1.030 g cm −3 , concluding the type I clathrates are marginally denser (1.040 g cm −3 ) than the sea water and type II significantly lighter (0.970 g cm −3 ). Figure 7 shows the average densities of gas hydrate particles of varying radius, each compositional variant coated in a layer of ice of thickness determined by the polarizability and amount of the entrapped gas species. These were calculated using equation 10 below. The equilibrium ice film thicknesses and densities are given in the text immediately below Figure 5. The value used for the density of pure ice was 0.9167 g cm −3 . Horizontal lines represent the estimated or measured density of the ocean/sea water on the various bodies.
It is quite apparent that for CO 2 gas hydrate particles, which are otherwise denser than most models for the water on Enceladus or in Lake Vostok, an equilibrium ice layer of the order of several nm has a significant impact on the buoyancy of the particles. When the radii of these is below approximately 20-100 nm, the average density drops below values estimated for the ocean water density on Enceladus and consequently will float. We use the following simple expression for the average density of a ice coated gas hydrate cluster (approximated as a sphere),
ρ av = ρ h r 3 h + ρ i [(r h + d) 3 − r 3 h ] (r h + d) 3 .(10)
Here ρ av is the average density of mixed particle comprising a clathrate hydrate core and a shell of water ice, ρ h densities are given in Tab. 1 for different gas hydrates, ρ i is given for ice above, and r h the radius of a gas hydrate cluster. Finally, d is the approximate thickness of each ice film at planar water-CO 2 gas hydrate and water-N 2 gas hydrate interfaces given above.
Conclusions
In analogy to the premelting layers of ice [19,23,22], we found that freezing of gas hydrates in ice cold water is caused by an energy minimum in dispersion energies. This is not expected at water surfaces [33] but predicted to occur at some water-solid interfaces [34]. We find that a significant difference between different gas hydrate surfaces in water lies in whether they are coated with a nano-sized interfacial ice cap or not. The result is sensitive to the details in the dielectric functions of the materials involved. However, our results indicate that some hydrates are more likely to have interfaces that are kept dry by an interfacial ice cap. We have seen this trend for three different volume fractions of CO 2 hydrates in water as well as for N 2 hydrate and crystalline CO 2 in water. Other hydrates, CH 4 hydrate in water, are more likely to stay wet and have no interfacial ice cap.
A review [47] a few years ago asked the question if gas hydrate surfaces in air are dry or wet. Our results are consistent with gas hydrate surfaces that are in equilibrium with water molecules in vapor phase. If a film of water is adsorbed on a gas hydrate surface, much thicker than say 10 nm, then our calculations can be extended to predict that a fraction of that water will form an interfacial ice layer between the water film and the surface of the CO 2 (or N 2 ) hydrates but not so for CH 4 (or H 2 S) hydrates. These differences for materials, whether their interfaces stay dry or wet, are expected to influence the fluxes of gas molecules into the liquid water and then further towards the surrounding atmosphere. Further, as we discussed above a dry surface may affect the growth and overall density of gas hydrate crystals. The density of type I CO 2 hydrate crystal densities are similar to that predicted for different ice coated ocean waters on Earth, Enceladus and Europa [12,13,14,15,9]. The density values in Tab. 1 for CO 2 hydrate suggest a water ice cap layer could make a significant difference in buoyancy when hydrate crystals have diameters in the range of approximately 20-100 nm, based on the 3-4 nm ice films we predict. Indeed if a layer of interfacial ice cap grows on a hydrate crystal early after nucleation, its growth may be restricted to such small sizes, leading to the formation of nanoscale, ice-capped CO 2 hydrate crystals with positive buoyancy.
Besides the requirement of accurate dielectric functions for quantitative predictions of such ice layer thicknesses, the restriction to interactions caused by dispersion forces yields a source of uncertainties. For non-polar systems, it would be sufficient to neglect electrostatic effects. However, water is a polar medium, thus interactions caused by permanent dipole moments will also play a role and will shift this theory to a more precise one. The extension of the theory of dispersion forces to include permanent dipole moments is of current interest for several groups and will also be part of further investigations. However, a simple estimation of such effects shows a small contribution to the dispersion forces which is smaller than in the vacuum case due to the shielding effect of the environmental medium.
We have notably shown that the above-mentioned density dependence of the gas hydrates induce a sinking or floating of the particles which is important for carbon capture and storage via gas hydrates [48]. The creation of an interfacial ice layer modify the average density of the particle, thus the buoyancy that determines the floating or sinking of the particle. When studying very small gas hydrates, the particle's curvature may be expected to play a role. It can easily be incorporated into theory by changing the geometry from a planar to a spherically layered system. However, since the size of the gas hydrate clusters are much larger than the predicted ice film layer a planar approximation is expected to give useful estimates. Such investigations will also effect the description of crystallization processes in particular for cloud creation [49] by treating the gas hydrate as cloud condensation nuclei.
Figure 2 :
2(Color online) The dielectric functions of crystalline CO 2[31], both ice models and water[19] at 273.16 K.
Figure 3 :
3(Color online) Product of the non-retarded reflection coefficients for the two interfaces.
Figure 4 :
4(Color online) The free energy per unit area (at 273.16 K) as a function of ice film thickness on the boundary between the surface of a crystalline CO 2 structure and liquid water. It is predicted that at equilibrium an ice film around d = 33 Å for the ice model from M. Seki et al. and d = 39 Å for J. Daniels' model.
Figure 5 :
5(Color online) The Lifshitz free energy per unit area (at 273.16 K) for a flat three-layer system (water-ice-gas hydrate) as a function of the ice film thickness d. For CO 2 gas hydrates and the N 2 gas hydrate, energy minimum exist corresponding in each case to an equilibrium ice film thickness: d CO2 =44, 43 and 37 Å for CO 2 volume fractions p = 5.75, 6 and 7.67, respectively, and d N2 =32 Å.
Figure 6 :
6(Color online) Polarisabilities of gas molecules at imaginary frequencies. The polarisability of a water molecule in ice is also shown for comparison.
Figure 7 :
7(Color online) The average densities of gas hydrate particles of varying radius for CO 2 hydrates with density fraction p = 5.75 (solid black line), p = 6.0 (dotted red line) and p = 7.67 (dashed blue line) and N 2 with p = 6.0 (dotted magenta line), each compositional variant coated in a layer of ice of thickness determined by the polarizability and amount of the entrapped gas species as specified above. As comparison we show the water densities in different systems. References for the water/gas number density ratios p are given in Tab. 1.
Prieto-Ballesteros et al.[13] considered buoyancy of type I CO 2 , SO 2 , CH 4 and H 2 S gas hydrates (space group 223) on Europa, where two extreme models for the density of the ocean water were considered, namely a eutectic brine of composition MgSO 4 -H 2 O system with density 1.19 g cm −3 and a low salinity water ocean of density 1.0 g cm −3 . Safi
DisclaimerThis document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in ACS Earth and Space Chemistry, copyright c American Chemical Society after peer review. To access the final edited and published work see:https://doi.org/10.1021/acsearthspacechem.9b00019
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| sample_539 | 0.5793 | arxiv | |
Sustainable AI Regulation
Philipp Hacker
Sustainable AI Regulation
Working Paper (this version June 1, 2023) Early draft for PLSC, footnotes missing * Prof. Dr. Philipp Hacker, LL.M. (Yale), Chair for Law and Ethics of the Digital Society, European New School of Digital Studies, European University Viadrina Frankfurt (Oder).
Current proposals for AI regulation, in the EU and beyond, aim to spur AI that is trustworthy and accountable. What is missing, however, is a robust regulatory discourse and roadmap to make AI, and technology more broadly, environmentally sustainable. This paper aims to take first steps to fill this gap.In computer science, AI and technology more generally are increasingly recognized as important contributors to climate change. And with good reason: Current estimates show that information and communication technology (ICT) contributes up to 3.9% of global greenhouse gas (GHG) emissions compared to roughly 2.5% for global air travel. The carbon footprint of machine learning more specifically has skyrocketed over the last years. Water consumption is another crucial factor. Regarding both energy and water, AI training is particularly resource intensive, and even more so with large generative AI models, such as ChatGPT or GPT-4.However, questions of climate change and sustainability still occupy a significant blind spot in AI regulation. This paper will therefore explore two key dimensions: legal instruments to make AI greener; and methods to render AI regulation more sustainable. Concerning the former, transparency mechanisms, such as the disclosure of the GHG footprint under Article 11 AI Act, could be a first step. However, given the well-known limitations of disclosure, regulation needs to go beyond transparency. Hence, in this paper, I propose a mix of co-regulation strategies; sustainability by design; restrictions on training data; and consumption caps.Within sustainability by design strategies, one important mechanism could be what I term "sustainability impact assessments". Crucially, during the modelling phase, developers should compare different AI model types (e.g., linear regression versus neural networks) not only regarding their performance but also their estimated GHG footprint. Already, effective tools exist to measure the GHG impact of such models. Simply put, if two model types exhibit similar performance, the developers would be obliged, under such a provision, to choose the more sustainable model for further development and deployment. In this way, the current fixation on performance measures may be complemented by climate change mitigation strategies. Importantly, pre-trained models, such as large AI models, may in the long run be more energyefficient despite their high upfront training costs. However, ironically, planned regulation might thwart these efforts. Pre-trained models, such as ChatGPT, are significantly dis-incentivized by the EU AI Act and the EU AI liability directives. Hence, regulatory endeavors should urgently be updated to better reflect the sustainability challenges AI raises.This regulatory toolkit may then, in a second step, serve as a blueprint for other information technologies and infrastructures facing significant sustainability challenges due to their high GHG emissions, for example: blockchain (e.g., bitcoin); Metaverse applications; and data centers. The regulatory toolbox described above, from transparency to sustainability
II assessments and hard consumption caps, can and must be flexibly adapted to these other areas of technology law.
The final dimension consists in efforts to render AI regulation, and by implication the law itself, more sustainable. Certain rights we have come to take for granted, such as the right to erasure (Article 17 GDPR), may have to be limited due to sustainability considerations. Imagine that a large AI model was trained on supposedly anonymized medical data and is used for cancer detection. Given new re-identification techniques, one data subject exercises her right to erasure. Not only may her data point have to be deleted from the training data, but the entire AI model may have to be re-trained-entailing significant GHG emissions. In my view, the subjective right to erasure, in such situations, has to be balanced against the collective interest in mitigating climate change. Here, I draw on the growing literature on data externalities and third-party effects of processing. The paper formulates guidelines to strike this balance equitably, discusses specific use cases, and identifies doctrinal legal methods for incorporating such a "sustainability limitation" into existing (e.g., Art. 17(3) GDPR) and future law (e.g., AI Act). Ultimately, law, computer science and sustainability studies need to team up to effectively address the dual large-scale transformations of digitization and sustainability. I.
III
Introduction
The next generation of AI systems is currently developed under the name of large generative AI models (or foundation models). 1 These involve popular applications like ChatGPT, GPT-4, or DALL-E 2. Training such models is complex and resource intensive. 2 Significantly, not only do they demonstrate the vast transformative potential of AI for society, 3 but they also underscore palpable and emerging risks posed by AI. 4 In this article, the focus will be on a crucial risk dimension that has hitherto been under-appreciated in the legal literature and regulatory: AI scholars are increasingly sounding the alarm on the contribution of machine learning to climate change because of its energy 5 and water consumption. 6 AI regulation therefore, arguably, needs a paradigm change: from trustworthy 7 to sustainable AI 8 regulation.
This paper takes first steps into this direction. In doing so, it seeks to move beyond the state of the art in three specific respects. First, it tackles specific regulatory challenges triggered by the advent of large generative AI models, 9 such as ChatGPT or GPT-4, which have so far received 1 See, e.g., Mark Chen and others, 'Evaluating large language models trained on code' (2021) arXiv preprint arXiv:210703374 ; Rishi Bommasani and others, 'On the opportunities and risks of foundation models' (2021) arXiv preprint arXiv:210807258 . Terminologically, foundation models are trained on large data at scale and are able to tackle diverse tasks; they can be adapted to diverse downstream use cases (ibid, 7). Large AI models overlap mostly-but not fully-with this definition. They typically contain several billion parameters, are trained on large datasets, and require significant compute infrastructure Joerg Bienert et al., Large AI Models for Germany: Feasibility Study (2023); specifically, generative models output content addressed towards communication, e.g., text, images, videos, or music, see, e.g., Patrick Meyer, 'ChatGPT: How Does It Work Internally?' Towards AI <https://pub.towardsai.net/chatgpt-how-does-it-work-internally-e0b3e23601a1> accessed January 30, 2023. The terms "large generative AI model" (LGAIM) and "foundation model" are used interchangeably in this paper unless specifically differentiated. 63-66. 9 "Large" refers to the number of parameters in the model (> 10 billion), the amount of training data, and the size of the necessary compute infrastructure for training; many, but not all, large AI models are generative, creating text, videos, images etc.; see, e.g., Bienert et al., LEAM Report (2023), 31-32 and n. 1. scant attention in the legal literature. 10 Second, it ventures beyond existing research paradigms to develop a comprehensive legal framework for addressing the growing importance of AI for environmental sustainability. In legal scholarship, the implications of the law for climate change, and vice versa, are increasingly discussed in the general legal literature. 11 Nonetheless, for AI regulation more specifically, questions of climate change and sustainability still occupy a significant blind spot. 12 In this domain, an interdisciplinary lens is necessary to tease apart the differential impact of machine learning modelling choices for, e.g., greenhouse gas (GHG) emissions and water consumption, and to suggest a pertinent regulatory framework. For example, it will often make a profound difference, in terms of the GHG footprint, if the developer uses a simple linear regression model or a complex, much more compute-intensive deep neural network. 13 The advent of large AI models, such as GPT-4, which are pre-trained once and may then be adapted to many different use cases, may change that equation, though: while their training is highly resource-intensive, 14 they may in fact harbour potential sustainability advantages in the long run by "replacing" a large number of smaller models. 15 In this context specifically, I will draw on a growing literature investigating the intersection of computer science, and machine learning more specifically, on the one hand and climate change on the other. 16 Against this background, second, the article reviews the EU AI Act, which is currently in the midst of the legislative process, regarding its sustainability requirements -which have, in fact, just been updated by the European Parliament (EP) in its latest vote on the Act (AI Act EP 3 Version). 17 The EP, however, chiefly focuses on soft rules, 18 such as lofty principles, 19 voluntary codes of conduct, 20 green labels, 21 and disclosure rules. 22 The paper goes beyond these suggestions to propose a number of policy options necessary to align AI development with sustainability, ranging from co-regulation instruments to sustainability by design and restrictions on AI training to consumption caps based on an AI model social utility. The article then uses the toolkit developed for sustainable AI regulation to envision a blueprint for sustainable technology regulation more broadly, for example in the context of blockchain, data centers, or the metaverse.
In the third step, I enquire into the specific challenges raised by the current climate crisis for technology law and, potentially, the law more generally: the article asks to what extent sustainability considerations may limit, or strengthen, certain subjective rights, such as the right to erasure, that we have come to take for granted. Overall, the article seeks to deliver the first comprehensive account of sustainable AI regulation -in the decidedly dual sense of making AI (and technology more broadly) and the law covering AI (and beyond) more sustainable.
More specifically, the remainder of the article is structured as follows. Part II provides an accessible introduction to the benefits as well as potential risks of AI, with a focus on the environmental dimension. The core topics of the article unfold in Parts III-VI. Here, the paper explores two key dimensions: legal instruments to "green" AI, both under the AI Act (Part III) and with respect to a number of policy proposals (Part IV). I will then briefly turn to digital technology more broadly to show how sustainable AI regulation may serve as a blueprint for solving urgent climate change issues raised by soaring GHG emissions other digital technologies, such as blockchain, the metaverse, and data centers (Part V). Finally, the paper considers methods to render AI regulation, and the law more generally, more sustainable (Part VI). The last section concludes (Part VII)..
II. AI and sustainability
AI and classical AI risks
In a nutshell, computer scientists continue to disagree on the concept of AI, with one leading definition referring to AI as computer programs that emulate human, rational behavior and thinking. 23 The concept of AI was one of the two main divisive questions which led to the delay of the AI Act in the EU Parliament.
What is certain, however, is that AI confers tremendous opportunities to our societies, 24 but also harbors several serious risks. 25 Classical risks associated with AI include a range of specific 17 characteristics. 26 First, the need for training data raises significant challenges for data protection and privacy. Second, deep learning systems in particular are opaque and it is difficult to explain why they generate a specific output. Third, due to their reliance on data, which may encode social and historical biases, AI are prone to exacerbate patterns of discrimination. Fourth, learning capabilities (machine learning) may lead to unforeseeable output and actions. Previous scholarship in AI regulation has largely focused on these four risks, 27 which are compounded by the growing interconnection between data, models, and applications. Indeed, these four risks need to be addressed by any AI labeled trustworthy. Fifth, large generative AI models in particular may take manipulation, fake news, and hate speech to unprecedented levels by automated mass generation, if not properly reined in. 28 This is another topic now addressed by a growing body of legal research. 29
Another perspective: environmental risks
Beyond theses more traditional risks, however, an increasing body of research points to environmental risks posed by AI training and deployment. 30 Current research operates with a threefold concept of sustainability, branching out into economic, social, and environmental aspects. 31 While these are all important goals, the present paper will focus on the IT law implications of environmental sustainability, which is key to solving the current climate crisis.
Why environmental sustainability?
The current climate crisis arguably poses an existential threat to the human species, at least when compared to the rather benign living conditions that have reigned for centuries in many regions of the world. Despite efforts by scientists, civil society, and policymakers, no clear legislative path or collective action scheme has emerged to date that would likely prevent crossing the threshold of 1.5°C of global warming, compared to the pre-industrial era. Hence, new approaches are needed that go beyond the traditional, but so far largely ineffective international climate summits and individual initiatives of certain climate-progressive states.
Effectively, in my view, every legal field-just like every industrial, administrative or consumption sector-will have to chart paths across its own territory to map possible contributions to the collective effort of mitigating climate change. Information and communication technology (ICT), and the concomitant field of IT law, are particularly well positioned to lead this effort as ICT arguably has an important role to play concerning both the mitigating at the contributing side of climate change, and the legal field is promisingly interdisciplinary in its general approach. 26
a) Promises to mitigate global warming
ICT more generally and AI particularly may be harnessed to combat climate change in various ways. This is an active field of research in various technical disciplines. It has resulted in numerous theoretical and empirical contributions demonstrating how a reduction of energy, water and material consumption can be achieved by bringing AI applications to bear on questions of project planning, documentation, and implementation. 32
b) Contributions of ICT and AI to climate change
In computer science, AI and technology more generally are increasingly recognized as important contributors to climate change. 33 And with good reason: Current estimates show that IT contributes up to 3.9% of global greenhouse gas (GHG) emissions 34 -compared to roughly 2.5% for global air travel. 35 The carbon footprint of machine learning more specifically has skyrocketed over the last years. 36 AI training is particularly resource intensive, both in terms of energy and water usage, and even more so with large AI models. 37 However, running a large AI model, such as GPT-4, also comes with sustainability costs. It not only consumes energy, but also significant amounts of water for cooling the data centers hosting the model: recent estimates posit that a standard conversation with ChatGPT consisting of 20-50 questions and answers consumes roughly the content of a 500ml bottle of water, depending on the circumstances of deployment. 38 Given the large number of conversations ChatGPT has powered since its inception, this adds up to a highly significant amount of water-an increasingly scarce resource in many parts of the world. Hence, regulatory guidance is arguably needed to make AI and technology more sustainable.
III. Sustainable AI and the EU AI Act
In the general legal literature, a growing discussion exists about the interrelated impacts of climate change on the law, and vice versa. 39 However, for AI regulation more specifically, 6 questions of climate change and sustainability still occupy a significant blind spot. 40 "The uptake of AI applications is beneficial for the environment," the Commission laconically concludes. 41 While AI does have a role to play here, 42 this analysis is dangerously one-sided and ignores recent developments in computer science reviewed above, suggesting a highly significant and rapidly growing contribution of AI, and ICT, to GHG emissions.
This section of the article will therefore explore how existing or forthcoming legal instruments may render AI more sustainable. As a key example, let us turn to the EU AI Act (for the GDPR, see below, Part VI.1.). Under the General Approach adopted by the Council of the EU on December 6, 2022 (AI Act Council Version), 43 the European legislator only encourages voluntary codes of conduct concerning environmental sustainability (Art. 69(2) AI Act, Council General Approach). Quite evidently, the General Approach fails to adequately tackle the issue of environmental sustainability.
However, significant progress was made on May 11, when two key committee votes 44 cleared the path for amendments to the AI Act by the European Parliament (AI Act EP Version 45 ). While the EP Version goes further in addressing environmental concerns, it still falls short of taking sufficient action. The amendments contain different sets of rules concerning sustainability. I will structure my analysis around five pillars: goals and principles; preferential access to research funding and sandboxes; information approaches; risk assessment; and guidance and review.
The first one focuses on goals and principles. Article 1 AI Act EP Version sets out the general objectives of the regulation, the prevention of including harm to the environment. Furthermore, environmental sustainability figures prominently among the new principles for AI development and deployment (Article 4a(1)(f) AI Act EP Version). However, arguably, they lack the necessary regulatory teeth to incentivize meaningful action. The Act, in these sections, sets lofty goals without providing concrete measures to ensure their implementation. If, eventually, the principles become part of the enforceable rules-such as the data protection principles in Article 5 GDPR 46 -then indeed they might qualify as backup rules offering a last resort in case some system circumvents specific AI Act rules, meeting requirements by the letter but violating them in spirit.
The second pillar concerns funding and support. It channels the provision of preferential access to research funding and sandboxes for AI systems promising to make a positive impact on the environment, as outlined in Article 54a. This provision aims to encourage the development of AI systems that prioritize environmental sustainability. However, further details and mechanisms for implementation are required to effectively promote these objectives; moreover, 7 to develop truly groundbreaking AI systems in the range of foundation models, significantly more funding in the provision of computer infrastructure will be necessary. 47 Information approaches are emphasized in the third pillar. Article 12(2a) AI Act EP Version requires the measurement and calculation of resource use and environmental impact throughout the lifecycle of high-risk AI systems, including energy consumption. Article 11 in conjunction with Annex IV 3(b) AI Act EP Version mandates the disclosure of energy consumption information during development and use, considering relevant Union and national legislation. Importantly, and rightly, the Commission is charged to develop a methodology for calculating Key Performance Indicators and references for the Sustainable Development Goals (SDGs), including environmental impact (Recital 46b; see also Recital 87a AI Act EP Version). Harmonized standards according to Article 40 will be essential to effectively compare and evaluate the environmental impact of different AI systems.
While transparency mechanisms such as logging and disclosing the greenhouse gas (GHG) footprint under Articles 11 and 12 are a step in the right direction, numerous studies indicate that standard disclosures are often ignored by recipients. 48 Nevertheless, such mechanisms can be beneficial for non-governmental organizations, information intermediaries, and regulatory agencies seeking to collect data on the environmental impact of AI systems.
The fourth pillar encompasses risk assessment, specifically addressed in Article 28b(2)(a) AI Act EP Version. Providers of foundation models need to assess and mitigate, and ultimately manage throughout the lifecycle (Article 28b(2)(f) AI Act EP Version), foreseeable risks not only with respect to health, safety, fundamental rights, democracy and the rule of law, but also the environment. While, as I have spelled out in detail elsewhere, 49 risk assessment and management should generally relate to specific use cases, addressing sustainability risks at the level of the model itself seems reasonable indeed: it is here that most resources for equipment and training are used, and where sustainable practices may have a large impact that propagates down the AI value chain. However, the provision needs to be suitably operationalized. The proposal made below concerning sustainability by design and sustainable impact assessments (see Part IV.0.) precisely ties into this risk management framework.
The fifth pillar involves guidance and review. Article 82b(1)(viii) AI Act EP Version calls for guidance by the European Commission on the practical implementation of environmental impact measurement and reporting methods, including carbon footprint and energy efficiency. However, Article 84(3)(bf), which pertains to review and potential update requirements, lacks specificity and does not prioritize urgent environmental concerns adequately.
Notably, there is a missing pillar in the EU AI Act: operationalizing sustainable ambitions and translating them into effective action. While the Act addresses various aspects, it fails to provide a comprehensive framework that actively promotes meaningful action to address the climate change impact of AI. Thus, in my view, the proposed AI Act EP Version still inadequately addresses the environmental consequences of AI.
IV. Policy proposals: sustainable AI regulation going forward
The preceding analysis has shown that current EU law, despite some promising steps in the latest version of the AI Act endorsed by the European Parliament, does not adequately address the climate risks posed by AI systems. In the following section, this article introduces and 47 Cf. al discusses for policy proposals, ranging from co-regulation instruments to sustainability by design and restrictions on AI training to consumption caps based on an AI model social utility.
Co-regulation
A first potential approach to regulating the use of AI and its impact on sustainability is through tools of co-regulation that have also been introduced in the GDPR. For example, Article 69 AI Act already encourages, as seen, the adoption of industry codes of conduct. These codes serve as voluntary agreements or standards developed and embraced by relevant stakeholders, such as companies, associations, or professional bodies, to guide their behavior and practices regarding AI. 50 For instance, the GDPR encourages the creation of codes of conduct to promote sector-specific data protection rules (Art. 40 GDPR). These codes may eventually be approved by national data protection authorities or even the Commission and thus be acquired general validity in the EU (Article 40(9) GDPR). Such a provision formalizing administrative oversight and endowing a limited binding effect on codes of conduct is missing in the AI Act and should be added to make them an attractive instrument, similar to a safe harbor provision in a legal act.
The key advantage of industry codes of conduct is their ability to harness the distributed knowledge and expertise of the various actors involved in the design, development, and deployment of AI systems. They can promote innovation and flexibility by allowing for customized solutions that are tailored to specific contexts and sectors, making them adaptable to evolving circumstances and needs. Additionally, they can enhance trust and legitimacy by demonstrating the industry's commitment and responsibility in addressing the ethical and social challenges posed by AI.
However, industry codes of conduct also have their drawbacks. One of these is the potential lack of sufficient incentives for compliance, particularly when effective monitoring and enforcement mechanisms are absent. Additionally, there is a risk of regulatory capture or fragmentation, as different groups or regions may adopt diverging or conflicting standards, which could undermine the coherence and consistency of the regulatory framework. Furthermore, these codes may not adequately represent the interests and values of all affected parties, such as consumers, workers, or civil society organizations, who may have limited participation or representation in the code development process. Similar arguments may be raised concerning sustainability seals (cf. Art. 42 GDPR). While they may also gain industry support and even provide guidance to downstream companies and consumers, there is a distinctive risk of industry tailoring certification mechanisms to their needs in order to facilitate "greenwashing". Such a provision is currently missing entirely in the AI Act and should be introduced. However, it will be crucial to ensure proper oversight of the certification mechanism to prevent opportunistic behavior by AI developing companies.
Therefore, industry codes of conduct related to sustainable AI and sustainability seals should not be viewed as a replacement for legal regulation. Instead, they should be seen as complementary measures that can enhance the effectiveness and legitimacy of AI governance. It is essential that these codes and seals undergo regular review and evaluation to ensure their ongoing relevance, reliability, and responsiveness to the evolving challenges and opportunities presented by the climate effect of AI.
Sustainability by design
A second and, in my view, more promising proposal is to integrate a requirement of sustainability by design into the AI Act. Inspired by the principle of data protection by design, which requires the integration of data protection safeguards into the design and operation of 50 Thilo Hagendorff, 'The ethics of AI ethics: An evaluation of guidelines' (2020) 30 Minds and Machines 99. information systems, sustainability by design aims to embed environmental considerations into the design and implementation of ML models and practices. As I will argue, a key tool for achieving this goal are sustainability impact assessments.
a) From data protection to sustainability by design
Over the past decades, data protection law has arguably taken a compliance turn. 51 Data controllers not only need to answer to data subjects exercising their subjective rights, and agencies nudging inquiries, but have to establish technical and organizational routines to ensure data protection compliance even in the absence of individual and administrative proceedings (Art. 24 et seqq. GDPR). This is based on the correct assumption that subjective rights, and administrative inquiries, often come too late and are exercised too rarely to effectively protect data protection principles and data subject on the ground. One of the most notable provisions embodying this compliance term is the principle of data protection by design and default (Article 25 GDPR). Data protection, in this way, is converted from a mere reactive tool of expost control to a proactive instrument of ex-ante design.
As political scholars have pointed out repeatedly, however, civil liberties and freedoms, such as data protection, are essentially worthless if their grantees lack the material resources to exercise them and to flourish in the protective frame afforded by them. 52 This limitation resurfaces with renewed urgency in the current climate emergency. While the capabilitarian tradition rightly stresses access to basic amenities and resources, even these preconditions of the enjoyment of subjective rights are threatened for a growing number of persons by hostile environmental conditions as a result of climate change.
Hence, in my view, data protection by design needs to be complemented by "sustainability by design". At the technical and organizational level, developers need to ensure that all reasonable levers are pulled to minimize the contribution of ICT to climate change. Such a paradigm change has been explored for consumption practices 53 and product design 54 in the literature, and is increasingly translated into the practice of supply chain management and other industrial sectors for the pursuit of corporate ESG goals. 55 Building on these approaches, sustainability by design should also become a leading principle in the governance and regulation of the ICT sector. If we cannot the climate crisis, data protection by design will ultimately be a futile effort, a luxury game played out in a few privileged jurisdictions whose citizens-or courts and regulators-may still afford to care about data protection and privacy.
b) Sustainability impact assessments
As always with "by design" principles, the devil is in the details of implementing such ideals in concrete technologies and practices. In the context of AI regulation more specifically, mandatory sustainability impact assessments may be effective instruments to firmly integrate climate change considerations into the development of AI models. 56 55 See, e.g., https://www.bcg.com/press/10february2022-bcg-cdp-build-tech-platform-scope-3-data-acceleratedecarbonization;
https://www.accenture.com/us-en/services/sustainability/sustainability-by-design; https://www.designorate.com/principles-of-sustainable-design/. 56 See also Hacker, 'The European AI Liability Directives -Critique of a Half-Hearted Approach and Lessons for the Future', 63 et seqq. on a large literature, and practical experience, concerning data protection, 57 social, 58 and algorithmic impact assessments. 59 While impact assessments are not a silver bullet 60 and embody important normative and design choices, 61 they do provide a promising route toward operationalizing sustainability considerations in the design and deployment of AI models.
More specifically, a mandatory sustainability impact assessment (SIA) should be a key component of the AI Act. Indeed, the EP has added such wording for high-risk models (Art. 9(2(a) AI Act EP Version) and for foundation models (Art. 28b(2)(a) AI Act EP Version). Both provisions call, inter alia, for a risk assessment and mitigation measures concerning environmental risks. While they present a step in the right direction, they should be simultaneously narrowed and expanded. First, Art. 28b(2)(a) AI Act EP Version should be restricted to an assessment of environmental hazards-the GHG emissions and water consumption are the main risks which already materialize during the training of foundation models, before their actual deployment in real uses cases. 62 Any mistakes in this domain will inevitably propagate down the AI value chain. Other risks, e.g., to health, safety, and fundamental rights, are generally best addressed at the application level. 63 However, the analysis of environmental risks more specifically should not be limited to high-risk (Art. 9(2)(a) AI Act EP Version) or foundation models (Art. 28b(2)(a) AI Act EP Version) only. Rather, the SIA should apply to developers of both high-risk and non-high-risk AI systems: the carbon footprint of AI systems is unrelated to their level of risk regarding health, safety, or fundamental rights, or their integration in Annexes II and III.
As part of the SIA, during the modeling phase, developers should compare different model and design types-such as linear regression versus deep learning, 64 federated versus non-federated learning, 65 or the use of a pre-trained models versus the training of a new model from scratch 66 -not only in terms of performance but also considering their estimated climate footprint. 67 As in the establishment of a design defect under product liability law, 68 only models and designs that are reasonably available to the developer, considering cost and utility, need to be integrated into the SIA.
Obviously, such a constraint depends on the availability of approximating and comparing the GHG emissions of different models and design choices. 69 Fortunately, tools already exist to measure the carbon impact of AI models. 70 Simply put, if two model types demonstrate similar performance, developers would be obliged under the new provision to choose the more sustainable model for further development and deployment. This approach would supplement the existing focus on performance measures with greater environmental awareness and practical, low-maintenance steps to integrate sustainability into the broader target function of ML development.
In fact, sustainability and performance may often align synergistically in many scenarios. One current trend in machine learning involves the utilization of pre-trained models, 71 such as ChatGPT or GPT-4. These models are initially trained on general data for a specific task class, such as image 72 or speech recognition 73 , and subsequently fine-tuned by developers using domain-specific data for a specific problem. 74 Pre-trained models not only exhibit superior performance and have become the state-of-the-art architecture for numerous tasks, 75 but may also consume less energy overall since the pre-training process needs to be performed only once for multiple model deployments. 76 However, ironically, regulations may hinder these efforts. The most powerful pre-trained models, including foundation models, are precisely the ones that the current version of the AI Act and AI liability directives discourage in their development. 77 Hence, as I have explained in detail elsewhere, the AI Act's rules on foundation models 78 and the concomitant liability 12 provisions 79 need to be adapted to the specificities and complexities of foundation models, such as GPT-4.
Restrictions on training AI models
One further entry point for a regulation is the time, location and type of training large AI models undergo. As mentioned, the large number of iterations necessary to calibrate state-of-the-art machine learning models consumes significant amounts of energy-leaving a large GHG footprint-and freshwater. A recent paper has shown how the GHG emissions of AI training might be lowered by (requiring) a shift to regions where large amounts of renewable are available to power AI training. Generally, this might lead to policy where AI developers might be bound to conduct training only at facilities that derive a certain percentage of their energy from renewable sources.
The devil, however, is in the details. One particularly attractive move to raise the renewable energy percentage would be to "follow the sun", i.e., to conduct training in regions with excellent opportunities for photovoltaic production of energy. Incidentally, these regions may also, precisely because of their sun exposure, exhibit higher average temperatures-leading to greater water needs to cool data centers. 80 Hence, factoring water consumption into the equation introduces potentially hard trade-offs between the conservation of scarce sources and GHG emissions. Federated learning strategies may offer a way out of this impasse, as they can be both water-81 and energy efficient. 82 Ultimately, these questions will probably have to be settled in a country-and region-specific way, depending on the available resources. For the time being, however, rules such as a minimum threshold of, e.g., 50% of renewable energy powering AI training should be considered, and federated learning strategies should be explored and incentivized further.
Consumption caps based on an AI model's social utility
The final, and most intrusive, regulatory mechanism contemplated here to render AI more sustainable is the establishment of energy consumption caps. ML systems have become ubiquitous in various domains, such as healthcare, education, entertainment, and security. Arguably, these sectors differ in their criticality for basic societal tasks. Hence, consumption caps could be formulated as a function of the sector and specific use case the model is deployed in-similar to the risk qualification undertaken in Annexes II and III AI Act. Significantly, many of the areas listed in Annexes II and III are, arguably, among the most important societal sectors in which machine learning could, if properly used, simultaneously have the greatest positive societal impact, e.g., medicine, employment, administration, transportation and automotive etc.
As a first step, lawmakers or regulators would have to define certain "social usefulness classes" based on the expected societal benefits of harnessing AI in a certain area. In a second step, consumption soft or hard consumption caps could be allocated to these classes. They would designate the amount of energy that can be used, or GHG that may be emitted, to train and run an ML system in that specific sector in use case. In this way, the permitted climate costs often AI model would depend on how valuable and beneficial the system is for society.
However, this approach raises the question of how to measure and compare the social value of different ML applications. Ultimately, this is a judgment call that depends on what we can 79 Hacker, 'The European AI Liability Directives -Critique of a Half-Hearted Approach and Lessons for the Future', 53 et seq. 80 Li and others, 'Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models', 9. 81 Ibid,8. 82 Güler and Yener, 'Sustainable federated learning'. 13 afford as a society in terms of energy and carbon emissions. It is a debate that, in terms of climate emergency, our societies must increasingly be prepared to have. The proposal is complicated further because, particularly in AI value chains where foundation models are finetuned, emissions cannot be simply mapped onto a specific use case as the climate costs of the foundation model factors into potentially a great variety of different applications. However, such measuring problems can, in my view, be overcome. One may either use a specific fraction (e.g., 1/1000) of the foundation models costs for each use case, or attempt to specifically measure only the cost for fine-tuning, deploying and running the model for a specific use case, with correspondingly lower consumption caps.
Eventually, I submit, there should indeed be a difference between training an ML system for medical diagnostics that could potentially, with the right guardrails in place, 83 save hundreds of lives, and developing an ML system for mere entertainment purposes. For example, this difference could also translate into greater leeway in the sustainability impact assessment that would be required before deploying an ML system. By giving more flexibility to ML systems with higher social utility, we could encourage more innovation and research in areas that are critical for human well-being and social welfare, while balancing the expected benefits of specific AI applications with their climate costs.
V. From sustainable AI to sustainable technology regulation 1. Sustainability challenges in technology AI models are, however, not the only digital tools or infrastructures suffering from significant GHG emissions. Indeed, many other digital technologies, beyond AI, face significant sustainability challenges due to their high GHG emissions: for example, blockchain (e.g., Bitcoin); 84 metaverse applications; 85 and data centres, 86 to name only a few. The energy demand of data centers, more specifically, is expected to grow substantially over the next years as cloud services and large compute infrastructures become ever more important to sustain advanced, data-intense IT applications, such as large AI models or the metaverse.
Sustainable AI regulation as a blueprint
In these areas, sustainable AI regulation may arguably serve as a blueprint. The regulatory toolbox described above, from co-regulation to sustainability assessments and hard consumption caps, can and should be flexibly adapted to these other areas of technology law.
[to be elaborated xxx]
VI. Sustainable and Climate-Responsive Law
Perhaps the biggest challenge in a regulatory framework for sustainable AI lies in the partially intertwined, but to a large extent also independent and accelerating dynamics of the respective fields -climate change and AI development. Making regulation future-proof concerning only 83 See, e.g., Brent Mittelstadt, Sandra Wachter and Chris Russell, 'The Unfairness of Fair Machine Learning: Levelling down and strict egalitarianism by default' (2023) 14 one of these critical societal transformations already is challenging; 87 combining both of them raises the stakes even further.
Hence, regulatory techniques must be developed to enable the flexible and continued adaptation of laws both to the level of climate change and to future developments of digitization and particularly in AI, which will certainly not stop with GPT-4. While the law may be harnessed to make AI and technology more sustainable, scholars also need to auto-reflexively develop pathways to render AI regulation, and the law more generally, more sustainable. Under such a perspective, sustainability emerges as a collective interest that may reconfigure certain existing rights we have come to take for granted.
A sustainability limit to existing rights
On a theoretical level, this questions links to the broader issue of the value and position of collective interests in law. 88 Arguably, from an economic perspective, sustainability and climate change mitigation qualify as a public good. 89 This not only points to the importance of regulatory intervention for its implementation but also raises important doctrinal questions concerning the relationship to subjective rights: using several examples drawn from data protection and non-discrimination law, the following sections explore to what extent existing subjective rights may have to be limited, or buttressed, by sustainability considerations. Taken together, these examples point to the larger question of the relevance and status of collective interests in sustainability in a body of the law that, in private law particularly, has for centuries been understood as structuring largely dyadic relationships (e.g., between seller and buyer; or more recently between data controller and data subject).
a) Data protection versus sustainability
To start with, we shall consider the right to be forgotten (Article 17 GDPR), which allows data subjects, under certain conditions, to request the erasure of their personal data. Now imagine that a large AI model was trained on supposedly anonymized medical data and is used for cancer detection. Some individuals whose data were contained in the training data set may be reidentified with novel technical tools. One of them exercises her right to erasure under Article 17(1)(a) GDPR. As a consequence, not only may her data point have to be deleted from the training data, but the entire AI model may have to be re-trained 90 -entailing significant GHG emissions.
In my view, the subjective right to erasure, in such situations, has to be balanced against the collective interest in mitigating climate change. Doctrinally, such a "sustainability limitation" might be based on Art. 17(3)(c) or (d) GDPR. According to the former, the right to erasure does not exist if processing is necessary for reasons of public interest in the area of public health, provided that the constraints of Article 9(2)(h) or (i) and Article 9(3) GDPR are heeded. This requires, importantly, a specific law under EU or Member State law authorizing the processing of sensitive data in the specific case and providing adequate safeguards.
While such a law would indeed be a favorable course of action, the question remains whether, in its absence, a possible defense against the erasure request in this and other cases might be based on Article 17(3)(d) GDPR. Pursuant to this provision, the erasure request may be denied if the processing is necessary for "for archiving purposes in the public interest, scientific or historical research purposes or statistical purposes in accordance with Article 89(1) [GDPR] in so far as [the erasure] is likely to render impossible or seriously impair the achievement of the objectives of that processing". Art. 17(3) GDPR establishes an exemption whose validity, in each single case, can only be ascertained by striking an equitable balance between the mentioned rights and interests.
Based on a grammatical interpretation of Article 17(3)(d) GDPR, one will hardly find that the erasure request will seriously impair reaching the objectives of the research purpose: the deletion of a single data point from the training data set will rarely have any noticeable effect. One could, potentially, argue that taken together, a multitude of erasure requests could have such an effect; but the extent to which such extrapolations might be considered in evaluating a single erasure request -particularly if the other requests have not yet been formulated -is unclear. Hence, the woman from the example stands a decent chance of seeing her erasure request granted under a literal interpretation of Article 17(3)(d) GDPR.
Arguably, however, Article 17(3) GDPR only imperfectly sketches and operationalizes a constitutionally required balancing exercise. As the CJEU spelled out in the infamous Google Spain case, the "right to be forgotten" requires a comprehensive assessment of the rights and interests of the respective parties to determine whether any erasure request must be granted. Hence, I submit that, a purposive, teleological interpretation of Article 17(3) GDPR must not be limited to the cases enumerated in letters (a) to (e). Rather, an unwritten exemption must be read into Art. 17(3) GDPR according to which erasure requests may be denied if a comprehensive balancing exercise including the constitutionally protected rights and interests of the involved parties finds a preponderance of the rights and interests of the data controller.
Importantly, Article 17(3)(c) and (d) GDPR demonstrate that collective interests, such as public health, archiving, or research may limit individual erasure requests. This links the right to erasure to a growing debate on the relevance of third-party interests for interpreting the GDPR. 91 That debate, however, has so far focused on the extent to which disclosure of individual data points, and their processing, may generate (negative) externalities to third parties, for example because ML models might inference their hitherto undisclosed preferences by aggregating enough data from similarly situated persons (triangulation). The impetus, then, would be to restrict data processing in the interest of the data subjects whose preferences might be the object of inference.
The question of sustainability puts this issue on its head: under this perspective, we must ask if the (climate) externalities of the exercise of individual data subject rights may effectively limit the reach or even existence of these individual rights. Again, as Article 17(3)(c) and (d) GDPR, such reasoning is not foreign to the GDPR and its right to erasure. Framed as a constitutionally required weighting exercise, it involves balancing the right of data protection against the right to, or at least interest in, saving energy and reducing GHG emissions for the sake of climate change mitigation. Importantly, while the latter is a collective interest, precisely the debate around data externalities shows that the right of data protection need not be understood as a merely individual right, but that it also embodies a collective dimension.
Ultimately, such cases will have to be resolved on a case-by-case basis. However, the guideline, in my view, should be that a clear discrepancy between the individual and collective harms flowing from the continued storage/use of the data point in question and the harms resulting from the climate costs of, e.g., retraining the model should indeed lead to an exemption from the right of erasure under Article 17(3) GDPR. This will depend, inter alia, on the nature of the personal data (e.g., its proximity to sensitive data and its importance for the exercise of other fundamental rights); the extent of the projected climate costs; potential alternatives the data controller might have used to minimize climate costs in the case of erasure requests (e.g., machine unlearning 92 , sharding 93 ). The social utility of the model itself, however, should not factor into the equation as the erasure will rarely generally not lead to the deletion of the model, but only it is (partial) retraining; if indeed the purpose of the model is defeated by the erasure request, Article 17(3)(d) GDPR provides the more specific norm for the balancing exercise.
In our example case, if indeed the GHG emissions from retraining model are significant (e.g., the yearly emissions of a small town) there is arguably a case to be made that the erasure request should, despite the sensitive nature of the data, eventually be denied.
b) Transparency versus sustainability
Transparent models may be, in some cases, more resource intensive than black box models. This holds particularly if a post hoc explanation algorithm must be deployed on top of the machine learning model. Conversely, the use of simpler models that are interpretable from the start may indeed reduce energy consumption.
For instance, consider a scenario where only a black-box model can solve a problem, such as detecting fraudulent transactions or diagnosing diseases. Suppose that the law requires the model to provide explanations for its predictions, and that a post-hoc explanation algorithm exists for this purpose. However, the post-hoc explanation algorithm is very resource intensive, as it needs to analyze the black-box model and generate explanations for each case. This may result in increased energy consumption and environmental impact. In such a situation, one might wonder whether the harm of opacity is less than the harm to sustainability. That is, would it be better to use a simpler and more transparent model that is interpretable from the start, even if it sacrifices some accuracy? Or would it be preferable to use a more accurate but opaque model that requires a costly post-hoc explanation method? How can we balance these conflicting objectives and values? These questions are not easy to answer, as they depend on various factors, such as the nature and importance of the problem, the availability and quality of the data, the expectations and preferences of the users and stakeholders, and the legal and ethical implications of the decisions. environment and sustainability. Adding post-hoc fairness algorithms to the original algorithmic process may increase the energy consumption and carbon footprint of the system, as they require additional computational resources and data processing.
However, between opacity and lack of non-discrimination, we argue that non-discrimination is more important and urgent to ensure in algorithmic systems, as long as the energy consumption of the system is reasonable and within acceptable limits. This is because lack of nondiscrimination has more severe and direct impacts on the affected persons than opacity. Lack of non-discrimination may lead to unfair outcomes, such as denial of opportunities, resources, or benefits, or exposure to risks, harms, or disadvantages. Moreover, lack of non-discrimination may disproportionately affect those who are already marginalized or underserved by society, such as minorities, women, or people with disabilities. Therefore, non-discrimination is a fundamental human right that should be respected and protected in algorithmic systems-even if climate costs are substantial.
Climate-responsive law
The previous use cases have shown how sustainability considerations may become factors irritating our traditional understanding of subjective rights, and limiting them if conditions warrant. These deliberations point to the larger question of how the law more generally may adapt to a changing climate. More specifically, the remaining part of the article will ask if and how legal provisions, particularly those of technology law covered in this article, could be coupled to the state of climate change going forward.
Ideally, one may imagine sustainability rules to become stricter if the climate crisis accelerates, and to soften if, at some future moment in time, the current trend of climate change is reversed. In this way, sustainability obligations could be adapted (tightened or loosened) depending on the "state of the planet". To this end, legal and sustainability scholars should explore suitable indices capturing the state of climate change-at regional and global levels-and propose ways to integrate the current value of these indices into the interpretation or even wording of the law.
While legal norms regularly refer to the state of the art in technical development, it its high time to adapt laws to the climate state of the world. This may, for example, take the form of flexible thresholds in technical standards and SIAs, coupled with relevant indices; of collective interest interpretation of general clauses; or of fundamental rights interpretation of secondary law if climate change mitigation does, indeed, gain the status of a Charter right. Again, the jurisprudence of the German Constitutional Court, binding the government to climate mitigation measure based on the current state of climate change, 94 may serve as an example here.
Generally, the task of formulating a climate-responsive law contains two steps: first, the development of suitable indices (below, Part a)); and, second, legal methods to reflect the value of these indices in the interpretation and making of the law (below, Part b)).
a) Measuring global climate challenges
In the efforts to confront the monumental task of addressing global climate challenges, accurate measurement and assessment of these challenges have become indispensable. The Intergovernmental Panel on Climate Change (IPCC), for example, compiles data and creates reports 95 to help scientists, industry leaders and policymakers understand and adapt to the rapidly evolving science behind it impact of climate change. 94 In-depth index for climate change An in-depth index for climate change that incorporates both long-term trends and short-term fluctuations could serve as a vital tool in this regard. Such an index, with sub-indices, would incorporate numerous variables, including but not limited to, average global temperatures, sealevel rise, ice cap measurements, CO2 concentration, and the frequency of extreme weather events. Utilizing such a rich index offers a robust and nuanced understanding of the climatic changes unfolding, and may act as a significant guide for legislative reform.
Institutionally, the pursuit and construction of such an index can link up with current initiatives at the EU level, for example. The European Climate Adaptation Platform (Climate-ADAPT), a partnership between the European Commission and the European Environment Agency (EEA), collects data and provides resources concerning climate change and adaptation in the EU. 96 More specifically, one initiative within that strategy, the European Climate Risk Assessment (EUCRA), maps out "current and future climate change impacts and risks relating to the environment, economy and wider society in Europe." 97 Drawing on publicly available data, projects like EUCRA, and Climate-ADAPT more generally, may facilitate tracking and disclosing various regional climate developments and indices, which may be taken up for legal interpretation and lawmaking.
ii.
Pragmatic proxies
The development of comprehensive indices suitably geared toward legal use will probably take time, however. Climate change is a highly complex process at the feasibility of a single index, while desirable from a law and policy perspective, may be scientifically challenging. In the meantime, the application of pragmatic, more readily available proxy indices can further contribute to our ability to measure climate change effectively and to base policy and law upon it. These proxies might include factors such as the frequency and severity of natural disasters; CO2 concentrations in specific regions; changes to the global or regional average temperature; or changes in seasonal patterns. Such proxies might serve as tangible, readily observable indicators to infer the broader climate trajectory and to inform law and policy.
Within the framework of Climate-ADAPT, a range of indicators are already made available as part of the European Climate Data Explorer (ECDE). 98 They include information on health, agriculture, forestry, energy, tourism as well as coastal and water resources. 99 Such categories can arguably be starting points for developing indices that can meaningfully be used by legal institutions, such as the courts, regulatory agencies, or parliaments.
b) Continuous adaption of legal provisions
Recognizing the dynamic nature of climate change, our laws should be adapted continuously to meet these shifting challenges effectively. Generally, there is an agreement that environmental protection laws, for example, need to be rendered more stringent as climate change proceeds, 100 and that it must inform current and future policy in a variety of sectors. 101 However, distinct legal methods can be brought to bear expand the impact of climate change insights beyond environmental law, both concerning existing and future law.
i.
General considerations
The vast majority of laws are not in the making, but already in existence and will not be changed in the immediate future. Hence, scholars have started to interpret legal norms in the light of climate change considerations, giving rise to what may be termed an "ecological analysis of law" 102 rivaling the more traditional "economic analysis of law". 103 General clauses, for example, have long been recognized as gate openers, facilitating the integration of broader societal and normative questions into the law. More specifically, they may be interpreted by incorporating the collective interest dimension of environmental sustainability. As the specific use cases discussed above show, a flexible understanding of general clauses and vague legal terms offers a window of opportunity to ventilate specific insights from sustainability studies and climate science in the law's realm proper.
Moreover, the evolution of climate change law might witness the reinterpretation of secondary EU legislation through the lens of fundamental rights, provided that climate change mitigation indeed gains recognition as a right under the EU Charter of Fundamental Rights. This development could significantly enhance the enforcement of climate change mitigation measures and hold greater accountability for environmental harm.
Under such an interpretation, secondary laws and regulations that have traditionally been seen as purely economic or technical could now be reevaluated based on their environmental impact and their consistency with the right to climate change mitigation. For example, laws relating to energy production, transportation, and agriculture might need to be reassessed to ensure they do not infringe upon the recognized fundamental right to climate change mitigation.
Beyond the interpretation of existing law, sustainability considerations should also increasingly inform the genesis of new legislation. Building on theories and practices of evidence-based legislation, 104 the imperative of climate change adaptation in lawmaking can take several forms, necessitating innovative approaches in interdisciplinary analysis and legal drafting. One such form can be the integration of flexible thresholds in technical standards, aligned with pertinent climate change indices. This would enable the law to dynamically respond to the severity and frequency of climate anomalies and extreme weather events. For instance, emission standards for industrial pollutants, in the realm of IT development and beyond, could be tied to indices of air quality and global warming, automatically adjusting to the prevailing conditions. This, in turn, could ensure that regulatory mechanisms remain relevant and proportionate to the degree of environmental degradation.
This transformative approach embodying a climate-responsive law, involving the adaptation of technical standards, the reinterpretation of general clauses and vague legal terms, and the recognition of fundamental rights, could prove to be a game changer in our global response to the climate crisis. Given the urgency of the climate crisis, the law should be leveraged to facilitate and accelerate climate change mitigation. Overall, laws should be interpreted acknowledging the collective interest in environmental sustainability, designed to be capable of evolving in accordance with scientific insights and understanding of climate change, and revised regularly-"manually" by legislative review or "automatically" by reference to a climate change index-to reflect the changing conditions of the planet the laws operate on.
ii. A case in point: Sustainability thresholds in sustainability impact assessments
Sustainability thresholds in sustainability impact assessments have a critical role to play in these adaptations of legal provisions, and may serve as a case in point. As discussed, sustainability impact assessments would cover the development and deployment of AI more specifically, and technology more broadly (see Part IV.2.). Such mandatory assessments would ensure that reasonable alternatives to specific models and implementations are considered, and chosen, if the trade-off between the performance of the alternative model and the benefits in terms of GHG emissions speaks in favor of the alternative.
Importantly, one way to operationalize the SIA could be the establishment of a threshold of performance loss-vis-à-vis the best performing model-below which even significantly more sustainable models need not be anymore. Conversely, the performance corridor delineated by the best-performing model and the threshold, the most sustainable model (or the model with the best performance-sustainability trade-off, depending on the exact design of the SIA) would have to be chosen.
This decisive threshold could arguably be tethered to the climate change index, or a meaningful sub-index or proxy: the more urgent the climate crisis, the broader the range of models that need to be considered as an alternative, and hence the greater the weight of sustainability considerations in the trade-off. Effectively, in terms of accelerating climate change, even alternative models with significantly lower performance could then be benchmarked against the best performing model. Similarly, the renewable energy threshold discussed above (see Part IV.3.) might be coupled to a climate change index, raising the threshold as the planet heats up. By calibrating thresholds in response to the climate change index, AI regulation and practice may be endowed with a scientifically grounded and continuously updated basis.
In conclusion, legal responses to climate change require both the understanding of scientific data and the ability to translate that understanding into effective, adaptive legislation. The proposed climate change index and use of pragmatic proxies provide a means to grasp the state of climate change more accurately, while continuous adaptation of legal provisions based on ecological interpretation of law and on sustainability thresholds offer a flexible and responsive strategy for maintaining balancing performance and innovation with climate change mitigation. Overall, this contributes to an understanding of the law that is not fixed and doctrinal, but responsive to the key challenges our society is facing, such as the dual large-scale transformations of digitization and sustainability.
VII. Conclusion
This paper suggests that AI regulation needs a shift from trustworthiness to sustainability. This desideratum has acquired urgency with the advent of large generative AI models like ChatGPT or GPT-4. While such large AI models may offer sustainability benefits in the long run, their training and deployment is highly resource intensive along several parameters, such as GHG emissions and water consumption.
Against this background, the paper articulates a framework for sustainable AI and technology regulation, in a dual sense. First, AI regulation needs to take contributions of AI to climate change and water scarcity seriously, establish provisions to make AI more environmentally sustainable. Second, AI regulation itself-and the law more generally-must be rendered more sustainable by recognizing the collective interest of climate change mitigation as a modifying factor in the analysis and enforcement of individual subjective rights.
Concerning the first dimension-regulating for a more sustainable AI development and deployment-I show that the significant challenges AI poses regarding environmental sustainability are only in adequately addressed by the upcoming EU AI Act. Hence, the paper suggests and develops a range of strategies, from transparency mechanisms to co-regulation, sustainability by design, including sustainability impact assessments, and restrictions on AI training to consumption caps.
Regarding the second dimension-bringing AI regulation and the law itself in line with sustainability desiderata-the paper explores the balance between individual rights, such as the right to erasure under the GDPR, and collective interests like mitigating climate change. It suggests that the right to erasure may need to be limited if it interferes with efforts to combat climate change. The authors also discuss the potentially increased energy consumption associated with more transparent models and fairness-aware algorithms implementing nondiscrimination provisions. While greater leeway exists for a restrictive integration of transparency provisions in cases of high climate costs, I suggest that non-discrimination provisions should generally prevail over climate concerns.
Finally, the paper argues for the development of a comprehensive index to measure the impact of climate change regionally and globally, and to use this as a variable to calibrate AI and technology regulation. More specifically, thresholds and sustainability impact assessments for restrictions for training data could be coupled to suitable indices, tightening regulatory requirements as the climate crisis accelerates (and vice versa). The overall goal is to facilitate a broadened, climate-responsive interpretation and making of the law to promote environmental sustainability. Overall, the law must be leveraged, beyond environmental law properly, to accelerate climate change mitigation efforts-before it is too late for good.
of Contents I. Introduction . 1 II. AI and sustainability . 3 1. AI and classical AI risks . 3 2. Another perspective: environmental risks . 4 3. Why environmental sustainability? . 4 a) Promises to mitigate global warming . 5 b) Contributions of ICT and AI to climate change . 5 III. Sustainable AI and the EU AI Act . 5 IV. Policy proposals: sustainable AI regulation going forward . 7 1. Co-regulation . 8 2. Sustainability by design . 8 a) From data protection to sustainability by design . 9 b) Sustainability impact assessments . 9 3. Restrictions on training AI models . 12 4. Consumption caps based on an AI model's social utility . 12 V. From sustainable AI to sustainable technology regulation . 13 1. Sustainability challenges in technology . 13 2. Sustainable AI regulation as a blueprint . 13 VI. Sustainable and Climate-Responsive Law . 13 1. A sustainability limit to existing rights . 14 a) Data protection versus sustainability . 14 b) Transparency versus sustainability . 16 c) Non-discrimination versus sustainability . 16
c) Non-discrimination versus sustainabilityIn ways similar to post hoc explanations, post-hoc fairness algorithms may mitigate bias in machine learning systems. However, these methods may have unintended consequences for the92 Thanh Tam Nguyen and others, 'A survey of machine unlearning' (2022) arXiv preprint arXiv:220902299 ; Ayush Sekhari and others, 'Remember what you want to forget: Algorithms for machine unlearning' (2021) 34 Advances in Neural Information Processing Systems 18075; Yinzhi Cao and Junfeng Yang, 'Towards making systems forget with machine unlearning' (2015) 2015 IEEE symposium on security and privacy 463. 93 Lucas Bourtoule and others, 'Machine unlearning' (2021) 2021 IEEE Symposium on Security and Privacy (SP) 141.
See n. FEHLER! TEXTMARKE NICHT DEFINIERT.. 95 See, e.g., Hans-Otto Pörtner and others, Climate Change 2022: Impacts, Adaptation and Vulnerability (2022); Valérie Masson-Delmotte and others, Climate Change 2021: The physical science basis (2021); Nebojsa i.
Table
//www.europarl.europa.eu/meetdocs/2014_2019/plmrep/COMMITTEES/CJ40/DV/2023/05-11/ConsolidatedCA_IMCOLIBE_AI_ACT_EN.pdf (= AI Act EP Version).40 But see Mario Martini and Hannah Ruschemeier, 'Künstliche Intelligenz als Instrument des Umweltschutzes'
(2021) 2021 Zeitschrift für Umweltrecht 515-521 et seqq. Pagallo, Sciolla and Durante, 'The environmental
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41 European Commission, Proposal for a Directive of the European Parliament and of the Council on adapting
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42 Cowls and others, 'The AI gambit: leveraging artificial intelligence to combat climate change-opportunities,
challenges, and recommendations'.
43 https://data.consilium.europa.eu/doc/document/ST-14954-2022-INIT/en/pdf.
44 Luca Bertuzzi, 'AI Act moves ahead in EU Parliament with key committee vote' EURACTIV
<https://www.euractiv.com/section/artificial-intelligence/news/ai-act-moves-ahead-in-eu-parliament-with-key-
committee-vote/> accessed May 11, 2023.
45 Draft Compromise Amendments on the Draft Report, Proposal for a regulation of the European Parliament and
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the
Council,
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9,
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Such a proposal may build 51 Meg Leta Jones and Margot E Kaminski, 'An American's Guide to the GDPR' (2020) 98 Denv L Rev 93. 52 See, e.g., Amartya Sen, The Idea of Justice (Harvard University Press 2011). 53 John Ehrenfeld, Sustainability by design: A subversive strategy for transforming our consumer culture (Yale University Press 2008). 54 Carlo Vezzoli and Ezio Manzini, Design for environmental sustainability (Springer 2008).
arXiv preprint arXiv:230202404 . 84 Johannes Sedlmeir and others, 'The energy consumption of blockchain technology: Beyond myth' (2020) 62 Business & Information Systems Engineering 599. Luca Bertuzzi, 'EU Commission moves to link 'fair share' debate with the metaverse' 2023) <www.euractiv.com/section/digital/news/eu-commission-moves-to-link-fair-share-debate-with-the-metaverse> accessed January 10 . 86 Technology Policy Council, TechBrief: Computing and Climate Change (Association for Computing Machinery 2021) 1.85
But see now, e.g., Philipp Hacker, Andreas Engel and Marco Mauer, 'Regulating ChatGPT and other Large Generative AI Models' (2023) ACM Conference on Fairness, Accountability, and Transparency (FAccT '23,
See, e.g., https://www.bcg.com/de-de/publications/2022/how-ai-can-help-climate-change; https://www.sueddeutsche.de/wirtschaft/ki-energie-sparen-industrie-eisengiesserei-aveva-1.5650707; OECD,
See, e.g., the recent decision of the Irish DPA of December 31, 2022, Meta Platforms, xx.
See, e.g., David Flaherty, 'Privacy impact assessments: an essential tool for data protection' (2000) 5 Privacy Law & Policy Reporter 85; David Wright and Paul De Hert (eds), Privacy Impact Assessment (Springer 2012);
The exact impact is not easy to measure. An index including Scope 1, 2 and 3 Emissions for necessary compute resources (e.g., energy; carbon emissions) for training and retraining could be used as a proxy. For a more
See, e.g., Solon Barocas and Karen Levy, 'Privacy dependencies' (2020) 95 Wash L Rev 555; Ben-Shahar, 'Data Pollution' (2019) 11 Journal of Legal Analysis 104; Hacker, Datenprivatrecht (Mohr Siebeck 2020), 64 et seqq.
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Training GPT-3 in Microsoft's state-of-the-art U.S. data centers can directly consume 700,000 liters of clean freshwater, enough for producing 370 BMW cars or 320 Tesla electric vehicles, and these numbers would have been tripled if GPT-3 were trained in Microsoft's Asian data centers. 2OECDMeasuring the Environmental Impacts of AI Compute and Applications: The AI Footprint, 5; Li and othersOECD, Measuring the Environmental Impacts of AI Compute and Applications: The AI Footprint, 5; Li and others, 'Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models', 2: "Training GPT-3 in Microsoft's state-of-the-art U.S. data centers can directly consume 700,000 liters of clean freshwater, enough for producing 370 BMW cars or 320 Tesla electric vehicles, and these numbers would have been tripled if GPT-3 were trained in Microsoft's Asian data centers."
Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models. Others Li, 3Li and others, 'Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models', 3.
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Another key risk at this level is discrimination; hence, Art. 10 AI Act should apply to foundation models as well, see Hacker, Engel and Mauer. Regulating ChatGPT and other Large Generative AI Models. Part 7.3Another key risk at this level is discrimination; hence, Art. 10 AI Act should apply to foundation models as well, see Hacker, Engel and Mauer, 'Regulating ChatGPT and other Large Generative AI Models', Part 7.3.
. Ibid, Part 7.2; but see also n. 62Ibid, Part 7.2; but see also n. 62.
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Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models', 9; below, text accompanying n. 80) have to be resolved on a case-by-case basis. Any trade-offs between GHG emissions and water consumption (see, e.g., Li and others. grounded in best practices, a reasonable weighting of all relevant factors, and regulatory guidelines69 Water consumption should be monitored as well, to the extent possible. Any trade-offs between GHG emissions and water consumption (see, e.g., Li and others, 'Making AI Less" Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models', 9; below, text accompanying n. 80) have to be resolved on a case-by-case basis, grounded in best practices, a reasonable weighting of all relevant factors, and regulatory guidelines.
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| sample_544 | 0.9963 | arxiv | |
Benjamin Auteurs
Rotenberg
Laboratoire PHENIX
Sorbonne Universités
UPMC Univ Paris 06
CNRS
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RS2E (Réseau sur le Stockage Electrochimique de l'Energie)
3459, 80039Amiens CedexFR CNRSFrance
Mathieu Salanne
Laboratoire PHENIX
Sorbonne Universités
UPMC Univ Paris 06
CNRS
4 place Jussieu75005Paris
RS2E (Réseau sur le Stockage Electrochimique de l'Energie)
3459, 80039Amiens CedexFR CNRSFrance
Patrice Simon
RS2E (Réseau sur le Stockage Electrochimique de l'Energie)
3459, 80039Amiens CedexFR CNRSFrance
CIRIMAT
Université de Toulouse
CNRS
INPT
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SupercapacitorsMolecular simulationIn situ experimentsNanoporous carbon
Vers des supercondensateurs plus performants: quand expériences et simulations permettent d'élucider les mécanismes à l'échelle nanométrique RésuméLes supercondensateurs sont des dispositifs de stockage de l'énergie électrique permettant notamment de délivrer une forte puissance. Ils sont constitués d'électrodes de carbone poreux plongées dans un électrolyte concentré. La charge est stockée par adsorption des ions sur la surface des électrodes. Les carbones nanoporeux permettent de stocker une plus grande quantité d'électricité grâce à un mécanisme de charge différent des carbones possédant des pores de plus grande taille. Ce mécanisme de charge a été récemment caractérisé en combinant des expériences in situ (Résonance Magnétique Nucléaire, microbalance à quartz) et des simulations moléculaires.Mots-clésSupercondensateur, Simulation moléculaire, Expériences in situ, Carbone nanoporeux Towards more efficient supercapacitors: When experiments and simulations uncover the mechanisms on the nanometer scale Abstract Supercapacitors are energy storage devices able to deliver electricity with a high power. They consist of porous carbon electrodes in a concentrated electrolyte. Charged is stored by the adsorption of ions at the electrode surface. Nanoporous carbons allow to store more electricity thanks to a charging mechanism that differs from carbons with larger pores. This charge storage mechanisms has recently been uncovered by combining in situ experiments (Nuclear Magnetic Resonance, Electrochemical Quartz Microblance) and molecular simulations.
I. Introduction
Le réchauffement de la planète, les réserves limitées en combustibles fossiles et la pollution des villes (les transports sont responsables de 30 % des émissions de CO 2 ) montrent, entre autres, combien il est important de se tourner vers une utilisation intensive et efficace des énergies renouvelables (ENR) et de trouver des solutions innovantes pour faciliter le passage progressif du véhicule thermique aux véhicules électriques. L'intermittence des énergies renouvelables ainsi que la nécessité d'embarquer une quantité suffisante d'électricité dans les véhicules électriques afin d'assurer une grande autonomie, font du développement de nouvelles technologies pour le stockage de l'énergie un des défis majeurs des vingt prochaines années: il s'agit d'une étape indispensable pour mieux gérer les ressources en énergie de notre planète. S'il existe une grande variété de solutions de stockage à grande échelle (stockage hydraulique, air comprimé, volants d'inertie…), la technologie la plus largement utilisée reste incontestablement le stockage électrochimique avec les batteries et les supercondensateurs [1]. Ce succès s'explique par l'avantage considérable qu'ils apportent par rapport à d'autres solutions : la mobilité. La mise au point de générateurs électrochimiques performants revêt donc une importance toute particulière [2,3].
Comme le montre la Figure 1a, les batteries permettent de stocker ou délivrer de grandes quantités d'énergie (200 Wh/kg) pendant des temps longs, typiquement de plusieurs heures ou dizaines d'heure. Cependant, de par le mécanisme de stockage des charges impliquant la rupture / création de liaisons chimiques par des réactions d'oxydo-réduction, elles restent limitées en terme de puissance. A l'inverse, les condensateurs diélectriques classiques ne stockent que peu d'énergie mais sont capables de la restituer en quelques millisecondes, permettant ainsi délivrer de grandes puissances.
Les supercondensateurs sont des systèmes intermédiaires entre les condensateurs classiques et les batteries. Ils peuvent fournir des densités de puissance très élevées (> 10 kW/kg) avec une densité d'énergie modeste (6 Wh/kg), ce qui définit une constante de temps allant de quelques secondes à quelques dizaines de secondes. Ces performances sont liées au mode de stockage de la charge : il n'y a en effet aucune réaction redox dans les supercondensateurs car le stockage est réalisé de façon électrostatique, par adsorption des ions d'un électrolyte à la surface de carbones poreux de surface très développée. Ce mécanisme peut être décrit en première approche en utilisant la notion de capacité de double couche électrochimique (Figure 1b), suivant le modèle proposé par Helmholtz en 1853 :
C = ε 0 ε r A d(1)
où ε 0 la permittivité du vide, ε r est la constant diélectrique de l'électrolyte, d l'épaisseur de la double couche électrochimique (distance de séparation des charges), et A l'aire de l'électrode.
On notera qu'excepté ε 0 , ces grandeurs sont difficiles à définir à l'échelle locale des interfaces. La capacité de cette double couche électrochimique est de l'ordre de 10 à 20 µF/cm². En remplaçant une électrode plane par un matériau poreux de grande surface spécifique comme le carbone activé (1000 à 2000 m²/g, Figure 1c), on atteint des capacités de plus de 100 F/g de carbone. La tension maximum de ces cellules est limitée par la décomposition de l'électrolyte : 2,7 à 3 V en électrolyte non-aqueux. Le stockage des charges en surface explique la grande puissance de ces systèmes par rapport aux batteries. L'absence numéro de l'Actualité Chimique consacré à la transition énergétique [8].
II. Modèles structuraux des carbones nanoporeux
Les carbones nanoporeux sont généralement constitués d'unités graphitiques nanométriques (substracting pore effect) [10]. Si l'on souhaite accéder, au-delà de la surface spécifique, à une mesure des tailles de pores et de leur distribution, on peut avoir recours à une analyse de type théorie de la fonctionnelle de la densité (Quenched Solid Density Functional Theory) [11].
Tout ceci illustre la difficulté de mesure la surface des carbones nanoporeux. En réalité, le concept même de surface est à manier avec précaution, car il dépend de l'approche (notamment, la sonde choisie) pour la mesurer. Il est donc pour cela nécessaire de compléter ces techniques d'adsorption par une caractérisation directe de la structure telle que la diffusion de rayons X aux petits angles (SAXS) ou la résonance magnétique nucléaire (RMN), et avoir ainsi accès au rapport surface sur volume accessible aux ions, c'est-à-dire dans des conditions pertinentes pour les applications électrochimiques. Malgré toutes les limitations évoquées cidessus, il reste possible de discuter l'évolution de la capacité par unité de surface en fonction [13].
Enfin, notons que la plupart des études ont pour l'instant porté sur la structure du carbone nanoporeux, alors que la capacité à prédire les paramètres structuraux cruciaux pour l'optimisation du stockage de charge nécessite également de comprendre la structure et la dynamique de l'électrolyte confiné.
III. Mouillage des pores sans différence de potentiel
Jusqu'à récemment, on croyait que la charge des supercondensateurs venait d'un mécanisme simple, à savoir l'entrée des ions dans le réseau de pores du carbone sous l'effet du champ Le développement de techniques in situ comme la microbalance à quartz électrochimique (EQCM) s'est révélé être particulièrement important pour réaliser ce type de mesures [17]. La
VI. Dynamique de charge et décharge
La caractéristique principale des supercondensateurs, par rapport aux batteries notamment, est leur grande puissance spécifique : ils se chargent ou se déchargent en quelques secondes.
Dans la perspective d'optimiser ces dispositifs, il ne faut donc pas que l'augmentation de la capacité se fasse au détriment de la puissance. Les théories habituelles prédisent que les liquides sous confinement extrême sont fortement ralentis, ce qui disqualifie en principe l'utilisation de carbone micro-ou nanoporeux pour les supercondensateurs. Heureusement, l'effet n'est pas si dramatique que cela dans des structures à porosité interconnectée comme les Les développements méthodologiques ne sont bien sûr pas en reste, avec par exemple pour les simulations une nouvelle approche pour la prédiction des propriétés interfaciales en fonction de la différence de potentiel entre les électrodes, qui exploite les fluctuations d'équilibre de la charge des électrodes sous l'effet de l'agitation thermique dans l'électrolyte [26].
Nous avons ainsi pu faire le lien entre des pics de la capacité différentielle et des transitions, induites par la différence de potentiel, au sein de l'électrolyte adsorbé [27,28].
Du point de vue des applications, on pourra exploiter les possibilités offertes pour la fabrication d'électrodes de carbone dont on contrôle la porosité, la composition (par activation ou par dopage) ou la microstructure, ainsi que la large gamme de liquides ioniques et de solvants disponibles. Ces matériaux carbonés pourraient également jouer un rôle important dans d'autres contextes, par exemple avec des solutions aqueuses pour la récupération "d'énergie bleue", en exploitant la différence de salinité entre l'eau de mer et celle des rivières [29,30].
présentant des défauts, avec des pores de tailles couvrant les micropores (taille < 2 nm) aux mesopores (taille entre 2 et 50 nm). Contrairement aux pores en fentes ou aux nanotubes, ils ne présentent aucun ordre tri-dimensionnel à longue portée [Figure 2]. Puisque les performances électrochimiques des carbones sont déterminées par l'interface entre le carbone poreux et l'électrolyte, il est nécessaire de pouvoir caractériser de façon fiable et précise le réseau poreux. Les surfaces spécifiques (surface par unité de volume ou de masse de matériau) ou les distributions de tailles de pores sont généralement obtenues à partir de mesures d'adsorption de gaz, via des modèles théoriques. Cependant ces méthodes présentent des limitations importantes lorsqu'on chercher à les appliquer aux carbones microporeux. Le choix de la sonde moléculaire est essentiel, car certains pores peuvent être inaccessibles aux molécules de gaz et l'être quand même pour les ions de l'électrolyte, selon les conditions thermodynamiques. Ceci est particulièrement vrai pour l'adsorption de N 2 à 77 K, qui ne donne pas des mesures précises pour les ultra-micropores (< 0,7 nm) dans les carbones. L'utilisation de l'argon, plus petit et sans quadrupôle, et ce à plus haute température (87 K), combinée à une analyse théorique plus simple des données expérimentales, est plus adaptée dans ce cas. L'adsorption de fluides super-ou sous-critiques (CO 2 ) à température ambiante offre une approche complémentaire pour caractériser la surface accessible dans des conditions plus proches de celle d'utilisation. Outre la sonde moléculaire et les conditions thermodynamiques, un autre défi doit être surmonté, car les propriétés microscopiques doivent être déduites des isothermes d'adsorption à travers un modèle approprié. L'analyse BET (Brunauer-Emmett-Teller) n'est pas recommandée pour les carbones microporeux, comme l'a confirmé récemment l'IUPAC [9] , car elle sous-estime les ultra-micropores et surestime les micropores de plus grande taille. Il est nécessaire d'avoir recours à des techniques plus élaborées telles que la méthode SPE
Figure 3a
3aprésente le schéma de principe d'une microbalance EQCM, dans laquelle un mélange de carbone poreux à étudier est placé sur un quartz piézoélectrique utilisé comme électrode de travail dans une cellule électrochimique. La variation de la fréquence de résonance du quartz est proportionnelle au changement de masse de l'électrode durant la polarisation. La Figure 3b montre la variation de masse (exprimée en nombre de mole d'anions et cations en divisant par la masse molaire des ions nus) en fonction de la charge lors de la polarisation d'une électrode de carbone. Les traits pointillés symbolisent la variation théorique de masse Δm d'après la loi de Faraday : la charge de l'électrode, F la constante de Faraday, M la masse molaire et z la valence de l'espèce échangée. En première approche, on peut considérer que les contre-ions seuls s'adsorbent : les anions sont adsorbés pour des charges positives (Q>0), et les cations pour des charges négatives (Q<0). La Figure 3b, qui correspond à un électrolyte organique avec des carbones de taille de pores contrôlée de 1 nm, montre trois zones de pentes différentes, correspondants à des mécanismes différents. A faible charge, il y a un échange entre anions et cations : les contre-ions s'adsorbent tandis que les co-ions (charge de même signe que celle de l'électrode) sont expulsés. A charge plus importante, seuls les contre-ions s'adsorbent. De ces courbes, on peut déduire le nombre de molécules de solvant accompagnant les ions lors de leur adsorption dans les pores. En plus de mettre en évidence deux mécanismes de stockage des charges différents pour des polarisations positives et négatives (voir plus loin), la différence entre la variation de masse théorique et expérimentale de l'électrode pour les charges négatives a permis de calculer un nombre de solvatation de 3 pour les cations 1-éthyl-3-méthylimidazolium confinés dans les pores, alors que ce cation est normalement entouré de 8 molécules de solvant dans le même électrolyte non confiné[15]. Ces résultats sont la preuve expérimentale de la désolvatation partielle des ions dans les nanopores, et viennent confirmer les simulations par dynamique moléculaire qui ont également montré ce phénomène[18].V. Mécanisme de stockage de chargeSi le principe de base du stockage de charge dans les supercondensateurs, à savoir l'adsorption d'ions à la surface de l'électrode, est bien établi, le mécanisme microscopique correspondant était bien moins clair jusqu'à récemment. La théorie de Gouy-Chapman-Stern (GCS) -qui prolonge le modèle de Helmholtz -reste la pierre angulaire de l'électrochimie théorique depuis plus d'un siècle ; elle prédit que près d'une surface étendue, la charge de l'électrode est compensée par la polarisation de l'électrolyte. La charge ionique et le potentiel électrostatique évoluent sur une distance caractéristique dite de Debye, de l'ordre de 1 à 10 nm en fonction de la concentration de l'électrolyte et la permittivité du solvant. Mais cette image est d'une utilité limitée dans le cas des supercondensateurs, à cause des effets de corrélation ionique à forte concentration en sel ou dans les liquides ioniques et des effets prononcés du confinement, qui est différent de la situation de l'électrode plane[19]. Les avancées récentes des techniques de simulations ont démontré la nécessité de décrire correctement la structure de l'électrolyte sur la surface.Pour des surfaces complexes (électrodes poreuses), la simulation a mis en évidence un point important dans le cas du confinement extrême : lorsque la taille des pores est comparable à celle des ions, la charge de l'électrode est compensée par un déséquilibre entre les nombres de co-et contre-ions dans le pore. Dans un tel état "super-ionique", la violation de l'électroneutralité dans le fluide interstitiel est compensée par l'apparition d'une charge opposée sur l'électrode, qui écrante la répulsion entre ions de même charge[20]. Plusieurs processus peuvent conduire à un excès global de contre-ions dans l'électrode: l'asdsorption de contre-ions, l'échange entre co-et contre-ions, ou la désorption de co-ions. Pour une combinaison donnée d'électrodes et d'électrolytes (nature des ions, présence et nature de solvant), l'un ou plusieurs de ces mécanismes peut être observé en fonction du potentiel. La simulation moléculaire, ainsi que les expériences de RMN, spectroscopie IR, SAXS et EQCM, suggèrent que l'échange d'ions est le processus le plus courant pour les faibles différences de potentiels, mais que pour des gros ions et/ou à fort potentiel l'adsorption des seuls contre-ions est aussi observée. La désorption des co-ions seule semble moins fréquente. Des mesures récentes de RMN in situ avec un électrolyte dans un solvant ont montré que le mécanisme de stockage de charge peut varier en fonction de la polarisation : alors que pour les polarisations positives l'échange d'ion était observé, c'est l'adsorption des contre-ions qui dominait pour les polarisations négatives. Ainsi, plusieurs facteurs contribuent à l'excès de charge, tels que la taille et la mobilité relatives des co-et contre-ions, ou encore la réorganisation des ions sur plusieurs cycles charges/décharges. Comme nous l'avons déjà mentionné, tant l'adsorption de contre-ions que l'échange d'ions sont accompagnés d'entrées et sorties de molécules de solvant. Dans les liquides ioniques purs, les simulations moléculaires indiquent que l'échange d'ions a lieu sans changer le volume de liquide dans l'électrode (voir
Figure 4 )
4[21]. Cette conclusion reste à renforcer pour d'autres combinaisons de cations et d'anions, et à confirmer expérimentalement.
carbones dérivés de carbures (CDCs), pour lesquels des temps caractéristiques de charge inférieurs à 20 secondes ont été observés pour les carbones présentant les pores de plus petite taille (0,8 nm en moyenne)[4]. Cette tendance est également confirmée par les mesures de spectroscopie d'impédance électrochimique, qui permet de sonder la résistivité de l'électrolyte à l'intérieur des pores dans le domaine des basses fréquences. Les valeurs obtenues (de l'ordre de 50 à 200 Ω.cm pour des électrolytes organiques dans l'acétonitrile, à température ambiante) ne sont pas beaucoup plus élevées que celles mesurées dans les liquides (non confinés).La charge rapide des supercondensateurs empêche l'utilisation des techniques in situ habituelles pour suivre leur évolution au cours du temps. Souvent, le temps nécessaire à l'enregistrement d'un spectre ou d'un diffractogramme est plus long que le temps de charge.Cependant, des techniques telles que la spectroscopie infrarouge ou le SAXS ont permis de suivre l'évolution de la structure à l'échelle des quelques secondes au cours de trifluorométhylsulfonyl)imide) dans une électrode CDC ou encore une solution aqueuse de CsCl dans une électrode de carbone activé[22,23]. La RMN et l'imagerie de résonance magnétique (IRM) permettent également de suivre l'évolution des ions, à condition d'utiliser des cellules de mesure in situ avec un design particulier qui permet d'enregistrer la signature d'une seule électrode à la fois.Enfin, la simulation moléculaire a permis de comprendre l'origine microscopique de la rapidité de charge. En particulier, l'étude des trajectoires de dynamique moléculaire permet d'extraire des propriétés de transport difficilement mesurables telles que les coefficients de diffusion des différentes espèces. Des travaux récents ont ainsi montré que les coefficients de diffusion des ions dans les électrolytes sont généralement diminués d'un ou deux ordres de grandeurs dans les électrodes (électrolytes confinés) par rapport au liquide (non confiné)[24], mais de fortes variations sont observées avec le remplissage des électrodes dans le cas des RTILs. Dans les CDCs, la connectivité du réseau de pore joue bien sûr un rôle important sur les propriétés de transport. A partir des résultats de simulation moléculaire, nous avons pu faire le lien avec un modèle de circuit électrique équivalent (voirFigure 5) et remonter ainsi au temps de charge pour une électrode réelle, de l'ordre de 1 à 10 s[25]. Ceci confirme les bonnes capacités prédictives de ces simulations, y compris du point de vue dynamique.VIII. Conclusion et perspectivesLa compréhension des mécanismes fondamentaux à l'échelle microscopique ces 5 dernières années fournit une base solide pour la conception de meilleurs supercondensateurs, en suggérant de nouvelles stratégies pour l'optimisation du stockage de la charge par une combinaison adéquate de structure des électrodes, d'ions et de solvant. L'utilisation à grande échelle des outils expérimentaux et de simulation développés pour établir ces mécanismes sera la clé du succès pour atteindre cet objectif.
Fig. 2 .
2(a) Capacité électrique par unité de surface obtenue pour le liquide ionique EMI-TFSI à 60°C avec des électrodes en carbones dérivés de carbures (CDC), en fonction de la taille moyenne des pores de l'électrode. Reproduit de Simon et Gogotsi, Nat. Mater. 2008, 7, 845-854 [5] avec la permission de Nature Publishing Group. (b) Exemples de structure de carbones: pores réguliers (fentes ou nanotubes) ou désordonnés (CDC). Reproduit de Salanne et al., Nature Energy, 2016, 1, 16070 [6] avec la permission de Nature Publishing Group.
Fig. 3 .
3(a) Schéma d'une microbalance à quartz électrochimique (EQCM). L'électrode de travail (WE) est déposée sur un quartz piézoélectrique qui permet de mesurer la variation de masse au cours de la charge (ici la contre-électrode CE est en platine). (b) La comparaison des résultats expérimentaux à la loi de Faraday (Equation 2) pour des ions nus ou solvatés permet de déduire les mécanismes qui interviennent en fonction de la polarisation de l'électrode.
Fig. 4 .Fig. 5 .
45Simulation moléculaire d'un supercondensateur constitué de deux électrodes nanoporeurses de Carbone Dérivé de Carbure (CDC), maintenues à une différence de potentiel constante, et d'un électrolyte liquide ionique à température ambiante. Les ions du liquide ionique, l'hexafluorophosphate de butyl-méthyl-imidazolium (BMI-PF 6 ), sont décrits par un modèle à "gros grains" (trois sites pour le cation, en rouge, un seul pour l'anion, en vert). Pour une différence de potentiel nulle (Ψ=0.0V), il y a autant de cations que d'anions dans chaque électrode, et la charge de ces dernières est nulle. Pour une différence potentiel de 1V, il y a un excès de cations dans l'électrode négative (Ψ=-0.5V) et un excès d'anions dans l'électrode positive (Ψ=+0.5V). Dans les deux cas, la charge nette du liquide dans l'électrode est compensée par la charge de cette dernière. La charge locale de l'électrode (négative en vert, positive en rouge) est illustrée, dans chaque cas, sur la partie droite de la figure correspondante. Ce mécanisme d'échange d'ions entre les électrodes diffère radicalement de ce qui se passe près d'une électrode plane de graphite. Reproduit de Merlet et al. Nat. Mater., 2012, 11, 306 [21] avec la permission de Nature Publishing Group. La dynamique de charge peut être étudiée par simulation moléculaire en mesurant la charge des électrodes en fonction du temps lorsque l'on passe d'une différence de potentiel nulle à une valeur non-nulle (où l'inverse). Compte tenu de la taille nanométrique du système simulé, on ne peut directement comparer ces résultats aux données expérimentales. On peut par contre les analyser à l'aide d'un modèle de circuit électrique équivalent similaire à ceux utilisés par les expérimentateurs. Les paramètres correspondant à un modèle de ligne à transmission (résistance de l'électrolyte R bulk , résistance et capacité par unité de longueur d'électrode R l et C i ) sont ainsi déterminés, ce qui permet d'extrapoler à un temps de charge pour un grain d'électrode de taille micrométrique (dans ce modèle, le temps de charge croît comme le carré de la taille) de quelques secondes, en accord avec la caractérisation électrochimique. Reproduit avec la permission de Péan et al., ACS Nano, 2014, 8, 1576 [25]. Copyright 2014 American Chemical Society. Encadré 1: Electrolytes pour les supercondensateurs Trois types d'électrolytes liquides sont utilisés dans les surpercondensateurs actuels. Les électrolytes aqueux sont avantageux du point de vue environnemental et de la sécurité, mais ils possèdent une fenêtre électrochimique limitée. Cette dernière peut être fortement élargie en utilisant des solvants organiques avec des ions dissous, voire des liquides ioniques à température ambiante. Ces derniers possèdent cependant des conductivités ioniques relativement faibles.
de variation de volume dans les électrodes au cours des cycles de charge/décharge (la charge Les supercondensateurs sont utilisés pour deux applications principales, qui sont la fourniture de pics de puissance et la récupération de l'énergie ; pour cette dernière, c'est la vitesse de recharge qui est exploitée[2]. On les retrouve en petit format (cellule de capacité de moins de 100F) en électronique de puissance. Les formats plus importants (capacité de plus de 100F Ils permettent également, en association avec les batteries, d'augmenter la durée de vie de ces dernières en fournissant les pics de puissance qui sont les plus contraignants pour la batterie.restant en surface) permet aux supercondensateurs d'atteindre des cyclabilités de plusieurs
millions de cycles à température ambiante, soit bien plus que pour les batteries (typiquement
quelques centaines). Enfin, l'utilisation de solvants comme l'acétonitrile permet un
fonctionnement entre -40°C et +70°C. Rappelons toutefois que la densité d'énergie est
environ 30 fois plus faible que celle des batteries.
par cellule) sont utilisés par exemple dans l'aéronautique (A380), l'automobile, les tramways
et les bus (fonction stop and start et récupération de l'énergie de freinage), ou encore les grues
portuaires (récupération de l'énergie potentielle)… Des applications récentes utilisent les
supercondensateurs pour la traction électrique dans les bus qui font des arrêts réguliers.
L'autonomie limitée (quelques minutes) reste suffisante pour rouler en mode tout électrique
entre deux arrêts, et la recharge se fait en moins d'une minute pendant l'échange de passagers.
Jusqu'en 2005, le modèle classique utilisé pour décrire l'adsorption des ions dans les pores
des carbones prévoyait que seuls les pores de taille comprise entre 2 et 10 nm (les mésopores)
permettaient un stockage efficace des ions ; la plupart des travaux étaient donc orientés vers la
synthèse de carbones mésoporeux pour maximiser la capacitance. La découverte de
l'augmentation de la capacité dans les nanopores (de taille inférieure à 1 nm, c'est-à-dire
inférieure à la taille des ions solvatés) a conduit à complètement repenser l'adsorption des
ions dans les pores confinés, et donc la charge de la double couche à l'échelle nanométrique
[4]. Du point de vue pratique, la première conséquence a été l'utilisation, dans les systèmes
commerciaux, de carbones microporeux dont tout le volume poreux provient de pores de taille
inférieure à 2 nm [5]. Du point de vue scientifique, il a fallu développer de nouvelles
techniques, expérimentales et théoriques, pour essayer de comprendre l'organisation des ions
de l'électrolyte dans les pores nanométriques et sub-nanométriques des carbones pour essayer
d'expliquer ces capacités élevées dans ces pores confinés [6]. Ces 5 à 10 dernières années, les
techniques de caractérisation in situ par diffusion aux petits angles des rayons X (SAXS) et
des neutrons (SANS), ainsi que les approches théoriques par dynamique moléculaire classique
ou ab initio [7] ont permis de faire des avancées importantes dans le domaine. Le
développement de techniques électrochimiques avancées, comme la microbalance à quartz
électrochimique couplée à des techniques spectroscopiques comme la RMN, ont également
été à l'origine de progrès notables, en contribuant à comprendre le transport et l'adsorption
des ions dans les pores. Nous développons ici le sujet abordé succinctement dans un récent
de la taille de pore à partir des mesures d'adsorption d'argon, pour comparer différents carbones. On préférera toutefois les capacités gravimétriques (F.g -1 d'électrode) ou volumétriques (F.cm -3 d'électrode) qui sont mesurables directement, sans avoir recours à des considérations théoriques ou structurales.Il est beaucoup plus délicat de caractériser la "vraie" structure des carbones nanoporeux, car il n'est à ce jour pas possible de le faire à partir d'approches purement expérimentales. On a ainsi recours à des combinaisons modélisation/expérience. Par exemple, la diffraction des rayons X et le SAXS permettent d'obtenir des informations structurales à courte et longue distance. Mais l'on obtient en général des informations structurales à 1D, et le passage à la structure 3D se fait souvent en recourant à des simulations de Monte Carlo hybride inverse[12]. Une approche combinant RMN, rayons X, spectroscopie Raman et simulation sur réseau a ainsi récemment permis d'estimer la taille des domaines graphitiques dans les carbones poreux, tandis que des simulations de trempe de dynamique moléculaire ont permis d'obtenir des structures de carbone réalistes sans partir de données expérimentales
électrique lors de l'application d'une différence de potentiel entre les électrodes. Les premières mesures de RMN in situ ont montré que ce n'est pas le cas. Même à faible concentration en électrolyte, on observe un décalage vers les basses fréquences du signal RMN, induit par les courants de cycle aromatique des domaines graphitiques et la susceptibilité magnétique du carbone [14]. Les résultats indiquent que les ions ainsi que le solvant sont bien présents dans les pores. La situation à 0 V est donc mieux décrite par l'interpénétration de deux structures hétérogènes: le carbone solide d'une part, et l'électrolyte d'autre part. Par des simulations de dynamique moléculaire, nous avons pu confirmer cette image, en montrant qu'un liquide ionique en contact avec une électrode de carbone nanoporeux entre spontanément dans les nanopores y compris en l'absence de différence de potentiel. diffusion au petits angles des rayons X ou de neutrons, en exploitant le contraste entre le carbone et l'électrolyte, pour préciser par exemple l'entrée ou non dans les pores de plus petite taille. résultats aient été obtenus avec des carbones à porosité contrôlée dans le domaine des micropores (<1,5 nm), ces techniques électrochimiques classiques ne donnent pas accès à des informations quantitatives sur, par exemple, le nombre de molécules de solvant perdues lors de l'adsorption dans les nanopores.La spectroscopie RMN permet de plus de quantifier la concentration des ions adsorbés au sein
de l'électrode [15]. Celle-ci est proportionnelle à la concentration dans le volume de
l'électrolyte, ce qui confirme l'affinité des ions pour le carbone. Cependant, à l'échelle de
temps de la mesure RMN, les ions diffusent dans la structure poreuse et sondent différents
environnements, ce qui conduit à des spectres larges. Il n'est donc pas aisé de préciser les
populations des différents sites d'adsorption par cette technique. On peut alors recourir à la
En combinant diffusion de neutrons et simulations moléculaires, Bañuelos et al. ont conclu
qu'un liquide ionique à température ambiante (RTIL) couvrait la surface des pores d'un
carbone à porosité hiérarchisé de manière uniforme, plutôt que de remplir certains pores
complètement avant de passer à d'autres. Différentes observations ont été faites dans le cas
des électrolytes aqueux, suggérant que la chimie de surface du carbone et la nature de
l'électrolyte jouent un rôle important sur les propriétés de mouillage. Récemment, Kondrat et
Kornyshev ont proposé d'utiliser des pores "ionophobes" pour la conception particulière d'une
nouvelle génération de supercondensateurs [16]. Cette idée, dont la faisabilité expérimentale
reste à démontrer, repose sur le fait que de tels pores se rempliraient seulement à haut
potentiel, ce qui ouvre des perspectives intéressantes en termes de densité d'énergie et de
vitesse de charge/décharge.
IV. Désolvatation dans les nanopores
La découverte que les ions d'un électrolyte pouvaient accéder et s'adsorber dans des pores de
dimensions inférieures à la taille des ions solvatés a été le point de départ d'un grand nombre
de travaux sur l'étude du confinement des ions dans les nanopores de carbone. Du point de
vue expérimental tout d'abord, les résultats des caractérisations électrochimiques classiques
(voltammétrie, chrono-potentiométrie ou encore spectroscopie d'impédance électrochimique)
ont conduit à proposer que l'accès à ces nanopores se faisait en perdant une partie de leur
cortège de solvatation. De plus, la capacité était fortement augmentée lorsque la taille des
pores était du même ordre de grandeur que celle des ions nus [4,5]. Cependant, bien que ces
RemerciementsLes auteurs remercient leurs collègues Pierre-LouisTaberna et Barbara Daffos à Toulouse
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. Figures, Figures et légendes
Les lignes diagonales indiquent le temps caractéristique de charge/décharge. (b) Représentation de la double couche électrochimique à la surface d'une électrode plane chargée négativement. Le modèle de condensateur plan prédit une capacité C proportionnelle à l'aire A de l'électrode et inversement proportionnelle à la distance d de séparation des charges. (c) Dans le cas d'un carbone poreux de grande surface spécifique. Le diagramme de Ragone représente les différents dispositifs de stockage de l'électricité en fonction de leur puissance spécifique (puissance par unité de masse) et de leur énergie spécifique (énergie par unité de masse). ici supérieure à 1000 m 2 .g -1 ), la prédiction de la capacité est plus délicateFig. 1. (a) Le diagramme de Ragone représente les différents dispositifs de stockage de l'électricité en fonction de leur puissance spécifique (puissance par unité de masse) et de leur énergie spécifique (énergie par unité de masse). Les lignes diagonales indiquent le temps caractéristique de charge/décharge. (b) Représentation de la double couche électrochimique à la surface d'une électrode plane chargée négativement. Le modèle de condensateur plan prédit une capacité C proportionnelle à l'aire A de l'électrode et inversement proportionnelle à la distance d de séparation des charges. (c) Dans le cas d'un carbone poreux de grande surface spécifique (ici supérieure à 1000 m 2 .g -1 ), la prédiction de la capacité est plus délicate.
| sample_545 | 0.9733 | arxiv | |
Future change in the solar wind and Central England temperature: implications for climate change attribution
Ian R Edmonds iredmonds@aapt.net.au
Physics Department
Queensland University of Technology
BrisbaneAustralia (Retired)
Future change in the solar wind and Central England temperature: implications for climate change attribution
1 FutureCETarxiv.docx
The recent increase in global temperature is attributed by the IPPC to anthropogenic global warming, (AGW), with a minor role for natural trends in temperature due to solar activity and volcanism. The IPPC estimates natural temperature (NAT) from climate models and attributes the difference from recent recorded temperature to AGW. This paper uses the temperature record to assess if trends in temperature are due to NAT or AGW effects. The method requires long records like the 362-year Central England temperature (CET) record. The CET was divided into a 262 year-long early part when only NAT was significant, and a 100 year-long later part. The early part was decomposed into eight components in the spectral range 15 to 257 years and the components were forward projected to the next 100 years. The projected NAT replicated the recorded cooling from 1950 to 1980 and the rapid increase from 1980 to 2010, indicating that the recent strong 50-year trend in CET was primarily NAT. Based on the small difference between the projected NAT and the recorded CET a minor role was attributed to AGW and a climate sensitivity to CO2 doubling, T2CO2 = 0.7 +/-0.2 C, was estimated. Components, at 514 and 1028 years, were derived from the CET record providing a means for validation of long projections against proxy records of past temperature. Future projection of combined NAT and AGW indicated a cooling of CET by 0.5 C from now to year 2060 before AGW becomes dominant. The possible cause of an imminent decrease in CET was explored by applying the same method of component estimation to temperature data from Melbourne, Australia (MET) and the geomagnetic aa index, a proxy for the solar wind. Comparing cyclic variations of the aa index and the CET and MET data indicated a complex relationship with the strong recent increase in CET and MET lagging the increase in the solar wind by ~15 years.HighlightsNovel method used to decompose the CET and aa index into cycles Forward projection of past CET onto recent CET demonstrates recent CET is primarily natural Observational determination of CET sensitivity to CO2 doubling = 0.7 +/-0.2 K Exploration of the complex lagged relationship between the solar wind and temperature
Introduction.
The prospect of catastrophic global warming, as a result of increasing anthropogenic emissions, has resulted in the prediction of future climate change becoming a critically important area of science, IPCC (2013b). The variation in long temperature records such as the Central England temperature, (CET), is due to natural variations and, in more recent times, according to the IPCC, the effects of anthropogenic emissions, principally CO2 and SO2, IPPC (2013a). The radiative forcing due to CO2 is given by F = 5.35ln(C/C0) Wm -2 , Myhre et al (1998). The change in temperature due to CO2 forcing is given by
∆ = ∆T = 5.35ln( / 0 )(1)
where C is the current CO2 concentration, C0 the pre industrial CO2 concentration, and is a sensitivity factor or attribution factor, the value of which depends on how much of recent temperature change is attributed to the forcing due to CO2 emissions, (IPPC 2013a, Hansen et al 2011. Natural temperature (NAT) variation is due to solar irradiance variation, volcanism, oceanic oscillations such as the Pacific Decadal Oscillation, and other factors such as cloud changes due to changes in cosmic ray flux, Dorman (2021). If is known equation 1 can be used to predict future AGW for various CO2 emission scenarios, (Stott et al 2006a, IPCC 2013b). However, due to uncertain feedback effects in the climate system is difficult to calculate from first principles. To estimate computer models of NAT are made and the difference between recorded temperature and the modelled NAT is attributed to different effects including AGW, (Stott and Kettleborough 2002, Stott et al 2006a, Knutson et al 2006, Stott et al 2006b. The temperature change attributed to CO2, T, and the current CO2 concentration, C, are used with equation 1 to determine a value for the sensitivity, . If all the temperature increase since 1850, 1.2 C, is attributed to the increase of CO2 from 300 to 400 ppm, the sensitivity factor = 0.8 K/Wm -2 . This is a very simplified description of attribution based on climate models, currently a complicated, vast, and expensive scientific endeavour. Attribution is the critical process and relies on accurate modelling of NAT.
The CET, extending over 362 years from 1659 to 2022, Figure 1, is the longest instrumental record of temperature, (Manley 1974, Parker et al 1992. The linear trend in CET is 0.28 o C/century and the variance of CET is high; the standard deviation of the detrended CET is 0.6 o C. The high variance in CET presents challenges in attributing the contribution of AGW to CET. One approach to attribution that can be used with long temperature records is to compare historic trends in NAT with recent trends in NAT. If a recent trend is uniquely high, the trend could be regarded as unlikely to be due to NAT and, on that basis, attributed to AGW. Karoly and Stott (2006) applied this approach to the CET and attributed the recent 50year trend in CET to AGW. The approach is valid only if the entire temperature record is considered. Karoly and Stott (2006) omitted the first part of the CET record that, according to recent work, shows a 50-year trend, 1690 to 1740, of 0.35 o C/decade, significantly stronger than the recent 50-year trend, 0.27 o C/decade, Zhou 2013, Gonzalez-Hildalgo 2020). If all the recent increase in CET is attributed to AGW, would be 0.8 K/Wm -2 and the projected increase in CET would follow the dotted line in Figure 1, a projection predicting an increase of CET of about 5 o C from present levels by 2100 and a climate sensitivity due to doubling of CO2, T2CO2 = 3.3 o C. The CET experienced a positive 50-year trend in the past, evident in Figure 1, between 1690 to 1740, significantly larger than the recent trend, Zhou 2013, Gonzalez-Hildalgo et al 2020), so the question of attribution arises: Is the recent high trend in CET primarily attributable to AGW or is it primarily attributable to the same natural effect that resulted in the earlier and larger trend? If the recent 50-year trend in CET was primarily natural the fitting of an AGW scenario to the recent trend as in Figure 1 would overestimate future temperature change: a viewpoint supported by several recent analyses of various temperature records, (Wu et al 2011, Loehle and Scafetta 2011, Tung and Zhou 2013, Abbot and Marohasy 2017.
Clearly, the strong variations in CET before 1900, Zhou 2013, Gonzalez-Hidalgo 2020), were due to natural effects. The earlier variation could be due to natural variation such as volcanism and/or due to some complex superposition of natural cycles originating from solar irradiance and cosmic ray variation, de Jager (2005). There is considerable evidence of cycles in the CET, (Plaut et al 1995, Baliunas et al 1997, Tung and Zhou 2013, as well as evidence of long-term persistence in the CET, Gonzalez-Hidalgo (2020). Spectral analysis of other long temperature records provides evidence of cyclic behaviour, , Humlum et al 2012, Scafetta 2010 CET CET trend 0.28 C/century AGW scenario than the CET record length was achieved with a new method of spectral decomposition. Cycles were fitted to the components and the cycles were projected and superposed to obtain back and forward projections of the CET. In section 4 the validity of this approach was assessed by back projecting the CET and comparing with proxy records of past temperature. In Section 5 the same process of component and cycle identification was applied to the CET data in the time range 1659 to 1921 and a forward projection to the 100 years from 1921 to 2021 was made and compared with the actual CET data for that interval, in particular the time interval 1950 to 2010 that exhibits the recent strong 50-year trend in CET, Figure 1. This forward projection was used to attribute the recent temperature variation between natural and secular effects and assess climate sensitivity. In the last part of Section 5 the change in temperature was compared with the change in aa index, a proxy for the solar wind. Section 6 discusses the validity of IPCC projections of catastrophic temperature increase in the light of the projection of this paper of imminent temperature decrease. Section 7 is a conclusion.
Data sources
Annual mean Central England temperature, (Manley 1974, Parker et al 1992 Figure 2, was assessed by standard Fourier analysis. There are narrow peaks in the short period range, 15 to 57 years, but, due to limited resolution of the Fourier analysis, in the longer period range peaks are replaced by bands; one broad band between 60 and 100 years and the other between 200 and 400 years. It was noticed that the periods of some of the narrow peaks corresponded closely to harmonics of the Uranus-Neptune conjunction period, TUN = 171.4 years. For example, 57 = TUN/3, 34 = TUN/5, 24 = TUN/7, and 15 = TUN/11. In the absence of other criteria, the spectral range was divided into bands with centre periods, T, based on harmonic and simple factors of TUN, i.e., selecting bands with centre periods, T, by using the relation nT = mTUN where n and m are small integers. The basis for selecting periods based on TUN is strong evidence, as outlined in detail in Appendix A3, that both solar activity and temperature records are dominated by cycles with periods close to harmonics and sub harmonics of TUN. Further, back projection of the CET, as developed later in this paper, reproduces both the coarse and fine detail of proxy temperature records over the last two millennia when the back projection is based on decomposing CET into cycles based on harmonics and sub harmonics of TUN, c.f. Section 5.4.
The centre periods used correspond to the labelled reference lines in Figure 2 with two exceptions. Spectral power at the period TUN is absent from the CET record for reasons outside the scope of the present article to discuss; but see McCracken et al (2014). The labelled period at 114 years, T = 2TUN/3, was omitted for reasons outlined in Appendix A1.
Method of decomposition of the detrended CET into cycles.
The detrended CET was decomposed into components based on eight frequency bands of centre frequency k/TUN where k = 2/3, 2, 5/2, 3, 4, 5, 7, and 11. For example, for k = 3, the band centre frequency is 3/TUN = 0.0175 yr -1 , corresponding to the period 57.13 years. The method of decomposition is illustrated in Figure 3 where the 24.5-year component, k = 7, is obtained. A Press band reject filter, Press et al (2007), as implemented in the DPlot application, is applied to the detrended CET. To reject the 24.5-year component the centre frequency of the Press filter was set to 1/24.5 = 0.0408 yr -1 and the filter bandwidth set to 10% of the centre frequency, 0.004 yr -1 . The filtered CET is then subtracted from the unfiltered CET yielding the 24.5-year component, indicated by the bold blue line in Figure 3. The time variation of this component is consistent with the time variation of the 24-year component in CET obtained by the more conventional method of continuous wavelet spectrum analysis, Tung and Zhou (2013). The eight components obtained are shown in Figure 4. As each component is decomposed from a frequency band the components, as expected, show significant variation in amplitude and phase. However, due to the narrow filter bandwidths the largest phase shift of any component over the 362-year record was a 1/2 cycle shift for the k = 11, 15-year component. The average phase shift of the eight components is 1/6 of a cycle indicating that fitting a cycle to each component, apart from the k = 11, 15-year component, is a very good approximation. A comparison of the sum of the eight components with a seven-year running average version of detrended CET, Figure 5, indicates that the sum of the eight components closely reconstitutes the detrended CET. The correlation coefficient, r = 0.92. In the following CET will refer to the seven-year running average of the annual mean CET. To project CET backward or forward it is necessary to approximate components with sinusoids. The approximation was obtained by fitting sinusoids of the form 0.15cos(2ki(t -ti)/TUN) to each of the components in Figure 4. Here ki/TUN defines the frequency of the ith sinusoid. For example, when ki = 3, ki/TUN = 0.0175 yr -1 corresponding to period 57.1 years. The year ti defines the phase of the sinusoid. The fit is obtained by adjusting ti to maximise the correlation coefficient between the component and the fitted cycle. The resulting eight cycles, the sum of the cycles, and the detrended CET are shown in Figure 6. The approximation of the detrended CET with the eight constant amplitude cycles, Figure 6, reduces the correlation coefficient to r = 0.68, Figure 6. However, the major features, the high warming trend 1690 to 1740, the cooling 1950 to 1980, and high warming trend 1980 to 2010 are retained.
The variation in CET due to long period cycles.
It is evident that the linear trend of CET, 0.28 o C per century, Figure 1, cannot extend indefinitely into the future or extend indefinitely into the past and must be due to long term cyclic variations in temperature imposed on the CET. Fourier analysis of the 362-year CET record, Figure 2, has insufficient resolution to uncover very long cycles. However, proxy records of solar activity and related quantities are available over much longer intervals (Castagnoli et al 1992, Rigozo et al 2010, Abreu et al 2012, Scafetta 2012, McCracken et al 2013, McCracken et al 2014. Fourier analysis of the records revealed the presence of long period cycles in solar activity several of which occur at periods close to harmonic and sub harmonic periods of TUN. The ~1000-year Eddy cycle, (Eddy 1976, Ma 2007 is close in period to 6TUN = 1028 years. Castagnoli et al (1992) identified six major components at 1100, 690, 500, 340, 250, and 90 years, closely corresponding to periods at factors of TUN, respectively, 6, 4, 3, 2, 3/2, 1/2. One of the major periodicities obtained from proxy cosmic ray data by McCracken et al (2013) occurred at 510 years, close to 3TUN, and two of the periodicities, 976 years and 1126 years, are both close to 6TUN. Scafetta (2012) found strong components in proxy total solar irradiance data at 499 years, ~3TUN, and at 978 years, ~6TUN. Ludecke and Weiss (2017) used worldwide temperature proxies to construct a mean global temperature over the last 2000 years. The harmonic analysis of the mean global temperature showed strongest components at periods at 1000 years, ~6TUN, and at 460 years, ~ 3TUN. used components at 1190 years, ~6TUN, and at 560 years, ~3TUN, to reconstitute the Central Greenland temperature as obtained from the GSIP2 ice core. Abbot (2021) applied spectral analysis to eight proxy temperature records for the northern hemisphere and found the dominant periodicities in the millennial and centennial time range were ~1000 years and ~500 years. Based on this observational evidence the same method of band reject filtering as outlined above was applied to the CET record to find the components of CET at 3TUN (514 years) and at 6TUN (1028 years). Cycles of the same amplitude as previously, 0.15 o C, were then fitted to the components by the same correlation method as outlined previously. The sum of the two long period cycles obtained is shown in Figure 7. Also shown in Figure 7 is the sum of the two components, the CET anomaly, and the linear trend of the CET anomaly. It is apparent that the linear trend of 0.28 o C/century in CET obtained in Figure 1 is partly due to the long period cycles and partly due to the short-term temperature depression around 1700 and the short-term temperature enhancement around 2000. The two long-term cycles were added to the eight-cycle approximation of CET, Figure 6, and the sum of the ten cycles was obtained using
= 0.15 ∑ cos( 2πk i (t−t i ) T UN ) + 9.27 ℃(2)
Here i = 1 …10. The ith value of ki is, in sequence, 11, 7, 5, 4, 3, 5/2, 2, 2/3, 1/3, 1/6, and the ith value of ti is, in sequence, 1993, 2000, 2005, 1998, 2005, 2002, 2000, 2005, 2000, and 2130 years. The periods, in sequence, are 15. 6, 24.5, 34.3, 42.8, 57.1, 68.6, 85.7, 257, 514, and 1028 years. The constant temperature, 9.27 o C, is the average value of CET 1659 to 2021. With the two long period cycles included in equation 2 the correlation coefficient between the ten-cycle approximation and the CET record is increased to r = 0.78, Figure 8.
Backward and forward projection of the cyclic content of CET using equation 2.
The forward projection of the cyclic content of CET using equation 2 to the year 2500 is shown in Figure 9. There is short term variation in temperature due to the seven cycles in the period range 15 to 257 years superimposed on a longer-term variation due to the two cycles of period 514 and 1028 years. The shorterterm variation repeats at intervals of 343 years and gives rise to the rapid temperature changes evident at 1650, 2000 and 2350 years. The longer-term cyclic variation of CET can be best appreciated by calculating equation 2 with only the 514-year and 1028-year cycles, i = 9 and 10, included, as in Figure 10, to cover both back and forward projection. Figure 10 shows that the long-term cycles of period 3TUN and 6TUN years combine to produce the broad swings in CET between the Warm Periods and the Little Ice Ages that occurred during the past two millennia, as labelled in Figure 10 with the common terminology relating to the events. The multiproxy reconstruction of temperature by Ljungqvist (2016)
Attribution of temperature change between secular and natural effects
Attribution of recent trends in temperature to different forcings is the critical problem of climate science.
The previous section has shown the detrended CET can be closely approximated by eight components and approximated moderately well, correlation coefficient r = 0.68, by eight cycles. Decomposing a record into components and cycles does provide a view as to how various cycles combine to produce extreme excursions and strong trends. For example, it is evident in Figures 4 and 6 that the strong trends in the early part and in the recent part of the CET record are due to the 57.1, 68.5 and 86.7-year components repeating an in-phase condition after an interval of about 340 years. However, the positive interference of cycles in different parts of the record is not in itself useful for attribution as the cycles may have resulted from different effects on temperature at different times in the record; for example, volcanism in the early part of the record and AGW in the recent part of the record. The only unambiguous conclusion is that the strong trends in the early part of the record were not caused by AGW.
Attribution based on climate models of NAT is problematic due to the large uncertainty in the NAT output of different models, e.g., (Karoly et al 2003, Karoly andBraganza 2005). Therefore, there is considerable interest in methods of attribution that avoid using climate models, Hegerl and Zwiers (2011). Wu et al (2011) used ensemble empirical mode decomposition to decompose the global mean surface temperature into a low frequency oscillation and a high frequency, approximately 65-year period, oscillation, and estimated about one third of late twentieth century warming was due to NAT. Another method is to decompose the temperature record into high and low frequency components using low pass filtering. The components of temperature are then compared with components of forcing decomposed from the same frequency range. For example, Tung and Zhou (2013) 50-to-90-year period signal in CET varied coherently with both the global mean temperature and with the Atlantic Multidecadal Oscillation (AMO) and attributed much of the recent CET variation to the AMO.
Attribution by forward projection of early CET onto later CET.
As discussed in Section 4, approximating components with sinusoids provides for projection beyond the temperature record. Projection is especially useful to separate cyclic effects from secular or "one off" effects. It is generally accepted that AGW is the result of secular forcings that become strong after 1950 and that temperature change before 1950 is due primarily to natural effects, (Karoly et al 2003, IPCC 2013, IPCC Report 2021, Figure SPM.1, SPM.2b). It follows that, if NAT is cyclic, and the cyclic content can be accurately decomposed from temperature data before 1950, the cycles can be projected forward to assess the NAT after 1950. Loehle and Scafetta (2011) (2011) projected three cycles of period 71.7, 24.9, and 15.3 years, obtained from the Svalbard temperature record forward to 2035 and concluded that the late 20 th century warming in Svalbard is not going to continue for the next 20 -25 years. Abbot and Marohasy (2017) fitted cycles to records of proxy temperature before 1830 and projected the cycles forward for comparison with the proxy records in the interval from 1880 to the present; finding that the increase in temperature over the last 100 years can be largely attributed to NAT. The results in section 3 of this paper indicate that the detrended CET can be accurately characterized by eight cycles covering the spectral range between 15 and 257 years, a spectral range relevant for the assessment of the 50-year trend in CET in the interval between 1950 and 2010.
The CET record was divided into a 262 year long earlier part, 1659 to 1920, and a 100 year long later part, 1921 to 2021. The method for deriving an eight-cycle simulation of the detrended CET as outlined above was applied to the 262 year long data to obtain components and the approximate cycles in the same eight spectral bands between 15 years and 257 years. The periods of the cycles and the constant amplitude, 0.15 o C, of the cycles was retained, however, the phases, ti, of the eight cycles obtained differ and were, in sequence i = 1 to 8, as follows: 1994, 1999, 2004, 1996, 2012, 1997, 1994, and 2016. The projected CET obtained with these values in equation 2 is shown as the red full line in Figure 11, where the projected CET is compared with (1), the actual CET, and (2), the projected CET based on the entire, 362 year long, data record. Clearly, the projection from the early part of the record replicates, reasonably accurately, the later, 1921 to 2021, part of the record including the warming between 1930 and 1950, the cooling between 1950 and 1980, and the strong warming from year 1980 to year 2010. It is noticeable in Figure 11 that the second very narrow warming peak in CET at 2018 was not reconstituted from the 1659 to 1921 data or from the 1659 to 2021 data. This is due to the 15-year period cycle approximation being half a period out of phase with the 15-year component towards the end of the record as discussed in Appendix A2. This phase shift between cycle and component is an inevitable consequence of approximating a narrow band component with a single period cycle. The two forward projections to 2200, the one based on the earlier part of the record and the one based on the entire record are, as evident in Figure 11, closely similar. The correlation coefficient between the projected CET and the actual CET in the time interval 1921
-2021 is r = 0.55 indicating that the forward projection of the eight cycles reproduces CET in this interval moderately well. The correlation coefficient of the projection and CET in the 1921 to 2010 interval is r = 0.79. The result provides confidence in the forward projection capability of the method and confidence that the warming, 1920 to 1950, the cooling, 1950 to 1980, and the strong warming, 1980 to 2010, is primarily natural. The type of natural forcing that leads to the strong warming trend from 1950 to 2010 is not defined by this method. However, the possible candidates are solar activity and/or volcanism 5.2 Climate sensitivity to AGW. Previous work, for example Karoly and Stott (2006), attributed all the recent 50-year trend in CET to AGW with the implication that the sensitivity of temperature to CO2 is high and the projected temperature increase due to increasing CO2 is high. The forward projection of this high sensitivity scenario is illustrated in Figure 12 The correspondence of the forward projection obtained from early CET data, before changes in CO2 or SO2 were significant, to the CET data 1921 to 2021 provides strong evidence that the recent 50-year trend in CET is primarily natural. However, estimating the small change in CET at year 2000 that could be attributable to AGW is subject to high uncertainty because the change in CET due to AGW is a small difference between two near equal values, the CET record itself and the projected natural contribution to CET, c.f. Figure 12. The low sensitivity projection in Figure 12 was based on estimating that, of the 1.2 o C increase in CET from 1850 to 2000, just 0.2 +/-0.1 o C, or about 15% of the 1.2 o C increase at year 2000 is attributable to AGW. From the level of this projection at the time of CO2 doubling, t2CO2, the temperature change due to CO2 doubling is T2CO2 is 0.7 +/-0.2 o C, c.f. Figure 12. Even with CO2 concentration increasing at an exponential rate like the RCP8.5 scenario, the indication of the low sensitivity projection in Figure 12 is that, in the next few decades, CET will fall to a temperature about 0.7 o C below the current sevenyear average CET of 10.5 C, and remain near that lower temperature, ~ 9.7 o C, until about 2070 when CET will briefly rise to slightly above the current temperature. The projection indicates that CET will not be consistently above present temperatures until 2150. The projected temperature change in this low sensitivity forward projection is lower than the RCP8.5 projections of climate models, (Stott and Kettleborough 2002, Stott et Figure 12. For example, the IPCC RCP8.5 temperature projection at year 2100 is 4 o C above present levels and at year 2300 is 8 o C above present levels, (IPCC 2013 Figure 12.5), whereas the low sensitivity temperature projection of Figure 12 at year 2100 is 0.5 o C below present levels and at year 2300 is 2 o C above present levels. While considerably different from IPCC projections the low sensitivity, T2CO2 ~ 0.7 o C, projection should be viewed in the light of the recent hiatus in global temperature increase, Tung and Chen (2018), the decreasing estimates of climate sensitivity over time, Gervais (2016), the low climate sensitivity estimates based on other observational determinations, e.g., T2CO2 ~ 0.7 o C by Lindzen and Choi (2011), T2CO2 ~ 0.7 o C by Abbot and Marohasy (2017), the low sensitivity obtained by other methods of climate modelling, e.g., T2CO2 = 0.6 o C by Harde (2014) It is noted that the projections in Figure 12 are based on an exponential increase in concentration of CO2, C(t), given by the relation C(t) = C0 + exp(0.028(t -t0)). The increase approximates the Mauna Loa CO2 data record and the RCP 8.5 scenario of CO2 increase, Tollefson (2020). There are numerous scenarios for longterm CO2 concentration increase, some more plausible than others, (Hansen et al 2013, Moss et al 2010, Tollefson 2020. However, on current trends, a CO2 concentration of 500 ppm by 2050 appears probable. Based on this anticipated CO2 level and the projected SO2 concentration decrease, Bellouin et al (2011), and using the high climate sensitivity of ~ 0.9 K/Wm -2 , as proposed by, for example, (IPCC 2013, Figure 12.40, IPCC 2018, Ma et al 2022), the CET would be 2 o C higher by 2050, as in Figure 12. Based on the low climate sensitivity estimate of this paper the CET would be 0.5 o C lower by 2050. Thus, the CET in the next few decades should provide a clear indication of the relative validity of deterministic projections and climate modelling projections of climate sensitivity and future climate change.
Attribution of recent temperature extremes.
It is obvious, for example from Figure 8 and 9, that the CET has increased by about 2 o C during the 340 years between the Little Ice Age around 1680 and the year 2021; and by about 1 o C from year 1850 to the year 2021. It is also clear from this paper that the increase is primarily natural and is largely due to the two long-term cycles coming into positive interference at around year 2000, c.f. Figure 10. Currently, there is concern that AGW is having a catastrophic effect on climate; for example, the statement by the UN Secretary-General at the 2022 United Nations Climate Change Conference: "We are on a highway to climate hell with our foot on the accelerator", The Guardian (2022); or "Assessing "Dangerous Climate Change"", Hansen et al (2013). There is evidence that daily maximum temperatures and daily minimum temperatures have increased recently, (Karoly and Braganza 2005, Fischer et al 2021, IPCC 2021). An edited collection of reports of this type of evidence appears in an annual series, now eight years long, published by the American Meteorological Society from 2013 to 2020 titled "Explaining Extreme Events of 2XXX From a Climate Perspective", e.g., Herring et al (2014). A very brief summary of the findings therein is that recent record high temperatures can be attributed to AGW. Examples of research specific to England are papers attributing the record high CET of 2014 to AGW, King et al (2015), and the paper by Christidis et al (2020) attributing the record temperatures in the UK in 2019 to AGW. CET has trended upward from a minimum during the Little Ice Age, Figure 1, so it is to be expected that in recent times CET will be exceeding temperature levels and records set at previous times, Rahmstorf and Coumou (2011). It is clear, from the attribution analysis in Section 5.1, that, if the same type of analysis had been made on CET data as it existed in 1920, a forward projection from 1920 would have anticipated a spate of temperature records in the 2000 to 2020 interval. If the increase in CET, 1950 to 2010, is attributed primarily to AGW the rate at which new CET records occur would increase with time in proportion with the increasing trend in CET indicated by the extreme scenario in Figure 12, Rahmstorf and Coumou (2011). Under the low sensitivity scenario of Figure 12 the indication is that the spate of new record high temperatures in the first two decades of this century is a temporary phenomenon and new high temperature records will not occur until 2070.
Attribution of past temperature extremes.
Proxy estimates of Earth's surface temperature during the past two millennia are of considerable and controversial interest with respect to attribution science; see Smerdon and Pollack (2016) for a review. As well as forward projection, equation 2 can be back projected. Because equation 2 is based on cycles at harmonic periods and simple factor periods of TUN and as TUN is a constant of the solar system, forward and back projection by equation 2 does not accumulate error due to period selection error and projections can be made over long time intervals. A back projection of CET to the year -500 AD is shown in Figure 13. The extended warm periods around 0 AD, 1000 AD and 2000 AD in the projection coincide closely with the Roman, Medieval, and Modern Warm Periods identified from historical and proxy records of temperature, e.g. (Esper et al 2002, Mann et al 2008, Ljungqvist 2010, Buntgen et al 2011 Assessment Report 2013, Figure 5.7, Smerdon andPollack 2016, Ludecke andWeiss 2017), that indicate a slow 0.5 C swing between the Medieval Warm Period and the Little Ice Age with short term temperature variation increasing the swing to approximately 1 C. The back projection in Figure 13 shows two CET peaks, at year 975 and year 1045, that replicate the double temperature peak form of the Medieval Warm Period evident in new paleo-climate reconstructions, (Esper 2002, Moberg 2005, Mann et al 2008 th Assessment Report 2013, Figure 5.7). The back projection also shows two strong peaks at -55 and + 15 years that replicate the double temperature peak form of the Roman warm Period, Buntgen et al (2011). The coincidence provides further validation of the accuracy of equation 2 for long projections. Figure 13 shows that extended warm periods return at intervals close to 6TUN = 1028 years and that strong positive and negative 50-year trends return at intervals close to 2TUN = 343 years. For example, the strong 50-year trends in Figure 13 evident at around years 1000, 1350, 1690, and 2000 in Figure 13 are also evident in proxy temperature records; for example, at around year 1000 and 1350 in proxy records of Norther Hemisphere temperature, Mann et al (2008). It is interesting that the times of occurrence of strong 50-year trends match almost exactly the times of high spatial deviation between proxy temperatures from different regions of the Northern Hemisphere, Christiansen and Ljungqvist (2012). When the 343-year cycle of rapid CET variation overlaps with the extended warm periods in the projection the CET attains levels of 10.4 o C, about one degree above the long-term average CET level and about two degrees above the minimum CET level. The indication from the back projection is that Central England is currently experiencing mean annual temperatures similar to the mean annual temperatures during the Medieval and the Roman Warm periods. Further, Figure 13 indicates that natural CET has increased by about 1.2 o C during the last century and is now passing through the Modern Warm Period peak. It is well known that in a temperature record exhibiting a normally distributed temperature variation the fraction of temperatures that exceed some specified high temperature will increase exponentially as the mean temperature increases, (Hansen et al 2012, IPPC 5 th Assessment Report 2013, Figure 1.8). The indication from Figure 13 is that the current spate of record temperatures in England, (King et al 2015, Christidis et al 2020, is due to a similar pattern of high temperatures and rapid temperature change imposed on long a term temperature cycle similar to the pattern that characterised temperature variation during the Roman and Medieval Warm Periods.
Temperature variation over the past two millennia as projected in Figure 13 and as observed in proxy temperature records, (Mann et al 2008, Ljungqvist 2010, Buntgen et al 2011 th Assessment Report 2013, Figure 5.7, Ludecke and Weiss 2017), presents a serious challenge to current attribution science. It is known from ice core records of trace gases, for example, Rubino et al (2019), that CO2 concentration was essentially constant during the past two millennia and only began to increase from a level close to 280 ppm after 1800. Therefore, the temperature extremes of the Medieval Warm Period and the Little Ice Age along with the accompanying strong 50-year trends cannot be attributed to AGW and must be due to some other form of forcing, Shindell et al (2001). However, if the extremes and trends of the Medieval Warm Period and the Modern Warm Period are similar, as Figure 13 indicates, the attribution of the extremes and trends of the Modern Warm Period entirely to AGW is challenged. Mann et al (2009), suggest that "a better understanding of the influence of radiative forcing on large-scale climate dynamics should remain priorities as we work toward improving the regional credibility of climate model projections."
Origin of recent natural variation in CET.
The IPCC attributes the recent rapid increase in temperature solely to AGW, (IPCC 2007(IPCC , 2013(IPCC , 2021. This paper attributes the recent increase in the CET primarily to natural effects. Attribution to natural effects was based on the forward projection of the cyclic content derived from the CET when only natural effects were significant. The projection to the recent 100-year interval coincided closely with the CET record in that interval indicating recent trends in CET were primarily due to natural effects. Attribution between natural warming and AGW by forward projection does not require specification of the natural effect, only that the cycles forward projected were obtained from a time in the record when AGW was insignificant. The two types of natural effect considered by the IPCC are volcanism and solar activity. As volcanism reduces temperature it is not relevant to the recent rapid increase in temperature. Increased solar activity would increase temperature. However, according to the IPCC, the effect of solar activity in recent times, is negligible.
The geomagnetic aa index, Figure 14, recorded since 1868, by magnetometers in England and Australia, is a proxy for the strength of the heliospheric magnetic field in the solar wind and is related to other forms of solar activity such as total solar irradiance, sunspot number and cosmic ray flux, Lockwood et al (1999).. The aa index roughly doubled between 1900 and 1990 due to the doubling of the solar magnetic flux emanating from the Sun, Lockwood et al (1999). This is the same interval during which the CET increased by about 0.6 C, c.f., Figure 1. The aa index fell sharply between 1990 and 2021 while the CET increased by another 0.6 C during the same interval, c.f. Figure 1. However, forward projection in this paper indicates an imminent fall in CET temperature suggesting that CET may follow a change in aa index after a significant lag. As the aa index record is long it is possible to apply the same decomposition into components method to the aa index as applied in section 4 to the CET record. As we are interested in trends over intervals of 50 years the aa index record was decomposed into components from frequency bands with centre periods at 34, 43, 57, 68, 86 and 257 years, Figure 15A. Also shown in Figure 15A is the average of the six aa index components. Figure 15B shows the six components derived from the CET anomaly for the same period bands, c.f., Figure 4. It is evident that a strong peak in the aa index, due to the positive interference of all six aa components, occurs in 1990, about 15 years before the strong peak in CET at year 2005 that is due to the positive interference of all six CET components. A similar result is obtained for the Melbourne TMAX anomaly (MET) with the six components coming into positive interference about 18 years after the peak in the aa index components. The average curves in Figure 15A, 15B and 15C show the same general trends of an increase from 1900 to 1940-1950, a decrease to year 1970-1980, an increase to peaks when the temperature peaks lag the aa index peak by about 15 years and then a sharp decrease from the peaks. The aa index additionally shows a minimum occurred at 2012. Provided the approximately 15-year lag of temperature relative to the solar wind is maintained in the next few decades, c.f., Figure 16, the implication is a minimum in CET and MET occurring at year 2027 -2030. The correlation coefficient at zero lag between the two average curves in Figure 15A and 15B is r = -0.06, suggesting an insignificant relationship. However, if the lag was considered the correlation would be high. Figures 15A, 15B and 15C indicate a strong but complex relationship between the cyclic variation of the aa index/solar wind and the cyclic variation of temperature. Close examination of Figures 15A, 15B and 15C shows that, aside from a lag that reaches a maximum lag of 15 years near year 2000, the 257, 68, 57 and 43-year components of aa index and temperature vary mainly in-phase. The 86 and 34-year components of aa index and temperature vary out-of-phase. This suggests that the response of temperature to the solar wind involves at least two internal oscillations, such as the Atlantic Multidecadal Oscillation, the North Atlantic Oscillation, the Pacific Decadal Oscillation, or the El Nino Southern Oscillation Zhou 2013, Power et al 2017), that are forced by the solar wind and directly influence temperature. The results in Figure 15 indicate that the response of temperature to the solar wind is not amenable to simple regression analysis, as in de Jager et al (2010). For example, Figures 15A and 15B indicate that, while the aa index and CET anomalies, at zero lag, are negatively correlated in the 40-year interval between 1980 and 2020, the peak in CET at 2005 is likely a lagged response to the peak in solar wind/aa index at 1990. Lockwood and Frohlich (2007) used a method to analyse longer-term trends in solar activity and temperature between 1975 and 2007 and, noting the negative correlation, concluded that the rapid rise in temperature after 1985 could not be ascribed to solar variability. However, Lockwood and Frohlich (2007) did not consider the possibility that temperature change would significantly lag multidecadal solar forcing. It is relevant here that Li et al (2013) demonstrated that the North Atlantic Oscillation (NAO) is connected to the Northern hemisphere mean surface temperature over multidecadal time scales, of approximately 60-year period, with the NAO leading the surface temperature by 15-20 years and thus acting as a useful predictor of temperature change. Both the aa index/solar wind and the NAO peak at the same time, 1990, suggesting the two variables are related, c.f. , Schaife et al 2013. Figures 15B and 15C indicate that the peak in regional temperature around 2010 is common at widely separated locations suggesting the influence of external forcing.
By fitting cycles to the aa index components in Figure 15A a six-cycle composite of the aa index can be obtained in an equation similar in form to equation 2:
= 1.5 ∑ cos( 2πk i (t−t i ) T UN ) + 9.55(3)
Here i = 1 …8. The ith value of ki is, in sequence, 5, 4, 3, 5/2, 2, 2/3, 1/3, 1/6, and the ith value of ti is, in sequence, 1991, 1991, 1967, 1999, 2000, and 2130years. The periods, in sequence, are 34.3, 42.8, 57.1, 68.6, 85.7, 257, 514, and 1028 nT, is the average value of the aa index 1868 to 2020. The ti values at i = 7, period 514 years, and at i = 8, period 1028 years, were not derived from the aa index record but are the same as the values obtained from the CET record, i.e., the phases of the 514 and 1028 period cycles were inferred to be the same as the phases of the corresponding cycles derived from the, much longer, CET record. Equation 2 and equation 3 can be used by interested readers to explore the time relationship between the aa index and CET. For example, the back and forward projection of the aa index and the CET, Figure 16, shows that the aa index mostly leads the CET but sometimes lags, e.g., 1900 to 1950, illustrating the complexity of the relation. The lag of the CET relative to the aa index/solar wind appears to be amplitude dependent, increasing to ~15 years when the aa index and the CET experience strong trends, e.g., near year 1650 and near year 2000. It seems likely that the delayed response of the CET to increase in the aa index is due to thermal inertia of the upper mixed layer of the ocean, Soldatenko (2022). Gray et al (2013) found that the sea surface temperature in the North Atlantic/European region lagged the 11-year solar cycle by 3 -4 years or about 1/3 of a cycle and suggested the mechanism was solar forcing of the NAO, see Scaife et al (2013). See also Shindell et al (2001) who found "relatively small solar forcing may play a significant role in century-scale NH winter climate change".
Discussion
The changes in CET, 1659 to 2021, are quite complicated, Figure 1; however, the changes in temperature from 1900, when CO2 emissions started to become significant is the current focus of climate science, (Hansen 2011, Hansen et al 2013, IPPC 2013, IPPC 2018 (2013), and Figure 12. If the temperature hiatus continues, as projected for global temperature (Loehle and Scafetta 2011, Abbot and Marohasy 2017 or the temperature decreases in the next few decades as projected in this report and Li et al (2013) the challenge to the current climate modelling approach where the influence of external forcing is regarded as negligible would be severe.
This report indicates that the slow increase in CET, 1900 to 1950, was due to the positive phases of the 57, 68, and 86-year period components in CET beginning to overlap; the 1950 to 1980 decrease due to the negative phases of the same components nearly overlapping; and the sharp rise 1980 to 2000 due to the positive phases of the same components closely overlapping, Figure 4 and Figure 5. The hiatus, 2000 to 2021, would appear to be the transition interval between a lagged response to the increase in solar activity to a peak in 1990 and the lagged response of CET to a fall in solar activity from the peak in 1990. The projected decrease in CET between 2020 and 2050 indicated in Figure 12 and Figure 16, if it occurs, will be due to the negative phases of the 57, 68 and 86-year components in CET again closely overlapping before moving progressively out of phase. Thus, the observationally determined projection of CET indicates that the hiatus is likely a crest between the recent rise and the imminent decrease in CET. The result in Figure 15C for the Melbourne TMAX anomaly where the decrease in temperature from 2010 is evident provides support for the idea that the hiatus is more likely a crest.
By inference, any decreased climate sensitivity to CO2 concentration requires an increased sensitivity to solar activity and the accompanying effects, such as variation in total solar irradiance, cosmic ray flux and cloud cover. The analysis in section 5.5 provides evidence that change in CET is a complex lagged response to variation in solar activity. Revised estimates of solar irradiance, Ergorova et al (2018), indicate the effect may be about six times higher than the estimates used by the IPCC. Forward projections of solar activity, as in Figure 16 and in other studies, (Rigozo et al 2010, Shepherd et al 2014, do predict a strong decrease in solar activity from the grand maximum around year 2000. It is interesting that decreasing solar activity from 2000 onwards has recently been the subject of global climate modelling; for example (Ineson et al 2015, Maycock et al 2015, and interesting that the Coupled Model Intercomparison Project (CMIP) has replaced the stationary-Sun scenario in CMIP5 with more realistic scenarios in CMIP6 that include solar activity falling to a grand solar minimum around 2100, Matthes et al (2017). A strong increase in future volcanic activity would also result in a decrease in temperature. There is evidence of an approximately a 50-70-year oscillation in volcanic forcing of temperature over the last two millennia e.g. (Mann et al 2021, Sun et al 2022. However, apparently, no projections of near-future volcanic activity have been made.
Conclusion
The analysis in this paper indicates that the CET is currently passing through a relatively short interval, about two decades long, of higher-than-average temperature that is primarily natural and is the result of several of the natural cycles that contribute to CET variation coming into constructive interference. This is the reason record high temperatures have recently been recorded in Central England. Comparison of the cyclic content of the CET with the cyclic content of the aa index indicates that forcing of the CET may be due to a complex interaction of solar activity, solar wind, cosmic ray flux and cloud cover with the global oscillatory systems such as the NAO that directly influence oceanic and atmospheric temperature. This report projects a decrease of about 0.5 o C in CET during the next few decades with CET temperature continuously exceeding present temperatures from 2100 onwards if CO2 emissions continue to increase exponentially. The climate sensitivity, T2CO2, is estimated to be 0.7 +/-0.2 K.
Appendix
A 1. Selection of component periods. Basing the method of decomposing CET into cycles at periods based on simple factors of TUN is somewhat controversial. As pointed out earlier several of the shorter period peaks in the spectrum of CET and other temperature records are close to harmonics of TUN, Figure 2. The longest period component of CET resolvable by Fourier analysis occurs at 257 years making 3TUN/2 = 257.1 years an obvious choice as one of the centre periods for filtering. The spectral content in the broad band between 70 and 130 years in Figure 2 has no resolved peaks, however, the periods 68, 86, and 114 years cover the band reasonably well. The period 114 years was not used in equation 2 because the component at that period suffers a phase shift in the middle of the CET record and cannot be approximated as a single sinusoid. It is closely approximated by the term 0.075cos(21.5(t -2019)/TUN).cos(2(t -2000)/3TUN) o C. However, when this term is added as an 11 th term in equation 2 the correlation coefficient of projected CET with the CET record in Figure 8 improves only marginally, from 0.78 to 0.79. For this reason and the benefit of keeping equation 2 simple the term was not included. Figure 17. This results in the short-term discrepancy between recorded and projected CET at around 2020 evident in Figures 6, 8, and 11. A 3. Basis for using TUN to decompose CET into cycles. Decomposing the CET record into cycles with periods, T, given by nT = mTUN is based on evidence that the long-term periodicity of solar activity varies at harmonics of TUN, McCracken et al (2014), and evidence that temperature on Earth varies with the variation in solar activity, (Usoskin et al 2005, Haigh 2007, Gray et al 2010, Bae et al 2022. The periods of the first ten harmonics of TUN are 85.7,57.1,42.8,34.3,28.5,24.5,21.4,19.0,17.1 and 15.6 years and four,15,24,34, and 57 years, are evident in the CET spectrum, Figure 2. Other evidence that the harmonics of TUN are relevant to temperature variation is as follows: Previous Fourier analyses of the CET record are dominated by components with periods close to harmonics of TUN. For example, the three long period cycles Baliunas et al (1997) identified in CET, were at periods of 102, 23.5, and 14.4 years, periods close to the first, sixth and tenth harmonics of TUN. The five long period components in the Svalbard temperature record identified by
Figure 1 .
1CET 1659 to 2021 and the linear trend in CET of 0.028 o C/century. If the recent positive trend in CET between 1950 and 2000 is attributed entirely to AGW an AGW scenario can be fitted to this trend and used to make a forward projection of CET, the dotted line in the graph. The fit is obtained by assuming an exponential increase in CO2 concentration, C, between C0 = 300 ppm in 1850 and C = 400 ppm in 2010 and a logarithmic dependence of temperature on CO2 concentration, T = F = 5.35ln(C/C0). The temperature increase obtained is constrained to fit the recent trend in CET by adjusting the temperature to CO2 sensitivity factor, , to the value 0.80 K/Wm -2 , corresponding to a T2CO2 of 3.3 o C on CO2 concentration doubling from an 1850 level of 300 ppm to 600 ppm by the time of CO2 doubling, t2CO2, marked by the vertical reference line.
Figure 2 .
2Periodogram of detrended CET obtained by padded Fast Fourier Transform. The dotted reference lines are at periods corresponding to harmonics or simple factors of TUN = 171.4 years. e.g., 15 = TUN/11, 24= TUN/7, 34 = TUN/5, 43 = TUN/4, 57 = TUN/3, 68 = 2TUN/5, 86 = TUN/2, and 257 = 3TUN/2 years.
Figure 3 .
3Illustrates the novel decomposition method. To obtain the component of CET in the band with centre period TUN/7 = 24.5 years the detrended CET, red line, is filtered using a Press band reject filter of centre frequency 0.0408 yr -1 with 10% bandwidth, 0.004 yr -1 , green dots. The difference between the original CET and the filtered CET yields the 24.5-year period component of CET, blue bold line.
Figure 4 . 0023 Figure 5 .
400235The eight components decomposed from the detrended CET using the method of Press band reject filtration outlined in the text. The centre frequency and 10% bandwidth of each frequency band are indicated. The average amplitude of the components is ~0.15 o C. .48 0.0408 bw 0.004 5 34.28 0.02917 bw 0.003 11 15.58 0.0642 bw 0.0064 3 57.13 0.0175 bw 0.0017 2 85.7 0.01166 bw 0.0011 2.5 68.56 0.01458 bw 0.0014 2/3 257.1 0.00389 bw 0.0004 4 42.85 0.0233 bw 0.Adding the eight components in Figure 4 closely reconstitutes the seven-year running average of the CET. Of particular interest are the high 50-year trend 1690 to 1740, the increase from 1900 to 1950, the decrease from 1950 to 1980, the rapid increase 1980 to 2010 and the hiatus 2000 to 2021.
Figure 6 .
6Shows the constant amplitude sinusoidal cycles fitted to the components of Figure 4. The sum of the eight cycles, blue bold line, and the detrended CET, dots, are also shown. The approximation of the components by cycles results in a moderately good approximation to the detrended CET, correlation coefficient r = 0.68.
Figure 7 .
7Shows the seven-year running average of CET anomaly, i.e., CET minus the 9.273 o C average. Also shown the sum of the 514-year and 1028-year components, the sum of the 514 and the 1028-year period cycles approximating the components, and the linear trend of the CET anomaly.
Figure 8 .
8The ten-cycle approximation, equation 2, closely reconstitutes the CET. The correlation coefficient in the time range 1659 to 2021 is 0.78. The high 50-year trend, 1690 to 1740, the 0.5 o C rise, 1900 to 1950, the 0.5 o C decrease, 1950 to 1980, and the 1 o C increase from 1980 to 2010 are accurately reproduced by the ten-cycle approximation.
Figure 9 .
9The forward projection of the cyclic content of CET as given by equation 2. Note that the pattern of strong short-term variation, evident near years 1650, 2000 and 2350 repeats at intervals of 343 years The short-term variation is superposed on the longer-term cycles illustrated inFigure 10.
this back projection providing strong confidence in the projection capability of equation 2.
Figure 10 .
10The longer-term cyclic component of CET accurately reproduces the warm and cold periods identified in historical and proxy records of temperature.
used this projection method, decomposing a 20year cycle and a 60-year cycle from the global surface temperature record in the interval 1850 to 1950 and projecting the two cycles forward to 2010 to compare with the temperature record 1950 to 2010. From the comparison Loehle and Scafetta (2011) attributed 60% of the warming observed since 1970 to NAT. Humlum et al
Figure 11 .
11The cyclic variation of CET derived from the CET record 1659 to 2021 compared with the detrended CET, line with diamond symbols. The vertical reference lines indicate the time interval 1921 to 2021 and the time interval 1921 to 2010. In the 1921 to 2021 interval the correlation coefficient between the CET forward projection and the detrended CET is r = 0.55. In the interval 1921 to 2010 the correlation coefficient is r = 0.79. The difference in correlation is due to phase shift of the 15-year cycle relative to the 15-year component as discussed in Appendix A2.
Figure 12 .
12CET simulation based on 1659 to 2021 and to 1921 data.The seven-year running average of CET is shown by the blue broken curve. When the increase in CET from 1950 to 2000 is attributed entirely to AGW and the CO2 concentration continues to increase at the present rate, a temperature increase of about five degrees at year 2100 can be projected. The projected natural CET, calculated by equation 2, is also shown, as the green broken line that closely overlaps the CET before 2021. With the 50-year trend from 1950 to 2000 attributed primarily to natural variation a much lower climate sensitivity, = 0.10 K/Wm -2 , rather than = 0.87 K/Wm -2 , is appropriate. With = 0.10 K/Wm -2 the CO2 contribution to CET is shown by the black long-dash line. The forward projection of CET due to combined AGW forcing and natural forcing of CET is shown by the broken red line. Reading off the graph at t2CO2, for the low sensitivity curve the T2CO2 is now 0.7 K compared with T2CO2 = 3.3 K for the high sensitivity curve, c.f.Figure 1.
al 2006, IPCC 2013, Knutti et al 2017, Tollefson 2020) that resemble the high NATURAL CET (10 cycle sum + 9.273) AGW 100% change in CET at 2010 AGW 15% of change in CET at 2010 AGW + NATURAL sensitivity projection in
, T2CO2 = 0.6 o C, Coe et al (2021), in the light of projections of imminent decrease in solar activity, (Clilverd et al 2006, Steinhilber and Beer 2013, Velasco Herrera et al 2015, Yndestad and Solheim 2016, Matthes et al 2017, Velasco Herrera et al 2021), the recent fall of the heliospheric magnetic field, c.f.Figure 14, and imminent reduction in global warming,(Loehle and Scafetta 2011, Omrani et al 2022)
Figure 13 .
13The back projection of CET using equation 2. Also shown, broken red line, is the back projection with only the 514-year and 1028-year cycles in equation 2. It is evident that CET experiences extended Warm Periods at intervals of ~1028 years and extended cool periods, Little Ice Ages, also at intervals of 1028 years. Strong positive enhancements in CET occur at intervals of 343 years, e.g., at ~ year 0 and ~ year 343. Strong positive enhancements also occur within the extended cool periods, e.g., ~ year 680 and ~ year 1680, and within the extended warm periods, e.g., ~ year 0, ~ year 1000, and ~ year 2000. CET projected NATURAL and OBSERVED -500 to 2500.CET projected NATURAL long period CET OBSERVED CET
Figure 14 .
14Annual mean level of the geomagnetic aa index.
Figure 15 .
15The components of the aa index anomaly, (A), and the CET anomaly, (B), and the Melbourne TMAX anomaly, (C), derived from decomposition based on the periods 34, 43, 57, 68, 86 and 257 years. The average curves show that all components of the aa index positively interfere at year 1990 and all components of the CET and Melbourne TMAX positively interfere about 15 years later between year 2005 and 2010.
Figure 16 .
16Forward and back projection of the aa index anomaly (reduced by a factor of 10) and the CET anomaly using cycles with periods 34, 43, 57, 68, 86, 257, 514, and 1028 years in equations 2 and 3.
compare aa index and CET dual axis 1600 to 2200.
A 2 .
2Phase shift between the 15-year component and cycle. Of the cycles that are included in equation 2 the 15-year cycle suffers the largest phase shift relative to the corresponding component, about half a cycle over the 362-year record,
Figure 17 .
17Compares the TUN/11, 15.6-year, period component with the cycle approximation. The close to /2 phase shift of the cycle relative to the component around year 2000 results in the short-term discrepancy between recorded CET and projected CET at this time.
). This paper builds on this evidence by decomposing the CET into several components; each component derived from one of a series of spectral bands covering the period range 15 to 1000 years. Section 3 outlines how the extraction of components with period longeryear
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). The changes in CET from 1900 are relatively simple; four trends in the temperature are evident, an increase of about 1 C from 1900 to 1950, a decrease of about 0.5 C from 1950 to 1980, an increase of about 1 C from 1980 to 2000, and a hiatus or a crest from 2000 to 2021. In climate modelling the increase 1900 to 1950 is attributed 80% to an increase in CO2 and about 20% to an increase in solar irradiance; the decrease 1950 to 1980 is attributed to the combined effect of increases in CO2, aerosols, and volcanism; the increase 1980 to 2000 is attributed primarily to the rapid increase in CO2. In climate models the contribution from natural effects, specifically solar irradiance, to the increase between 1950 and 2000 is effectively zero,(Hansen et al 2011, IPCC 2021. The hiatus in CET, 2000 to 2021, presents a challenge for climate modelling and the hiatus generally is the subject of some controversy, e.g.,Fyfe et al (2016). With the CO2 concentration record continuing to increase exponentially at a rate equivalent to the RCP8.5 scenario and with the high climate sensitivity attributed to CO2 for the 1950 to 2000 change in CET, an increase of about 0.3 C would be projected by climate models for the interval 2000 to 2021, IPCC
are at periods83, 62, 36, 26, and 16.8 years, close to the first, second, fourth, sixth, and ninth harmonics of TUN respectively. The five significant periods identified in six central European instrumental temperature records,Ludecke et al (2013) were at 248, 80, 61, 47 and 34 years; close to the 257, 86, 57, 43 and 34 year-periods used here.Mann et al (2021) identified oscillations in global mean temperature over the last millennium with periods at66, 58, 43, 28, 24, 19, and 14 years all close to harmonics of TUN apart from 66 years. The period, 66 years, is close to period 2TUN/5 = 68.5 years that was used in this paper.
Acknowledgment. I acknowledge the use of CET data published by the Met Office, Hadley Centre for Climate Prediction and Research and aa index data from Geosciences Australia. I acknowledge useful comments by Don Field and Glen Johnston.
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| sample_555 | 0.9989 | arxiv | |
Don't Trust, Verify: Towards a Framework for the Greening of Bitcoin
2 May 2023
Juan Ignacio Ibañez j.ibanez@ucl.ac.uk
Alexander Freier freier@energiequelle.de
DLT Science Foundation
LondonUK
Centre for Blockchain Technologies
University College London
LondonUK
Facultad de Ciencia Política y Relaciones Internacionales
Universidad Católica de Córdoba
CórdobaArgentina
Energiequelle GmbH
FeldheimGermany
Don't Trust, Verify: Towards a Framework for the Greening of Bitcoin
2 May 2023Version: May 4, 2023Index Terms-BlockchainCarbon FootprintDecarbonizationSustainabilityRenewable Energy Sources
For more than a decade, Bitcoin has gained as much adoption as it has received criticism. Fundamentally, Bitcoin is under fire for the high carbon footprint that results from the energy-intensive proof-of-work (PoW) consensus algorithm. There is a trend however for Bitcoin mining to adopt a trajectory toward achieving carbon-negative status, notably due to the adoption of methane-based mining and mining-based flexible load response (FLR) to complement variable renewable energy (VRE) generation. Miners and electricity sellers may increase their profitability not only by taking advantage of excess energy, but also by selling green tokens to buyers interested in greening their portfolios. Nevertheless, a proper "green Bitcoin" accounting system requires a standard framework for the accreditation of sustainable bitcoin holdings. The proper way to build such a framework remains contested. In this paper, we survey the different sustainable Bitcoin accounting systems. Analyzing the various alternatives, we suggest a path forward.
I. I
Spearheaded by the revolutionary Bitcoin protocol and its cryptocurrency bitcoin, blockchain technology is evolving beyond mere promise and becoming a reality. However, blockchain in general and Bitcoin in particular have been starkly criticized for the high-energy consumption of the PoW consensus algorithm [1], [2]. This is mostly due to concerns that mining could aggravate climate change. Nevertheless, a growing body of literature is beginning to highlight that Bitcoin has the potential to be not only decarbonized, but furthermore to act as a net-negative carbon asset [3], [4].
In short, the contention is that the process of Bitcoin mining has unique characteristics that make it an exceptionally good complement to renewable energy generation, as it provides a load that is flexible, interruptible, non-rival, available, stable and reliable, highly price sensitive, scale agnostic, and portable, while at the same time producing an output whose price is not correlated to electricity prices and provides an additional source of revenue for the renewable energy seller [3]. This complementarity is expected to grow over time as mining profits fall (due to increased competition in the mining market and the Bitcoin halving) and as renewable energy imbalances grow (due to renewable penetration) [3].
Although the argument is plausible, whether such a phenomenon will act as a mere mitigation factor on Bitcoin's carbon footprint or as a true net-decarbonizing force for the energy grid as a whole remains an empirical issue. However, this does not mean that it is merely exogenous, as miners may have the ability to influence the protocol towards becoming the latter.
Specifically, if miners manage to monetize the green attributes associated with their activities, this may give them a competitive edge over other miners [4]. In turn, this ¿ could act as a tipping point factor, tilting the scale towards decarbonization.
A. State of the art and our contribution
Over time, a number of works have been produced seeking to give green Bitcoin miners an additional source of profit. Cross and Bailey [5] systematized the effects of holding and mining bitcoin for sustainability, and suggested an incentive offset scheme on this basis. Martinez [6] outlined a framework for carbon markets in Bitcoin that are consistent with existing environmental, social and governance (ESG) reporting standards, whereas SBP [7] did so by exploring the interplay of Bitcoin with energy attribution certificates (EACs). Nevertheless, no significant analysis systematizes the state of the art. We provide an up-to-date framework that fills this gap.
To do so, this paper is structured in the following form. First, we review forms of Bitcoin carbon accounting, comparing different estimation methods. Second, we survey proposed schemes to account for and incentivize Bitcoin greenness, exploring their advantages and disadvantages. We then discuss the findings and extract the key conclusions.
II. C B
The elaboration of a framework to account for green bitcoin attributes in terms of greenhouse gas (GHG) requires an understanding of carbon accounting for bitcoin emissions in the first place. We identify two sets of systems addressing different aspects of Bitcoin emissions. Firstly, systems that ascertain what percentage of the total emissions of a system are attributable to a particular subsystem (in this case the, Bitcoin protocol). Secondly, systems discussing the event that is causally associated with the emissions and which should act as the denominator for the emissions (emissions per event).
A. Estimation methods for total emissions
Calculating the total emissions of the Bitcoin protocol in a given grid requires the previous adoption of a philosophical position. Although in some cases of off-grid mining or arrangements between a miner and an energy seller that is putting in place additional generation to meet its obligations (giving rise in turn to external verification issues such as those associated with self-reporting), emissions accounting is not usually straightforward as it requires the prioritization of some emissions over others.
To analyze each method, we resort to the 3 carbon accounting constraints identified by Cross [8]:
1) "Compositionality. The sum of carbon footprints of actors in a system must equal the total footprint of the system. 2) "Marginality. The footprint of an action must reflect the difference between that action being taken and (counterfactually) not being taken." 3) "Fungibility. The footprint of any two users of the same energy over the same duration must be equal." a) Marginal emissions accounting: The marginal emissions method is a form of a before-and-after causal inference. If a miner plugged into the grid starts their operations, the difference between the grid emissions after the start of their operations and the emissions before the start is attributable to the miner. This can also be formulated as a hypothetical exante: the additional new emissions that the grid would have, if the miner started operations, are attributable to the miner. This can also be performed in reverse: the difference between the emissions that the grid would have if the miner turned off and the emissions that the grid actually has are the emissions that should be imputed to the miner. This approximation tends to highlight the fact that the baseline energy needs are met with renewable energy and only the net load once renewable energy is exhausted is met with fossil energy. In other words, fossil energy sources are the marginal seller.
This approach is intuitive and is usually employed by Bitcoin critics, presumably because Bitcoin is a rather new source of energy demand [9]. However, there are four problems with it.
1) It arbitrarily assigns "green energy" to the old energy consumers and "brown energy" to the new energy consumers, despite they are all consuming fungible electrons from the same energy grid, for no other reason than a first-come-first-served principle. Therefore, it sacrifices the fungibility of load (see discussion below). 2) If applied consistently to all energy buyers, it leads to results where the total emissions of the grid are much smaller than the sum of the individual emissions of all buyers. Therefore, it sacrifices the compositionality of the load. 3) It displays a very significant short-term bias that is inconsistent with how other loads are usually viewed, e.g.
batteries. An additional load may create an incentive for renewable buildout (demand leads to investment) resulting in a new equilibrium not considered by the marginal emissions figure. For instance, a battery may have high marginal emissions while at the same time enabling the deployment of additional renewable capacity. 4) Short-run marginal emissions may not coincide with long-run marginal emissions (and increasing marginal emissions may coexist with decreasing average emissions [10]).
b) Attributional accounting: Attributional accounting is the form of carbon accounting that takes the totality of a grid's emissions and attributes them to all the energy consumers. By starting from the total grid emissions, it preserves compositionality. The simplest form of attributional accounting is a simple average ("average emissions"), which results in a form of grid mix egalitarianism. Ryan et al [11] have identified numerous variants of attributional accounting.
Average emission factors preserve fungibility as well. Overall, their usefulness relative to marginal emission factors depends on the research questions (for instance, average emission factors are considered more appropriate for the attribution of responsibility [11]. However, they do not necessarily account for marginality, which is a useful notion.
c) Emissions based on EACs: Using EACs such as Renewable energy certificates (RECs) or guarantees of origin (GOs) could be considered a form of attributional accounting. However, due to their relevance to understanding the functioning of energy markets, we treat them separately. Under an EACs system, whether a miner has mined with green or brown energy is not directly related to miner's share of the grid mix or to the additional effect arising subsequently to the beginning of the miner's operations, but to whether the miner has purchased EACs or not.
B. Estimation methods for emissions per event
Once the total emissions have been established, it is useful to identify an event that causally leads to the generation of these emissions, so as to establish the emissions per event, and to facilitate cost-benefit analysis based, for instance, on the event's benefits and the emissions' costs. a) Origin accounting: Origin accounting is the perspective that focuses on each "coin", considering the environmental impact of each individual coin as given by the energy expenditures and energy mix used to mine them historically. In a way, it maintains an idea that the energy mix used to mine each given coin eternally accompanies the coin throughout its life, such that "older" coins mined with little electricity will always be much greener than newer, more electricity-intensive coins. Under this paradigm, if tracing each coin to its origin is technically feasible, their economic fungibility is eroded.
However, holding bitcoin drives up bitcoin price, incentivizing additional mining. Whether the coin being held is old or new, green or not, has no bearing on this. In other words, even if it were possible to hold green bitcoin, doing so would create an incentive to mine more bitcoin, which may be green or brown. This incentive effect should be accounted for in a green Bitcoin framework. b) Transaction accounting: Transaction accounting is the practice of taking all the emissions (or electricity consumption) in a given time frame and dividing them by the number of transactions in the period, to arrive at a carbon (or electricity consumption) per transaction metric. This is usually framed to imply a causal effect from the transactions to the electricity consumption or emissions, and hence that additional transactions would entail additional emissions.
This method has received criticism because it overlooks the fact that, unlike in proof-of-stake (PoS) systems, electricity consumption from transaction processing is minimal in most PoW systems. Instead, the overwhelming majority of the computational effort is derived from the mining process. Furthermore, by sidestepping Bitcoin's functioning as a wholesale payment system that can support a very large number of transactions through layer-2 (L2) solutions, as well as by failing to account for the Bitcoin halvings which regularly reduce incentives for mining, the predictions tying additional emissions with every additional transactions are, as a rule, seriously flawed [12], [13].
c) Maintenance accounting: To address the shortcomings outlined above, Cross and Bailey [5] suggest the maintenance accounting approach, which the Crypto Carbon Ratings Institute denominates "holding-based approach" [14]. This considers that all holding of bitcoin creates a proportional incentive to mine bitcoin for the period of the holding. One may additionally, and in a symmetric manner to the transactionbased approach, divide all the emissions over a time period by the percentage of holding of each holder during the time frame.
This method is gaining increasing praise as it reflects the economic reality of Bitcoin mining much more accurately. Nevertheless, it also encounters some limitations. The fact that transaction processing represents a negligible part of the computational effort in the Bitcoin protocol does not mean that transaction processing is only responsible for equally negligible electricity consumption. This is because transaction processing itself may create an incentive to mine that is much more than proportional to the share of computational effort attributed to it. Therefore, the maintenance accounting approach accurately attributes emissions caused by bitcoin holding but fails to account for emissions caused by bitcoin "All the carbon gets mapped to hodlers in proportion to the amount of Bitcoin they own." [15] Note also that although all non-lost bitcoin must be held at any given moment, including for transaction purposes, this is of little relevance from an incentive perspective (see next footnote).
transactions.
d) Hybrid accounting: For a more integral approach, one may attribute holders emissions derived from the pursuit of the block subsidy (in proportion to their holdings, maintenance accounting) and emissions derived from the pursuit of transaction fees to transactions (transaction accounting). This hybrid approach has been proposed by the CCRI [14] (but also Cross [16]):
"From an incentive perspective, miners receive both block subsidies and transaction fees. While transaction fees are paid by entities that execute transactions, it might not be intuitive why the block subsidy is paid by all holders. To understand the relationship between holders and block subsidies, we need to consider the creation of new currency. As miners propose new blocks, they are rewarded with new coins. While the supply of the currency inflates, the value of the overall currency stays the same. Therefore, the value of the individual coin is decreasing; the value of every holding in the respective cryptocurrency gets devalued; the difference in form of new coins is paid to the miner as the block subsidy. This results in an indirect payment of all holders towards the miners which in turn use this money to purchase electricity to run their mining devices. Therefore, all holders are responsible for the share of the block subsidy of the overall reward. The hybrid approach accounts for these phenomena and distributes the total network emissions to both all holders and all entities executing transactions. The share between holders and transactions is weighted by the respective share of both components." [14, p. 14]
III. A B
Having covered frameworks to address Bitcoin GHG emissions, we turn to frameworks to account for green bitcoin attributes.
A. Colored coins
A first solution to Bitcoin's energy "problem" is to distinguish between "green", "grey" and "brown" coins [17]- [19]. This amounts to storing a record of the energy type used to mine each particular coin on-chain. The proposal dates back to at least 2013, when the project "Coin Validation" was put forward [18] (and was received with strong criticism [20], Cross and Bailey [5] argue that block rewards and fees are both denominated in bitcoin and thus depend on bitcoin's price, which in turn is influenced by the investors who hold bitcoin. While all of this is true, we do not expect transaction fees to be a function of bitcoin price simply because they are denominated in bitcoin. Rather, transaction fees are determined by the supply and demand of block space, which in turn will be given by the expected utility payers find in Bitcoin as a payment protocol. For practical purposes, it is better to think of block rewards as denominated in bitcoin, but of transaction fees as denominated in fiat.
Alternatives include HODLing only green "virgin" coins, see https://www.hiveblockchain.com/. [21]). Similar proposals have been suggested for KYC/AML purposes [22].
Colored coins suffer from two main problems. Firstly, distinguishing between green coins and grey/brown ones comes at the cost of substantially impairing bitcoin fungibility, which is a key element to the cryptocurrency's moneyness [5], [21] (see also [23]). Secondly, usage of colored coins assumes "origin accounting" [5].
B. Incentive offsets
In 2021, Cross and Bailey [5] formalized this perspective by suggesting an incentive offset system from a maintenance accounting perspective. Their framework suggests that, in order to completely offset any emissions caused by holding bitcoin, any bitcoin holder should co-invest in sustainable bitcoin mining (however the individual defines sustainable) in proportion to their holdings. Thus, if a person holds 1% of all bitcoin, they should invest in sustainably mining 1% of the total bitcoin hash rate.
The mechanism behind this proposal relates to the incentives given by holding and by mining bitcoin. First, holding bitcoin creates an incentive to mine bitcoin, as the price of bitcoin is driven upwards and mining profitability is increased. Second, mining bitcoin creates an incentive not to mine bitcoin, as the hash rate is driven upwards and mining profitability likewise decreases. Hence, Cross and Bailey suggest co-investing in green mining proportion to the holdings so as to neutralize any incentive effect given by the holding of bitcoin.
This proposal presents some strong advantages, including its adaptability to each person's own definition of sustainability, the lack of a need to know the global Bitcoin grid mix, and, most importantly, that this proposal is profitable as long as mining is also profitableas well. However, scaling this proposal may present some implementation challenges as it may collide with existing systems leading to double-counting of green attributes (see IV-D).
C. Traditional environmental market instruments
Insofar bitcoin mining leads to net positive GHG emissions, a miner, holder or payer in bitcoin (depending on the estimation method per event used) may choose to green their bitcoin holdings by purchasing environmental instruments in the market. a) Carbon offsets: Carbon offsets are reductions of GHG emissions or removal thereof. A carbon offset certificate is an instrument (a "token" in the more general sense of the word) that not only certifies the offset but furthermore allows the bearer or owner to claim the offset as their own so as to compensate their emissions. A bitcoin miner with positive GHG emissions may purchase carbon offsets to achieve, for instance, net carbon neutrality. Offset certificates may be considered environmentally beneficial in that the more they are demanded, the higher their price, the higher rewards for offsetors, and, thus, the higher the incentive to continue offsetting.
However, carbon offsets have received criticism:
1) That they act as a "free pass" for emitting parties to continue doing so and "greenwash" their activities [24]- [26]. 2) That they are not trustworthy, and that the claimed quantities of "sunk" GHGs are grossly overestimated, would have been sunk irrespective of the offsetor's activity, that the emissions will "bounce back" after a period, or that they suffer from other empirical problems such as double-counting, lack of additionally, etc. [27], [28] 3) That, from a financial perspective at least, they constitute a pure loss for the buyer, who gains no revenue from them [5]. Note also that if a miner with negative GHG emissions wants to sell carbon offsets to create a green premium on their hash rate and thus be incentivized to invest further in renewable mining, it may be unable to do so. This is because one of the main ways in which green miners may achieve net negative emissions is by either driving brown miners out of the market by increasing the global hash rate, or by facilitating additional renewable buildout through FLR [3]. Both of these are second-order effects and subject to uncertainty and many other factors, and hence cannot be verified, audited and certified even if the incentive effect is there.
b) Carbon credits: Carbon credits are instruments similar to carbon offsets, except that they are usually the result of regulation and that they do not represent sunk a quantity of GHG but rather a right to legitimately emit such a quantity. For this reason, a miner or holder may purchase them. They share some of the criticism received with carbon offsets, namely that they may enable greenwashing [31] and that they do not produce revenue for the buyer [5].
c) RECs and GOs: If purchasing energy from the grid, where green energy electrons and brown energy electrons are indistinguishable, a miner may purchase EACs to be able to claim that its activities are green. This approach has the benefit that it is in line with how existing energy markets currently operate (i.e. through the commercialization of environmental attributes) and that it provides an incentive for renewable buildout as it effectively provides a "green premium" on electricity from RES. [32] However, EACs have also been criticized under greenwashing pretenses. Specifically, it is argued that the incentive A more charitable perspective may recognize the incentive generated by carbon offset purchases on additional offsetting projects but nevertheless find that offsets partially act as a free pass if low-quality offsets are cheaper than (and thus, prioritized over) highly reliable in-house GHG reductions, in a Gresham's law of sorts [25].
Note that this is not the case for methane miners, who can easily certify an emissions reduction at the only cost of assuming that methane is more "harmful" than carbon dioxide (see [3], [29], [30]).
One could also argue that, unlike offset certificates, carbon credits do not produce in themselves any incentive for additional offsetting or renewable buildout as they do not directly reward offsetors or renewable energy sources (RES) producers. However, this is not obviously the case. A high price for carbon credits may incentivize firms to lower or offset emissions so as to avoid having to purchase the credits. created by the green premium is not leading to additional renewable buildout (if there are new renewable investments these would be attributed to other factors, not income). This, the revenue from the sale of EACs would be acting, effectively, as a windfall profit for RES energy sellers whose facilities had already been built. However, an emissions reduction achieved directly by a company in the real world trades on par with an emissions reduction achieved indirectly through the purchase of EACs, in spite of the latter leading to much less of the former. This would result, again, in a Gresham's Law analog of sorts, where bad emissions reductions displace good emissions reductions. [33]- [36]
D. Sui generis environmental Bitcoin market instruments
We discussed above the difficulties miners face in selling the green attributes of their operations when these are net negative. To address this, proposals to tokenize these attributes have emerged. The Sustainable Bitcoin Protocol and Clean Incentive have designed Sustainable Bitcoin Certificates and Clean Bitcoin Certificates, respectively, each with some differentiating factors. These tokens store on-chain (on the Bitcoin-based Stacks blockchain and on ordinals-based Bitcoin inscriptions, respectively) a record that a coin has been mined sustainably, producing one token for every coin sustainably mined (following a verification process). A portfolio manager may green their bitcoin portfolio by holding one token for every coin held.
The benefits of these instruments are that they offer an additional revenue stream for the miner, that they are consistent with existing systems (especially the markets for environmental attributes) but also tailored to the specificities of bitcoin (these tokens may be minted for methane mining, off-grid mining, EACs-based mining, etc.), and that they facilitate ESG reporting. In turn, one of the challenges faced by these projects is the construction of technically sound ecosystems with sufficient buyers to make these tokens liquid.
IV. D Throughout this paper, we have surveyed and systematized the various elements composing the systems to green Bitcoin and to account therefor. We have highlighted the pros and cons of different approaches. In the remainder, we interpret these findings and extract our key takeaways.
A. Second-order causal effects and incentives
Our research shows that properly accounting for the degree of sustainability of Bitcoin requires looking beyond the immediate, proximate short-term effects of a given event. Not doing so obscures important facts, such as how marginal electricity consumption (even if high in marginal emissions), how flexible loads, how carbon offsets and even how carbon credits may incentivize renewable buildout. Similarly, it could be the case that pessimism about the usefulness of carbon credits, carbon These systems includes tokenomic schemes to green not just new coins but also coins already mined.
See https://www.sustainablebtc.org/ and https://www.cleanincentive.com/.
offsets and EACs is the result of a short-term bias and a neglect of the long-term incentives at play.
B. Philosophical presuppositions
An additional finding is the often-overlooked relevance of philosophical assumptions in the analysis of Bitcoin's "greenness" or "brownness." If applied to attribute responsibility (instead of other, much more narrowly defined applications of the method), marginal emissions accounting is tied to the philosophical position that the legitimacy of an energy buyer is given by its relative age, a rather heterodox stance. This could suggest that an attributional framework is more adequate for this goal, whether through the egalitarianism of a simple average or the coherence of the EACs-based methods. Overall, it is of paramount importance to apply a philosophical perspective consistently, both in all the dimensions of the analysis of a single industry as well as across industries.
C. Coherence with the existing system
The initiatives identified in this paper highlight the importance, for any Bitcoin greening scheme, of coherence with existing systems already in place, such as the market for environmental attributes. Frameworks developed that do not take them into account risk implementation obstacles and slower adoption.
D. The problem of double-counting
These constitute a genre of the former. The overlap of multiple frameworks can generate an ironic consequence for the technology created to solve the double-spending problem: the double-spending of environmental attributes. If a miner claims that their activities are green due to the energy mix of the grid to which they have plugged, but simultaneously EACs have been sold for all the energy in the grid, there is double-counting as the greenness of the energy mix has been spent twice, once in the average attributional scheme and once in the EACs scheme. Similarly, if an individual seeks to neutralize their bitcoin holding with Cross's incentive offset scheme by investing in a miner that claims the grid mix but did not purchase RECs, the greenness of green energy may also be spent twice.
E. The need for an ESG reporting framework
Carbon-negative second-order effects in Bitcoin must be accounted for in manners that adequately fit existing reporting practices (as per the previous discussion of "coherence"). A potentially fruitful avenue to this end would be the application of the concept of "Scope 4" emissions (avoided emissions) [37], [38].
We previously established that second-order avoided emissions cannot be reliably "verified", but that the incentive effect to avoid is real nonetheless. The additional renewable buildout that is incentivized through existing instruments such as RECs or carbon offsets also cannot be demonstrated, and yet we admit e.g. EACs as a valuable tool in carbon accounting. A similar understanding could guide Scope 4-based instruments.
V. C
We surveyed and systematized the state of the art pertaining to Bitcoin carbon accounting. As a result, we are inclined to highlight the importance of making philosophical assumptions clear, considering second-order effects, integrating any green Bitcoin frameworks into existing schemes, and avoiding double-counting.
A
We thank Troy Cross, Casey Martinez, and Elliot David for comments that greatly improved the manuscript. J.I.I. was supported by the DLT Science Foundation and the University College London Centre for Blockchain Technologies. A.F. was supported by the University College London Centre for Blockchain Technologies and Energiequelle GmbH.
C
I The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
A EACs energy attribution certificates ESG environmental, social and governance FLR flexible load response GHG greenhouse gas GOs guarantees of origin L2 layer-2 PoS proof-of-stake PoW proof-of-work RECs Renewable energy certificates RES renewable energy sources VRE variable renewable energy
This circles back to the original issue of philosophical presuppositions: the attribution of responsibility between the two parties spending an attribute twice is not entirely obvious.
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| sample_565 | 0.9924 | arxiv | |
Global temperature projections from a statistical energy balance model using multiple sources of historical data
May 23, 2022 20 May 2022
Mikkel Bennedsen mbennedsen@econ.au.dk
Department of Economics and Business Economics and CREATES
Aarhus University
Fuglesangs Allé 48210Aarhus VDenmark
Eric Hillebrand ehillebrand@econ.au.dk
Department of Economics and Business Economics and CREATES
Aarhus University
Fuglesangs Allé 48210Aarhus VDenmark
Jingying Zhou Lykke jzlykke@econ.au.dk
Department of Economics and Business Economics and CREATES
Aarhus University
Fuglesangs Allé 48210Aarhus VDenmark
Global temperature projections from a statistical energy balance model using multiple sources of historical data
May 23, 2022 20 May 20221two-component energy balance modelstate space methodsnon-stationaritymulti- ple data sourceshistorical observationsscenario analysis
This paper estimates the two-component energy balance model as a linear state space system (EBM-SS model) using historical data. It is a joint model for the temperature in the mixed layer, the temperature in the deep ocean layer, and radiative forcing. The EBM-SS model allows for the modeling of non-stationarity in forcing, the incorporation of multiple data sources for the latent processes, and the handling of missing observations. We estimate the EBM-SS model using observational datasets at the global level for the period 1955 -2020 by maximum likelihood. We show in the empirical estimation and in simulations that using multiple data sources for the latent processes reduces parameter estimation uncertainty. When fitting the EBM-SS model to eight observational global mean surface temperature (GMST) anomaly series, the physical parameter estimates and the GMST projection under Representative Concentration Pathway (RCP) scenarios are comparable to those from Coupled Model Intercomparison Project 5 (CMIP5) models and the climate emulator Model for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC) 7.5. This provides evidence that utilizing a simple climate model and historical records alone can produce meaningful GMST projections.
Introduction
In this paper, we propose a state space representation (EBM-SS model) of the two-component energy balance model (EBM) (or two-layer EBM), which is initially introduced in Paltridge (1981) and subsequently extended in Gregory (2000) and Held et al. (2010). Like other versions of EBMs (e.g., North et al., 1981), the two-component EBM is a simplified mathematical representation of the complicated dynamics underlying temperature changes as energy imbalance between the incoming solar radiation and the outgoing terrestrial radiation for the earth system. It extends the zero-dimensional EBM (e.g., Budyko, 1969;Sellers, 1969;North et al., 1981;Imkeller, 2001) by accounting for the vertical resolution of the Earth system and two distinct time scales of the global temperature response to external perturbations (Hasselmann et al., 1993;Held et al., 2010;Geoffroy et al., 2013).
The EBM-SS model enables statistical inference to evaluate parameter estimation uncertainties. Climate modeling is inevitably accompanied with parameter uncertainty (e.g., Winsberg, 2012;Reyer et al., 2016;Gillingham et al., 2018). Accounting for parameter uncertainty plays a crucial role in obtaining reliable evaluations of climate change and conducting robust projection.
Other approaches to quantify parameter uncertainty for the two-component EBM include sensitivity analysis (Soldatenko & Colman, 2019;Colman & Soldatenko, 2020), Monte Carlo simulation (Gillingham et al., 2018;Smith et al., 2018;Jiménez-de-la Cuesta & Mauritsen, 2019), and Bayesian estimation (Jonko et al., 2018;Nijsse et al., 2020). The main drawback of sensitivity analysis is its disconnection with any measure of probability, while Monte Carlo simulation assumes the input parameter estimates as the true values. (e.g., Cox & Baybutt, 1981). The performance of Bayesian estimation depends on the prior distributions (e.g., Kim et al., 2020). Alternatively, state space methods obtain maximum likelihood estimators based on the frequentist principle and easily quantify parameter uncertainty using asymptotic properties (Durbin & Koopman, 2012).
The EBM-SS model reduces estimation uncertainty by using multiple data sources. There are different datasets available for GMST. All of the GMST anomalies series from separate research groups can be regarded as different measurements for the same variable of interest -the temperature in the mixed layer in the two-component EBM. As we will show, employing different data sources reduces information loss and improves estimation accuracy.
The EBM-SS model provides alternatives and extensions to two current contributions by Pretis (2020) and Cummins et al. (2020), who obtain parameter values of the two-component EBM using maximum likelihood. Pretis (2020) shows the mathematical equivalence between the twocomponent EBM and a cointegrated VAR model (EBM-CVAR). Instead of including the temperature in the deep ocean layer, he includes ocean heat content (OHC) in his model. In his discretization, two of the parameters of the two-component EBM, heat capacity in the mixed layer and the coefficient for the heat transfer, are not recovered in the output EBM-CVAR model. In this paper, we maintain the original parametrization by modeling the temperature in the deep layer but also incorporate OHC as an additional measurement for it, which helps constrain the parameters. We maintain a one-to-one mapping relationship between the two-component EBM and our state space model so that all of the physical parameters can be estimated and interpreted accordingly. Cummins et al. (2020) present a state space representation of the k-layer EBM and report parameter estimates for the cases where k = 2 and k = 3. Our paper only considers the case k = 2 and differs from Cummins et al. (2020) in several ways: (1) we employ observational datasets instead of the abrupt 4×CO 2 experiment data from CMIP5; (2) we model radiative forcing as a non-stationary process instead of a stationary red noise process; (3) we use instrumental records of ocean temperature, OHC, and effective radiative forcing instead of top-of-the-atmosphere net downward radiative flux as measurements in the state space model; and (4) we incorporate multiple data sources for the latent states.
In this paper, using historical datasets, we obtain estimates for the physical parameter in the two-component EBM that are comparable to the estimates in Cummins et al. (2020) that are obtained from CMIP5 model outputs. Meanwhile, the GMST projection results under RCP 2.6, RCP 4.5, and RCP 6.0 scenarios have a high degree of agreement with the outputs from the climate emulator MAGICC 7.5 and CMIP5 models. These results require two ingredients. One is the inclusion of multiple historical records as different data sources into the EBM-SS model. The other is the inclusion of both ocean temperature and OHC datasets. Our results indicate that utilizing a simple climate model with historical records alone can produce meaningful physical parameter estimates and GMST projections.
The remainder of the paper is organized as follows: Section 2 presents the two-component EBM. Section 3 describes the method and technical details on mapping the two-component EBM into a state space representation. Sections 4 presents simulation results on the performance of the EBM-SS model. Sections 5 and 6 introduce the datasets and their use as measurements in the empirical study. Section 7 contains an application of the EBM-SS model to GMST projections using RCP scenarios. Section 8 concludes.
Two-component energy balance models
The two-component EBM (e.g., Gregory, 2000;Held et al., 2010) divides the earth system into two thermal reservoirs (also referred to as "layer" , "box" , or "component") that are characterized by different heat capacities to measure thermal inertia. Each of the reservoirs contains components of global climate responses with both fast and slow time scales.
The first layer is usually called the "mixed layer" and consists of the atmosphere, the land surface, and the upper ocean layer. The second layer is called the "deep ocean layer". The depth of the upper ocean layer varies seasonally and geographically. Hartmann (2015, Chapter 7) argues that the global mean depth of the ocean in the mixed layer is 70 m. Gregory (2000) considers the upper ocean layer as the part that shows consistent temperature variations with the surface temperature. He chooses 150 m as the depth for the upper layer based on the temporal correlation between the heating rates of different ocean layers and that of the surface. In addition, he defines 2,400 m as the lower bound for the deep layer and describes the part beyond this level as an "isolated basin". .1 gives a graphic illustration of the dynamics underlying the two-component EBM. The change in the heat content of the mixed layer is driven by two sources in opposite directions: external and internal. The external source comes from the net heat flux, which is characterized as F − λT m , where the incoming heat radiation is represented by the effective radiative forcing F (measured in Wm −2 ), and the outgoing longwave radiation (OLR) is modeled as a linear function of the temperature in the mixed layer T m with the slope λ (known as the climate feedback parameter, Wm −2 K −1 ). The practice of using λT m to approximate OLR follows a linear approximation widely used in physical science. The linearity between T and OLR is validated by satellite measurements and can be explained in physics by the offsetting of two non-linear processes (Koll & Cronin, 2018). The internal source involves a downward heat transport H (measured in Wm −2 ) from the mixed layer to the deep ocean layer, which changes proportionally to the temperature difference T m − T d between these two layers with a coefficient γ (Wm −2 K −1 ). This term is deemed a reasonable approximation of all of the small perturbations constituting the heat transfer (Gregory, 2000). The heat exchange term, H = γ (T m − T d ), poses the only source of energy for the deep ocean layer. Summarizing the dynamics described in Figure 2.1 into a differential equation system, the two-component EBM is specified as:
C m dT m dt = F − λT m − γ (T m − T d ) , C d dT d dt = γ (T m − T d ) ,(2.1)
where C m and C d (measured in W year m −2 K −1 ) denote heat capacities of the mixed layer and of the deep ocean layer, respectively. It holds that C m < C d , indicating that the deep ocean requires a greater amount of energy than the upper layer for a unit change in the temperature. The terms C m dTm dt and C d dT d dt describe the rates at which the corresponding temperatures change. In this framework, the radiative forcing F is generated exogenously to the system (e.g., by anthropogenic factors). There are four physical parameters to be estimated: λ, γ, C m , and C d . In the next sections, we map the two-component EBM into a state space model and estimate the values of these physical parameters using maximum likelihood methods.
Including ocean heat content in the system
Ocean heat content (OHC) (measured in J m −2 ) measures the amount of heat stored in the ocean. Mathematically, ocean heat content O between ocean depths h 1 and h 2 is calculated as:
O = ρC h1 h2 T (x)dx, (2.2)
where ρ, C, and T (·) denote the seawater density, heat capacity, and the temperature at a specific depth, respectively (Dijkstra, 2008). We denote ρC as C d and h1 h2 T (x)dx as T d , which represents the integrated average ocean temperature between h 1 and h 2 . Then, Equation (2.2) is rewritten as:
O = C d T d . (2.3) This relationship implies the heat content expression C d dT d dt = dO dt for the term C d dT d dt in the two- component EBM (2.1).
Relating the temperature to heat content in this way is a common practice in energy balance models, and it is motivated by empirical evidence (Schwartz, 2007).
In our state space model of the two-component EBM introduced later, we include OHC in the measurement equation using the linear relationship O = C d T d . In our specification, OHC plays the role of a second measurement for the latent state T d , in addition to the direct empirical observations of T d as the first measurement. As shown in Equation (2.2), OHC is a function of the deep ocean temperature, and in practice, the observational OHC series is compiled using the records of ocean temperature data plus salinity information (Levitus et al., 2012). Hence, our choice to include OHC as an additional measurement for T d is grounded on both the theory and the empirical data construction process. In Section 6, we will show that using information of both ocean temperature and OHC helps constrain the parameter estimates to be more realistic compared with using ocean temperature alone.
Mapping the two-component EBM into a state space model
The objective of this section is a discrete-time state space representation of the two-component EBM that enables estimation using empirical data. Particularly, we focus on the multivariate linear Gaussian state space model. For details on the estimation of these models, see Durbin and Koopman (2012). State space models distinguish unobserved states from observations, where the observations are employed to infer the states. They also allow for using multiple observation series as measures of the latent state of interest.
Decomposition of radiative forcing
We decompose the state of radiative forcing, F , into two components by source and treat them separately. Total radiative forcing is disaggregated into natural forcing and anthropogenic forcing, where the latter can be further decomposed by the forcing agents. Figure 3.1 shows the decomposition employed in the fifth IPCC assessment report Myhre et al. (2013, Chapter 8). As seen in Figure 3.1, natural forcing is mainly driven by two contributors: solar irradiance and volcanic forcing. Anthropogenic forcing is subject to human influences and consists of forcing from greenhouse gases, land surface changes, and human-made aerosols. We obtain the latest version of the effective forcing dataset from Hansen et al. (2011) as the measurement for F t and show the data in Figure 3.2. It provides information on forcing from different greenhouse gases and summarizes the forcing due to the land surface changes and human-made aerosols into a category "TA+SA" (tropospheric aerosols and surface albedo forcings combined).
As seen in Figure 3.2a, the observation-based natural forcing Y N,t is dominated by the volcanic forcing, which appears as negative spikes due to temporary cooling periods lasting approximately three years after major volcanic eruptions, while solar irradiance varies around zero over time and exhibits cyclical behavior. Anthropogenic forcing is attributed to human activities, of which the dominant contributors are the well-mixed greenhouse gases. Figure 3.2b shows the two time series for natural forcing and anthropogenic forcing we use in this paper. Natural forcing exhibits large negative spikes and remains otherwise close to zero, while anthropogenic forcing is upward trending.
As natural forcing and anthropogenic forcing have distinct time series characteristics, we treat
F t = A t + N t ,
where A t is anthropogenic forcing and N t is natural forcing. We model A t but we treat N t as an exogenous regressor and use historical data for it. Considering the small magnitude of solar irradiance, we do not introduce extra structure to model its cyclical feature explicitly. Anthropogenic greenhouse gas emissions following industrialization increase anthropogenic forcing (denoted as Y A,t ) and render it non-stationary (Kaufmann et al., 2013;Chang et al., 2020). In the two-component EBM system, the increasing anthropogenic forcing raises temperatures at the surface and in the ocean, thus, temperatures become non-stationary, too. Anthropogenic forcing is external to the system of surface temperature and ocean heat uptake, and, hence, it can be regarded as the major source of non-stationarity in the system. Non-stationarity poses statistical challenges such as spurious regression (e.g., Granger & Newbold, 1974). State space methods can be used to specify systems of non-stationary variates while retaining valid statistical inference (Caines, 1988). As shown in Figure 3.3a, the first-order difference of anthropogenic forcing, ∆Y A,t , appears (a) first-order difference:
∆Y A,t (b) second-order difference: ∆ 2 Y A,t
non-stationary with both trends and shifts of trends. The second-order difference in Figure 3.3b exhibits an abrupt increase in variance in the 1950s. The shifts in the trends and the variance are mainly the result of changes in measurement methods. For example, greenhouse gases are initially measured using ice core records and later measured directly from the atmosphere (e.g., Raynaud et al., 1993). This switch applies since the year 1958 for CO 2 and 1978 for CH 4 and N 2 O. These structural shifts may indicate the existence of wide-sense non-stationarity in anthropogenic forcing, which invalidates the method of obtaining a stationary process by taking differences (Castle & Hendry, 2019, 2020). An in-depth analysis of wide-sense non-stationarity is beyond the scope of this paper, but we investigate the integration order of anthropogenic forcing. Unit root test results are reported in Table A.1 in Appendix A.1. As shown in Table A.1, the components of forcing exhibit different integration orders. Total radiative forcing, Y F,t , is an I(1) process, i.e., it becomes stationary after taking first-order difference. This observation is consistent with the statement in Pretis (2020) that the individual forcing components integrate to an I(1) total forcing upon summation. Table A.1 also implies that total anthropogenic forcing, Y A,t , is an I(1) process when no lag or only the first-order lag is included in the unit root test equation, but it is an I(2) process if a higher-order lag is included. Guided by the unit root tests and visual inspection of Y A and its differences, we represent A t using a local linear trend model (Durbin & Koopman, 2012, Chapter 3), where A t is a random walk process with a stochastic trend β t :
A t =β t + A t−1 + η A,t , β t =β t−1 + η β,t , (3.1)
where η A,t and η β,t are independent Gaussian white noise processes with variances σ 2 η A and σ 2 η β , respectively. The second-order difference ∆ 2 A t is thus a linear function of two white noise processes and hence stationary:
1 ∆ 2 A t = η β,t + η A,t − η A,t−1 . (3.2)
As a result, A t is modeled as an I(2) process. Figure 3.3b shows a variance increase and hence suggests the existence of heteroskedasticity in ∆ 2 A t . One method to accommodate such a variance shift is to impose a multiplicative constant on the variance of the measurement error of forcing σ 2 ε,Y F from the year where the measurement scheme shifts onwards, and this constant can be estimated using maximum likelihood. Inclusion of such a constant yielded insignificant estimates on the sample period 1955 -2020, and hence we omit it from the model.
EBM-State Space (EBM-SS) model -state equation
The state equation in a state space model describes the dynamics of the latent state variables as a first-order autoregressive process. For our EBM-SS model, we define the following five variables as unobservable latent states: the temperature in the mixed layer T m , the temperature in the deep 1 If we set σ 2 η A = 0, Equation (3.2) is reduced to ∆ 2 A t = η β,t , which is called integrated random walk model (Young et al., 1991;Durbin & Koopman, 2012). ocean layer T d , natural forcing N , anthropogenic forcing A, and the stochastic trend β.
According to the dynamics in the two-component EBM (differential equation system (2.1)) and the decomposition of F in Section 3.1, we formulate the state equation system as the following system of linear equations:
T m,t = 1 − (λ + γ) C m T m,t−1 + γ C m T d,t−1 + 1 C m (N t−1 + A t−1 ) + η Tm,t , T d,t = γ C d T m,t−1 + 1 − γ C d T d,t−1 + η T d ,t , N t =Y N,t , A t =β t + A t−1 + η A,t , β t =β t−1 + η β,t ,(3.3)
where η Tm,t , η T d ,t , η A,t , respectively, and η β,t are the state disturbances to the states T m,t , T d,t , A t and β t , and they capture the deviations from the assumed linear relations implied by the two-component EBM and the local linear trend model (Equation (3.1)). We assume the state disturbances to be independent and η ·,t ∼ N (0, σ 2 η,· ). The system of equations (3.3) allows for modeling non-stationarity. It establishes temperature changes as a response to perturbations in radiative forcing and represents the non-stationarity in radiative forcing using a local linear trend model, which is the only source of a stochastic trend in the system, and the stochastic trend propagates to temperatures at the surface and in the ocean through linear relationships. The equation N t = Y N,t captures that we use observational data Y N,t on natural forcing for the latent process N t , i.e., we treat it as exogenous.
EBM-SS model -measurement equation
The measurement equation in a state space model connects the observational data vector to the latent state vector linearly. We consider the following measurement equations:
Y Tm,t =T m,t + ε Tm,t , Y T d ,t =T d,t + ε T d ,t , Y O,t =C d T d,t + ε O,t , Y F,t =N t + A t + ε F,t , (3.4)
where Y * ,t denotes the measurement for the latent process * . Following the assumption O = C d T d , the third equation in (3.4) expresses the OHC series, Y O,t , as an alternative measurement for T d . Note that the data for Y O,t and Y T d ,t are retrived from the same institution and cover the same ocean depth. We assume that ε ·,t ∼ N (0, σ 2 Y· ), and the correlation Corr (ε T d ,t , ε O,t ) = ρ, where ρ can be estimated using maximum likelihood like other parameters. Allowing for correlation between the measurement errors of ocean temperature and OHC accounts for the highly correlated data compilation processes for these two series.
Incorporation of multiple measurements
Cummins et al. (2020) fit a two-box EBM to datasets from 16 Earth System Models (ESMs) in CMIP5 separately and further consider a joint data series that is the average of these 16 datasets. The parameter estimates vary across different datasets due to the heterogeneity of the ESMs. We employ an alternative strategy. We include different data sources simultaneously in the measurement equation as multiple measurements for the latent states. This approach only produces one set of parameter estimates regardless of the number of measurements we include. We focus on using multiple data sources of GMST, ocean temperature, and OHC. 2 The two latent processes T m,t and T d,t are linearly linked to multiple observational measurements. For example,
the K (K ∈ N) GMST anomalies Y 1
Tm,t , ..., Y K Tm,t share the same driver -the latent process T m,t . They are distinguished from each other by separate measurement errors ε 1 Tm,t , ..., ε K Tm,t . For ocean temperature and OHC, we include series from the same institution in pairs, as they are correlated measurements for T d . The measurement equations that include J and K (J ∈ N) data sources for GMST and ocean data are formulated as:
Y 1 Tm,t = T m,t + ε 1 Tm,t , . . . Y K Tm,t = T m,t + ε K Tm,t , Y 1 T d ,t = T d,t + ε 1 T d ,t , Y 1 O,t = C d T d,t + ε 1 O,t , . . . . . . Y J T d ,t = T d,t + ε J T d ,t , Y J O,t = C d T d,t + ε J O,t , Y F,t = N t + A t + ε F,t . Similar to the one-data-source case, ε k Tm,t ∼ N 0, σ 2 ε,Y k Tm , ε j T d ,t ∼ N 0, σ 2 ε,Y j T d , ε j O,t ∼ N 0, σ 2 ε,Y j O , ε F,t ∼ N 0, σ 2 ε,Y F , and Corr ε j T d ,t , ε j O,t = ρ j .
EBM-SS model -matrix form
In this section, we integrate Section 3.2 and Section 3.3 and present the matrix form of the EBM-SS model. We only discuss the specification with multiple data sources, which nests the one-data-source case. We denote X t = T m,t T d,t N t A t β t 1 as the state vector and
Y t = Y 1 Tm,t · · · Y K Tm,t Y 1 T d ,t · · · Y J T d ,t Y 1 O,t · · · Y J O,t Y F,t
as the observational vector. The processes in X t are unobserved, with the exceptions of natural forcing N t and the constant state "1". The latter is a technical way to equate the state N t with observations Y N,t without errors, or in other words, to treat them as an exogenous regressor, as seen in Equation (3.6). The observational vector contains data on the elements of the state vector and on OHC (
Y 1 O,t , ..., Y J O,t ). We write the state disturbances into a vector η t = η Tm,t η T d,t 0 η A,t η β,t 0 and the mearsurement errors into a vector ε t = ε 1 Tm,t · · · ε K Tm,t ε 1 T d ,t · · · ε J T d ,t ε 1 O,t · · · ε J O,t ε F,t ,
where the two 0's in η t are due to the absence of state disturbances for the natural forcing state and the constant state. The EBM-SS model is written as a standard discrete-time state space form, as defined in, e.g., Durbin and Koopman (2012):
X t+1 = TX t + η t , η t ∼ N (0, Q), Y t = ZX t + ε t , ε t ∼ N (0, H). (3.5)
The matrices T, Q, H, and Z are time-invariant. The state equation X t+1 = TX t + η t is written explicitly as:
T m,t+1 T d,t+1 N t+1 A t+1 β t+1 1 = −(λ+γ) Cm + 1 γ Cm 1 Cm 1 Cm 0 0 γ C d − γ C d + 1 0 0 0 0 0 0 0 0 0 Y N,t+1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 T m,t T d,t N t A t β t 1 + η Tm,t η T d ,t 0 η A,t η β,t 0 , (3.6) and η t ∼ N (0, Q), where Q = σ 2 η,Tm 0 0 0 0 0 0 σ 2 η,T d 0 0 0 0 0 0 0 0 0 0 0 0 0 σ 2 η,A 0 0 0 0 0 0 σ 2 η,β 0 0 0 0 0 0 0 . (3.7)
The measurement equation Y t = ZX t + ε t with multiple data sources is written explicitly as:
Y 1 Tm,t . . . Y K Tm,t Y 1 T d ,t . . . Y J T d ,t Y 1 O,t . . . Y J O,t Y F,t = 1 0 0 0 0 0 . . . . . . . . . . . . . . . . . . 1 0 0 0 0 0 0 1 0 0 0 0 . . . . . . . . . . . . . . . . . . 0 1 0 0 0 0 0 C d 0 0 0 0 . . . . . . . . . . . . . . . . . . 0 C d 0 0 0 0 0 0 1 1 0 0 T m,t T d,t N t A t β t 1 + ε 1 Tm,t . . . ε K Tm,t ε 1 T d ,t . . . ε J T d ,t ε 1 O,t . . . ε J O,t ε F,t , (3.8) and ε t ∼ N (0, H), where H = σ 2 ε,Y 1 Tm 0 · · · 0 0 0 · · · 0 0 · · · 0 0 0 σ 2 ε,Y 2 Tm . . . 0 0 0 · · · 0 0 · · · 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 . . . σ 2 ε,Y K−1 Tm 0 0 · · · 0 0 · · · 0 0 0 0 · · · 0 σ 2 ε,Y K Tm 0 · · · 0 0 · · · 0 0 0 0 · · · 0 0 σ 2 ε,Y 1 T d . . . 0 ρσ ε,Y 1 T d σ ε,Y 1 O . . . 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 · · · 0 0 0 . . . σ 2 ε,Y J T d 0 . . . ρσ ε,Y J T d σ ε,Y J O 0 0 0 · · · 0 0 ρσ ε,Y 1 T d σ ε,Y 1 O . . . 0 σ 2 ε,Y 1 O . . . 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 · · · 0 0 0 . . . ρσ ε,Y J T d σ ε,Y J O 0 . . . σ 2 ε,Y J O 0 0 0 · · · 0 0 0 · · · 0 0 · · · 0 σ 2 ε,Y F . (3.9)
Since the observation vector Y t contains data measurements of the latent states, the measurement equation matrix Z contains 1's on the diagonal with the exception of the equation for OHC, where the heat capacity parameter C d enters. When K = J = 1, the model collapses to the specification with one data source for the latent states. The EBM-SS model with multiple data sources is schematically depicted in Figure 3.4.
T m,t T d,t F t Z Z Z η t X t−1 T X t Y 1 Tm,t Y K Tm,t Y 1 T d ,t , Y 1 O,t Y J T d ,t , Y J O,t Y F,t ε 1 Tm,t ε K Tm,t ε 1 T d ,t , ε 1 O,t ε J T d ,t , ε J O,t ε F,t
Estimation and simulation of the EBM-SS
The parameters to be estimated in EBM-SS model include the four physical parameters λ, γ, C m , and C d ; the parameters in the variance-covariance matrices of the state disturbances, Q, and of the measurement errors, H; and constants µ T d for the observations of T d . These parameters are collected in the parameter vector θ. The estimate of θ is obtained by maximum likelihood, where the log-likelihood function is evaluated using the Kalman filter, see Durbin and Koopman (2012). We implement the EBM-SS model using the R package KFAS (Helske, 2017) and optimize the log-likelihood value using a combination of "solnp" 3 (Ye, 1988) and the Nelder-Mead simplex method (Nelder & Mead, 1965). For initialization, we adopt the "Big K" technique (illustrated in Durbin and Koopman (2012)) to approximate the diffuse initialization, and we set the initial variances of the non-stationary states as 10 6 . We conduct a Monte Carlo simulation to explore the small-sample properties of the EBM-SS model. We choose a sample size of 66, the length of the historical dataset, and perform 1,000 simulation replications. We consider the EBM-SS base model, where there is one data source for each latent state, and the EBM-SS full model, where there are eight GMST series, two pairs of ocean temperature and OHC series, and one radiative forcing series, all of which are simulated in this exercise. We also allows for correlations between each pair of ocean temperature and OHC. For the EBM-SS full model, we employ the empirical estimates reported in panel A in Table 6.1 as the data-generating parameters to simulate the data. First, we simulate the data for the EBM-SS full model, and we chose the first GMST, first ocean temperature, first OHC, and the radiative forcing series from this set of data as the simulated data for the EBM-SS base model. Hence, these two sets of simulated data share the same source of randomness.
As shown in Equation (3.2), the anthropogenic forcing state A t is of integration order 2, as it cumulates a stochastic trend β t . Simulating the anthropogenic forcing series unrestrictedly inevitably generates trajectories with downward trends, which contradicts the pronounced upward trends observed in the historical series (Figure 3.2b). To obtain simulated paths that are comparable with the observational records, we apply rejection sampling (Wells et al., 2004) and only retain the ith simulated trajectory Y i,sim
A,t T t=1
, if it satisfies that:
Y i,sim A, T 2 ≥ 0.75Y A, T 2 and Y i,sim A,T ≥ 0.75Y A,T , (4.1) where Y A, T 2
and Y A,T are the mid-point and the endpoint in the historical anthropogenic forcing series from Hansen et al. (2011). This ensures that the simulated trajectories are consistent with the historical series in trending upward.
We calculate equilibrium climate sensitivity (ECS) using the relationship as in, e.g., the IPCC Sixth Assessment Report (AR6) (Forster et al., 2021, Chapter 7
) : ECS = F 2×CO 2 λ
, where F 2×CO 2 is the radiative forcing in response to a doubling of the CO 2 concentrations in the atmosphere. We use the updated best estimate of F 2×CO 2 ≈ 3.93 (±0.47, 5% − 95% CI) W m −2 from the IPCC AR6 (Forster et al., 2021, Chapter 7). Table 4.1 reports data-generating parameter values, estimation biases, standard deviations, root mean squared errors (RMSEs), and mean absolute errors (MAEs) of the simulation exercise. Table 4.1, together with the distributions in Figure 4.1, demonstrate good finite-sample properties of the EBM-SS model.
σ 2 ε,Y 1 Tm σ 2 ε,Y 2 Tm σ 2 ε,Y 3 Tm σ 2 ε,Y 4 Tm σ 2 ε,Y 5 Tm σ 2 ε,Y 6 Tm σ 2 ε,Y 7 Tm σ 2 ε,Y 8Tm
variances of measurement errors (II) constant of
T d ρ T d ,O σ 2 ε,Y 1 T d σ 2 ε,Y 2 T d σ 2 ε,Y 1 O σ 2 ε,Y 2 O σ 2 ε,Y F µ T d ,1 µ T d ,σ 2 ε,Y 1 Tm σ 2 ε,Y 2 Tm σ 2 ε,Y 3 Tm σ 2 ε,Y 4 Tm σ 2 ε,Y 5 Tm σ 2 ε,Y 6 Tm σ 2 ε,Y 7 Tm σ 2 ε,Y 8Tmρ T d ,O σ 2 ε,Y 1 T d σ 2 ε,Y 2 T d σ 2 ε,Y 1 O σ 2 ε,Y 2 O σ 2 ε,Y F µ T d ,1 µ T d ,
Comparing the simulation results for the base model and for the full model in Table 4.1, we note that estimation biases, standard deviations, RMSEs, and MAEs decrease, as we include more data series. This provides evidence that including multiple data sources helps decrease the estimation uncertainty.
Data
This section presents the historical records of anomalies employed in the empirical investigation and the synchronization of these anomalies to a common baseline. For the empirical analysis in this paper, we have collected eight observational GMST datasets from separate research groups, three pairs of ocean temperature and OHC data series, and one effective radiative forcing series (summarized in Table 5.1) as the measurements for the latent processes in the state equation (3.3) of the EBM-SS model. (Berrisford et al., 2011), and the Japanese 55-year reanalysis (JRA-55) (Kobayashi et al., 2015). We assume that each of these datasets represents an independent assessment of the global mean temperature variations.
All of these eight GMST series are in the form of anomalies, i.e., they measure the departures from an average of the observations over a long period (called "reference period" or "baseline") that usually spans thirty years or longer. It is common practice to record and construct the anomalies rather than the absolute value of the observations (Hawkins & Sutton, 2016). Figure 5.1a indicates that, despite having different lengths, these eight GMST series share similar upward trends and fluctuation trajectories, but the ranges they span vary to some extent, which is mainly due to the different reference periods. The datasets for the ocean (including both ocean temperature anomalies and OHC anomalies) are from two research bodies, NOAA National Centers for Environment Information (NOAA) and Institute of Atmospheric Physics (IAP), and cover 0-700 and 0-2,000 meter, respectively (see Table 5.1 for details). The OHC anomaly series are estimated based on the in-situ subsurface ocean temperature measurements combined with salinity series (Levitus et al., 2012), and they have the same coverage and baseline as their ocean temperature counterparts. The 0-700m ocean series from NOAA (Levitus et al., 2012) is available since 1955, while the IAP (Cheng et al., 2020) series begins in 1940. As we aim to only use the data based on direct observations, we choose 1955 -2020 as the time horizon for the empirical study. While the baseline periods for NOAA ocean temperature and OHC anomalies are not documented, IAP benchmarks the ocean series against the 30-year period from 1981 to 2010. Figure 5.1c shows that all of the OHC series agree on a warming trend but exhibit slightly different yearly variations. According to Von Schuckmann et al. (2020), the global heating rate over the period 1971 -2018 is estimated as 0.47 ± 0.1 Wm −2 , 89% of which is contributed by the global ocean (thereof 52% from the layer 0-700m, 28% from the 700-2,000m, and 9% beyond 2,000m).
We test the stationarity properties of the GMST, ocean temperature, and OHC anomalies, and we report the results in Table A.2 in Appendix A.1. They indicate that all of these anomaly series are I(1) processes. As shown in Table A.1, total radiative forcing is also I(1), and therefore all of the measurements we consider share the same integration order. As shown in Table 5.1, the data series have different baselines. The parameter estimates can be distorted if we include several data series with different reference periods simultaneously in a system. Therefore, it is necessary to reconcile these datasets to the same baseline by either synchronizing them before fitting into the model or introducing some structures in the model specification to offset the discrepancies across various baselines. The differences in the baselines across different data sources can be eliminated by synchronizing these anomalies to a common reference period. The simple mathematical arguments for synchronization is given in Appendix A.2.
The pre-industrial era is a natural choice for this common baseline, as it is commonly used as a benchmark to measure and evaluate climate change. We follow the IPCC Global Warming of 1.5 • C report (IPCC, 2018) to specify 1850 -1900 as the pre-industrial base period for GMSTs. The synchronized GMST series are exhibited in Figure A.1a in Appendix A.2. The forcing series we employ in the paper is already benchmarked against 1850. To maintain consistency with the pre-industrial benchmark of GMSTs, we synchronize the anthropogenic forcing as anomalies relative to 1850 -1900. It is infeasible to synchronize the ocean series relative to the pre-industrial era, as the ocean information during this period is very sparse. We benchmark the NOAA ocean series against 1981 -2010 for comparability with IAP series, as shown in Figures A.1b and A.1c in Appendix A.2. What remains to be accommodated is the baseline difference between 1981 -2010 and the preindustrial era. A solution we consider here is to introduce a constant µ j T d to the jth measurement equation of ocean temperature and to the jth measurement equation of the corresponding OHC accordingly:
Y j T d ,t =µ j T d + T d,t + ε j T d ,t , Y j O,t =C d µ j T d + C d T d,t + ε j O,t , (j = 1, 2, · · · J).
(5.1)
Empirical results
In this section, we fit the EBM-SS model defined in Section 3 to the datasets described in Section 5. The sample period is 1955 -2020. The ERA-Interim and JRA-55 GMST anomalies have a shorter length of 51 years, from 1970 to 2020, but the missing observations during 1955 -1969 are treated in the state space model using the techniques illustrated in Durbin and Koopman (2012). Table 6.1 shows the parameter estimates using all of the eight GMST anomalies presented in Section 5. Using the delta method, we account for the uncertainty of the estimates of both λ and F 2×CO 2 when calculating the standard error for the ECS estimate, where F 2×CO 2 denotes the radiative forcing in response to a doubling of the atmospheric CO 2 concentrations. The estimation results with only one data source for each of the latent states are presented in Table A.4 in Appendix A.3. Of the four physical parameters (λ, γ, C m , and C d ) in the two-component EBM, the estimates . Panel B includes the ocean temperature and OHC series covering 0-2,000m from IAP. All of the GMST anomalies and the ocean series have been synchronized relative to the pre-industrial period and 1981 -2010, respectively, where the constants for the ocean series offset the baseline difference. The standard errors for estimates are obtained using the delta method and presented in parentheses. H andQ denote the estimated variance-covariance matrices of the measurement errors and state disturbances, respectively, andL denotes the maximized log-likelihood. ρ NOAA of the climate feedback parameter λ, of the coefficient of heat transfer γ, and of the heat capacity of the deep ocean layer C d show pronounced increases when 0-2,000m ocean data series are employed, which account for more ocean heat uptake. The last column in Table 6.1 reports the estimated two linear relationships specified by the EBM-SS model, i.e., between the state T m,t and the lag terms of the three latent states T m,t−1 , T d,t−1 , and F t−1 , and between the state T d,t and the lag terms T m,t−1 and T d,t−1 . The estimated coefficients are similar regardless of whether ocean 0-700m or 0-2,000m data are employed. Table 6.2 compares the estimates of the physical parameters from the EBM-SS model with those from other studies. Comparing panel A and panel B reveals that, when fitting the eight GMST series and 0-700m ocean datasets from NOAA and IAP, our estimates are comparable to those obtained by the CMIP 4×CO 2 experiment data (Cummins et al., 2020;Smith et al., 2021, Chapter 7 supplementary material). Our estimate of the ECS is 3.63 • C, which is close to the upper bound of the estimated range of 2.5 • C−3.5 • C using instrumental records in the IPCC AR6 (Forster et al., 2021, Chapter 7). It is also close to the emergent constrained ECS mean estimates from CMIP5 and CMIP6 (Schlund et al., 2020;Smith et al., 2021, Chapter 7 supplementary material). Panel D in Table 6.2 reports heat capacity values indicated by physical relations. As we employ ocean data covering 0-700m and 0-2,000m in this paper, we also examine the physics-implied heat capacities at these two depths to evaluate the estimation accuracy. Here we have two benchmarks that define different depths for the mixed layer. The first benchmark is by Hartmann (2015), who declares the average depth of the mixed ocean layer that interacts with the atmosphere on a scale of one year is 70 m, and the corresponding heat capacity is 9.32 W year m −2 K −14 . Another benchmark considers 150 m as the mean depth (Gregory, 2000) and the heat capacity value for this benchmark is 14.33 W year m −2 K −15 . Our estimates of the heat capacities for the mixed layer and deep ocean layer C m and C d are noticeably close to Hartmann's benchmarks. give graphic summaries of the model fit for the EBM-SS full model to two pairs of 0-700m ocean datasets from NOAA and IAP, and to 0-2,000m ocean series from IAP, respectively. These two figures indicate that the smoothed states of the latent states, which are the estimated states given the entire observational trajectory, closely catch the data.
Parameter estimates by fitting historical observations
ε Y T d ,ε O and ρ IAP ε Y T d ,ε O denoteT d,t−1 + η T d ,t C d 98.49 (0.26) σ 2 ε,Y NOAA O 1.53 (0.05) σ 2 η,β 0.00001 (0.000006) ECS 3.63 (0.89) σ 2 ε,Y IAP O 1.28 (0.008) σ 2 ε,Y F 1.6 × 10 −11 (1.9 × 10 −17 ) ρ NOAA ε Y T d ,
As described in Section 3.4, we assume the state disturbances and measurement errors to be serially uncorrelated and normality distributed. Then, ideally, the standardized one-step ahead prediction errors are also serially uncorrelated and follow a standard normal distribution (Durbin & Koopman, 2012). In Figure A.2 and Figure A.3, the residuals after the fit, the standardized onestep ahead prediction errors, appear centered around zero. Diagnostic statistics of the residuals are reported in Table A.5 in Appendix A.5. The residual series have means close to zero and standard deviations close to one. There is no violation of Gaussianity except for the residuals of ocean temperature 0-2,000m and OHC 0-2,000m from IAP due to the outliers in 1958. There are a few standardized prediction error series showing autocorrelation. This can be attributed to using a single state to fit variations from multiple data series. Overall, the EBM-SS model provides a good fit for the data.
Empirical evidence for estimation uncertainty reduction by using multiple data sources
In Section 4, we have shown in simulations that the multiple-data-source structure in the EBM-SS model is effective in reducing parameter estimation uncertainty. In this section, we examine if the same conclusion can be drawn in the empirical exercise.
In the simulation study, we can directly compare the simulation performances of the EBM-SS base model (single data source) and of the EBM-SS full model (multiple data source). This is because the simulated data for these two models are generated from the same simulations and thus have the same parametrization and randomness. However, the standard errors using different empirical datasets are incomparable due to the varying magnitudes of the mean estimates of the parameters. Therefore, we use the coefficient of variation (CV), defined as the standard error divided by the estimate of the mean, to measure the relative estimation uncertainty.
In Table 6.3, we compare CVs in the EBM-SS base model with those in the EBM-SS full model. Under the EBM-SS base setting, there are sixteen and eight combinations of different series when ocean data 0-700m and ocean data 0-2,000m are employed, respectively. As shown in Table A.4 in Appendix A.3, both the physical parameter estimates and CVs are diverse across the different combinations of series, and thus we use the median of the CVs for the EBM-SS base model. Table 6.3 shows clearly that the EBM-SS full model with 0-700m and 0-2,000m ocean series produces a lower CV than the medians of CVs for the EBM-SS base model. The last row in Table 6.3 indicates that the majority of individual CVs are equal to or greater than the CV of the EBM-SS full model. One exception isγ when IAP 0-2,000m ocean data is employed. Table 6.3 provides Table 6.3: Comparing coefficients of variation (CVs) of the physical parameters for the EBM-SS full model and the medians of CVs for the EBM-SS base model. CV is calculated as the standard error of the estimate divided by the estimate of the mean. "% CV ≥ *" reports the percentage where the individual CV of EBM-SS base model is not smaller than the CV of the EBM-SS-full model (denoted as * ). empirical evidence that including multiple data sources reduces the estimation uncertainty.
Setting
Scenario Analysis
In this section, we study long-term projections from the EBM-SS full model using the Representative Concentration Pathway (RCP) scenarios of Meinshausen, Smith, et al. (2011). RCPs are adopted by IPCC (2014) tories in the future until 2100. The four scenarios RCP 2.6, RCP 4.5, RCP 6, and RCP 8.5 denote different levels of radiative forcing values (Wm −2 ) 2.6, 4.5, 6, and 8.5, respectively, in 2100. The reduced complexity climate model MAGICC6 was influential in constructing the RCP pathways. The RCP radiative forcing time series during 2021 -2100 are shown in Figure 7.1. Except for RCP 2.6, which shows a peak in around 2030 and then decline, the other three pathways are rising over the period. They exhibit cyclical patterns from solar irradiance. We focus on the projection of GMST for 2021 -2100 conditional on the RCP forcing series. To take parameter uncertainty into account, we assume that the physical parameter vector follows a multivariate normal distribution N (θ * ,Σ * ) and draw 10,000 sets of parameters from this distribution, whereθ * andΣ * denote the estimated mean vector and the estimated variance-covariance matrix of the physical parameter set in the empirical exercise in Table 6.1. We fix the other parameters, such as the variances of measurement errors, at their empirical estimates. We insert each of the parameter sets into the EBM-SS model, which produces point predictions of GMST at T + h (T = 2020, and h = 1, 2, ..., 80). We show the median values and the 90% projection confidence intervals in Figure 7.2 under each of the four RCP scenarios. We produce GMST projections for both the EBM-SS base and the EBM-SS full models. The EBM-SS base model is specified using HadCRUT5 GMST anomalies, together with ocean series (ocean temperature and OHC) from NOAA for 0-700m and from IAP for 0-2,000m. We choose these series because they produce parameter estimates and CVs that are closest to the medians of the values using all combinations of data series (see Table A.4 in Appendix A.3).
In Figure 7.2 and Table 7.1, we compare our GMST projections with the outputs from CMIP5 models and the emulator MAGGIC 7.5, where all of the values are relative to 1850 -1900. The global scale averaged time series of CMIP5 projections under various RCP scenarios are aggregated by Nicholls et al. (2021). Considering data availability, we include the projection series from 21, 29, 16, and 28 CMIP5 models for RCP 2.6, RCP 4.5, RCP 6.0, and RCP 8.5 scenarios, respectively. The 2081 -2100 mean results from MAGGIC 7.5 runs use historical observational GHG concentration levels until 2015 and then switch to emission-driven runs (Lee et al., 2021). Figure 7.2 and Table 7.1 show that our GMST projections produced using the EBM-SS full model and eight GMST historical datasets largely agree with those from CMIP5 models and MAG-GIC 7.5. The EBM-SS base model generates both a higher mean projection and a wider confidence band. The wider confidence band is mainly due to the larger estimation uncertainty in the base case. It corroborates the crucial role of multiple data sources in producing more precise projection values. The results are robust to the depth the ocean data (ocean temperature and OHC) covers. Although employing 0-2000m ocean data generates wider confidence bands than using 0-700m, the differences are not large and the medians remain almost unchanged (Table 7.1).
Conclusion
In this paper, we present a statistical climate model (EBM-SS model), which is a multivariate linear Gaussian state space representation of the two-component EBM. The EBM-SS model provides a framework to quantify the temperature change in response to radiative forcing, while taking the thermal inertia of the ocean into account. We incorporate ocean heat content (OHC) as a second measurement of the temperature in the deep ocean, so that the heat capacity for the deep ocean, C d , can be constrained using both ocean temperature and OHC historical records. We incorporate multiple data sources as measurements for the latent states to reduce estimation uncertainty. To account for the different baseline periods in different anomaly series, we synchronize the eight GMST series and the anthropogenic forcing series with respect to the period 1850 -1900 using the information by IPCC (2018). We include constants for the ocean temperature and OHC series to offset their baseline discrepancies relative to the GMST anomalies and radiative forcing series. Both the empirical and simulation exercises indicate that including eight GMST anomaly series and two pairs of ocean data series as multiple data sources reduces estimation uncertainty of the parameters compared to the models that use only one data source. We obtain physical parameter estimates that are comparable to the ones reported in Cummins et al. (2020) and Smith et al. (2021, Chapter 7 SM).
We show that fitting the EBM-SS model to a comprehensive data set of GMST anomalies, ocean temperature, and OHC over the period 1955 -2020 from separate research groups produces projections for GMSTs that are comparable to those of CMIP5 (Nicholls et al., 2021) and MAG-ICC 7.5 (Lee et al., 2021) for RCP 2.6, RCP 4.5, and RCP 6. Our results thus corroborate earlier findings from both complex climate models and reduced-complexity models, where our statistical model exclusively uses historical data. Our model is, in contrast to earlier models, a small-scale statistical model that can be estimated using standard software packages on standard office computers. Its statistical nature allows for the assessment of parameter uncertainty. (Dickey & Fuller, 1979) for unit roots on level and first-order difference of the observational series for different components of anthropogenic forcing, total anthropogenic forcing Y A,t , and total forcing Y F,t during 1955 -2018. The null hypothesis of the ADF test is the existence of a unit root, i.e., non-stationarity. "f + greenhouse gas name" indicates the forcing from a specific greenhouse gas. ** and * mark significance at 1 % and 5 %, respectively. We report the test statistics when lag order k equals to 0, 1, 2, and 3, respectively. The values in bold indicate the optimal lag order selected by Bayesian information criterion (BIC) (Schwarz, 1978). The maximum order of lags considered is 15. γ j ∆y t−j + εt. Under the null hypothesis π = 0, the regression equation is reduced to a random walk process with drift. b ADF test regression with constant and trend: ∆yt = α + βt + πy t−1 + k j=1 γ j ∆y t−j + εt. Table A.2: ADF test for unit roots on level and first-order difference series of different GMST, ocean temperature, and OHC anomalies during 1955 -2020. ** and * denote significance at 1% and 5%. As in Table A.1, we conduct the tests with constant alone or both constant and trend included (the explicit expressions are reported in the footnote for Table A.1). Subtable (a) reports the test statistics for each of these specifications examined under lag order 0, 1, 2, and 3. The values in bold indicate the optimal lag orders selected by Bayesian information criterion (BIC). The maximum order of lags considered is 15. Subtable (b) reports the optimal lag orders and test statistics for NOAA OHC 0-700m, IAP OHC 0-700m, and IAP OHC 0-2,000m, where the optimal lag orders exceed 3. IAP OHC 0-2,000m 0.84 1.24 1.52 2.53 −9.45 * * −7.14 * * −5.76 * * −4.24 * * −9.72 * * −7.50 * * −6.78 * * −5.12 * *
A Appendix
A.1 Unit root tests on the historical data
Level series
(b)
Level series First-order difference (1). with constant (2). with constant (3). with constant and trend
optimal lag order t-stat optimal lag order t-stat optimal lag order t-stat
NOAA OHC 0-
A.2 Synchronizing anomalies to a common baseline
We show that we can directly synchronize anomaly series of different reference periods to a common baseline. Take a yearly global-level anomaly series T anom,1 t T t=1 such that T anom,1
t = f T grid j,τ − T ref1 j , where T grid j,τ
is the raw gridded temperature level at time τ and location j, τ is the time index at higher frequency than a year, and T ref1 j is the average of the temperatures at location j over a pre-defined reference period ref1. f (·) is the linear operator that integrates high-resolution data into a yearly global value. Suppose we would like to get the anomalies over another reference period ref2, e.g., 1981-2010. Using linearity of f (·), the new anomaly T anom,2 t at time t can be obtained by:
T anom,2 t = f T grid j,τ − T ref2 j = f T grid j,τ − f T ref2 j + f T ref1 j − f T ref1 j = f T grid j,τ − T ref1 j − f T ref2 j − f T ref1 j = T anom,1 t − T ref2 − T ref1 , (A.1)
where T ref2 − T ref1 is the difference between the two average global yearly temperatures over the two reference periods ref1 and ref2. Then we can synchronize the anomalies to ref2 by subtracting T ref2 − T ref1 from the original anomalies.
We use Equation (A.1) and the information in the IPCC report 1.5 • C report (IPCC, 2018) to get the average GMST values during the pre-industrial era, T pre-ind , for each of the data sources.
The results are reported in Table A.3. The downloaded ERA-Interim and JRA-55 datasets are already transformed relative to the pre-industrial level using the same method as in this paper, and hence we leave them as they are. We subtract T pre-ind from other GMST series to get the synchronized series. Figure A.1a shows that these eight GMST anomalies after the synchronization have a substantial agreement, especially since the twentieth century. Figures A.1b and A.1c indicate that, after aligning to the same baseline, the NOAA 0-700m ocean temperature and OHC series are also comparable to their counterparts from IAP. A.4 Fitted estimates and standardized prediction errors using 0-2,000m ocean series Figure A.2: Fit of EBM-SS full model to eight GMST series, two 0-700m ocean temperature, two OHC 0-700m, and one radiative forcing series. Panels (a), (c), (e) show the observational series and the smoothed states from the Kalman filter, which are the estimated states conditional on the entire observational paths. Panel (g) shows the fit to OHC series using the assumption O = C d µ T d . Panels (b), (d), (f), and (g) report the standardized one-step ahead prediction errors. "constant" in the legends of (c) and (g) are the estimated constants for the IAP ocean temperature series. (Jarque & Bera, 1980). The null hypothesis is that the sample is normally distributed.
b Portmanteau test statistic for serial correlation by Ljung and Box (1978): Q(k) = n(n + 2) k j=1 ρ 2 j n−j , where k is the order of lag, and ρ j is the sample autocorrelation at lag j. H 0 : the sample exhibits no serial correlation.
Figure 2 . 1 :Figure 2
212Dynamics of the two-component EBM Incoming radiation Radiative forcing F Mixed Layer (Net radiative flux: F − λT m ) Outgoing radiation λT m Heat transport H γ (T m − T d ) Deep ocean layer
Figure 3 . 1 :
31Components of radiative forcing
Figure 3
3separately. In our state space model, we let
Figure 3 . 3 :
33First and second-order differences of the time series of anthropogenic forcing Y A,t Wm −2 during 1850 -2018. The two vertical dashed lines mark the year 1958 and 1978 when the measurement scheme method changes. The gray area is the time horizon 1955 -2020 for the empirical study in this paper.
Figure 3 . 4 :
34Diagram of the state space model with multiple data sources, i.e., K GMST anomalies, J pairs of ocean temperature and OHC anomalies, and one forcing as measurements.
Figure 4 . 1 :
41Simulated distributions of θ i − θ 0 i for the five physical parameters from 1,000 Monte Carlo simulations of the EBM-SS base model and the EBM-SS full model. "d" in the titles denotes the difference between the estimate in the simulation and the data-generating value, i.e., the bias. The red, blue, and yellow vertical lines represent the data-generating parameter values, the means, and the medians of the 1
Figure 4 .
41 shows the distributions of the deviations of the physical parameter estimates in the simulation relative to the true values (denoted as d·), which are centered around zero. Among these physical parameters, dγ and dC d exhibit the feature of normality, and dC d appears much less dispersed for the full model. Under both models, dλ is slightly positive-skewed. Due to the inverse relationship between ECS and λ, the small magnitudes of the estimates of λ produce large ECS estimates, thus the long right tail in dECS. There are positive skewness and a long right tail in dC m as a result of a few large outliers. The small values of the deviations measures in
Forcing
Effective Radiative Forcing Hansen et al. (2011) 1850 -2018 1850 c,d The ERA 5 and JRA 55 yearly series are downloaded from the Copernicus Climate Change Service (C3S)Climate Data Store, which are processed according toSimmons et al. (2017). These two datasets have already been transformed with respect to the pre-industrial period.Our choice of the eight GMST datasets is in accordance with that in the IPCC Global Warming of 1.5 • C report (IPCC, 2018), which includes: the GISS Surface Temperature Analysis (GIS-TEMP) (GISTEMP Team, 2021; Lenssen et al., 2019), the NOAA Merged Land Ocean Global Surface Temperature Analysis (NOAAGlobalTemp) (NOAA National Centers for Environmental Information, 2021), HadCRUT5 by the Met Office Hadley Centre (Morice et al., 2020), the Berkeley Earth Surface Temperatures Land + Ocean (BEST) (Rohde & Hausfather, 2020), the Cowtan-Way temperature series (CW2014) (Cowtan & Way, 2014), JMA annual anomalies (Japan Meteorological Agency, 2021), ERA-Interim reanalysis
Figure 5
5Figure 5.1: GMST, ocean temperature, and OHC anomaly series before synchronization. The light gray area corresponds to the time horizon 1955 -2020 in the empirical study. (a) GMST Anomalies ( • C) (1850 -2020) (b) ocean temperature ( • C) (1940 -2020)
Figure
Figure A.2 and Figure A.3 in Appendix A.4 give graphic summaries of the model fit for the EBM-SS full model to two pairs of 0-700m ocean datasets from NOAA and IAP, and to 0-2,000m ocean series from IAP, respectively. These two figures indicate that the smoothed states of the latent states, which are the estimated states given the entire observational trajectory, closely catch the data. As described in Section 3.4, we assume the state disturbances and measurement errors to be serially uncorrelated and normality distributed. Then, ideally, the standardized one-step ahead prediction errors are also serially uncorrelated and follow a standard normal distribution (Durbin & Koopman, 2012). In Figure A.2 and Figure A.3, the residuals after the fit, the standardized onestep ahead prediction errors, appear centered around zero. Diagnostic statistics of the residuals are reported in Table A.5 in Appendix A.5. The residual series have means close to zero and standard deviations close to one. There is no violation of Gaussianity except for the residuals of ocean temperature 0-2,000m and OHC 0-2,000m from IAP due to the outliers in 1958. There are a few standardized prediction error series showing autocorrelation. This can be attributed to using a single state to fit variations from multiple data series. Overall, the EBM-SS model provides a good fit for the data.
Figure 7 . 1 :
71to represent different possible GHG concentration trajec-Global annual mean radiative forcing (Wm −2 ) constructed under RCP scenarios(Meinshausen, Smith, et al., 2011) during 2021 -2100.
Figure 7
7Figure 7.2: Probabilistic projection of GMST during 2021 -2100 conditional on RCP 2.6, RCP 4.5, RCP 6, and RCP 8.5 forcing series from Meinshausen, Smith, et al. (2011). (a) RCP 2.6 -0-700m ocean data (NOAA & IAP) (b) RCP 2.6 -0-2,000m ocean data (IAP)
0.26 0.83 −11.05 * * −8.80 * * −7.64 * * −4.68 * * −10.99 * * −8.85 * * −7.84 * * −4.94 * * NOAAGlobalTemp −1.27 −0.95 −0.07 0.59 −10.59 * * −8.86 * * −7.50 * * −4.70 * * −10.51 * * −8.85 * * −7.64 * * −4.91 * * HadCRUT5 −1.07 −0.57 0.15 0.70 −11.36 * * −8.89 * * −7.70 * * −4.78 * * −11.30 * * −8.93 * * −7.88 * * −5.00 * * BEST −1.17 −0.61 0.16 0.76 −11.53 * * −9.02 * * −7.88 * * −4.83 * * −11.47 * * −9.06 * * −8.09 * * −5.08 * * CW2014 −1.22 −0.66 0.12 0.69 −11.32 * * −9.07 * * −7.82 * * −4.88 * * −11.26 * * −9.11 * * −8.02 * * −5.15 * * JMA −1.59 −1.30 −0.37 0.24 −10.45 * * −8.77 * * −7.76 * * −4.73 * * −10.37 * * −8.73 * * −7.83 * * −4.84 * * ERA-Interim −1.12 −0.85 −0.29 0.02 −9.39 * * −7.69 * * −5.75 * * −4.18 * * −9.30 * * −7.64 * * −5.77 * * −4.12 * JRA-55 −1.22 −0.94 −0.36 0.08 −9.47 * * −7.82 * * −6.01 * * −4.26 * * −9.37 * * −7.76 * * −6.04 * * −4.19 * * NOAA Ocean Temp 0-700m 0.49 1.39 1.52 1.99 −10.97 * * −6.98 * * −5.35 * * −3.05 * −11.50 * * −7.47 * * −6.29 * * −3.81 * IAP Ocean Temp 0-700m 0.24 0.81 1.19 2.35 −10.46 * * −7.51 * * −6.52 * * −4.66 * * −10.60 * * −7.77 * * −7.48 * * −5.52 * * IAP Ocean Temp 0-2,000m 0.91 1.27 1.58 2.62 −9.28 * * −7.05 * * −5.78 * * −4.24 * * −9.56 * * −7.43 * * −6.85 * * −5.16 * * NOAA OHC 0-700m 0.40 1.19 1.56 2.02 −10.75 * * −7.61 * * −5.61 * * −3.11 * −11.19 * * −8.11 * * −6.56 * * −3.86 * IAP OHC 0-700m 0.24 0.87 1.26 2.38 −10.80 * * −7.69 * * −6.45 * * −4.60 * * −10.96 * * −7.97 * * −7.44 * * −5.51 * *
Figure A. 1 :
1GMST, ocean temperature, and OHC anomaly series after synchronization. The light gray area corresponds to the time horizon 1955 -2020 in the empirical study.
results using one GMST and one pair of ocean temperature and OHC series
Figure A. 3 :
3Fit of EBM-SS full model to eight GMST series, one 0-2,000m ocean temperature, one OHC 0-2,000m, and one radiative forcing series. Panels (a), (c), (e) show the observational series and the smoothed states from the Kalman filter, which are the estimated states conditional on the entire observational paths. Panel (g) shows the fit to OHC series using the assumption O = C d µ T d . Panels (b), (d), (f), and (g) report the standardized one-step ahead prediction errors. "constant" in the legends of (c) and (g) are the estimated constants for the IAP ocean temperature series.(a) smoothed state of T m and 8
Well-mixed greenhouse gasses Ozone (O 3 )(tropospheric and stratospheric) Stratospheric water vapourLand surface changes:Total radiative forcing
Natural forcing
Solar irradiance
Volcanic radiative forcing
Anthropogenic forcing
Greenhouse gases:
Land use changes
snow albedo changes
Human-made aerosols:
Reflective aerosols
Aerosol Indirect Effect
Black carbon in snow and ice
Table 4
4.1: Data-generating parameter (DGP) values, estimation biases, standard deviations, and root mean squared errors (RMSEs), and mean absolute errors (MAEs) of the Monte Carlo simulation for the EBM-SS base model and EBM-SS full model. Here, σ 2 denote the variance of measurement error of the kth GMST series, of the jth ocean temperature series, and of the jth OHC series, respectively.ε,Y k
Tm
, σ 2
ε,Y j
T d
, and σ 2
ε,Y j
O
EBM-SS base model
physical parameters
variances of state disturbance
λ
γ
Cm
C d
ECS
σ 2
η,Tm
σ 2
η,T d
σ 2
η,A
σ 2
η,β
DGP value
1.0828
1.3027
9.6376
98.4886
3.6294
0.0122
3.66 × 10 −5 4.73 × 10 −5 9.72 × 10 −6
estimation bias
0.0139
0.0308
0.2696
−0.0279
0.1993
−0.0012
−8.59 × 10 −6 −1.82 × 10 −5 6.51 × 10 −6
standard deviation
0.2745
0.2674
2.6176
0.8397
1.0595
0.00354
3.54 × 10 −5 1.72 × 10 −5 6.67 × 10 −6
RMSE
0.2747
0.2691
2.6301
0.8397
1.0776
0.00375
3.65 × 10 −5 2.5 × 10 −5 9.32 × 10 −6
MAE
0.2137
0.2049
1.9236
0.6438
0.7705
0.00295
2.33 × 10 −5 2.03 × 10 −5 7.2 × 10 −6
variances of measurement errors (I)
Table 5 . 1 :
51Summary of the anomaly datasets employed in the empirical analysis. The last column "baseline" indicates the reference period or the year upon which the anomalies are constructed.Variable
Acronym/Type
Institution/Authors
Coverage Baseline
GMST Anomalies
GISTEMP
NASA
1880 -2020 1951 -1980
NOAAGlobalTemp
NOAA
1880 -2019 1901 -2000
HadCRUT5
Met Office Hadley Center
1850 -2020 1961 -1990
BEST
Berkeley Earth
1850 -2020 1951 -1980
Table 6 . 1 :
61Parameter estimates from fitting the EBM-SS model to eight synchronized GMST and the radiative forcing series fromHansen et al. (2011). Panel A includes two pairs of ocean temperature and OHC series covering 0-700m from NOAA Y NOAAT d
, Y NOAA
O
and IAP Y IAP
T d , Y IAP
O
the correlations between the ocean temperature and OHC series from NOAA and from IAP, respectively.A. ocean temperature and OHC 0 -700m from both NOAA and IAP included
phys. para.μ Y T d
elements inĤ
diagonal ofQ estimated linear relationshipŝ
λ 1.08
(0.25)μ
Y NOAA
T d
−0.27
(0.09)
σ 2
ε,Y Tm
0.0003 ∼ 0.012
(0.0001) (0.002)
σ 2
η,Tm 0.012
(0.002)
γ 1.30
(0.34)μ
Y IAP
T d
−0.28
(0.09)
σ 2
ε,Y NOAA
T d
0.00014
(0.00005)
σ 2
η,T d
0.00004
(0.00002)
Tm,t = 0.75
(0.09)
T m,t−1 + 0.14
(0.06)
O t−1 + 0.10
(0.03)
F t−1 + η Tm,t
Cm 9.64
(2.86)
σ 2
ε,Y IAP
T d
0.00015
(0.00005)
σ 2
η,A 0.00005
(0.00001)
T d,t = 0.01
(0.003)
T m,t−1 + 0.99
(0.003)
Table 6 . 2 :
62Comparison of estimates for the physical parameters between EBM-SS full model and other studies.The standard errors of the estimates are reported in parentheses, while some standard errors are unavailable. "Chapter 7 SM" represents the supplementary material to Chapter 7 in IPCC AR6.A. evaluation of the two-component EBM using historical datamodelλγĈ mĈdÊ CS
EBM-SS full, 0-700m ocean data (NOAA & IAP)
1.08 (0.25) 1.30 (0.34) 9.64 (2.86) 98.49 (0.26)
3.63 (0.89)
EBM-SS full, 0-2,000m ocean data (IAP)
0.66 (0.31) 1.82 (0.45) 9.35 (2.61) 269.30 (0.42) 5.91 (2.77)
B. evaluation of the two-component EBM using 4×CO 2 experiment data
modelλγĈ mĈdÊ CS
CMIP6 means (Smith et al., 2021, Chapter 7 SM)
0.84 (0.38) 0.64 (0.13) 8.1 (1.0)
110 (63)
3.0
CMIP5 means (Cummins et al., 2020)
1.21
0.77
6.88
97.18
3.41
C. estimates of ECS using different datasets and methods
model and dataλγĈ mĈdÊ CS
Instrumental records (Forster et al., 2021, Chapter 7)
-
-
-
-
2.5 -3.5
CMIP6 means (Schlund et al., 2020; Smith et al., 2021)
-
-
-
-
3.78 (1.08)
CMIP5 means(Schlund et al., 2020; Smith et al., 2021)
-
-
-
-
3.28 (0.74)
D. heat capacity by physical relationship
literature
C m
C at 700m
C at 2000m
Hartmann (2015)
9.32
93.17
266.2
Gregory (2000)
14.33
66.85
191
Table 7
7.1: 5% -95% ranges and medians of GMST ( • C) projections in 2100 under RCP scenarios by EBM-SS
full model.
0-700m ocean data (NOAA & IAP)
0-2,000m ocean data (IAP)
RCP 2.6 RCP 4.5 RCP 6.0
RCP 8.5
RCP 2.6 RCP 4.5 RCP 6.0 RCP 8.5
Base
median
2.10
3.02
3.51
4.90
1.96
2.81
3.28
4.58
5% quantile
1.45
2.17
2.63
3.77
0.91
1.39
1.71
2.49
95% quantile
2.56
3.55
4.05
5.62
2.34
3.34
3.87
5.41
Full
median
1.73
2.57
3.08
4.42
1.61
2.37
2.84
4.06
5% quantile
1.34
2.02
2.46
3.56
1.21
1.80
2.20
3.17
95% quantile
2.14
3.14
3.75
5.35
1.97
2.91
3.51
5.02
MAGGIC 7.5 runs 2081 -2100 means
CMIP5 outputs
RCP 2.6 RCP 4.5 RCP 6.0
RCP 8.5
RCP 2.6 RCP 4.5 RCP 6.0 RCP 8.5
median
1.6
2.35
2.8
4.2
1.78
2.62
3.06
4.27
5% quantile
1.2
1.75
2.2
3.2
0.97
1.95
2.48
2.93
95% quantile
2.0
3.2
3.7
5.6
2.36
3.32
3.95
6.09
Table A . 1 :
A1Augmented Dickey-Fuller (ADF) test
Table A . 3 :
A3Averages of the GMST series over 1986 -2005 T , changes of the averages over 1986 -2005 relative to the pre-industrial era (1850 -1900) ∆T 1986-2005 pre-ind , and averages over 1850 -1900 T pre-ind i ( • C).GISTEMP NOAA HadCRUT 5 BEST CW2014 JMA ERA-Interim JRA-55for the HadCRUT 5 dataset is not avaiable in IPCC (2018), and thus we use that for HadCRUT 4.6 instead.1986-2005
i
T
1986-2005
i
0.420
0.445
0.349
0.382
0.305
0.014
0.626
0.635
∆T 1986-2005
pre-ind
(IPCC, 2018)
0.65
0.62
0.60 a
0.73
0.65
0.59
-
-
T
pre-ind
i
−0.230
−0.175
−0.251
−0.210 −0.345 −0.576
-
-
a The temperature change ∆T 1986-2005
pre-ind
Table A . 4 :
A4Mean estimates of the physical parameters from fitting the EBM-SS base model to different GMST and ocean (ocean temperature + OHC) datasets. The numbers in parentheses are the coefficients of variation.One ocean temperature and one OHC series are included -0-700mOne ocean temperature and one OHC series are included -0-2,000mNo. of GMST GMST(s) included
NOAA 0-700m
IAP 0-700m
λγĈ mĈd
ECSλγĈ mĈd
ECS
1 GMST
GISTEMP
0.63
1.45 21.44 96.13 6.24
0.44
1.21 25.52 98.23 8.91
(0.47) (0.2) (0.38) (0.01) (0.47) (1.1)
(0.36) (0.59) (0.002) (1.1)
NOAA
0.82
1.59 18.29 96.14 4.79
0.63
1.31 22.42 98.23 6.19
(0.34) (0.21) (0.36) (0.01) (0.34) (0.65)
(0.35) (0.55) (0.002) (0.66)
HadCRUT5
0.74
1.3
20.3 96.15 5.29
0.63
1.15 22.12 98.23 6.29
(0.41) (0.22) (0.37) (0.01) (0.41) (0.61)
(0.3) (0.48) (0.002) (0.62)
BEST (Berkeley)
0.39
1.56 29.16 96.14 10.09
0.00017 1.13 43.18 98.23 231033.26
(1.18) (0.24) (0.59) (0.01) (1.19) (0.00015) (0.29) (0.2) (0.002) (0.07)
CW2014
0.55
1.61 26.52 96.13 7.15
0.07
1.21 42.28 98.23 60.06
(0.64) (0.21) (0.43) (0.01) (0.65) (12.56)
(0.33) (0.72) (0.002) (12.56)
JMA
1.01
2.28 15.81 96.13 3.88
0.8
1.83 21.38 98.22 4.93
(0.26) (0.21) (0.34) (0.01) (0.27) (0.51)
(0.38) (0.61) (0.002) (0.52)
ERA5
0.85
1.2
15.8 96.14 4.61
0.87
1.14 14.11 98.22 4.52
(0.32) (0.26) (0.37) (0.01) (0.33) (0.26)
(0.27) (0.32) (0.002) (0.27)
JRA55
0.85
1.32 17.74 96.15 4.61
0.87
1.26 15.85 98.22 4.51
(0.37) (0.27) (0.43) (0.01) (0.38) (0.3)
(0.28) (0.38) (0.002) (0.31)
Median of estimate
0.78
1.51
19.30
96.14
5.03
Median of CV
(0.39)
(0.22)
(0.37)
(0.01)
(0.40)
No. of GMST GMST(s) included
IAP 0-2000m
λγĈ mĈd
ECS
1 GMST
GISTEMP
0.18
1.84 21.72 269.28 22.36
(1.9)
(0.18) (0.37) (0.002) (1.9)
NOAA
0.33
2.00 19.04 269.28 12.08
(1.01) (0.19) (0.36) (0.002) (1.01)
HadCRUT5
0.25
1.73 20.95 269.28 15.89
(1.40) (0.20) (0.36) (0.002) (1.40)
BEST (Berkeley)
0.03
1.93 27.2 269.28 148.48
(14.61) (0.19) (0.48) (0.002) (14.61)
CW2014
0.10
1.98 26.16 269.28 39.12
(3.67) (0.19) (0.42) (0.002) (3.67)
JMA
0.47
2.65 16.9 269.28 8.44
(0.70) (0.19) (0.35) (0.002) (0.71)
ERA5
0.51
1.55 13.58 269.29 7.64
(0.49) (0.21) (0.27) (0.002) (0.49)
JRA55
0.53
1.7
14.81 269.3 7.44
(0.49) (0.21) (0.3) (0.002) (0.5)
Median of estimate 0.29
1.89 19.99 269.28 13.98
Median of CV
(1.20) (0.19) (0.36) (0.002) (1.21)
Table A . 5 :
A5Diagnostic statistics of the one-step ahead standardized prediction errors for the EBM-SS full model.The upper panel shows the results for 0-700m ocean data. The lower panel shows the results for 0-2,000m ocean data. ** and * denote significance at 1% and 5%.A. ocean temperature and OHC 0-700m from both NOAA and IAP are included GISTEMP NOAA HadCRUT5 BEST CW14 JMA JRA55 ERA5 Y T NOAA B. Ocean temperature and OHC 0-2,000m from IAP is included GISTEMP NOAA HadCRUT5 BEST CW14 JMA JRA55 ERA5 Y T IAP a Test statistic of the Jarque-Bera normality testd,700 m
Y O NOAA
700 m
Y T IAP
d,700 m
Y O IAP
700 m
forcing
mean
0.284
0.004
−0.225
0.753 0.381 −0.138 0.080 0.045
0.053
0.182
−0.074
0.163
0.149
std
0.945
0.989
0.935
0.724 0.944 0.962 1.067 1.052
1.033
0.930
1.044
0.928
0.989
skewness
−0.102
0.054
−0.115
−0.079 −0.106 0.072 −0.255 −0.160
0.432
−0.167
0.309
−0.180 0.093
kurtosis
2.720
2.598
2.649
2.651 2.612 2.260 2.689 2.427
2.567
2.731
2.444
2.909
3.860
t JB
a
0.325
0.461
0.476
0.399 0.528 1.539 0.759 0.898
2.529
0.498
1.873
0.375
2.034
Q(1) b
4.979 *
3.129
4.707 *
5.591 * 2.533 1.168 2.739 * 4.057 * 6.076 * *
3.703
9.895 * *
2.482
0.000
d,2,000 m
Y O IAP
2,000 m
forcing
mean
0.259
−0.025
−0.251
0.735 0.358 −0.161 0.065 0.028
0.118
0.089
0.148
std
0.949
0.985
0.941
0.720 0.937 0.943 1.078 1.056
1.006
1.005
0.988
skewness
−0.109
0.053
−0.126
−0.093 −0.118 0.086 −0.267 −0.168
0.456
0.483
0.095
kurtosis
2.703
2.629
2.641
2.660 2.628 2.282 2.719 2.493
4.222
4.289
3.858
t JB
0.368
0.396
0.520
0.407 0.527 1.478 0.772 0.772
6.290 *
7.020 *
2.026
Q(1)
4.465 *
3.292
4.012 *
5.714 * 2.880 0.737 2.144 3.737
0.234
0.132
0.000
We use one data source for radiative forcing. This is because we could not find an alternative observation-based dataset that provides complete information on the total radiative forcing and its components as the one byHansen et al. (2011).
The "solnp" optimizer implements the general nonlinear augmented Lagrange multiplier method.
The ocean heat capacity at a specific depth d is:C = d × 0.1331WK −1 m −2 m −1(Hartmann, 2015). 5 According toGeoffroy et al. (2013), C = d × 0.0955WK −1 m −2 m −1 .
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On adjustment for temperature in heatwave epidemiology: a new method and toward clarification of methods to estimate health effects of heatwaves
Honghyok Kim honghyok@uic.edu
Division of Environmental and Occupational Health Sciences
School of Public Health
University of Illinois Chicago
ChicagoIllinoisUSA
Michelle L Bell
School of the Environment
Yale University
1086 SPHPI MC 923, 1603 W. Taylor St60612New Haven, ChicagoCT, ILUSA, USA
On adjustment for temperature in heatwave epidemiology: a new method and toward clarification of methods to estimate health effects of heatwaves
Corresponding author: Honghyok Kim Conflicts of Interests The authors declare they have nothing to disclose.
Defining the effect of exposure of interest and selecting an appropriate estimation method are prerequisite for causal inference. Understanding the ways in which association between heatwaves (i.e., consecutive days of extreme high temperature) and an outcome depends on whether adjustment was made for temperature and how such adjustment was conducted, is limited. This paper aims to investigate this dependency, demonstrate that temperature is a confounder in heatwave-outcome associations, and introduce a new modeling approach to estimate a new heatwave-outcome relation:where HW is a daily binary variable to indicate the presence of a heatwave; R(Y) is the risk of an outcome, Y; T is a temperature variable; OT is optimal temperature; and Z is a set of confounders including typical confounders but also some types of T as a confounder. We recommend characterization of heatwave-outcome relations and careful selection of modeling approaches to understand the impacts of heatwaves under climate change. We demonstrate our approach using real-world data for Seoul, which suggests that the effect of heatwaves may be larger than what may be inferred from the extant literature. An R package, HEAT (Heatwave effect Estimation via Adjustment for Temperature), was developed and made publicly available.
INTRODUCTION
Heatwaves have become more frequent, severe, and prolonged due to climate change (1).
Epidemiology have shown health impacts and health disparities during heatwave events (2)(3)(4), thereby informing policy to save lives by improved heat responses and preparedness (5). Timely location-specific epidemiological evidence can provide valuable information on how to address public health burdens (6,7).
Time-series and case-crossover studies on the effects of heat on health typically investigate single days of high temperature (8,9), whereas studies on heatwaves focus on consecutive days with extreme high temperatures (10,11). Both single days of heat and heatwaves are detrimental to human health and such harms are projected to be more severe and frequent due to climate change. Understanding the differences between the health impacts of heatwaves and high temperatures is important to inform policies aimed to protect public health, such as heat action plans.
Some epidemiological studies on heatwaves and health adjust for temperature (12)(13)(14)(15) whereas others do not (16,17). The meaning and interpretation of heatwave-outcome associations, depending on whether such adjustment was made, is not well studied. Some studies discussed this issue from a statistical standpoint (13,18). However, understanding the meaning of heatwave-outcome associations requires conceptualizing the effect of heatwaves and identifying estimation methods relevant to the conceptualized effects (19,20).
We demonstrate that heatwave-outcome associations depend on whether adjustment for temperature is conducted and how such adjustment is made. We propose a novel modeling approach to estimate heatwave-outcome relations and propose a conceptualization of the effect of heatwaves with causal diagrams. We demonstrate how modeling approaches impact causal inference using an example with real-world data.
DEFINING A HEATWAVE
Heatwaves are not defined consistently in research and policy (11,21,22), although they are generally defined based on duration and intensity. For example, the U.S. National Weather Service defines a heatwave as "a period of abnormally hot weather generally lasting ≥2 days" (22). Heat warning systems sometimes rely on heat indices (23,24) which are designed to measure thermal comfort by integrating ambient temperature (T) and humidity. It is unclear whether heat indices are better causal factors of health outcomes than T alone (25,26). A multicountry epidemiological study (26) found that humidity does not appear to be a causal factor to non-accidental mortality risk. Numerous epidemiological studies have defined a heatwave based on T, without consideration of humidity (11). We follow this convention.
Commonly used methods to define heatwaves considers duration (at least a certain number of continuous days, often ≥2 days) and intensity (T exceeding a specified threshold value, THW such as the 98 th percentile of T distribution) (11). Epidemiological research often uses a daily binary variable to indicate the presence of a heatwave for day t, HWt. For example, using a definition of a heatwave as ≥2 consecutive days with T≥THW, if Tt<THW, HWt=0. If Tt≥THW, and either of the surrounding days exceed THW thereby generating two consecutive days exceeding THW (i.e., Tt-1≥THW or Tt+1≥THW), HWt=1, meaning that day t is categorized as a heatwave day. While high temperature is one characteristic of a heatwave (i.e., intensity), high temperature may occur for conditions other than a heatwave with a single day of heat or consecutive days that are hot but do not exceed THW. For clarification, we define high temperature, HT, as T>optimal temperature (OT), a temperature at which risk of a health outcome is minimal such as minimum mortality temperature (27,28). We refer to conditions where HT<THW (i.e., days with T>OT but T<THW)
or HT≥THW (i.e., days with T>THW) as moderately HT (MHT) or extremely HT (EHT), respectively.
For this paper, we define heatwaves as having at least two consecutive days with EHT, meaning days with T≥THW, as has been applied previously (11). There is no standard value for THW, and a variety of THW approaches have been applied (e.g., 95 th , 97 th , 98 th , and 99 th temperature percentiles).
DEFINING THE EFFECT OF A HEATWAVE
Defining the effect of exposure of interest with knowledge about potential causal pathways is a prerequisite for causal inference (19,20). Reflecting available public health or surveillance data (e.g., vital records, national insurance claims)(10), time-series and case-crossover studies investigated associations of heatwaves with mortality, hospitalizations, and emergency department visits in general populations, often with different methods. The findings of such studies are sometimes discussed without articulation of how different modeling approaches can affect the meaning of associations (not estimates). In this section, we conceptualize the effect of a heatwave; in the following section, we address the dependence of heatwave-outcome associations on estimation methods.
Multiple causal pathways and causal effects of interest
Causal pathways through which exposure to EHT on consecutive days (i.e., heatwave) impacts health differ from those for single days of HT that includes MHT. There are many dimensions to consider, such as difference in susceptibility between cumulative biological stress by extreme heat and the stress by moderate heat, adaptive behaviors to extreme heat, and disrupted social, economic, and health systems during heatwave events (7,(29)(30)(31)(32)(33). The Intergovernmental Panel on Climate Change (IPCC)'s Sixth Assessment Report (1) highlights cascading effects by weather-related disasters, meaning that heatwaves can indirectly increase health risks by impacting socioeconomic infrastructures (1) in addition to direct health impacts (i.e. physiological effects by heat exposure). We formulate potential causal pathways. Figure 1A is the simplest directed acyclic graph (DAG) that shows the causal effect of HW on a health outcome (Y): HW→Y. HW indicates the occurrence of a heatwave in ambient environment, not exposure to a heatwave. Figure 1B is an extension of Figure 1A including exposure to a heatwave (E): HW→E→Y. Figure 1C is an extension of Figure 1B that considers protection (P) to avoid E. For example, people can use air conditioning, visit cooling centers, and avoid outdoor activities during a heatwave: HW→P1→E→Y. There may be a set of factors, Q, that impact P1. For example, some people may need to stay outside (e.g., workers of essential services) or may not avoid exposure (e.g., not using air conditioning due to worry about energy costs and being unaware of governmental subsidies (5)). There is another protection regardless of HW such as indoor built-environment (e.g., architecture designed with natural ventilation and cooling): P2→E→Y. In a population, HW is unlikely to be perfectly correlated with E because some people may be exposed to a heatwave and others may not (e.g., different indoor/outdoor activity patterns). Figure 1D is another extension of Figure 1B, including the effect of HW on the infrastructure (I) (HW→E→I and HW→I) and directly heat-related outcome, Y1 and other outcome, Y2 due to impacted I: I→Y1 and I→Y2. I collectively denotes socioeconomic infrastructure (e.g., health systems, transportation networks, power supplies). Recall cascading effects discussed in IPCC's report (1). For example, whether health systems are heat-resilient to prevent a systemic failure of health services should be considered as a causal component (7). Critical patients with heatrelated illness can be at risk of losing receiving timely treatment if emergency departments are overwhelmed by incoming patients exposed to excess heat. Overburdened hospitals may struggle to provide timely medical treatments to patients with conditions other than heat-related illnesses.
This can exacerbate their health issues, as highlighted in Y2. A heatwave can increase the risk of power outages (34) and traffic chaos (e.g., increased risk of traffic crashes (35), road closures, rutting, and buckling (36)) may occur, impacting accessibility to necessary services and hospitals. Grocery stores and pharmacies may temporarily close, especially under national/state of emergency and/or power outages, resulting in water, food, and medicine insecurities. Figure 1E In causal mediation context, we can define the effect of HW as the relation between: 1) HW and Y1 through E and P; 2) HW and Y1 through I; and 3) HW and Y2 through I. We call #1 a direct effect of HW. We call 2# and #3 indirect effects of HW. These definitions presume that physiological pathways (e.g., heat toxicity through heat exposure) are subsumed in the direct effect. The indirect effects work through I. We define the relation between HW and Y (Y1+Y2) as the sum of these three effects. We call this HW-Y relation the total effect of HW as the main interest in this paper, representing the population-averaged effect. Many studies have used HW rather than E (10,11), and such data is more readily available.
There are many reasons why HW is used. For example, aside from policy implications, the use of HW may avoid unmeasured confounding that would arise if E is used. We relegate detail to Appendix A.
HW-Y relation
We define HW-Y relation as E[R(Y)|HW=1, Z]/E[R(Y)|T=OT, Z], where R(Y) is the risk of Y and
Z is a set of confounders. Z includes typical confounders such as seasonality, time-trend, and humidity but also lag effects/cumulative exposure effects of T not related to a heatwave on R(Y) at HW=1 and lag effects of a heatwave on R(Y) at T=OT. Note that T=OT means HW=0 (i.e., OT<THW). We relegate the definition of lag effect and cumulative exposure effect to Appendix B.
Confounding by temperature is not widely discussed in heatwave epidemiology. We will discuss this in the first sub-section of the next section.
Counterfactuality for a reference risk
Many counterfactuals for HW-Y relation could exist: the concept that a heatwave increases R(Y) from 'a' reference risk (i.e., the risk would have been if the episode had not occurred). This T=OT), given that many studies have estimated heat-related premature mortality as HT deviated from OT (8,9).
A reference risk could be what R(Y) would have been with T<THW. Some studies estimate an excess mortality risk during a heatwave event by comparing the mortality rate during the event with a historically mean mortality rate during non-heatwave periods (37,38). That periods could include days with T<OT, days with T=OT, and days with T<THW. Such average risk appears to serve as another counterfactual risk because the average may differ from the mortality risk at OT.
Other studies estimate an effect of heatwaves in comparison to the risk related to single days of heat, referred to as an added effect of heatwaves (18). The counterfactual risk of this added effect is not straightforward due to the gap between statistical concepts and epidemiological concepts.
We will review this added effect in the first sub-section of the next section.
ISOLATING THE EFFECT OF A HEATWAVE FROM THE EFFECT OF TEMPERATURE
The health effect of HW may differ than that of MHT for physiological pathways, including susceptibility by predisposing factors (e.g., drug use, illness, genetics) (30,33). We propose to distinguish HW and MHT considering whether HW can increase R(Y) by impacting I. Health systems, transportation networks, and power grids can be disrupted during extreme heat (1). Heat safety actions and responses can be activated if temperature exceeds a certain intensity threshold, including disaster preparedness of health systems (7), governmental subsidies for electricity bills (5), electricity demand management (39), and railroad speed limits (40). Evidence shows higher association with for extreme heat than for moderate heat fatal traffic crashes (35) and with road buckling (36). Studies suggest that R(Y) can depend on I and this dependence may be more strongly related to HW than MHT, meaning that potential causal pathways related to I should be considered in interpreting heatwave-outcome associations. For example, authors hypothesized that temporal decrease in heatwave-mortality associations resulted from prevention plans, although they did not directly measure such plans (41).
To isolate HW from T, we introduce DAGs for the effect of T on Y ( Figure 2A). Given epidemiological studies on both heatwaves and temperature and their policy implications, we propose that temperature effect should be regarded as two parts: heatwave effect (HW) and temperature effect not related to a heatwave (T NH ) ( Figure 2B). Some investigators may be interested in temperature effect including extreme heat (waves) (Figure 3: T effect). Others may want to investigate only heatwaves ( Figure 3: HW effect (i.e., HW-Y relation)).
Dependency of HW-Y association on how to address temperature
Traditionally, HW-Y association is estimated by comparing health risk on heatwave days and risk on non-heatwave days (11). For example, suppose a Poisson regression model in time-series studies,
log( [ ! ]) = + " ! + (Model 1)
where Yt is an outcome at day t and exp( " ) is rate ratio (RR), which could be approximately risk ratio when temporal change in the population-at-risk is negligible (e.g., mortality in a general population). Confounders typically include seasonality, time-trend, and humidity.
There exist two methods to address T (12)(13)(14)(15)(16)(17)(18) in efforts to disentangle effects of HW from those of HT. We review these two herein. Some studies do not adjust for T when estimating effects of HW (16, 17) (Model 1) because EHT is one component of HW (i.e., intensity). Other studies adjusted for basic T (e.g., T of the same day (Lag0), previous day(s) (e.g., Lag1, Lag2 temperatures (12-15))). We use Tt, Tt-1,…, Tt-L to denote Lag0, Lag1,…, LagL T. We refer to these two methods as traditional approaches: non-adjustment for T (Traditional Approach #1); adjustment for basic T (Traditional Approach #2).
HW-Y association not adjusted for T (Traditional Approach #1) indicates the difference between
R(Y) on heatwave days and a weighted average of R(Y) on non-heatwave days. The latter risk would be averaged from that of three different types of non-heatwave days: non-heatwave days with T<OT, non-heatwave days with T=OT, and non-heatwave days with T>OT, the latter of which is a day with HT but not satisfying the heatwave definition. The weight would be the number of days for each type of non-heatwave days. Thus, the counterfactual risk of this HW-Y association would be R(Y) at an unclear T<THW.
The approach of estimating the HW-Y association without adjustment for T may not be relevant for causal inference on HW-Y relation. This association is confounded by T NH due to the backdoor path of Y-T NH -T-HW ( Figure 2B). T NH is correlated with HW: for m≥0, if HWt-m=0, (42)). This confounding by T NH t-l and/or HWt-l can be articulated by clarifying R(Y). R(Y) on a heatwave day depends on increased risk due to HW but also increased risks due to lagged effects or cumulative exposure effects (27,28,(43)(44)(45)(46) of T NH before the heatwave if they exist. In a similar vein, R(Y) on a non-heatwave day depends on increased risks due to T NH but also increased risks due to lagged effects of HW preceding that day if they exist. Thus, adjustment for T NH and HWt-l is required for analysis that aims to estimate " as the causal impact of HW on Y. See Appendix C for additional illustrations.
|T NH t-m|>0 and if HWt-m=1, T NH t-m=0
Traditional Approach #2 adjusts for basic T. For example, in a piecewise Poisson regression, The meaning of this adjusted association is statistically straightforward, but its epidemiological concept is not straightforward. By adjusting for Tt,…,Tt-L, the effects of Tt,…,Tt-L of heatwaves are not subsumed into the estimand. How much lag effects and cumulative exposure effects of T including T NH or HW are adjusted for depends on L and methods to adjust for basic T (e.g., linear terms or splines in regression models). These two complicate the definition of what effect of a heatwave is targeted by this adjusted association regarding its counterfactual risk and causal components of that effect. We relegate our investigation on this effect to Appendix D.
log( [ ! ]) = + " ! + #,% ! #& + ',% ! '& + ⋯ + #,( ! !)( ! #& + ',( " !)( '& ' + (Model 2) where T LT =OT -T if T ≤OT,
Another issue to consider is perception and communication across stakeholders. The concept of this added effect (18), that a heatwave poses additional risk on top of the risk already increased by high temperatures, refers to a different aspect of heatwave risk than the total effect. News media outlets, political authorities, and local communities commonly discuss a heatwave episode in terms of increases deaths/hospitalizations by a certain number compared to the risk that would have been if T had been under normal conditions, not to the risk already increased by single days of T (3,47,48). Our defined HW-Y relation aligns with this perception (Figure 3: HW effect).
Novel approach to estimate HW-Y relation
Therefore, we propose a novel modeling approach to estimate HW-Y association that represents the defined HW-Y relation. We replace T HT in Model 2 with T HT* . We set T H* =T H if HWt=0 and T H* =0 if HWt=1 and adjust for a vector, V: Only summer seasons (June-August) were analyzed. T was daily 24-hour mean temperature. We defined heatwave as T exceeding the 99 th percentile (28.7 o C) of the year-round T distribution for at least two consecutive days (11). We fit quasi-Poisson regression models and Models 1-3.
log( [ ! ]) = + " ! + #,% ! #& + ',% ! '& * + ⋯ + #,( ! !)( ! #& + ',+ !)+ '& * + ! + (Model 3).
Adjustment for Tt and Tt-1 was considered. A natural cubic spline (NCS) of the day of season, dummy variables of year, and interaction between these two were included to adjust for timetrend and seasonality. Dummy variables of day of the week and NCS of two-day moving average of PM10 and O3 were added. We conducted analyses with NCS of Tt and NCS of Tt-1 without HWt to identify OT (21.7°C). Table 1 presents associations between HW and non-accidental mortality, including for Lag1 of HW (the second row). The first row shows associations without the lag effect presented in Figure 4. Associations including the lag effect was generally higher than associations without the lag effect. We should note subgroup-specific HW-Y association. Subgroup-specific HW-Y relations depend on the distribution of I, P, Q, and/or risk factors to Y (not drawn in Figure 1) (49) and the reference risk. The associations can further depend on confounding by temperature if the confounding is differential and is not adequately addressed. Our novel approach adjusts for this confounding is based on the well-defined reference risk.
Results
Figure 4 presents associations between
DISCUSSION
While no standard definition for a heatwave exists, we followed the convention of defining a heatwave based on intensity and duration (11). Stakeholders often use weather-based metrics and health impact-based approach (11,21). The implications of how different definitions of a heatwave impacts health estimates merits further research. We suggest that a health impact-based approach should consider total, direct, and indirect effects and clearly define a reference risk.
In
Figure 2. Directed acyclic graphs for the relation between ambient temperature (T) and a health outcome (Y). A. A simple conceptualization; B. A conceptualization of distinguishing a heatwave (HW) and non-heatwave related T (T NH ).
Note. Subscripts t, and t-1 denote time t and time t-1. Tt-1→Tt and Yt-1→Yt denote an autocorrelation process.
HW Y HW E Y A. B. C. D. E. HW E Y 1 I Y 2 HW E Y P 1 P 2 Q I Y 2 HW E Y P 1 P 2 Q ! ! "# ! !$% "# "# ! "# !$% $ ! $ !$% ! ! ! !$% B. $ ! $ !$% ! ! ! !$% A. … …
A. The use of HW rather than E
Many epidemiological studies use T measured from monitoring stations or modeled estimates of T at residence (10,11), not E, and although they are correlated, not perfectly so. Some may argue that such use of T introduces exposure misclassification because individuals are not necessarily exposed to a heatwave (i.e., through P1 and P2 in Figure 1C). This viewpoint holds if E-Y relation is the causal effect of interest. However, there are other viewpoints that advocate the use of HW and T. First, HW-Y relation can be of interest, which is policy-relevant. Some institutions and organizations (e.g., government agencies, community organizations) have policies related the occurrence of heatwaves in their jurisdictions (e.g., heatwave action plans) and are interested in how public health is impacted by heatwaves in the population through many causal pathways ( Figure 1). HW-Y relation would represent a population averaged total effect that presents an overall picture of the health impact in a population of interest, including exposed and unexposed groups. We call this crude HW-Y relation 'with respect to E' because this would be a weighted average of two stratum-specific relations: HW-Y relation for E=1 (those who would be exposed to heatwaves during heatwaves) and HW-Y relation for E=0 (those who would be unexposed to heatwaves during heatwaves). If a heatwave is harmful, HW-Y relation for E=1 will be positive and HW-Y relation for E=0 will be the null. Crude HW-Y relation would be meaningful to estimate the health impact of the total effect of HW (e.g., attributable fractions/numbers) when the size of the population is (usually) known but the size of exposed and unexposed groups is unknown. If HW-Y relation is of interest, the use of HW, not E, will not necessarily result in exposure misclassification, demonstrating that the use of HW or E should depend on what to infer. Second, even if E-Y relation is of interest, the use of E may introduce confounding by a set of unmeasured factors, U, that impact E and Y. Figure A1 shows why. The use of an ambient variable, X, can be seen as an instrumental variable method to avoid unmeasured confounding (50). For example, very short-term variation of individuals' behaviors and moods (e.g., working under stressful conditions outside) is not related to the occurrence of a heatwave in the atmosphere but may impact Y and affect behavioral patterns that thereby impact E. Built environment may also differ, impact E (e.g., insulation, greenspace) and Y (e.g., chemical emissions from building materials), but is not related to the occurrence of a heatwave. The use of HW can avoid this unmeasured confounding.
Figure A1. Instrumental variable (X) methods: similarity between the use of an ambient variable (X) in environmental epidemiology and the use of a treatment assignment variable (X) in randomized clinical trials instead of an actual exposure/treatment variable (E) in order to avoid confounding by a set of unmeasured factors (U) that increase the likelihood of E and increase the risk of an outcome (Y)
While the use of HW has the aforementioned benefits, HW-Y association may not be generalizable to another population regarding either HW-Y or E-Y relations because the existence and the degree of causal pathways in Figure 1 would differ across populations, which is analogous to a lack of generalizability of instrumental variable analyses such as intent-to-treat effect estimates due to different degrees of non-adherence across populations (51). While meta-analyses suggest consistently positive estimates of HW-Y associations (e.g., HW-mortality association), estimates are variable across study populations (10,11). This highlights why location-specific HW-Y association is needed for public health protections.
X E Y U
B. Epidemiological concept of lag effects and cumulative exposure effects
In disciplines outside environmental epidemiology, the term lag may have the connotation of induction period in epidemiology taxonomy (52). We adopt the term induction period for clarification, henceforth. Then, lag(ged) effect should mean the health effect of exposure with an induction period. For example, there exist Lag0 effect (i.e., the induction period is zero day, thus instantaneous effect) of one-day exposure, Lag1 effect (i.e., the induction period is one day) of one-day exposure, and so on. We call them L0(1d), L1(1d), and so on. Effects of cumulative exposure to T are possible because one-day exposure to high T may not be enough to exceed a certain biological threshold to manifest the effect of T (e.g., thrombosis advanced by heat stress from one-day exposure is not adequate to progress pathological responses leading to death), which may differ by predisposing factors of individuals. We refer to Lag0 effect of two-day exposure as L0(2d), refer to Lag1 effect of two-day exposure as L1(2d), refer to Lag0 effect of three-day exposure as L0(3d), and so on. For mortality and hospitalizations, a few days of induction periods are plausible through other pathways aside from biological pathways. For example, suppose that a person was expected to heat, had symptoms, and got hospitalized. That person received a medical treatment in an intensive care unit for two days but was pronounced dead unfortunately. In this case, the induction period for the effect of heat on this death is two days. Suppose that a person with diabetes was unable to use insulin treatments due to an out-of-electricity refrigerator due to power outage during the episode. That person got hospitalized after the episode when hospitals that were overburdened during the episode became available but eventually passed away after the heatwave. In this case, the induction period for the (indirect) effect of that heatwave on the death or the hospitalization is not zero day. Suppose two people who lived in a different community got cardiac arrest during a heatwave. One person was timely transported to a hospital by an ambulance and survived. Transportation of the other person to a hospital was delayed due to traffic chaos, underwent to a critical stage, and passed away after a few days of medical treatments. The induction period for the (total) effect of that heatwave on the death of the second person is a few days. The findings of many epidemiological studies suggest acute effects of HT on mortality (e.g., L0(1d), L0(2d), L1(1d), L1(2d)) (9,14,27,43,53,54), which are plausible, considering multiple causal pathways (e.g., impacted infrastructure), including biological plausibility and cascading effects ( Figure 1).
C. Confounding by temperature in estimating HW-Y relation
We illustrate why lag effects and cumulative exposure effects of T can confound HW-Y association by clarifying R(Y) at HW=1 and R(Y) at HW=0. The bottom graph of Figure A2 shows representation of different lag effects and cumulative exposure effects of HT as time-series of increased daily outcome rates on non-heatwave days (u-2, u-1) and on heatwave days (u, u+1).
The size of the increased risks is hypothetical for illustration. The top graph of Figure A1 shows hypothetical T time-series. Increased risks on heatwave days can come from not just HT of heatwave days, but also HT of non-heatwave days via lag effects (e.g., L1, L2) and/or partial cumulative exposure effects (e.g., L0(2d), L1(2d), L0(3d)): See Appendix B for L0, L1, L2, (1d), (2d), and (3d) notations. Some of the effects of HT of non-heatwave days would be subsumed to " in Model 1 (orange boxes on u and u+1), which is confounding. We note that the possibility of effects of low T of non-heatwave days on the risk on heatwave days may not be ruled out for some populations, which is not presented in Figure A2, considering global variation of temperaturemortality associations and temperature distributions (43).
This figure also shows why R(Y) of non-heatwaves would be a weighted average from R(Y) of three different types of non-heatwave days, which impacts " in Model 1: non-heatwave days with T<OT (not displayed in Figure A1), non-heatwave days with T=OT (e.g., u-2 in Figure A2), and non-heatwave days with T>OT (e.g., u-1 in Figure A2).
Figure A2. An illustration of how the increased risk on heatwave days and non-heatwave day can be decomposed into different increased risks by lag effects and cumulative exposure effects of T.
We provide an illustration of the confounding in the context of regression models. First, we show how regression coefficients of basic T are related to the effects presented in Figure A2 for illustrational simplicity. Suppose Lag0 HT (HTt), Lag1 HT (HTt-1), Lag2 HT (HTt-2) variables.
These three variables can be used to capture L0(1d), L0(2d), L0(3d), L1(1d), L1(2d), and L2(1d).
For example, in a cumulative exposure model,
log( [ ! ]) = + ( , ! , !)" , !), )
where ( ,•) denotes a function that represents the effect of three-day exposure to HT and indicates a set of the regression coefficients with respect to HTt, HTt-1, and HTt-2. One example of this model is an (unweighted) moving average model (55)
L0 (3d) L0 (1 st ,1d) L0 (2 nd ,1d) L0 (1d) L1 (1d) L2 (1d) L1 (1 st ,1d) L1 (2d) L0 (2d)
Temperature
Daily temperature (T)
Effect of one-day exposure (1d) to T of the non-heatwave day before the first day of a heatwave (i.e., u-1) on the risk at that day (Lag0 effect, L0), at the next day (Lag1 effect, L1), or at the day after next (Lag2 effect, L2):
L0 (1d)
This color indicates an increased risk by an effect of exposure to T of heatwave day(s) (i.e., u and/or u+1) on the risk at that day or later (i.e., u or u+1)
This color indicates an increased risk by an effect of exposure to T of the non-heatwave day before the first day of a heatwave (i.e., u-1) on the risk at that day or later (i.e., u-1, u, or u+1)
L0 (3d) L1 (1d) L2 (1d) L0 (1 st ,1d)
Effect of one-day exposure (1d) to T of the first day (1 st ) of a heatwave (i.e., u) on the risk at that day (Lag0 effect, L0), or at the next day (Lag1 effect, L1):
L0 (2 nd ,1d)
Effect of one-day exposure (1d) to T of the second day (2 nd ) of a heatwave (i.e., u+1) on the risk at that day (Lag0 effect, L0) L0 (1st,2 nd ,2d)
Effect of cumulative two-day exposure (2d) to T of the first two days of a heatwave (1 st ,2 nd ) (i.e., u and u+1) on the risk at the second day (Lag0 effect, L0)
L1 (1 st ,1d)
Effect of cumulative three-day exposure (3d) to T of three days (one-day exposure to T of the nonheatwave day before the first day of a heatwave (i.e., u-1) + cumulative two-day exposure to T of the first two days of a heatwave (i.e., u and u+1) on the risk at the the third day (i.e., u+1) (Lag0 effect, L0)
L1 (2d) L0 (2d)
Effect of cumulative two-day exposure (2d) to high T of two days (one-day exposure to T of the non-heatwave day before the first day of a heatwave (i.e., u-1) + one-day exposure to T of the first day of a heatwave (i.e., u)) on the risk at the second day (Lag0 effect, L0), or at the day after the second day (Lag1 effect, L1):
that day (i.e., u-1) the next day (i.e., u) the day after next (i.e., u+1)
that day (i.e., u) the next day (i.e., u+1)
the second day (i.e., u) the day after the second day (i.e., u+1) log( [ ! ]) = + * ! + !)" + !), 3
Instead, an unconstrained distributed lag model can be used as follows:
log( [ ! ]) = + % ! + " !)" + , !), * would differ from % + " + , if the contribution of each HT on ! through all the effects of HT is unequal (42,56). Otherwise, * would be equal to % + " + , . In time-series analysis and case-crossover analyses, the estimation of these coefficients is affected by mortality displacement as a set of unmeasured risk factors (57) and competing risk (45), which is beyond the scope of this paper. All these models may capture the effects of HT as the sum of the effect of T NH and the effect of HW (Figure 2 and Figure 3). Note that * , % , " , and , cannot distinguish lag effects and cumulative exposure effects if both types of the effect co-exist because they are represented by the regression coefficients simultaneously (45). With respect to % , " , and , , we list only the effects presented in Figure A2 as follows:
• % is related to the L0 effects of HW (i.e., L0(1 st , 1d), L0(2 nd , 1d) and L0(1 st , 2 nd , 2d)), the L0 effects of T NH (i.e, L0(1d), L0(2d), L0(3d)).
• " is related to the L1 effect of HW (i.e., L1(1 st , 1d)), a L0 effect of HW (i.e., L0(1 st , 2 nd , 2d)), the L1 effects of T NH (i.e., L1(1d), L1(2d)), and L0 effects of T NH (i.e., L0(2d), L0(3d)).
• , is related to the L2 effect of T NH (i.e., L2(1d)) and a L0 effect of T NH (L0(3d)).
While HWt is correlated with T NH variables, Model 1 does not include T NH variables such that the rate ratio of HWt is confounded by T NH and HWt-l. Traditional Approach #2 includes HT variables such that they may adjust for T NH and HWt-l, but they may adjust for some of the effects of HWt, meaning possible overadjustment for the rate ratio of HWt, which is reviewed in the main text and Appendix D.
D. Added effect of heatwaves from Traditional Approach #2
Here, we provide additional illustrations of how the estimand can differ when Traditional Approach #2 is used. Figure A3A illustrates the concept of the estimand of Traditional Approach #2. Basic T are expected to capture the increased risks by T deviated from OT. HW is expected to capture the increased risk that is not fully explained by basic T. The latter can be seen as the increased risk adjusted for single days of T.
D.1. Statistical concepts
Note that splines may be used instead of piecewise linear terms for parameterization of basic T. In this case, the increased risk not fully explained by basic T may differ because a spline function may explain some data points at EHT that is also categorized as a heatwave ( Figure A3B). The degree to which basics Ts explain increased risks depends on the specification of a spline function (e.g., spline types, degrees of freedom) and distribution of data points.
D.2. Epidemiological concepts of the added effect of heatwaves
The illustration above, which is statistical, does not fully describe the meaning of HW-Y association adjusted for basic T in epidemiological sense. To discover its meaning, we need to fill the gap between this statistical concept and the epidemiological concepts (i.e., lag effects of T and effects of cumulative exposure to T in terms of the manifestation of R(Y)) (Appendix B) (e.g., Figure A2). To fill this gap, Figure A4 shows how adjustment for basic T can adjust for components of increased risks in time-series, which is an extension of Figure A2. Figure A4A illustrates what basic Lag0 T would adjust for (dashed lines). The more lagged variables are adjusted for, the more components of increased risks would be adjusted for (dashed lines in Figures A4A-C). HW-Y association adjusted for basic T would be estimated to represent the remaining components of increased risks. For adjustment for basic Lag0 T or for basic Lag0 T and basic Lag1
T, the estimated association would be positive, but this may not necessarily represent the effects of heatwaves on R(Y) because HT of non-heatwave days also increases R(Y) on heatwave days (yellow plain boxes in Figures A4A and A4B). As an extreme case, HW-Y association adjusted for Lag0, Lag1, and Lag2 Ts may be null because Lag0, Lag1, and Lag2 Ts explain away all the increased risks due to heatwaves ( Figure A4C), whereas the association may be positive if the effect of heatwaves lasts for than three days. We stress that HW-Y association adjusted for basic T may not represent HW-Y relation because the association may also include the increased risk from T NH if there exist lag effects or cumulative exposure effect of T NH (See yellow boxes on heatwave days in Figure A4A and Figure A4B). and made it publicly available at the first author's GitHub (hyperlink to be added). Researchers can use this package to apply our novel modeling approaches to estimate HW-Y relation.
E.2. Adjustment for confounding by temperature to estimate HW-Y relation.
This sub-section elucidates Model 3 regarding adjustment for confounding by temperature. We illustrate this with an excerpt of the time-series dataset for South Korea, Seoul ( Figure A5). All variables except for FHWt-1, !)" '& * * * , * s, and * * s were introduced in the main text; we will introduce these below. For illustrational simplicity, we consider only Lag0 T (Tt)and Lag1 T (Tt-1).
Our R package, HEAT, allows researchers to consider ≤Lag7 in analysis.
Recall that we need to adjust for Ts (See Appendix C) and to avoid adjustment for some of the increased risks due to HW on heatwave days (i.e., overadjustment (58)) that arises when Traditional
D. Novel approach
, a cyclic graph, integrates Figures 1C-D, where the compromised infrastructure can impact P1, such as power outages resulting in the failure of air conditioning: HW→I→P1.
E
-Y relation would be the effect of interest if how much an individual's exposure to heatwaves increases the risk of Y via physiological pathways. HW-Y relation represents the health impacts of heatwaves via both physiological pathways and other pathways, which is policy-relevant.
counterfactual statement can reflect many forms. The defined HW-Y relation is based on E[R(Y)|T=OT, Z], meaning what R(Y) would have been if there had been no effects of T deviating from OT-the absence of the lag effects/cumulative exposure effects of T on R(Y) at
;
Tt is autocorrelated with Tt-l for l>0. For the perfect negative correlation between HWt and |T NH t|, this confounding corresponds to the aforementioned weighted average of R(Y) on non-heatwave days as a counterfactual risk because the effects of T NH t on R(Y) exist for only HWt=0, not HWt=1. Regarding correlations of HWt with T NH t-l and correlations of HWt-l with T NH t, if there exist lagged effects of cumulative exposure of T or lagged effects of HW, which is likely (9, 13), this association is further confounded by these effects: backdoor paths of Yt-T NH t-l-Tt-l-Tt-HWt and/or Yt-HWt-l-Tt-l-Tt-HWt (when lag effects of HW are not measured or considered in the association
which indicates low temperature (LT) and T H =T-OT if T>TO, which indicates HT, #& indicates the regression coefficient for LT, and ' indicates the regression coefficient for HT. JH is the maximum lag period for JH+1 of the effective exposure time-window for HT. JL is the maximum lag period for JL+1 of exposure time-window for LT. HW-Y association adjusted for basic T does not represent HW-Y relation because the effect of T on R(Y), including EHT that is a component of HW, is explained away by the adjustment. This adjusted association has been called an added effect of heatwaves (18), meaning how much consecutive days of EHT additionally increases risk after the risk from increased single days of T (Tt,…,Tt-L).
,
is a vector of the coefficients corresponding to each element of Vt. All the components of Vt differ depending on day t. If day t is the first day of a heatwave, ! = ( !)" '& , !), '& , … , !)+ '& ); if t is the second day of a heatwave, ! = (0, !), '& , … , !)+ '& ); …, if t is the K-1 th day of a heatwave, !)+ '& ); and if t is the K th day of a heatwave, ! = (0,0, … , 0, !)+ '&
conclusion, causal inference on health impacts of heatwaves should be based on clarifications of the effect of interest and estimation methods relevant to a defined effect. Diligent selection of modeling approaches and careful interpretation of heatwave-outcome associations are necessary to understand actual impacts of heatwaves under climate change and guide policymakers. Our findings indicate that traditional modeling approaches may underestimate the public health burden of heatwaves.
Figure 1 .
1Directed acyclic graphs (A-D) and a directed cyclic graph (E) for clarifying the effect of heat waves.
Figure 3 .
3An illustration of the difference between the effect of HW and the effect of T NH .
Figure 4 .
4Percentage increases in the risk of non-accidental mortality associated with heatwaves by sociodemographic factors and by different modeling approaches regarding how to address temperature. The vertical lines indicate 95% confidence intervals.
Figure A3 .
A3An illustration for the statistical concept of the estimand of Traditional Approach #2. Each circle indicates a hypothetical data point. G indicates an (weighted) average of temperature lagged variables, based on the link between weights of a moving average and coefficients of distributed lag (non-linear) models(56). An added effect of a heatwave An effect of single days of HTs An effect of single days of LTs High temperature (An added effect of a heatwave An effect of single days of HTs A.B.
Figure A4 .
A4An illustration of how adjustment for temperature can differently adjust for increased risks E. The novel modeling approaches E.1. R package, HEAT We created an R package, HEAT (Heatwave effect Estimation via Adjustment for Temperature)
). K can be the maximum duration of heatwaves in dataset minus 1 or JH. We relegate detailed illustrations of Model 3 and how to consider lag effects of HW to Appendix E, including our R package to help researchers apply our approaches.APPLICATION
Methods
We conducted time-series analysis for Seoul, South Korea, 2006-2013 to demonstrate how HW-
Y association can vary by modeling approaches to address temperature. This dataset, which has
been described previously (45), includes daily 24-hour average of temperature and PM10, daily 8-
hour moving average maximum of O3, holidays, calendar time, and daily non-accidental deaths
(International Classification of Disease 10th Revision, A00-R99). Using mortality data from
Statistics Korea, we calculated non-accidental deaths by age (≤64 years, ≥65 years), sex (male,
female), educational attainment (<high school graduation (<12 years), ≥high school graduation
(≥12 years)).
Clarifying the effect of interest and using appropriate epidemiological methods relevant to estimate the effect is essential for causal inference. Our conceptualization for the effect of heatwaves using causal diagrams considers multiple pathways through which heatwaves can impact health directly and indirectly. Our approach is aligned with IPCC's recent report on impacts of climate change, with cascading effects, and is relevant for policy implications. We showed how the HW-Y association depends on modeling approaches to address temperature. Since traditional approaches do not estimate our defined HW-Y relation, we proposed novel modeling approaches to estimate that relation. Our data analysis indicates that the effect of heatwaves on mortality in Seoul, SouthKorea is higher, based on our novel approach, than what would have been estimated using traditional approaches, suggesting that the traditional approaches underestimate the impacts of heatwaves on health. Our estimate may reflect the total effect of heatwaves on non-accidental mortality.There are direct and indirect effects of heatwaves. Epidemiological research on separating them will provide unique insights into heat responses and preparedness. This requires additional data that are rarely used in studies of heatwave epidemiology, as commonly used datasets, including our analyses presented for Seoul, addressed only total effect. For example, to identify indirect effects of HW via I-related pathways, data for compromised infrastructure, such as overburdened health systems and power outages, are necessary. Some studies used data on the prevalence of air conditioning that can indirectly imply P, meaning that the prevalence may be a surrogate of HW-E correlation and HW-Y relation may differ across strata of the prevalence. This type of variable may be useful, although this is an indirect measure (not measuring the actual use of personal protection). To separate Y1 and Y2, outcome classification should be performed considering causal pathways in future research.
Table 1 .
1Percentage increases (95% confidence intervals) in the risk of non-accidental mortality associated with heatwaves with and without one-day lag effect of heatwaves using our novel approach.Sex
Age
Educational attainment
Model
All
Male
Female
20-64yr
65+yr
Low
High
3
15.2
(1.3, 30.9)
8.6
(-8.9, 29.5)
23.6
(2.5, 49.0)
6.0
(-18.7, 38.2)
19.0
(1.9, 39.0)
20.5
(2.1, 42.4)
4.5
(-16.2, 30.3)
3 + Lag1
22.1
(-1.4, 51.1)
-2.2
(-26.7, 30.7)
60.0
(17.1, 118.5)
12.0
(-27.7, 73.4)
29.1
(-0.2, 67.1)
21.7
(-7.8, 60.5)
17.3
(-18.5, 68.9)
L0(1 st ,2 nd ,2d) L0 (1 st ,1d) L0 (2 nd ,1d)Increased riskThis pattern indicates adjustment for increased risks that T of a non-heatwave day contributes to This pattern indicates adjustment for increased risks that T of a heatwave day contributes toL0 (1 st ,2 nd ,2d) L0 (1 st ,1d) L0 (2 nd ,1d) Increased risk L0 (1 st ,2 nd ,2d) L0 (1 st ,1d) L0 (2 nd ,1d) Increased risk A. Adjustment for basic Lag0 T B. Adjustment for basic Lag0 T and Lag1 T C. Adjustment for basic Lag0 T, Lag1 T, and Lag2 T L0 (1 st ,2 nd ,2d) L0 (1 st ,1d) L0 (2 nd ,1d) L0 (1d) Increased riskL1 (1d)
L2 (1d)
L1 (1 st ,1d)
L0 (2d)
Heatwave days
Non-heatwave
day with high
temperature
u
u+1
u-1
L0 (1d)
L1 (2d)
L0 (3d)
L1 (1d)
L2 (1d)
L1 (1 st ,1d)
L0 (2d)
Heatwave days
Non-heatwave
day with high
temperature
u
u+1
u-1
L0 (1d)
L0 (3d)
L1 (1d)
L2 (1d)
L1 (1 st ,1d)
L0 (2d)
Heatwave days
Non-heatwave
day with high
temperature
u
u+1
u-1
L0 (1d)
L0 (3d)
L1 (2d)
L1 (2d)
Non-heatwave
day with high
temperature
L1 (1d)
L2 (1d)
L1 (1 st ,1d)
L0 (2d)
Heatwave days
u
u+1
u-1
L0 (3d)
L1 (2d)
AppendixApproach #2 is used (See Appendix D). For example, in terms of theFigure A1example, Model 3 estimates HW-Y relation as only the red boxes inFigure A4D.We introduce the variables, ! '& * and !)" '& * that were introduced in the main text. ! '& * and !)"'& * adjust for any increased risks due to HT of non-heatwave days on these non-heatwave days because their values are >0 when HW=0 (See red boxes inFigure A5B). They do not make the overadjustment because their values are zero when HW=1 (See the yellow-shaded rows in the green boxes inFigure A5B). Model 3 also adjusts for ! #& and !)" #& because there may be increased risks due to LT (See red boxes inFigure A5B). !)" '& * also adjusts for one-day lag effect of HW on the following non-heatwave day, which can be separately estimated instead of being adjusted for by !)" '& * (See the next subsection). By adjusting for them, the counterfactual risk of HW-Y relation is set to be the risk at OT. This is because any increased risks on non-heatwave days due to T deviating from OT are adjusted for.Lastly, we introduce the variable, ! , that was introduced in the main text. This variable adjusts for the increased risks on heatwave days due to HT of the preceding non-heatwave days (See the value in the blue box for ! inFigure A5B). This adjustment is necessary because lag effects or any partial cumulative exposure effects of HT from non-heatwave days are not the effect of heatwaves (e.g., orange boxes on days u and u+1 inFigure A2).E.3. Lag effects of HWThis sub-section illustrates how to separately estimate lag effects of HW, not adjusting for them by variables that adjust for confounding by temperature. We note that the other difference between !)" ' * and !)" ' * * is the values in the blue boxes inFigure A4C. !)" ' * * contains the information of ! . So, if !)" ' * * is used, ! is redundant. In this case, one may not use ! or may use !)" ' * * * that does not contain the information of ! . The difference between !)" ' * * and !)" ' * * * in terms of estimation is that the parameter is restricted to be identical for both !)" ' * * * and ! or not. Either of these two would be fine to use for the adjustment, unless lag effects of HT of non-heatwave days on R(Y) on heatwave days are likely to be different than effects of HT of non-heatwave days on R(Y) on non-heatwave days.We stress that how to generate lagged variables of ' * makes difference. One way is /,!)0if HWt=0 and /,!)0 ' * =0 if HWi,t=1 for j>0. This way creates /,!)0 ' * . Another is to generate lag variables using /,! ' * itself. This way creates /,!)0 ' * * . As shown earlier, the use of either of these two must be based on whether researchers want to estimate lag effects of HW (by using FHWt-j) or adjust for them.It is possible that exposure to HT of a heatwave may have its health effect with a long induction period such that it would increase the risk on the next heatwave. ! adjusts for this effect. We need not to adjust for this but to subsume such increased risks into 1 . Then, l-th component in ! must be set as 0 if t-l is a day of the previous heatwave. We denote the corrected ! as ! * Thus, to estimate lag effects of HW, Model 3 will becomeE.3. Splines in place of piecewise regression for adjusting for confounding by temperature.Model 3 is a piecewise regression regarding T. For adjustment purposes, non-linear temperatureresponse association can also be modeled by using a spline function such as natural cubic spline Lag variables of T * , !)+ * can be generated in the two ways as described above.To include 4 !,4 , !)5 * * or !)5 * * * should be used instead: !)5 * * is set as 0 during heatwave days.Also, l-th component in ! 23 must be set as 0 if t-l is a day of the previous heatwave. We refer to the corrected as ! 23 * . Then the model becomesFigure A5. An excerpt of daily time-series for temperature variables, a heatwave indicator, and an indicator of the subsequent day after heatwavesNote: The yellow-highlighted rows indicate heatwave days. For illustration, here, we defined heatwave as T exceeding the 97 th percentile (27.6 o C) of the year-round T distribution for at least two consecutive days. The data analysis in the main text used the 99 th percentile (28.7 o C), not the 97 th percentile.A. Data-structureYear Month Day Day of the Week(New variable introduced in this study)Variables to adjust for temperature as a confounder (piecewise regression) Note. !"# & * * * = !"# & * * − ! to remove redundancy(New variable introduced in this study)Variables to adjust for temperature as a confounder (splines) Note. !"# * * * = !"# * * − ! to remove redundancy (New variable introduced in this study) An indicator variable to estimate one-day lag effect of HWB. Highlights for adjustment for confounding by temperatureYear Month Day Day of the WeekC. Highlights for adjustment for or estimation of lag effects of heatwaves.Year
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| sample_607 | 0.7382 | arxiv | |
Laboratoire Gestion des Risques et Environnement
Université de Haute-Alsace
CNRS EP J0082
25 rue de Chemnitz68200MulhouseFrance
direct solar floorsolar energysolar heatingbioclimatic habitationsolar collectorcovering solar ratiosolar systems
Revue Générale deThermique -tome 34 -n° 408 -décembre 1995 -pp769-786 1 PLANCHER SOLAIRE DIRECT MIXTE À DOUBLE RÉSEAU EN HABITAT BIOCLIMATIQUE Conception et bilan thermique réel par T. DE LAROCHELAMBERT ( * ) Article reçu le 17.03.1995, accepté le 30.11.1995 Résumé. L'article présente une nouvelle technique de Plancher Solaire Direct épais à double réseau permettant l'utilisation conjointe du chauffage solaire et d'un chauffage d'appoint. Conçue pour garantir le stockage et la diffusion de la totalité de l'énergie solaire disponible en régulant physiquement l'appoint par l'apport solaire sans gestion informatique centralisée, cette technique simple est testée et suivie dans des conditions réelles d'utilisation en habitat bioclimatique pour étudier l'influence d'une enveloppe sans inertie à grand apport solaire passif sur la productivité de l'installation solaire. Des bilans journaliers, mensuels et annuels effectués sur trois ans, complétés par des mesures en temps réel sur site, ont permis de vérifier les propriétés fonctionnelles attendues de cette technique (stockage solaire, déphasage et lissage thermique, asservissement du circuit d'appoint, économie de l'énergie d'appoint). Une analyse du fonctionnement et du bilan global à travers les concepts de productivité solaire horaire, d'énergie primaire économisée et de taux de couverture solaire corrigé est proposée pour comparer les performances énergétiques de différents types d'installations solaires.Abstract. This study presents a new Direct Solar Floor Heating technique with double heating network whichallows simultaneous use of solar and supply energy. Its main purpose is to store and to diffuse the whole available solar energy while regulating supply energy by physical means without using computer controlled technology. This solar system has been tested in real user conditions inside a bioclimatic house to study the interaction of non-inertial and passive walls on the solar productivity. Daily, monthly and annual energy balances were drawn up over three years and completed by real-time measurements of several physical on-site parameters. As a result the expected properties of this technique were improved. The use of per-hour solar productivity, saved primary energy and corrected solar covering ratio is recommended to analyze the performances of this device and to allow more refined comparisons with other solar systems.Mots-clés: plancher solaire direct ; énergie solaire ; chauffage solaire ; habitat bioclimatique ; capteur solaire; taux de couverture solaire ; système solaire
INTRODUCTION
La technique du Plancher Solaire Direct (P.S.D.), conçue et mise au point par l'École Supérieure d'Ingénieurs de Marseille (E.S.I.M.) il y a une quinzaine d'années [1], a permis une diffusion plus importante du chauffage solaire dans l'habitat individuel grâce à la réduction des coûts d'investissement et la simplicité de mise en oeuvre qu'elle entraîne par rapport aux systèmes conventionnels de chauffage solaire [2].
Dans ces derniers en effet, l'énergie absorbée par les capteurs solaires est stockée dans de grands réservoirs d'eau par l'intermédiaire d'échangeurs, l'eau ainsi chauffée étant distribuée à basse température dans les émetteurs de chaleur (radiateurs et planchers chauffants). Les inconvénients de ces systèmes sont principalement: -une perte importante de rendement due à la présence d'échangeurs; -les déperditions thermiques importantes des ballons de stockage, généralement extérieurs au volume habitable; -un coût très élevé dû à l'échangeur (titane ou cuivre) et aux ballons -une multiplication des circulateurs, des régulations, des vannes motorisées et donc des risques de pannes, de fuites ou de dysfonctionnement.
Le P.S.D. dans son principe non seulement pallie ces inconvénients mais offre de surcroît des atouts décisifs que nous rappelons brièvement [3]: -stockage thermique de l'énergie solaire dans le plancher en béton, intérieur au volume habitable; -inertie thermique importante; -absence d'échangeur; -régulation simplifiée, généralement réduite à un thermostat différentiel contrôlant un circulateur unique; -avantages des planchers chauffants: confort basse température, uniformité de température de l'air ambiant, suppression possible des radiateurs muraux; -économie d'investissement importante.
Depuis la mise au point de la technique de chauffage par P.S.D., plusieurs centaines d'installations à P.S.D. ont été réalisées, presqu'exclusivement en France, essentiellement dans le secteur de l'habitat individuel et quelques unes dans le petit collectif ou le secteur hospitalier. Divers suivis et campagnes de mesures ont permis de vérifier le bon comportement des dalles solaires et leur apport positif dans les bilans énergétiques, annonçant des « taux de couverture solaire » généralement compris entre 30 à 50% [4][5] [6] [7].
Cependant, un des obstacles majeurs à une diffusion plus générale de la technique P.S.D. est la nécessité d'investir dans un chauffage d'appoint performant, devant couvrir la totalité de la puissance de chauffe du bâtiment pendant d'éventuelles longues périodes sans ensoleillement en hiver, sans pouvoir disposer du chauffage par le sol. La solution consistait jusqu'à présent à doubler le P.S.D. d'un système complet de chauffage classique par radiateurs ou par poêles à bois, fuel ou charbon, ou par cheminées à insert. Seule la perspective d'importantes économies de chauffage engendrées par le P.S.D. pouvait compenser le surinvestissement dans le chauffage d'appoint et la perte de confort du plancher chauffant en l'absence de soleil [8].
COUPLAGES SOLAIRE-APPOINT DANS LE PLANCHER CHAUFFANT
Divers travaux récents ont tenté d'apporter une solution économique au problème, en cherchant à utiliser les dalles de P.S.D. comme planchers chauffants utilisés simultanément par les circuits solaires et par les circuits de chauffage d'appoint.
P.S.D. mince à appoint intégré
Cette solution a été étudiée et mise en oeuvre par P.PAPILLON [9][10] et G.ACHARD et al. [11] et la société T2I, fabricant de panneaux et de systèmes solaires en Savoie (France). Elle consiste pour l'essentiel en un couplage hydraulique et thermique des circuits d'appoint et solaire dans un seul et même réseau de tubes chauffants noyés dans le plancher solaire en béton, dont l'épaisseur est diminuée de moitié par rapport aux P.S.D. classiques (15 cm au lieu de 30 cm). Les auteurs ont simulé numériquement le fonctionnement d'un tel système, basé sur une gestion centralisée de l'ensemble par microprocesseur, avec identification de paramètres in-situ et auto-adaptation, puis vérifié leur modèle sur un P.S.D. expérimental. Il apparaît que l'épaisseur de la dalle est un paramètre fondamental du comportement thermique du P.S.D. et de son interaction avec l'enveloppe de l'habitation.
Ainsi une dalle épaisse (supérieure à 20 cm) offre une inertie suffisamment importante pour rendre négligeable l'effet du type d'isolation (intérieure ou extérieure) des murs de l'habitation. Les auteurs soulignent que l'apport thermique du chauffage solaire "actif" par un P.S.D. est d'autant plus faible que les apports solaires "passifs" à travers les vitrages sud sont plus élevés; ils concluent à l'incompatibilité d'une enveloppe à isolation intérieure (faible inertie) et à grands apports solaires passifs vis à vis des performances d'un P.S.D., et préfèrent une solution dalle mince (15 cm) dans un habitat classique (forte inertie des murs pour compenser la perte d'inertie de la dalle; peu d'apports solaires passifs). La baisse de productivité solaire ainsi engendrée est alors compensée par une diminution du coût d'investissement et par une augmentation de la production solaire d'eau chaude sanitaire (E.C.S.).
Il est clair que cette solution présente un intérêt majeur en habitat collectif où l'emploi de dalles minces s'impose, et devrait permettre au chauffage solaire de pénétrer plus efficacement ce secteur où d'énormes économies d'énergie pourraient ainsi être engendrées.
En revanche l'opposition entre performances du P.S.D. et performances thermiques de l'habitat ne nous apparaît pas justifiée si l'on considère l'ensemble {chauffage solaire + chauffage d'appoint + enveloppe bioclimatique + E.C.S.} conçu autour d'un plancher chauffant à double nappe de chauffage tel que nous le présentons ci-dessous.
P.S.D. mixte à double réseau
Installation solaire à P.S.D. mixte
Le Plancher Solaire Direct Mixte est constitué d'une dalle de béton épaisse (26 cm) coulée sur toute la surface de rez-de-chaussée sur hourdis en béton armé Fricker, fortement isolée sur sa face inférieure côté cave par 23 cm de polystyrène et fibralith, comportant un double réseau de tubes de chauffage (figure 2):
• le réseau solaire directement relié aux capteurs solaires: de forte densité (pas de 20 cm entre tubes), il est noyé à environ 3 cm du fond de la dalle de manière à charger thermiquement tout le volume de la dalle et à imposer un gradient de température vers le haut. Cette position basse assure au P.S.D. ses fonctions de stockage et de déphasage indispensables à une bonne productivité solaire et au confort thermique. Un thermostat électronique différentiel commande le circulateur du réseau en tout-ou-rien;
• le réseau d'appoint relié à la chaudière (le gaz naturel a été choisi pour son faible coût, sa souplesse de régulation et son entretien réduit) par le biais d'une vanne motorisée trois voies assurant le bouclage du réseau et sa liaison à une bouteille de mélange chauffée à 65°C par la chaudière (qui alimente par ailleurs les petits radiateurs d'étage). Ce réseau est noyé en surface de dalle, à environ 7 cm sous le carrelage de manière à répondre rapidement aux variations des besoins de chauffe par une régulation classique de plancher chauffant par vanne mélangeuse à sondes extérieure, d'ambiance et de départ de circuit, tout en assurant une diffusion de chaleur suffisante pour homogénéiser la température superficielle de la dalle. Ce réseau est 1,5 fois moins dense que le réseau solaire (30cm entre tubes). Le principe physique autour duquel est conçu le P.S.D. mixte repose sur l'interaction thermique unidirectionnelle des deux réseaux: l'apport solaire en fond de dalle crée une densité de flux de chaleur ascendante dont la période caractéristique est d'une journée, qui assure l'asservissement thermique de l'appoint dans le réseau de surface par le biais de deux phénomènes, à savoir le temps de transit caractéristique des variations thermiques entre le réseau solaire et le réseau d'appoint ∆t SA = 3,9 h (calculé selon un modèle monodimensionnel de diffusion en régime établi du flux solaire injecté par journées ensoleillées successives dans une dalle isolée sur une face, avec coefficients d'échange constants) suffisamment faible pour permettre une influence rapide après une période sans soleil, et la température moyenne du P.S.D. qui dépend des apports solaires antérieurs. Le rôle du réseau d'appoint se limite alors approximativement aux 10 cm superficiels de la dalle car les variations de sa température, de périodes plus courtes que la journée, sont plus fortement amorties et se propagent plus rapidement.
C'est à ce niveau qu'intervient la conception bioclimatique de l'habitation: la régulation de l'appoint dans le réseau de surface est classiquement déterminée selon la loi de chauffe (cf. § 3.3) par la température de son départ (élevée si la dalle a été chauffée antérieurement par le circuit solaire), la température extérieure et surtout la température intérieure de l'habitation. La très faible inertie thermique des parois associée aux grandes ouvertures Sud et Est permet une élévation suffisamment rapide de la température ambiante pour que la régulation du circuit d'appoint réagisse très rapidement aux apports solaires passifs grâce à sa fonction de correction d'ambiance qui abaisse la température de départ du réseau d'appoint de la quantité C(T CI -T I ), réalisant ainsi une véritable accélération de l'effacement de l'appoint devant le solaire. Cette action est renforcée par l'absorption de chaleur par la surface du P.S.D. directement éclairée par le soleil à travers les vitrages.
L'effet prévu est de refermer rapidement la vanne de bouclage du circuit d'appoint pour éviter le maintien du chauffage de la partie supérieure de la dalle par ce circuit alors que le réseau solaire doit charger celle-ci. Comme l'enveloppe de l'habitation est très isolée, peu inerte et fortement passive, il est vérifié qu'il ne résulte pas de baisse de température ambiante de cet effacement de l'appoint en surface de dalle, les dix centimètres superficiels restituant la chaleur stockée suffisamment lentement à l'air ambiant.
Le choix de l'épaisseur totale de la dalle est fait en fonction du temps de stockage prévu (deux à trois jours en intersaison), du niveau moyen de température de dalle souhaité pour permettre l'autonomie journalière en hiver par période d'ensoleillement continu (température ambiante 19°C compte tenu des apports passifs), du déphasage voulu entre l'éclairement maximal et la restitution de chaleur en surface. Une trop grande épaisseur (supérieure à 30 cm) conduit à une température moyenne trop basse, à un ∆t SA et à un temps de transit ∆t SO du flux de chaleur solaire jusqu'à la surface trop grands (supérieurs à 5 h et 7,5 h respectivement). Inversement, une trop faible épaisseur (inférieure à 20 cm) entraîne un risque de réchauffement du circuit solaire par le circuit d'appoint et de surchauffe de la dalle en intersaison, un inconfort dû aux amplitudes thermiques trop fortes en surface de dalle, et conduit à une diminution du stockage solaire, ayant pour conséquence une demande d'appoint plus grande pour assurer les besoins. L'épaisseur de dalle retenue de 26 cm (avec carrelage), la distance de 16 cm environ entre les deux réseaux, et de 7 cm entre le réseau d'appoint et la surface de dalle constituent une bonne solution de compromis compatible avec le caractère bioclimatique de l'enveloppe (∆t SO = 6h, ∆t SA = 3,9 h, temps de déstockage de 3 jours en octobre), une dalle de compression de 17 cm étant coulée sur la structure en hourdis isolants avec armature. Ces chiffres peuvent évidemment varier de ± 1 cm lors de la mise en oeuvre du P.S.D.. La distance de 7 cm entre circuit d'appoint et surface peut être légèrement diminuée jusqu'à 5 cm, mais avec des risques d'inconfort (le réseau étant lâche, la température au droit des tubes est alors plus élevée ainsi que ses variations spatiales en surface) et de retard de l'action du circuit solaire sur le circuit gaz de près d'une demi-heure.
L'objectif premier du P.S.D. mixte est donc de rendre compatible le chauffage solaire et la structure bioclimatique d'un bâtiment. Cette technique offre en outre l'avantage de la simplicité dans la mise en oeuvre et dans la gestion simultanée de l'appoint et du chauffage solaire. En effet, toutes les régulations électroniques sont classiques et fiables cf. § 3.3). D'autre part, l'indépendance hydraulique totale des deux réseaux évite tout risque de fuite thermique de vannes de mélange, préjudiciable au rendement solaire, et permet une maintenance séparée des deux chauffages.
En outre, la chaudière peut également assurer le chauffage complémentaire de l'étage par petits radiateurs à robinets thermostatiques qui répondent très rapidement aux apports solaires passifs.
La fonction production d'E.C.S. est assurée simultanément par un circuit solaire, parallèlement au circuit P.S.D., avec circulateur et thermostat différentiel indépendant, et par la même chaudière d'appoint à travers un double échangeur à l'intérieur d'un ballon fortement calorifugé de 500 dm 3 . Le circuit solaire chauffe tout le stock par l'échangeur du bas à 100% en été et le préchauffe tout le reste du temps (au moins en intersaison). L'appoint ne chauffe la moitié supérieure du stock que si sa température descend au-dessous de 45°C, ce qui provoque le basculement d'une vanne de zone permettant à la chaudière de chauffer en priorité l'eau chaude sanitaire; cette opération est rendue possible par l'inertie suffisante de la dalle et l'excellente isolation des murs sans que l'on ressente l'absence de chauffage durant cette période, même sans apport solaire.
La configuration de l'ensemble de l'installation schématisée en figure 3 appelle quelques remarques supplémentaires:
• le circuit solaire du P.S.D. mixte est automatiquement coupé dès que la température de fond de dalle près du tube retour T SRD dépasse une valeur de consigne T CD fixée par aquastat réglable (la plage de 21°C≤ T CD ≤ 23°C convient). Ceci évite toute surchauffe de dalle solaire en intersaison et permet de transférer alors intégralement l'énergie solaire captée au ballon d'E.C.S., ce qui augmente le rendement global de l'installation [9]; un second aquastat en série avec le précédent n'autorise le redémarrage du circuit solaire P.S.D. que si la température du fluide solaire en sortie des capteurs est inférieure à une température maximale de protection T CP de l'ordre de 45 °C pour éviter de l'injecter trop chaud dans le circuit refroidi de la dalle (conformité à la réglementation , D.T.U. 65. 8 [14]); • lorsque l'énergie solaire absorbée par l'installation risque de dépasser les besoins d'E.C.S. en été, une soupape de sécurité permet un soutirage automatique d'E.C.S., récupéré ou évacué à l'égout selon les besoins, dès que la température de l'eau en haut de ballon d'E.C.S. dépasse une température de consigne T CB = 95°C. De la sorte, le fonctionnement et la sécurité de l'installation sont garantis même en l'absence des propriétaires;
• la mise en parallèle des circuits solaires P.S.D. et E.C.S. avec circulateurs, thermostats différentiels et vannes d'isolement indépendants offre une grande simplicité de réglage et de maintenance;
• l'investissement global dans les circuits d'appoint est réduit (chaudière de petite puissance à ventouse sans préparation d'appoint séparé).
Dimensionnement de l'installation et bilan énergétique prévisionnel
L'utilisation de la méthode de calcul de l'E.S.I.M. et des données de la station de Mulhouse de la Météorologie Nationale a conduit à une première approche classique du dimensionnement par bilans mensuels moyens, largement utilisée dans les bureaux d'étude, mais dont la simplicité et les hypothèses de base amènent à sous-estimer les pertes
Métrologie
Le suivi énergétique de l'habitation a été réalisé à partir des données suivantes: • comptage quotidien de l'énergie solaire distribuée dans l'installation, de la durée de fonctionnement de l'installation solaire, de la consommation de gaz par la chaudière seule, de l'énergie d'appoint gaz distribuée en sortie de chaudière et dans le réseau de surface P.S.D., de l'eau chaude sanitaire consommée;
• acquisition permanente par centrale informatique autonome sur batterie de l'éclairement solaire global hémisphérique par pyranomètre dans le plan des capteurs; de la température extérieure à 1,5m sous abri; de la température intérieure au centre de l'habitation; des températures départ-retour des réseaux solaire et appoint dans le P.S.D.; des températures départ-retour du circuit solaire E.C.S.; et du débit volumique total du fluide caloporteur des capteurs solaires; • relevés de la Météorologie Nationale des stations les plus proches (Mulhouse et Colmar). Le concept d'énergie économisée repose sur la substitution de l'énergie solaire à l'énergie d'appoint: c'est l'énergie primaire qu'aurait dû consommer la chaudière en l'absence de système solaire pour fournir la même énergie. Le rendement de production de la chaudière est pris en compte dans ses deux fonctions chauffage et E.C.S.; pour les chaudières de type mural à ventouse, il est généralement pris égal à 75%, mais les mesures effectuées sur site donnent des valeurs inférieures: 68,2% en chauffage seul; 51,3% en production d'E.C.S. seule; 62,5% en mode chauffage + E.C.S. (ces chiffres sont mesurés à ± 7% près). Les rendements de distribution et de stockage sont sensiblement identiques pour les circuits solaires et d'appoint, tant en chauffage qu'en E.C.S.. On peut donc estimer ici l'énergie économisée par la relation EE= (ES D /0,682) + (ES ECS /0,513).
BILANS ÉNERGÉTIQUES RÉELS DE L'INSTALLATION SOLAIRE
Le concept de taux de couverture solaire corrigé est de ce fait beaucoup plus proche de la réalité énergétique puisqu'il englobe à la fois tous ces rendements et tous les types de consommation habituels dans une maison, y compris ceux liés à la vaisselle, au sèchage et au lavage de linge, au renouvellement d'air. Il tient compte d'autre part des exigences modernes de confort, en particulier la quasi uniformité de température entre étage et R.d.C.. Il est facilement mesurable sur site, contrairement au taux de couverture théorique classique, rapport entre l'énergie solaire utile et les besoins totaux hors rendements, dont il est assez proche. On remarque une assez bonne corrélation entre la durée de l'insolation mesurée à la station la plus proche et la durée de fonctionnement de l'installation pour les mois de chauffe de novembre à mars, l'écart se creusant pour les autres mois ou la production d'E.C.S. devient importante. L'économie d'énergie globale par rapport à une habitation classique est en réalité plus élevée si l'on tient compte des apports solaires passifs gratuits qui représentent ici 69% de l'énergie solaire directe produite par les capteurs en hiver et intersaison: les apports passifs, évalués par la méthode C.S.T.B. [15], sont de l'ordre de 3500 kWh.an -1 pour une année moyenne; ils ont représenté entre 14% et 17% des besoins de l'habitation de 1992 à 1994, l'énergie économisée par l'installation solaire active couvrant alors 36% à 42% de ces besoins, ce qui donne pour l'ensemble des apports solaires {actifs + passifs} un taux de couverture solaire total de 48% à 59%. De fait, une habitation de mêmes surface et volume habitables, d'isolation réglementaire standard (G = 0,9 W.m -3 .K -1 ) consommerait en conditions moyennes environ 24000 kWh par an, hors rendements et E.C.S. (méthode C.S.T.B.), soit plus de 2,5 fois l'énergie consommée ici (plus de 4,4 fois en tenant compte des rendements de chaudière).
Bilans énergétiques annuels et mensuels
ANALYSE DU FONCTIONNEMENT DU P.S.D. MIXTE
Le bilan énergétique réel très satisfaisant du système solaire à P.S.D. mixte établi précédemment peut être expliqué et analysé par une étude plus fine des relevés et des enregistrements automatiques quotidiens effectués sur l'installation, sur des séquences caractéristiques. Les prévisions de comportement de l'installation reposent sur l'effet d'asservissement de l'appoint par les deux informations physiques que sont la température globale de la dalle −qui contient elle-même l'information thermique sur la séquence solaire couvrant les trois journées précédentes− et la température intérieure de l'habitation, représentative de l'ensoleillement du moment grâce à la conception bioclimatique de l'habitation (grands apports solaires passifs, faible inertie des parois internes) . C'est l'ensemble de ces paramètres de couplage qui assure la bonne performance du système; on peut ainsi représenter le fonctionnement du système par le schéma de principe de la figure 9.
Chauffage solaire + chauffage d'appoint en période hivernale très froide
La séquence du 18 au 22 février 1992 fait suite à plusieurs jours couverts très froids (figures 10,11,12,13). Au début de la première belle journée de la séquence, le 19 février, pour maintenir une température ambiante minimale de 19°C après une température extérieure nocturne entre -5°C et -12 °C, le circuit d'appoint en surface de dalle se referme totalement 50 minutes après le démarrage du chauffage solaire, et ne se rouvre que légèrement le lendemain, pour se refermer entièrement moins de 15 minutes après l'enclenchement du circuit solaire, grâce à l'effet de stockage solaire dans la dalle. Le lendemain, il ne se rouvre que très peu pendant environ 2,6 heures, et pas du tout le surlendemain, l'apport solaire étant suffisant malgré une température extérieure toujours négative. Le temps de transit ∆t SA enregistré est de l'ordre de 4,1 h ± 0,2 h (l'inertie thermique des tubes fortement isolés en chaufferie explique l'apparente durée de fonctionnement du P.S.D. plus longue que la durée d'ensoleillement; ce phénomène n'existe pas pour le réseau d'appoint dont le circulateur est constamment en fonction).
L'étude des rendements solaires journaliers et de la productivité solaire horaire (tableau III) montre que l'influence du chauffage d'appoint est négligeable sur ces paramètres et non corrélable, contrairement à la température extérieure qui joue un rôle dans le temps et l'énergie nécessaires à la mise en température des capteurs. Ainsi les deux journées les plus froides du 19 et du 20 février, autour de -5°C en moyenne jour-nuit montrent un même rendement de 45% et une productivité solaire horaire identique à 306 W.m -2 , alors que l'appoint a fourni près de trois fois moins d'énergie à la surface de la dalle. Les deux jours suivants voient le rendement s'élever à 49,4% du fait de l'élévation de température, alors que l'appoint gaz a été à peu près identique du 20 au 21. Enfin, la journée du 24 montre un rendement et une PSH nettement supérieurs de 54,2% et 315 W.m -2 respectivement pour une quantité d'énergie d'appoint fournie à la dalle similaire à celle du 22 car la température extérieure moyenne est passée à 1,9°C. Le cas des journées peu ensoleillées du 18 et du 23 février montre que la productivité solaire horaire est restée élevée (et même meilleure le 18 alors que l'appoint était important) et le rendement identique mais plus faible, ce dernier étant sensible à la valeur de l'irradiation solaire. Les énergies enregistrées sont données à 1 kWh près.
Chauffage solaire sans aucun appoint en période hivernale très froide
Une séquence quasi identique s'est déroulée du 23 au 27 février 1993 avec des températures extérieures similaires entre 0°C et -12°C (figures 14, 15, 16) mais le chauffage d'appoint a été coupé depuis le 22 février et remis en fonction le 2 mars. On constate que l'énergie solaire suffit à maintenir la température intérieure entre 17 à 18°C la nuit et 20 à 21°C le jour, et il est intéressant de comparer les paramètres de l'installation solaire durant cette période à celles de la séquence précédente avec appoint. Les résultats sont regroupés dans le tableau IV.
On constate que la productivité solaire horaire varie dans une fourchette identique (compte tenu des incertitudes de mesure d'énergie à 1 kWh près) à celle de la séquence de février 1992 ; elle est plus sensible aux passages nuageux et au rapport éclairement diffus/éclairement direct, alors que le rendement solaire est plus sensible à la température extérieure.
Chauffage solaire seul en intersaison, avec effet de stockage
L'inertie du P.S.D. est particulièrement importante en intersaison: combinée aux apports passifs de l'habitation, elle permet de se passer totalement de chauffage d'appoint lors de périodes comportant deux à trois jours sans soleil. On peut à cet égard examiner les enregistrements effectués du 5 au 10 novembre 1992, séquence caractérisée par une alternance de belles journées et de jours sans soleil par une température de 7,5°C en moyenne (figures 17, 18, 19). Là encore, l'énergie solaire suffit à maintenir la température ambiante autour de 20°C. Les performances de l'installation sont résumées dans le tableau V. On remarquera la valeur plus grande du rendement et de la productivité solaire horaire en intersaison du fait de la basse température du PSD et de la température extérieure encore clémente.
Chauffage et E.C.S. solaires seuls sans appoint en intersaison
Le fonctionnement en intersaison où l'autonomie totale ou quasi totale en chauffage et E.C.S. est atteinte peut être étudié lors de la séquence du 7 au 12 avril 1992 (figures 20, 21, 22, 23) lorsque la température de consigne de surchauffe de dalle T CD est dépassée, le circuit solaire du P.S.D. s'arrêtant alors pour laisser le circuit solaire E.C.S. absorber seul l'énergie solaire. Les résultats sont rassemblés dans le tableau VI.
On observe la baisse de rendement entraînée par l'arrêt du chauffage solaire, qui passe d'environ 56% lorsque les deux circuits solaires fonctionnent en parallèle, à 24% lorsque seul le circuit solaire E.C.S. est en fonction. La productivité solaire horaire est maximale en cette période (chauffage solaire + stock E.C.S. froid), et peut être élevée même avec un mauvais rendement global par journée faiblement ensoleillée comme celle du 13 avril.
Les mesures manuelles de température de surface de dalle ont montré qu'en aucun cas, elle n'a dépassé 25°C, que ce soit dans cette période charnière de forts apports passifs ou dans la période hivernale. Les pointes de 24 à 25°C relevées les 11 et 12 avril sont dues aux apports passifs incontrôlés en l'absence des propriétaires. We obtain a very good energy balance which can be described by the following results: • the annual corrected solar covering ratio τ AC , which represents the ratio of the energy saved EE A to the total energy need (EE A +EA A ), ranges from 40 to 55%; it depends only on meteorological conditions (fig. 8);
• total energetic autonomy is obtained during 179 to 213 days a year (49% to 58.3% of a year); heating period is reduced to a very short time (92 to 118 days a year − 25.2 % to 32.3% of a year), compared to at least eight months, as usual in this region ( fig. 6 and 7); • the annual solar productivity PS A ranges between 267 and 293 kWh.m -2 ( fig. 4); the solar efficiency η of the installation is independent of the fact that complementary energy is supplied or not at heating floor surface, but depends on external temperature and solar energy production mode (heating-floor / E.C.S.) (tables III-VI); • the per-hour solar productivity PSH is a very representative factor of the solar system performance; it remains almost constant over characteristic periods in the year ranging between 180 and 300 W.m -2 ( fig. 5) and really independent of complementary energy supply;
• the examination of automatic records leads to a good understanding of the real functioning of the Mixed Direct Solar Floor Heating when coupled with bioclimatic architecture ( fig. 10-23).
Conclusion
This new solar heating technique seems to be very efficient and can be applied at least to all types of well-oriented and well-insulated habitations. It allows the benefit of floor-heating comfort. Its simplicity and low cost implementation can lead to a rapid expansion in the field of domestic habitation and thus, to considerable energy saving.
Fig. 1 .
1-Vue de l'habitation bioclimatique à PSD mixte près de Mulhouse (France) Fig.1. -View of bioclimatic house with mixed direct solar floor near Mulhouse (France) 3. CONCEPTION DU SYSTÈME SOLAIRE À P.S.D. MIXTE 3.1. Enveloppe thermique de l'habitation La conception bioclimatique de l'habitation repose sur les caractéristiques suivantes: • orientation sur les points cardinaux avec vitrages principaux au sud, dont une grande verrière intégrée, occultable extérieurement; • toiture entièrement au nord jusqu'au sol, en tuiles épaisses de terre cuite, avec 30 cm de laine de verre, sans grenier; • une seule ouverture vitrée à l'ouest (pluies et vents dominants); • protection des entrées à l'est et vitrages plus nombreux; • cave (garage, cellier et chaufferie-buanderie-sèchoir) sous toute la maison; • conception interne: communication ouverte entre rez-de-chaussée (R.d.C.) et étage par escalier ouvert sous la verrière et mezzanines, dans le but d'uniformiser la température, de transmettre le rayonnement du P.S.D. à l'étage et l'éclairement de la verrière au R.d.C.; • choix des matériaux: l'ossature et les murs extérieurs sont en bois, avec double isolation laine de roche, laine de verre; le plancher d'étage est en bois avec isolation phonique. Le choix du bois permet une forte isolation thermique et une très faible inertie thermique. Cette faible inertie est également recherchée pour les parois intérieures en placostil doublé avec laine de verre. Les huisseries extérieures sont en PVC, et tous les vitrages sont doubles à faible pouvoir émissif. L'ensemble de ces choix conduit aux caractéristiques générales suivantes: • surface habitable S H = 132 m² (S HP = 187 m²) • volume habitable V H = 330 m 3 • coefficients thermiques calculés G = 0,642 W.m -3 .K -1 , B = 0,375 W.m -3 .K -1 • ventilation mécanique contrôlée simple flux Q v = 100 m 3 .h -1 .
Fig. 2 .
2-Schéma simplifié du PSD mixte (coupe transversale)
Fig. 3 .
3-Schéma hydraulique de l'installation complète de chauffage et d'ECS Fig.3. -Hydraulic flowsheet of mixed heating and SHW plant
inférieures de dalle et les couplages avec l'E.C.S. et l'enveloppe du bâtiment. Elle fournit cependant une valeur indicative assez représentative de la productivité annuelle globale et du taux de couverture solaires dont nous ferons plus loin une étude critique. La disposition du P.S.D. mixte sur plancher Fricker n'étant pas prise en compte dans la méthode E.S.I.M., divers dimensionnements ont été effectués pour déterminer une fourchette de taux de couverture mensuels et annuels amenant à une autonomie quasi totale d'avril à octobre inclus, en faisant varier les épaisseurs de dalle et d'isolant, la surface des capteurs et leur inclinaison i. La configuration retenue est présentée ci-dessous: • installation solaire: -capteurs solaires: S C = 17 m 2 ; i = 58°; B opt = 0,68; K C = 4,2 W.m -2 .K -1 ; R = 0,191; type sélectif intégré en façade; -circuit P.S.D.: S D = 89 m 2 ; réseau de tube polyéthylène réticulé de pas 20 cm sur toute la surface (pas de zonage Nord/Sud); thermostat électronique différentiel tout-ou-rien avec sondes à résistance métallique; -circuit E.C.S. V ECS = 0,5 m 3 ; thermostat électronique différentiel, identique au précédent; • chauffage d'appoint: -chaudière murale à ventouse au gaz naturel de 10 kW (modèle 18 kW installé) sans préparateur d'E.C.S.; -réseau de surface P.S.D. en polyéthylène réticulé de pas 30 cm sur toute la surface; puissance 7000 W; régulation de plancher chauffant pente 0,4; calage jour 19°C (nuit 18°C); correction d'ambiance C = 9; -radiateurs d'étage à robinets thermostatiques: puissance totale 3000 W; radiateur buanderie: 2000 W; • particularités: -aucun autre appoint n'est utilisé (poêle, cheminée, radiateur électrique, etc.); -la fonction sèchage de linge est assurée en hiver par le radiateur de buanderie sous étendoir; -la fonction lavage de vaisselle est assurée uniquement par l'eau chaude du ballon d'E.C.S. (pas d'électricité) -le lave-linge utilise l'E.C.S. du ballon par mélangeur (économie quasi totale d'électricité). • site météorologique: les données moyennes de 1951-1970 de la station de Mulhouse sont résumées dans le tableau I. Elles seront comparées aux données de 1992 à 1994 et aux mesures effectuées sur la maison. • bilan énergétique global: -chauffage : 9980 kWh dont 4160 à 4300 kWh solaires -E.C.S. : 2070 kWh dont 710 à 720 kWh solaires -total : 12050 kWh dont 4880 à 5020 kWh solaires. -taux de couverture solaire annuel : 40,5 à 41,7% ; productivité solaire annuelle : 287 à 295 kWh.m -2 .an -1 . TABLEAU I -TABLE I Données météorologiques (1951-1970) -Meteorological data (1951-1970) Mois JAN FEV MAR AVR MAI JUN JUL AOU SEP OCT NOV DEC ANNÉE DJU(K.jour)
Les données recueillies permettent d'établir des bilans énergétiques quotidiens, mensuels et annuels précis du système solaire que constitue l'habitation bioclimatique, son installation de chauffage et d'E.C.S. mixte solaire-appoint gaz en conditions réelles d'utilisation.Nous étudions dans un premier temps les principaux paramètres permettant un diagnostic clair du comportement global du système, pour lequel nous proposons des critères d'analyse comparative caractérisant le fonctionnement de l'installation et son potentiel énergétique, et nous exposons les bilans réels utiles que l'on peut en déduire, pour les comparer aux bilans prévisionnels classiques présentés précédemment (cf. schéma méthodologique).Dans un second temps, une analyse plus fine du fonctionnement du P.S.D. mixte et de son couplage avec l'enveloppe et la production d'E.C.S. dans diverses séquences climatiques journalières caractéristiques permet d'éclairer ces bilans globaux (voir paragraphe 5).
4. 1 .
1Paramètres d'analyse énergétique de l'installation solaire L'analyse du fonctionnement réel de l'installation solaire nous a amenés à utiliser plusieurs paramètres d'analyse énergétique et d'en proposer de nouveaux, afin de cerner au mieux les propriétés fonctionnelles des systèmes solaires basse température et permettre leur comparaison dans des contextes de couplages variés avec l'appoint et l'enveloppe. À partir des grandeurs globales mensuelles et annuelles mesurées par relevé quotidien (ES M , ES A , EA D , EA M , EA A , D M ) et de EA 0 , nous déterminons les paramètres d'analyse énergétique globaux suivants : • énergies économisées mensuelles et annuelles EE M et EE A : c'est l'énergie primaire d'appoint que la chaudière aurait dû consommer en plus en l'absence de l'installation solaire ; elle est obtenue par addition des énergies solaires distribuées au P.S.D. et au ballon d'E.C.S. divisées par les rendements de distribution et de production du système d'appoint dans les fonctions chauffage et production d'E.C.S. ; • taux de couverture solaire mensuels et annuels bruts courants τ MB et τ AB : ils sont définis par les relations suivantes τ MB = 100 ES M /(ES M + EA M ) et τ AB = 100 ES A /(ES A +EA A ) et ne représentent que les rapports de l'énergie solaire effectivement captée et distribuée à l'énergie totale primaire utilisée dans l'habitation ; • taux de couverture solaire mensuels et annuels corrigés τ MC et τ AC : ils donnent la part réellement couverte par l'énergie solaire active compte tenu de tous les rendements de production et donc plus proches de la réalité et de l'économie solaire ; nous les définirons par τ MC = 100 EE M /(EE M +EA M ) et τ AC = 100 EE A /(EE A +EA A ) ; • productivités solaires journalières, mensuelles et annuelles PS J , PS M et PS A : classiquement utilisées en ingénierie solaire, elles mesurent l'énergie produite par mètre carré de capteur solaire installé pour une journée, un mois et une année; ces grandeurs dépendent du type de production (chauffage / E.C.S.), de la conception de l'installation (échangeurs, P.S.D., ratios R et R B , i) et surtout des données locales du site (latitude, altitude, climat) ; • productivité solaire horaire PSH : nous utiliserons ce concept pour mieux définir la productivité réelle de l'installation quand elle fonctionne. Nous la définirons par PSH J = ES J /(S C .D J ) lorsque nous la calculerons sur une journée et par PSH M = ES M /(S C .D M ) sur un mois de fonctionnement. Nous verrons par la suite que c'est un paramètre représentatif de l'efficacité de fonctionnement du système, permettant la mesure de l'influence de l'appoint et de l'impact du choix de l'inclinaison i à la conception. Il représente la puissance effective moyenne de l'installation en production sur une journée, un mois (voire un an) ; • rendements solaires journaliers et mensuels η J et η M : également classiques, ils mesurent le rapport de l'énergie réellement produite par l'installation solaire à l'énergie solaire globale incidente sur les capteurs. Ce sont des paramètres représentatifs du type de fonctionnement de l'installation (chauffage et/ou E.C.S.) car très sensibles aux niveaux de températures de stock et de température extérieure.
La figure 4
4représente les productivités solaires mensuelles PS M produites en 1992, 1993 et 1994. La productivité solaire est plus élevée en mars -avril (entre 25 et 40 kWh.m -2 .mois -1 ) comme on le prévoit car les besoins de chauffage restent importants alors que le rayonnement solaire est quasi perpendiculaire au plan des capteurs; elle reste comprise entre 15 et 25 kWh.m -2 .mois -1 de mai à octobre et descend à des valeurs comprises entre 5 et 17 kWh.m -2 .mois -1 de novembre à janvier. La production solaire est donc assez importante en hiver pour couvrir une part significative des besoins.On peut comparer utilement les productivités solaires annuelles qui en résultent aux heures d'insolation mesurées à la station météorologique de Mulhouse et aux heures de fonctionnement effectif de l'installation solaire (tableau II).
Les trois années ayant été nettement moins ensoleillées qu'en moyenne, il convient de corriger les productivités solaires mensuelles et annuelles en tenant compte de la durée d'insolation, mais également des températures extérieures afin de connaître leurs valeurs moyennes: la productivité solaire annuelle pour une année moyenne est comprise entre 267 et 293 kWh.m -2 .an -1 . Cette fourchette correspond aux résultats de calcul les plus significatifs obtenus par différentes régressions linéaires multiples effectuées sur les durées d'insolation mensuelles de Mulhouse et/ou Colmar, les températures extérieures moyennes mensuelles de Mulhouse et éventuellement les températures moyennes de stock mensuelles observées sur les trois années; les régressions effectuées par saisons-types de fonctionnement (P.S.D. continu ; P.S.D intermittent ; E.C.S. seule) donnent également d'assez bonnes corrélations, et les régressions utilisant simultanément les deux stations sont généralement les meilleures. Ces valeurs sont très proches des valeurs obtenues dans le dimensionnement par méthode E.S.I.M.; cependant l'étude mensuelle montre que la méthode E.S.I.M. sous-estime la productivité solaire d'hiver (novembre à février inclus) du fait de la réduction du chauffage d'appoint permis par les apports passifs, ainsi que celle d'été (juin à août) par sous-estimation des consommations d'E.C.S.; elle surestime celle d'intersaisons car elle ne prend pas en compte de la production d'ECS dans cette période où les besoins en chauffage pour une maison bioclimatique sont plus réduits. Les couplages avec l'enveloppe du bâtiment et la régulation du chauffage d'appoint par les apports solaires passifs et actifs ne sont donc pas correctement évalués par la méthode E.S.I.M. qui est une méthode globale mensuelle.
Fig. 4 .
4-Productivité solaire de l'installation Fig.4. -Solar productivity of
La figure 5
5permet de mieux comprendre l'importance du choix de l'inclinaison i des capteurs dans la gestion de la ressource solaire. La productivité solaire horaire moyenne mensuelle PSH M présente une homogénéité remarquable autour de 230 W.m -2 , avec une plage une peu plus élevée autour de 280 W.m -2 en intersaison et un peu plus faible vers 200W.m -2 en période estivale. Cette régularité est liée au choix d'optimisation du fonctionnement par l'inclinaison à 58° pour une latitude de 47,6° permettant une très bonne productivité en hiver, une autonomie maximale de chauffage en intersaison et une autonomie totale de production d'E.C.S. en été sans beaucoup d'excédent. Les figures 6 et 7 confirment ce choix de manière évidente, l'autonomie énergétique totale (chauffage + E.C.S.) étant assurée de mai à septembre compris. Les relevés quotidiens révèlent une autonomie totale pendant 179 à 213 jours par an (soit 49% à 58,3% de l'année) et une saison de chauffe effective réduite entre 92 et 118 jours par an (soit 25,2% à 32,3% de l'année), dans une région où la saison de chauffe débute en septembre et termine en mai, voire en juin. La figure 8 montre que le taux de couverture solaire annuel corrigé τ AC fluctue selon les conditions tre 38,2% et 50,3% en 1993 et 1994; ces taux sont excellents, malgré des températures extérieures sur site systématiquement plus faibles qu'à la station de Mulhouse en hiver et intersaison, un ensoleillement inférieur à la moyenne et une consommation d'énergie prenant en compte tous les besoins domestiques hormis la cuisine. Ils seraient de l'ordre de 45,6% à 47,9% pour une année standard. Seul un recul sur une dizaine d'année permettra de donner une estimation statistique fiable du taux de couverture solaire corrigé annuel.
Fig. 5 .
5-Productivité solaire horaire de l'installation Fig. 5. -Per-hour solar productivity of solar plant
Fig. 6 .
6-Énergie d'appoint totale mensuelle Fig. 6. -Monthly total supply MAR AVR MAI JUN JUL AOU SEP OCT NOV DEC EAM (kWh/mois)
Fig. 7 .
7-Taux de couverture solaire mensuelle corrigé de l'installation Fig. 7. -Monthly corrected solar covering ration of solar plant
Fig. 8 .
8-Taux de couverture solaire annuel corrigé Fig. 8. -Annual corrected solar covering ration of
Fig. 9 .
9-Couplage solaire-appoint-enveloppe dans le PSD mixteFig. 9. -Coupling between solar energy-supply energy-habitation in mixed direct solar
Fig. 10 .
10-Éclairement solaire global E dans le plan des capteurs (du 18 au 22 février 1992) Fig. 10. -Global solar flow E received on solar collectors plan (1992, 18 to 22 February) Fig. 12. -Températures du circuit d'appoint en surface de dalle (du 18 au 22 février 1992) Fig. 12. -Supply energy heating tube network temperatures (1992, 18 to 22 February) Fig. 11. -Températures du circuit solaire dans la dalle (du 18 au 22 février 1992) Fig. 11. -Solar heating tube network temperatures in floor (1992, 18 to 22 February) Fig. 13. -Températures intérieure et extérieure (du 18 au 22 février 1992) Fig. 13. -Inner and outer temperatures (1992, 18 to 22 February)
Fig. 14 .
14Ainsi les journées du 26 février 1993 et du 21 février 1992, toutes deux autour de -3°C, donnent un rendement d'installation solaire d'environ 48,5% ; en revanche, la productivité solaire horaire est de 363 W.m -2 pour la première journée et de 309 W.m -2 pour la seconde du fait d'un éclairement solaire ES 0 nettement plus élevé dans le premier cas. De même les journées du 24 février 1993 et du 19 février 1992, de même température moyenne, donnent le même rendement de 45,5% et une productivité PSH moins grande dans le premier cas du fait d'un moindre éclairement solaire. Si l'on compare enfin deux journées quasi identiques comme celles du 23 février 1993 et du 20 février 1992 (T E ≈ -4,2°C ; ES 0 ≈ 62 kWh), on observe une productivité solaire horaire un peu moins bonne pour la première mais un rendement un peu -Éclairement solaire global E dans le plan des capteurs (du 23 au 27 février 1993) Fig. 14. -Global solar flow E received on solar collectors plan (1993, 23 to 27 February) Fig. 15. -Température du circuit solaire dans la dalle (du 23 au 27 février 1993) Fig. 15. -Solar heating tube network temperature in floor (1993, 23 to 27 February)
FigFig
. 17. -Éclairement solaire global E dans le plan des capteurs (du 5 au 10 novembre 1992) Fig. 17. -Global solar flow E received on solar collectors plan (1992, 5 to 10 November) . 18. -Température du circuit solaire dans la dalle (du 5 au 10 novembre 1992) Fig. 18. -Solar heating tube network temperature in floor (1992, 5 to 10 November) TABLEAU V -
Fig. 19 .
19-Températures intérieure et extérieure (du 5 au 10 novembre 1992) Fig. 19. -Inner and outer temperatures (1992, 5 to 10 November) TABLEAU VI -
Fig. 20 .Fig. 21 .
2021-Éclairement solaire global E dans le plan des capteurs (du 6 au 13 avril 1992) Fig. 20. -Global solar flow E received on solar collectors plan (1992, 6 to 13 April) -Température du circuit solaire dans la dalle (du 6 au 13 avril 1992) Fig. 21. -Solar heating tube network temperature in floor (1992, 6 to 13 April) Fig. 22. -Température du circuit solaire d'ECS (du 6 au 13 avril 1992) Fig. 22. -SHW solar tube temperature (1992, 6 to 13 April) Fig. 23. -Températures intérieure et extérieure (du 6 au 13 avril 1992) Fig. 23. -Inner and outer temperatures (1992, 6 to 13 April) consumption were measured every day and several physical factors (such as solar energy flow, external and internal temperatures, solar floor and E.C.S. heating temperatures and pipe flow, complementary heating temperatures) were computer recorded, so that we are able to draw up a precise energy balance of this solar system over the last three years. A short description of the solar and complementary energy systems can be given as follows (fig. 3): • heating floor surface and thickness: 89 m² and 26 cm respectively; habitable surface and volume of the house: 132 m² and 330 m 3 ; sanitary hot water storage volume: 0.5 m 3 • surface of solar collectors: 17 m²; optical coefficient: 0.68; thermal conductance: 4.2 W.m -2 .K -1 ; incline: 58°; heating-floor solar tubes spacing: 20 cm • complementary supply energy: natural gas; heating power of boiler: 18 kW; tubes spacing of the floor heating: 30 cm
Nous avons étudié dès 1990 la faisabilité technico-économique d'un système de chauffage global, basé sur le concept de couplage thermique asservi du réseau de chauffage d'appoint par le réseau de chauffage solaire dans un seul et même plancher chauffant, avec découplage hydraulique total. Cette étude, basée sur la méthode E.S.I.M. [1][2] et complétée par une modélisation monodimensionnelle, a été menée dans le cadre global d'un habitat moderne performant de type bioclimatique de manière à intégrer les deux paramètres thermiques fondamentaux caractérisant la réponse de l'enveloppe, à savoir les apports solaires passifs gratuits (que l'on cherche à maximiser) et l'inertie des parois extérieures (que l'on rend minimale). Elle s'est inscrite dans une action incitative régionale basée sur un programme de dix-huit installations à P.S.D. réunissant l'Agence de l'Environnement et de la Maîtrise de l'Énergie (A.D.E.M.E.), la Région Alsace et l'association Alter Alsace Énergies [12]. Elle s'est fixée comme objectifs l'évaluation expérimentale précise sur une longue période (plusieurs années) de la réponse thermique d'une dalle solaire à double nappe en habitat bioclimatique à toutes les séquences climatiques possibles, et la détermination comparée des performances énergétiques mensuelles et annuelles de ce système obtenue à partir des mesures expérimentales d'une part, et par la méthode E.S.I.M. d'autre part. Les objectifs ultérieurs sont la mise au point d'une simulation numérique globale du système et l'affinement des critères de dimensionnement et des bilans prévisionnels mensuels et annuels. installation à P.S.D. mixte et de l'habitat, et de vérifier le comportement thermique du P.S.D. mixte dans les situations les plus diverses en fonctionnement réel, la maison étant habitée depuis août 1991[13].Ce travail mené en collaboration avec l'Atelier
Architecture et Soleil de Strasbourg (67) et la société
Éco-Chauffage de Ribeauvillé (68) a conduit à la
construction en 1991 d'une maison prototype
bioclimatique à ossature bois dans la plaine d'Alsace, à
la latitude de MULHOUSE, sur un site parfaitement
dégagé près du Rhin, exposé à tous les vents et aux
brouillards fréquents dans cette région (figure 1). On
peut le considérer comme un cas représentatif de
conditions
climatiques
défavorables.
Une
instrumentation résidente complétée par des relevés
continus par acquisition informatique nous permet de
dresser un bilan énergétique expérimental précis de
l'
TABLE II Productivités
IIsolaires mensuelles de l'installation
Monthly solar productivity of the plant
1992
1993
1994
Mois
HS M
D M
T E
PS M
HS M
D M
T E
PS M
HS M
D M
T E
PS M
JAN
78,5
61,5
0,7
14,7
73,9
65,6
4,6
16,8
68,8
63,5
3,7
15,8
FEV
111,8
86,7
3,5
25,7
91,8
65,4
1,3
18,9
49,0
71,5
3,6
17,1
MAR
103,3 104,2
7,2
30,6 177,6 134,0 6,1
40,8 104,0 102,6 10,3 24,7
AVR
157,8 115,4
9,9
34,4 177,0 107,0 12,3 26,0 114,6 110,2
9,1
23,4
MAI
214,6 123,9 16,1 24,7 179,3 76,8 15,7 16,9 152,5
70,7
14,6 15,3
JUN
150,9
83,9
18,0 16,9 200,3 72,6 18,0 15,6 212,6 114,3 18,6 20,6
JUL
214,3 124,2 20,8 20,8 209,5 70,7 18,8 15,4 265,0 124,3 22,9 22,3
AOU
222,0 135,1 21,9 23,3 255,6 115,5 19,1 25,6 237,0 108,0 20,8 21,4
SEP
168,0
96,4
16,1 15,2 120,2 82,3 14,6 19,2
95,6
79,0
15,3 13,2
OCT
47,6
38,8
8,6
11,7
42,9
40,0
9,2
11,5 130,5 105,0 10,3 24,5
NOV
51,7
51,6
7,6
16,3
31,1
28,8
1,9
6,7
67,0
65,0
9,1
14,0
DEC
58,6
50,1
2,6
11,9
27,4
21,3
5,5
5,4
46,5
48,6
4,8
11,3
TABLE III
IIISéquence chauffage solaire + appoint en période hivernale très froideSolar + complementary heating during very cold winter periodFEVRIER 1992
18
19
20
21
22
23
24
MOIS
ES 0 (kWh)
33,7
77,5
64,8
59,7
61,9
37,4
70,6
1028,5
ES (kWh)
13,0
34,8
29,4
29,4
30,7
12,3
38,2
437,5
D (h)
2,44
6,66
5,66
5,60
6,05
2,48
7,14
86,7
T E (°C)
-3,1
-5,8
-4,2
-2,9
-0,53
4,1
1,9
2,5
T I (°C)
19,3
20,2
20,2
20,1
20,8
19,9
20,2
20,0
EA D (kWh)
44
40
15
12
8
0
7
651
η (%)
38,5
44,9
45,3
49,2
49,6
32,8
54,2
42,5
PSH (W.m -2 )
313
307
305
309
299
291
315
296,8
ECLAIREMENT SOLAIRE GLOBAL
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
18
19
20
21
22
23
FEVRIER 1992
kW/m²
CIRCUIT SOLAIRE PSD
15
20
25
30
35
40
18
19
20
21
22
23
FEVRIER 1992°C
RETOUR
DEPART
CIRCUIT APPOINT PSD
15
20
25
30
35
40
18
19
20
21
22
23
FEVRIER 1992°C
RETOUR
DEPART
TEMPERATURES INTERIEURE ET EXTERIEURE
-15
-10
-5
0
5
10
15
20
25
18
19
20
21
22
23
FEVRIER 1992°C
TEMPERATURE INTERIEURE
TEMPERATURE EXTERIEURE
Fig. 16. -Inner and outer temperatures(1993, 23 to 27 February) supérieur. L'explication est à rechercher dans la répartition journalière du flux solaire lors de ces deux journées, l'irradiation solaire instantanée ayant atteint 760W.m -2 le 23 février 1993 et seulement 610 W.m -2 le 20 février 1992 (voirfigures 10 et 14). On peut conclure de l'examen de ces deux séquences que la productivité solaire du P.S.D. mixte est apparemment insensible au chauffage d'appoint en surface de dalle; il en est de même du rendement solaire, à température extérieure égale.TABLEAU IV -TABLE IVSéquence chauffage solaire sans appoint en période hivernale très froide Solar heating without complementary heating during very cold winter periodTEMPERATURE INTERIEURE
TEMPERATURE EXTERIEURE
Fig. 16. -Températures intérieure et extérieure
(du 23 au 27 février 1993)
Février 1993
23
24
25
26
27
Mois
ES 0 (kWh)
60,0
63,3
80,1
77,3
57,1
846.8
ES (kWh)
30,9
29,1
40,9
37,3
29,1
321,2
D (h)
6,20
6,40
7,20
6,05
6,29
65,4
T E (°C)
-4,2
-5,8
-5,7
-3,2
1,2
0,37
T I (°C)
19,0
18,1
19,4
19,9
20,1
19,0
EA D (kWh)
0
0
0
0
0
_
η (%)
51,6
46,0
51,1
48,2
51,0
37,9
PSH (W.m -2 )
293
268
335
363
272
288,9
TABLE V
VSéquence chauffage solaire seul en intersaison, avec effet de stockage Solar heating alone during interseason, with storage effectNovembre 1992
5
6
7
8
9
10
Mois
ES 0 (kWh)
67,6
10,9
70,92
6,4
50,63
6,7
580,0
ES (kWh)
38,2
0
37,31
0
24,57
0
276,6
D (h)
6,75
0,05
6,24
0,00
5,06
0,03
51,59
T E (°C)
7,0
6,7
8,1
7,8
8,1
7,6
7,3
T I (°C)
20,7
20,6
21,0
21,0
20,9
20,9
19,6
EA D (kWh)
0
0
0
0
0
0
_
η (%)
56,6
0,0
52,6
0,0
48,5
0,0
47,7
PSH (W.m -2 )
333
0
352
0
286
0
315,3
TABLE VI
VISéquence chauffage et E.C.S. solaires autonomes en intersaison Autonomic solar heating and sanitary warm water production during interseasonAvril 1992
6
7
8
9
10
11
12
13
MOIS
ES 0 (kWh)
66,97
81,43
77,13
76,90
74,12
81,72
82,27
81,77 1565,1
ES (kWh)
37,54
47,09
43,68
39,58
28,66
30,03
19,79
9,55
584,9
D (h)
7,43
8,42
7,76
7,51
4,41
5,04
5,25
1,80
115,4
T E (°C)
4,0
5,4
8,0
8,9
9,3
8,7
11,0
10,8
9,8
T I (°C)
19,5
21,3
22,9
23,3
23,4
23,5
23,6
22,8
21,6
EA (kWh)
57,8
8,3
6,2
0
0
0
0
0
398,7
η (%)
56,1
57,8
56,6
51,5
38,7
36,7
24,1
11,67
37,4
PSH (W.m -2 )
297
329
331
310
382
350
222
312
297,7
ECLAIREMENT SOLAIRE GLOBAL
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
6
7
8
9
10
11
12
13
14
AVRIL 1992
kW/m²
ABRIDGED ENGLISH VERSIONDOUBLE DIRECT SOLAR FLOOR HEATING IN BIOCLIMATIC HABITATION Design and real thermal balanceThe Direct Solar Floor Heating Technique (Plancher Solaire Direct in french) was invented several years ago by the E.S.I.M. (the Engineering High School of Marseille)[1]and is largely employed in heating systems using solar energy in France, essentially in domestic habitations[4][5][6][7][8]. This technique is simpler and more economic than the previous ones[2]since there are no heat exchangers between solar collectors and heat storage equipment, and because the heating floor acts as a heat emitter as well as a storage device by means of its concrete thickness (approximately 30 cm). However an important disadvantage still remains since another heating installation providing complementary energy and full heating power during sunless periods, is necessary.Several authors[9][10][11]made an attempt in reducing the investment cost by reducing the thickness of the floor by a factor of two and by using the same heating tubes for both solar and complementary energies. They used a computer controlled technology in order to regulate the complete system and tested it in an experimental plant. By numerical simulation they decuced that it is a convenient way to produce solar energy even if this reduction leads to a light decrease of solar productivity. They pointed out that this Integrated Supply-Direct Solar Floor Heating System is efficient only if the thermal inertia of the house walls is sufficiently high and if the passive solar heating capability of the house is small enough.We studied another way of improving the Solar Direct Floor Heating technique consisting in a thick concrete floor that is very well insulated on the underside, with two heating tubes networks embedded in it (fig. 2): the solar one at the bottom of the floor in order to warm its whole mass; the second one − which is heated by complementary energy (gas)− a few centimeters under the upper surface of the floor. This disposition allows a thermal regulation of the latter by the former. We showed that this new technique is very efficient when coupled with a bioclimatic architecture − that is to say in a well oriented and insulated building with low thermal inertia walls and great passive solar energy flow through the windows (fig. 9).We have implemented this Mixed Direct Solar Floor Heating Technique (P.S.D Mixte in french) in a bioclimatic house that was built in Alsace (France) which is a cold and not very sunny region (fig. 1, table I).The gas consumption, solar production, working time of solar pumps, sanitary hot water (E.C.S. in french)
Une température moyenne inférieure à 23°C est maintenue sans problèmes. Le choix de l'épaisseur de la dalle a également des conséquences pour la tenue thermique de l'habitation en été; pendant cette saison, les enregistrements effectués (non donnés ici) montrent que l'habitation reste fraîche (entre 20 et 25°C) en plein été grâce à l'inertie thermique de la dalle sur cave et à la très bonne isolation de l'enveloppe, à condition que les surfaces vitrées soient correctement occultées au sud. Les relevés des années suivantes montrent une meilleure gestion de ces apports gratuits en avril-mai, et les risques de surchauffe en intersaison sont effectivement nuls, l'aquastat de coupure jouant parfaitement son rôle. le rafraîchissement naturel de nuit par les ouvrants suffisant à abaisser la température et la dalle restant suffisamment froide même en journéeLes relevés des années suivantes montrent une meilleure gestion de ces apports gratuits en avril-mai, et les risques de surchauffe en intersaison sont effectivement nuls, l'aquastat de coupure jouant parfaitement son rôle. Une température moyenne inférieure à 23°C est maintenue sans problèmes. Le choix de l'épaisseur de la dalle a également des conséquences pour la tenue thermique de l'habitation en été; pendant cette saison, les enregistrements effectués (non donnés ici) montrent que l'habitation reste fraîche (entre 20 et 25°C) en plein été grâce à l'inertie thermique de la dalle sur cave et à la très bonne isolation de l'enveloppe, à condition que les surfaces vitrées soient correctement occultées au sud, le rafraîchissement naturel de nuit par les ouvrants suffisant à abaisser la température et la dalle restant suffisamment froide même en journée.
La réalisation et le suivi d'une installation de chauffage solaire par Plancher Solaire Direct Mixte épais dans une habitation bioclimatique en région à climat continental de faible ensoleillement a permis de démontrer la bonne complémentarité du chauffage solaire actif. et du chauffage solaire passifLa réalisation et le suivi d'une installation de chauffage solaire par Plancher Solaire Direct Mixte épais dans une habitation bioclimatique en région à climat continental de faible ensoleillement a permis de démontrer la bonne complémentarité du chauffage solaire actif et du chauffage solaire passif.
Les mécanismes physiques de cette régulation expérimentalement observée font intervenir de nombreux paramètres physiques, climatiques et architecturaux, caractérisés par des couplages élevés dont il reste à simuler l'étendue. Cependant, l'étude énergétique du système a montré le très bon comportement de l'installation solaire dont le rendement et la productivité ne semblent pas affectés par l'utilisation conjointe de la dalle et du stock d'eau chaude sanitaire par les circuits d'appoint, au vu des mesures et des essais effectuées sur les trois années de 1992 à 1994. Les logiciels couramment utilisés en ingénierie solaire, s'ils permettent une évaluation globale des performances des P.S.D. en moyenne annuelle, ne rendent cependant pas compte du comportement dynamique d'une telle installation et des couplages solaire-appoint en interaction avec l'enveloppe. Des modèles bidimensionnels de dalle à double nappe, associés à des modèles numériques zonaux plus fins de type modulaire pour l'enveloppe doivent encore être développés pour simuler les interactions entre circuits solaires et circuits d'appoint, tant en chauffage qu'en production d'E.C.S.; vérifier que l'apport d'énergie d'appoint en surface de dalle solaire n'obère pas les performances solaires; affiner les choix de dimensionnement présentés plus haut; et approcher les productivités journalières, mensuelles et annuelles avec une précision satisfaisante. L'emploi des critères de productivité solaire horaire, d'énergie économisée et de taux de couverture solaire corrigé offre l'avantage de pouvoir comparer les installations solaires en fonctionnement réel, leurs performances intrinsèques et les performances globales des systèmes couplés {installation solaire / appoint / enveloppe du bâtiment}, ainsi que leur évolution sur plusieurs années. La technique de chauffage solaire basse température par P.S.D. mixte avec appoint indépendant en surface, de grandes fiabilité et simplicité, doit donc permettre une meilleure diffusion de l'utilisation de l'énergie solaire à tous les types d'habitation individuelle, y compris les bâtiments à hautes performances énergétiques caractérisées par une très grande isolation thermique. P S D Le, mixte assure la double fonction de stockage solaire par inertie thermique, complémentaire de la faible inertie de l'enveloppe de l'habitat, et de régulation de l'énergie d'appoint en surface de P.S.D. par asservissement thermique grâce à la fois aux apports passifs, à la faible inertie thermique de l'enveloppe de l'habitation et à l'épaisseur de la dalle. une faible inertie intérieure des parois et de grandes ouvertures vitrées du côté ensoleillé. Elle doit permettre également une meilleure prise en compte du chauffage solaire actif dans les règles d'urbanisme, les réglementations à venir et l'architecture de demain. A cet égard, elle complète utilement la technique du P.S.D. mince à appoint intégré particulièrement adaptée aux bâtiments collectifs et aux habitations individuelles classiquesLe P.S.D. mixte assure la double fonction de stockage solaire par inertie thermique, complémentaire de la faible inertie de l'enveloppe de l'habitat, et de régulation de l'énergie d'appoint en surface de P.S.D. par asservissement thermique grâce à la fois aux apports passifs, à la faible inertie thermique de l'enveloppe de l'habitation et à l'épaisseur de la dalle. Les mécanismes physiques de cette régulation expérimentalement observée font intervenir de nombreux paramètres physiques, climatiques et architecturaux, caractérisés par des couplages élevés dont il reste à simuler l'étendue. Cependant, l'étude énergétique du système a montré le très bon comportement de l'installation solaire dont le rendement et la productivité ne semblent pas affectés par l'utilisation conjointe de la dalle et du stock d'eau chaude sanitaire par les circuits d'appoint, au vu des mesures et des essais effectuées sur les trois années de 1992 à 1994. Les logiciels couramment utilisés en ingénierie solaire, s'ils permettent une évaluation globale des performances des P.S.D. en moyenne annuelle, ne rendent cependant pas compte du comportement dynamique d'une telle installation et des couplages solaire-appoint en interaction avec l'enveloppe. Des modèles bidimensionnels de dalle à double nappe, associés à des modèles numériques zonaux plus fins de type modulaire pour l'enveloppe doivent encore être développés pour simuler les interactions entre circuits solaires et circuits d'appoint, tant en chauffage qu'en production d'E.C.S.; vérifier que l'apport d'énergie d'appoint en surface de dalle solaire n'obère pas les performances solaires; affiner les choix de dimensionnement présentés plus haut; et approcher les productivités journalières, mensuelles et annuelles avec une précision satisfaisante. L'emploi des critères de productivité solaire horaire, d'énergie économisée et de taux de couverture solaire corrigé offre l'avantage de pouvoir comparer les installations solaires en fonctionnement réel, leurs performances intrinsèques et les performances globales des systèmes couplés {installation solaire / appoint / enveloppe du bâtiment}, ainsi que leur évolution sur plusieurs années. La technique de chauffage solaire basse température par P.S.D. mixte avec appoint indépendant en surface, de grandes fiabilité et simplicité, doit donc permettre une meilleure diffusion de l'utilisation de l'énergie solaire à tous les types d'habitation individuelle, y compris les bâtiments à hautes performances énergétiques caractérisées par une très grande isolation thermique, une faible inertie intérieure des parois et de grandes ouvertures vitrées du côté ensoleillé. Elle doit permettre également une meilleure prise en compte du chauffage solaire actif dans les règles d'urbanisme, les réglementations à venir et l'architecture de demain. A cet égard, elle complète utilement la technique du P.S.D. mince à appoint intégré particulièrement adaptée aux bâtiments collectifs et aux habitations individuelles classiques.
MANDINEAU (D.) et CHATEAUMINOIS (M.). -Calcul des planchers solaires directs. Edisud. Aix-en-Provence140 p.ROUX (D.), MANDINEAU (D.) et CHATEAUMINOIS (M.). -Calcul des planchers solaires directs. Edisud, Aix-en-Provence, 140 p., 1983.
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| sample_658 | 0.9407 | arxiv | |
On the use of Deep Generative Models for "Perfect" Prognosis Climate Downscaling
27 Apr 2023
Jose González-Abad
Santander Meteorology Group and Advanced Computing and e-Science Group Institute of Physics of Cantabria (CSIC-UC
SantanderSpain
Jorge Baño-Medina
Santander Meterology Group Institute of Physics of Cantabria (CSIC-UC) Santander
Spain
Ignacio Heredia Cachá
Advanced Computing and e-Science Group Institute of Physics of Cantabria (CSIC-UC) Santander
Spain
On the use of Deep Generative Models for "Perfect" Prognosis Climate Downscaling
27 Apr 2023
Deep Learning has recently emerged as a "perfect" prognosis downscaling technique to compute high-resolution fields from large-scale coarse atmospheric data. Despite their promising results to reproduce the observed local variability, they are based on the estimation of independent distributions at each location, which leads to deficient spatial structures, especially when downscaling precipitation. This study proposes the use of generative models to improve the spatial consistency of the high-resolution fields, very demanded by some sectoral applications (e.g., hydrology) to tackle climate change.
1 Motivations for generative models in "perfect" prognosis downscaling Global Climate Models (GCMs) are the main tools used nowadays to study the evolution of climate at different time-scales. They numerically solve a set of equations describing the dynamics of the climate system over a three-dimensional grid (latitude-longitude-height). In climate change modeling, these models are utilized to produce possible future pathways of the climate system based on different natural and anthropogenic forcings. However, due to computational limitations these models present a coarse spatial resolution -between 1 • and 3 • ,-which leads to a misrepresentation of important phenomena occurring at finer scales. The generation of high-resolution climate projections is crucial for important socio-economic activities (e.g., the energy industry), and they are routinely used to elaborate mitigation and adaptation politics to climate change at a regional scale.
Statistical Downscaling (SD) is used to bridge the scale-gap between the coarse model outputs and the local-scale by learning empirical relationships between a set of large-scale variables (predictors) and the regional variable of interest (predictands) based on large simulated/observational historical data records [1]. In this study we focus on a specific type of SD, named the "Perfect" Prognosis (PP) approach. PP downscaling leans on observational datasets to learn empirical relationships linking the predictors and the predictands. For the former, reanalysis data -a global dataset which combines observations with short-range forecasts through data assimilation,-is typically used, whilst for the latter either high-resolution grids or station-scale records can be employed. Once the relationship is established in these "perfect" conditions, we feed the model/algorithm with the equivalent GCM predictor variables to obtain high-resolution climate projections. A wide variety of Tackling Climate Change with Machine Learning: workshop at NeurIPS 2021. statistical techniques have been deployed to establish these links, such as (generalized) linear models [2], support vector machines [3], random forests [4], classical neural networks [5], and more recently deep learning (DL). In particular, DL has recently emerged as a promising PP technique, showing capabilities to reproduce the observed local climate [6,7,8], whilst showing plausible climate change projections of precipitation and temperature fields over Europe [9]. Nonetheless, currently the regression-based nature of most of the existing PP methods, leads to an underestimation of the extremes when the predictors lack from sufficient informative power -i.e., given a particular predictor configuration there are many possible predictand situations,-since they output the conditional mean [10]. To account for the uncertainty describing the possible extremes is crucial for some activities, and the community has driven its attention to probabilistic regression-based modeling. The probabilistic models used mostly estimate the parameters of selected probability distributions conditioned to the large-scale atmospheric situation. The choice of the distribution depends on the variable of interest to be modeled -for instance, the temperature follows a Gaussian distribution, whilst wind or precipitation fields present a heavy-tailed structure which better fits with Gamma, Poisson or log-normal density functions,-and the regression-based models are trained to optimize the negative log-likelihood of the selected distribution at each site [5,7,11,12,13]. To model the spatial dependencies among sites, ideally we would estimate multivariate distributions representing the whole predictand domain, instead of predicting independent probability functions at each predictand site. Nonetheless, this was in practice computationally intractable, and very few procedures aimed to downscale over low-dimensional predictand spaces have been successfully deployed [14,15,16].
Recently, deep generative models have been developed that seek to approximate high-dimensional distributions through DL topologies. Based on previous merits in other disciplines, such as imagesuper-resolution (see e.g., [17,18]), some studies have searched for an analogy between this task and downscaling, deploying Generative Adversarial Networks (GAN, [19,20]) to obtain stochastic samples of high-resolution precipitation and temperature fields conditioned to their counterpart low-resolution ones. Despite these first studies are far from the PP approach, -since they lean on surface variables in their predictor set, which are not well represented by GCMs (see [1,21] for guidelines/details on PP),-they show the potential of generative models to attain impressive levels of spatial structure in their stochastic downscaled predictions. Following this idea, we state that these topologies may provide a tractable alternative to model multivariate conditional distributions over high-dimensional domains in a PP setting, providing stochastic and spatially consistent downscaled fields very demanded by some sectoral applications for climate impact studies. To prove the potential of this type of DL topologies for PP-based downscaling, we show in the next section a use-case where Conditional Variational Auto-Encoders (CVAE) are deployed to produce stochastic high-resolution precipitation fields over Europe.
A downscaling case study over Europe with CVAE
We develop a simple use-case 1 which seeks to illustrate the promising capabilities of CVAE topologies to generate spatially consistent stochastic downscaled fields, especially as compared to the recent state-of-the-art PP DL-based topologies, which are based on the estimation of conditional Bernoulli-Gamma distributions at each predictand site (we refer the reader to [7] for more details). To this aim, we deploy the CVAE in the same conditions than [7], which builds on the validation framework proposed in the COST action VALUE [22]. VALUE proposes the use of ERA-Interim [23] reanalysis variables as predictors -trimmed to an horizontal resolution of 2 o ,-and the regular gridded 0.5 o E-OBS dataset [24] as predictand. For the predictor set we use five thermodynamical variables (geopotential height, zonal and meridional wind, temperature, and specific humidity) at four different vertical levels (1000, 850, 700 and 500 hPa), whilst as predictand we use the daily accumulated precipitation over Europe. The models are trained on the period 1979-2002 and tested on 2003-2008. Figure 1 shows the scheme of the CVAE proposed. This models builds on three different neural networks -an embedding network, an encoder and a decoder,-to produce stochastic samples of precipitation by sampling from a latent distribution which represents the complex interactions between predictors and predictands. During training, the embedding network transforms the high-dimensional predictors X to a low-dimensional array z x . This array is then stacked with the high-resolution predictand fields Y to feed the encoder network. The encoder outputs the parameters of a Gaussian distribution (i.e., the mean µ and the standard deviation σ), which encodes the spatial dependencies between both predictor and predictand fields. During both training and inference phases, stochastic realizations z sampled from this latent distribution are stacked with the low-dimensional predictor's embedding z x . This is used to feed the decoder network, which outputs the precipitation values Y at each E-OBS predictand site considered. Therefore, different samples Y conditioned on the same large-scale atmospheric situation X can be generated by sampling different vectors z from the latent distribution (see the three maps obtained for a particular day). We refer the reader to [25] for more details on CVAE.
For the sake of comparison, we select CNN1, which was one of the models that ranked first in [7], as an example of univariate model and compare its stochastic downscaled fields with those of CVAE. It can be seen how CNN1 fields present a spotty structure, characteristic of the sampling performed over the independent Bernoulli-Gamma distributions at each E-OBS site. In contrast, CVAE does not suffer from this problem improving the spatial consistency of the downscaled fields, as can be seen in the smoothness of the predictions.
3 Pathway of generative models to tackle climate change
Overall, we have showed the ability of CVAEs to produce spatially consistent stochastic fields in PP setups on a use-case over Europe. The generation of these high-resolution fields through generative models may foster the use of this type of downscaling into climate impact studies, since their products are very demanded by different sectors (e.g., agriculture, hydrology) to tackle climate change. In this line there are several challenges to address. For instance further research is needed in the evaluation of these models on aspects such as temporal consistency, and reproducibility of extremes. Also, in order to apply them to climate change projections, a study of its extrapolation capabilities is also required. The CVAE model developed here is a first approach, but further tuning this architecture may translate in improvements in the generated downscaled fields. For example, [26,27] propose the use of normalizing flows to generate more complex latent distributions which could help capturing the complex non-linearities of the distribution of precipitation fields. Finally, the DL ecosystem offers a wide catalog of additional topologies which are of interest for PP downscaling (e.g., Conditional GANs [28]).
Figure 1 :
1CVAE model architecture. Red lines represent the path followed by the model in the inference phase, during training both paths (green and red lines) are covered. At the bottom, a comparison between three different downscaled fields sampled from CVAE and CNN1 models, alongside the actual observation for 19/02/2004.
The code of the use-case is available at https://github.com/jgonzalezab/CVAE-PP-Downscaling
Acknowledgements. The authors acknowledge support from Universidad de Cantabria and Consejería de Universidades, Igualdad, Cultura y Deporte del Gobierno de Cantabria via the "instrumentación y ciencia de datos para sondear la naturaleza del universo" project. J. González-Abad would also like to acknowledge the support of the funding from the Spanish Agencia Estatal de Investigación through the Unidad de Excelencia María de Maeztu with reference MDM-2017-0765.
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| sample_679 | 0.9999 | arxiv | |
Political Strategies to Overcom e C lim ate Policy Obstructionism
Cameron Hepburn
Jacquelyn Pless
William O'sullivan
Matthew Ives
Sam Fankhauser
Thomas Hale
Joris Bücker
Marion Leroutier
Tim Dobermann
Linus Mattauch
Sugandha Srivastav
Ryan Rafaty
Political Strategies to Overcom e C lim ate Policy Obstructionism
† For thoughtful feedback at various stages of this paper's development, we thank Mike Thompson and INET-Oxford EOS seminar participants. Financial support from the Oxford Martin School Programme on the Post-Carbon Transition is gratefully acknowledged. 1. Smith School of Enterprise and the Environment, University of Oxford 2. Institute for New Economic Thinking at the Oxford Martin School 3. Climate Econometrics, Nuffield College, University of OxfordJEL Codes: D72 (Political ProcessLobbyingVoting Behaviour)D74 (Conflict)D78 (Policy Formulation) Suggested citation: SrivastavS and RafatyR2022 Political Strategies to Overcome Climate Policy Obstructionism Perspectives on PoliticsFirst View: pp1-11 2
A bstractGreat socio-economic transitions see the demise of certain industries and the rise of others. The losers of the transition tend to deploy a variety of tactics to obstruct change. We develop a political-economy model of interest group competition and garner evidence of tactics deployed in the global climate movement. From this we deduce a set of strategies for how the climate movement competes against entrenched hydrocarbon interests. Five strategies for overcoming obstructionism emerge: (1) Appeasement, which involves compensating the losers; (2) Cooptation, which seeks to instigate change by working with incumbents; (3) Institutionalism, which involves changes to public institutions to support decarbonization; (4) Antagonism, which creates reputational or litigation costs to inaction; and (5) Countervailance, which makes lowcarbon alternatives more competitive. We argue that each strategy addresses the problem of obstructionism through a different lens, reflecting a diversity of actors and theories of change within the climate movement. The choice of which strategy to pursue depends on the institutional context.
1 Introduction
Great socioeconomic transitions involve significant shifts in power. Such was the case for universal suffrage, the abolition of slavery and the end of apartheid. The transition to a postcarbon society will not be different.
Energy systems built around hydrocarbons will have to transition to a zero-carbon paradigm which will entail large shifts in the composition of firms and economic activity. This will inevitably create winners and losers, even if it society as a whole is better off. The existential politics of the post-carbon transition (Colgan, Green and Hale 2020), notably the $10 trillion worth of assets at risk of stranding (Mercure et al. 2018;Tong et al. 2019), makes it particularly prone to obstructionism by entrenched interests.
The climate change countermovement (CCCM) has received growing scholarly attention in recent years (e.g. Brulle 2014;Farrell 2016). The CCCM lobby consists of industry associations, carbon-exposed firms, utilities, workers, unions, corporate-funded think tanks and state-owned enterprises who engage in tactics to weaken climate policies rather than adapt to them. Finding ways to address this obstructionism is important, not only because climate change will affect inequality, conflict, migration, economic development and governance, but also because progress has been stalled in large measure by lobbying and inertia in the political system (Stokes 2020).
The corollary to an active CCCM lobby is the climate movement. The strategic operations of the climate movement have received relatively scant attention in the lobbying literature. To address this gap, we develop a framework that documents five key strategies to overcome obstructionism:
-A ntagonism , which increases the reputational and economic costs of participating in obstructionism and "business as usual" activities; -A ppeasem ent, which offers monetary relief, retraining and restitution to the losers of the transition; -Co-optation, which seeks change from within by co-opting the opposition to reform and diversify their business model; -Institutionalism , which involves regulatory and structural changes at the level of public institutions to make obstructionism harder; and -C ountervailance, which bypasses direct confrontation with political opponents by supporting alternative technologies and strengthening their disruptive market potential.
Each strategy advances a different theory of change, contains distinct tactics and is best suited to different actors ( Figure 1). We validate our framework by collecting evidence on the climate movement's activities and categorising that by the five strategies (see database in Supplementary Material). Finally, we develop a political economy model of interest group 3 competition and show how the five strategies, and the tactics within them, change a politician's incentives to enact stronger policy.
We find that the choice of strategy is sensitive to three macro-structural parameters: (i) "democratization", which we define as the bargaining power of citizens relative to corporations (ii) "climate consciousness" which is the bargaining power of citizens who support climate policy relative to those who are against it, and (iii) "green business interests" which is the bargaining power of businesses that support climate policy relative to those that are against it. Once deployed, the strategies themselves affect these variables creating feedback dynamics (Farmer et al. 2019).
Much of the existing literature in climate politics focuses on international climate negotiations. Relatively few studies have investigated how domestic politics and interest group competition constrain climate policy (Keohane 2015). Studies that build on this line on inquiry include Aklin and Urpelainen (2013), Meckling (2019), Brulle (2014Brulle ( , 2019, Farrell (2016), Brulle (2018), Gullberg (2008), McKie (2019), Stokes (2020), andMildenberger (2020). Our aim is to further build on this literature and make sense of disparate claims on the best path forward towards decarbonisation and overcoming obstructionism.
The rest of this article is structure as follows: Section 2 discusses the issue of climate policy obstructionism and the various forms it takes, Section 3 introduces our theoretical framework which coceptualises a politician's incentives to increase climate ambition and how the five strategies influence this, Section 4 discusses the five strategies in detail with a US case study and Section 5 looks at strategy choice. . 4 Figure 1. Five P olitical Strategies 2 C lim ate P olicy Obstructionism
The history of climate policy reveals the extent to which it has been a tug-of-war between different interest groups (Stokes 2020). The global policy landscape is replete with examples of the reversal of climate commitments such as the Australian government's removal of a carbon price only two years after its enactment, the Bolsanaro government's accelerated focus on land-grabbing across the Amazon and Cerrado biomes after years of effectively curbing deforestation (Rochedo et al. 2018) and the US's participation in the Paris Climate Accord which vacillates with which party is in power. The persistent difficulty in phasing out global fossil fuel subsidies is a testament to the degree of hysteresis within the political arena (Skovgaard and van Asselt 2018 CCCM lobbying dwarfs climate movement lobbying on all dimensions including the diversity of tactics, the cultivation of deep political networks (Farrell 2016), and the extent of expenditure (Brulle 2018;Ard, Garcia, and Kelly 2017). For example, lobbying expenditure by the CCCM in the US Congress between 2000-2016 was over USD 2 billion (4% of total lobbying expenditure), which is an order of magnitude higher than the political expenditures of environmental organizations and renewable energy companies (Brulle 2018).
However, the effects of CCCM lobbying extend well beyond the paradigmatic US case. Patterns of obstructionism are manifest in other major fossil-fuel producing countries. For example, in 2013 an estimated one-third of media coverage of climate change in Australia was biased in favour of climate scepticism, with disinformation campaigns openly sponsored by media mogul Rupert Murdoch (Bacon 2013). In India, the government's majority stake in Coal India Limited, the world's largest coal company, creates perverse incentives. In China, provincial politics is tilted in favour of high-carbon prestige projects (Nelder 2021). Even in the European Union, which is considered an innovator in climate policy, carbon-intensive industry associations have actively endorsed the emissions trading scheme (ETS) during periods of reform but have used it as a Trojan Horse to pre-empt stricter regulations. Industry has also negotiated substantial exemptions such as the grandfathering of free allowances and the carbon leakage list which exempts trade-exposed carbon-intensive industries from a carbon price all together (Markard and Rosenbloom 2020).
Passing legislation for decarbonization is difficult because of the sheer value of fossil fuel assets that will be impacted. In monetary terms, the situation is not dissimilar to the abolition of slavery. Slaves made up almost one-fifth of household "assets" back in 1860 and, like fossil fuels, were estimated to be worth around 10-20 trillion USD (Hayes 2014). Abolitionists had to deploy a range of tactics to overcome obstructionism.
Several reasons may explain the CCCM's superior political organization: (i) by virtue of its incumbency, it has greater material resources and political connections at its disposal; (ii) the CCCM lobby is a tightly defined group of actors while the climate movement is relatively more dispersed, making organization costlier; and (iii) existing laws and institutions cater to a highcarbon paradigm which creates inertia in the reform process.
3 P olitical Econom y M odel 6 To explore interest group competition, we develop a simple political-economy framework that models how a politician's incentives to enact more stringent climate policy are affected by different agents and institutional factors. While the literature has looked at political competition from the lens of "green" vs. "brown" governments (Aklin and Urpelainen 2013), we extend it to the case of citizens vs. business interest groups (first tier) and, climate conscious citizens and businesses vs. anti-climate citizens and businesses (second tier).
In the model, we assume a politician selects the level of policy ambition, , such that she maximizes the perceived welfare, , of citizens and business interest groups (Equation 1). The politician's chance of election or re-election increases in . 1 The politician cares about citizens as they supply votes and businesses since they supply campaign finance.
In our model represents climate ambition i.e. the target level of emissions reduction. However, in other applications, may represent the ambition to universalize access to free healthcare, gain autonomy from a subjugating party, or reform the food industry.
( ) = [β 1 + (1 − β 1 ) ] + (1 − )[ + (1 − ) ]
(1) α, β 1 , ∈ [0,1] describe the relative bargaining power of citizens versus businesses, climate conscious citzens versus anti-climate citizens, and green business interests vs. CCCM business interests respectively. 2 The perceived welfare of G citizens/businesses increases with greater policy ambition ( ′ ( ) > 0) and decreases for citizens/businesses ( ′ ( ) < 0). 3
Citizen and business interests are considered separately to capture numerous cases of divergent interests. For example, the interests of the youth who are very active in the climate movement have little overlap with that of large business interests.
We focus on perceived welfare because the true level of welfare an agent experiences in response to different scenarios may differ from how the agent perceives the matter ex ante, due to misinformation and biases (Druckman and McGrath 2019;Mildenberger and Tingley 2019).
In the case of climate change, evidence shows that weather extremes and the promulgation of scientific information do little to change aggregate opinions. Instead, political mobilization by elites and advocacy groups is critical in influencing climate change concern (Brulle, Carmichael and Jenkins 2012).
A politician's incentives to increase policy ambition to advance a social movement's agenda can be increased via the five strategies whose tactics change different parts of the politician's objective function. From a static perspective, the choice of strategy is sensitive to initial conditions related to democratization (α), climate consciousness ( 1 ) and green business incentives ( ). From a dynamic perspective, the strategies start to influence these parameters. Table 1 gives an example of how initial conditions influence strategy choice.
8 This section reviews the five strategies in detail.
Antagonism
Antagonism springs from grassroots movements by civil society, which aim to awaken public consciousness about climate change, diminish the reputational capital and "social license to operate" of CCCM entities, and pressure governments to act with greater urgency to reduce emissions.
Advocates pursuing this strategy employ tactics which name, shame, sue and boycott the CCCM lobby, thereby increasing the climate consciousness of the citizenry and threatening the business of hydrocarbons. Mass mobilizations, such as those galvanised by Fridays for Future, Extinction Rebellion and the Sunrise Movement fit within the realm of antagonism.
The antagonistic philosophy is well-captured by abolitionist Frederick Douglass' 1857 speech:
"If there is no struggle there is no progress. Those who profess to favour freedom and yet deprecate agitation are men who want crops without ploughing up the ground; they want rain without thunder and lightning. They want the ocean without the awful roar of its many waters…Power concedes nothing without a demand. It never did and it never will (Douglass 1979, 204). "
In institutional contexts in which there is "political opportunity" (Gamson 1996), that is, a high level of democratization as suggested by citizens having the freedom to assemble, voice demands, exert influence on politicians, and trust the judiciary to remain independent, antagonism may be an effective strategy. One very successful example of antagonism is the Beyond Coal campaign, run by Bloomberg Philanthropies and the Sierra Club, which has retired 60% of US domestic coal-fired power plants (349 out of 530 plants till date) 4 through public awareness and litigation (Sierra Club 2021a; Sierra Club 2021b).
Similarly, condemnatory exposure of alleged wrongdoing can reduce the social license to operate in a business as usual manner. The Exxonknew campaign exposed how the company was aware of the dangers of rising CO 2 emissions as early as 1968 but publicly sowed doubt and funded climate denialism, thereby delaying decades of climate action (Oreskes and Conway 2011;Robinson and Robbins 1968). This provided the evidentiary basis for numerous lawsuits filed by states such as New York and California.
Where there is a strong and independent judiciary climate litigation can also be used by citizens against the government. A high-profile case was the Urgenda Foundation v. the State of the Netherlands (2019), in which Dutch citizens sued their government over its failure to adopt ambitious climate mitigation measures. The court ruled in favour of citizens arguing that the government was in violation of citizens' constitutional right to secure adequate protection from environmental harm. Such litigation can not only result in direct changes to government policy but also increase how politicians weigh the welfare of climate conscious citizens. There may also be a valid legal case to challenge the issuance of fossil fuel permits when there are low-cost energy alternatives (Rafaty, Srivastav, and Hoops 2020).
Institutionalism
Institutionalism involves structural changes to incentivize climate compatible behaviour on a system level. Many institutionalists require "windows of opportunity" to push through their reforms which may arise after elections, mass mobilisations, and exogenous shocks, such as the COVID-19 pandemic, that force the system to do things differently (Farmer et al. 2019).
Examples of institutionalist measures that can negatively affect the operations of CCCM corporations include: the establishment of independent climate committees, mandatory disclosure of climate risks, green quantitative easing, conditional bailouts, and negative screens on stock exchanges to ensure listed companies are net-zero compatible (Dafermos, Nikolaidi and Galanis 2018;Hepburn et al. 2020;Farmer et al. 2019). Institutionalism is a strategy best leveraged by those in government, the judiciary, or the technocrats who advise them.
Institutionalism can also involve the establishment of independent oversight committees that shield climate policy from the vagaries of electoral cycles. For example, under the 2008 Climate Change Act, the UK established the Committee on Climate Change (CCC) which was tasked with setting science-based carbon budgets every five years, giving independent advice to the government, and reporting to the Parliament on progress. Independent commissions such as the CCC ensure that there are checks and balances against political short-termism. In many political systems, the creation of arm's length bodies of this sort may be decisive in enhancing the credibility of long-run emissions targets.
Appeasement
Appeasement provides compensation to the losers of the transition as a means of quelling their resistance. Leveraging this strategy is typically the prerogative of governments, local authorities, and courts. Common forms of appeasement include worker re-training programmes; pay-offs for workers and asset owners due to early closures of mines; and regional transition funds to support economic diversification in localities that are dependent on climate-forcing assets (e.g. coal, oil, gas, etc.). Appeasement for workers relies on the theory of change that successful strategy uplifts the economic hopes and developmental prospects of low-income communities, fostering a just transition. For example, compensation to miners and their communities was a core element of the climate proposal that US President Joe Biden advanced on the campaign trail when visiting the deindustrialized towns of the Rust Belt.
Appeasement for capital owners, on the other hand, is based on the idea that it may be politically expedient to compensate powerful lobbyists who may otherwise excoriate important reforms -the same way slave-owners were compensated during the abolition of slavery.
Starting in 2015, the Climate Leadership Council (CLC) in the US put forward a national "carbon dividends" proposal that included a provision to establish a legal liability shield, which would statutorily exempt oil and gas companies from all tort liability in court cases seeking restitution for the monetary damages attributed to their historical emissions. This provision was motivated by a theory of change which believed that no comprehensive climate legislation will ever pass through Congress without bringing the oil supermajors to the table. To bring oil supermajors to the table, the policy must not only provide sticks but also carrots (appeasement). This proposal did not prevent the outrage that many environmental groups expressed towards the liability provision. However, there was another segment of environmentalists who preferred to focus on the emissions abatement that could be achieved if "carbon dividends" were adopted.
Holding no particularly strong moral conviction about historical liability for emissions, they were willing to endorse the CLC's proposal as a compromise. CLC dropped the proposal in 2019.
Countervailance
Countervailance involves supporting green technologies via industrial policy to create a countervailing power to the CCCM lobby. Governments are best placed to leverage the countervailance toolkit through instituting measures such as: R&D tax credits, innovation incubators, subsidies for green innovation, renewable portfolio standards, renewable energy auctions, government procurement for green technologies, and policies that de-risk green investments. The aim of the countervailance toolkit is to increase the uptake of green technologies and bring down their costs so that they can displace carbon-intensive incumbent technologies.
An example of countervailance is Germany's feed-in-tariff for solar energy passed in 2000. One of the authors of the feed-in tariff law argued that history would call it the "Birth Certificate of the Solar Age", since it created assured demand for renewable energy that led to increased production and learning-by-doing (Farmer and Lafond 2016).
Countervailance bypasses head-on engagement with the CCCM lobby and helps dissipate a large portion of the political conflict by enabling market forces to drive rapid deployment (Breetz, Mildenberger and Stokes 2018). As green technologies acquire market share, novel political realignments tend to emerge (Meckling, Sterner and Wagner 2017;Meckling 2019). "Politically active green tech clusters" can become powerful advocates of stronger climate policies, deter policy backsliding, and create further windows of opportunities for institutionalist reform. This feedback dynamic can help advance the energy transition even in the absence of global coordination (Meckling 2019).
An instructive example occurred in Denmark after a centre-right coalition government abandoned several renewable energy commitments in the late 1990s. Vestas, the country's largest wind turbine manufacturer, threatened to leave Denmark and take its suppliers. It formed an ad hoc green lobbying coalition within the Danish Board of Industry. The government quickly realised that it was in its best interest to heed the demands of the green business coalition. They 12 subsequently re-instated various support measures for the wind industry, admitting that they had underestimated the sentiments of big green businesses.
Co-optation
Co-optation involves bringing climate policy obstructionists to the side of the climate movement. Co-opters can push for a number of different changes within business organisations such as: commitments to stop funding CCCM lobby groups; linking executive pay to measurable emissions reductions and adopting internal carbon pricing. Co-opters navigate the art and politics of persuasion, and their required skillset is not unlike that of an effective politician.
The theory of change is based on the idea that by convincing a relatively small number of elite individuals, such as the CEOs of large, energy-intensive companies or top government officials, great sums of capital can be reallocated away from climate-forcing assets. Compared to the other strategies, co-optation is available to relatively few members of the climate movement, and perhaps for this reason, its potential is frequently discounted.
Examples of co-opters in the climate movement include Pope Francis who has used his moral authority to summon oil and gas executives to change strategy; family members of executives who are in a unique position to change hearts and minds; and, majority shareholders, high profile advisors, CEOs and elite academics who have a sense of climate consciousness. Co-optation is likely to be a strategy of choice in contexts where ordinary citizens have relatively less bargaining power compared to corporations.
Looking ahead, strategists of co-optation could move beyond attempts to persuade hydrocarbon businesses and start building new alliances with businesses in sectors that have been largely overlooked in climate policy but can play a pivotal role in precipitating change. Google, Amazon, Facebook (Meta) and other technology companies have plans to eliminate or neutralize their carbon footprints. These companies have market-moving power and their actions across supply chains, data centres, and global distribution networks could amplify net-zero efforts in other areas of the economy.
Box 1 gives examples of how the five strategies have been deployed in the climate movement in the US.
B ox 1: U S A rchetypes of the Five Strateg ies
A ntagonism : Sierra Club (1892 -present):
N G O litigating to close 340+ coal plants across the U S
The Sierra Club, founded in the 19 th century, uses litigation and grassroots campaigns to decommission coal plants across the US, with 349 plants having closed (amounting to 905 coal-plant production units) and "181 to go" (Sierra Club 2021a; Sierra Club 2021b). The Sierra Club claims to have brought about almost 170MM of clean energy in place of decommissioned coal plants and avoided 2,322 miles of gas pipeline (Sierra Club 2021a). Institutionalism : Regional Greenhouse Gas Initiative (RGGI) (2009 -present):
A cap-and-trade schem e in Eastern states
The Regional Greenhouse Gas Initiative Program (RGGI) was the first mandatory, CO2-limiting cap-andtrade programme in the US. Since its inception, the initiative has held 50 auctions, selling 1.11 billion CO2 allowances (worth $3.78bn in total) to electric power generators in the ten eastern states participating in the program. In 2020, the emissions cap, which drops each year, was 96.2 million tonnes, with an aim of being 86.9 million tonnes in 2030 (Potomac Economics 2010).
A ppeasem ent: The POWER+ Plan (2016 -present):
C om pensation to coal com m unities
The Obama Administration introduced the POWER+ Plan to invest federal resources in regions that were historically reliant on the coal economy and vulnerable to the energy transition (The White House 2015). The Plan allocated funds to affected workers ($20m), economic development ($6m), the Environmental Protection Agency ($5m), and rural communities ($97m) (The White House 2016). Since 2015, the Appalachian region in the Northeast (comprised of states like Virginia, West Virginia and Pennsylvania) has received almost $300m in grants to revive and rebuilt communities (ARC 2021).
C hoosing Strategies
We now move to a dynamic perspective and consider how the five strategies build-off each other. Strategy choice depends, in the first instance, on initial conditions related to the macro-structural parameters (democratization, climate consciousness and green business interests) but subsequently, on how the deployment of strategies affects these variables. Therefore, from a dynamic perspective, strategy sequencing is important. To see why, consider the following examples:
Example 1:
Consider a setting where the state is heavily captured by business interest groups ( ≈ 0) and citizens have low climate consciousness ( 1 < 0.5). This setting could, for example, represent a Middle Eastern petrol producing state. In this context, the strategist will want to focus on increasing the strength of green business interests relative to CCCM interests (i.e., increasing ) through co-optation or countervailance. Co-optation could be used to convince the ruling elite that global demand for hydrocarbons is likely to diminish and there is a need to diversify towards fast-growing low-carbon industries. Countervailance could play a role in demonstrating the feasibility and disruptive market potential of low-carbon alternatives. Strategies that require political opportunity such as antagonism are unlikely to succeed since ≈ 0. If democratic institutional reforms are pursued that increase democratization i.e. = 0.25, then the climate movement's agenda will still face uncertainties since most citizens are against more ambitious climate policy. The pathway in this case would be to first increase green business interests, which may then translate into greater climate consciousness.
Example 2:
Let's now consider a case where democratization and green business interests are low but citizens' preferences are tilted strongly in favour of high climate ambition ( 1 > 0.5). This could be parts of the United States where citizens favour climate action but the political elite is captured by CCCM lobbies. In this case, if a strategist pursues structural democratic reforms (i.e. raising ) via institutionalism, then the politician will have stronger incentives to support emissions reductions because the voice of climate conscious citizens suddenly has more weight. In the absence of being able to pursue structural democratic reforms that raise , the climate strategist could continue pursuing co-optation and countervailance to increase green business incentives.
Example 3:
Finally, for a strategist in a setting where most citizens favour stronger climate policy and democratization is high (e.g. the Netherlands), there is greater political opportunity through which climate conscious citizens can pursue strong antagonistic tactics such as climate lawsuits. This can directly increase climate policy ambition (e.g. the Urgenda case). The creation of stronger green business interests can also create clusters of green industrial lobbies that can help support institutional reform such as mandatory disclosure of climate risks and countervailance tactics such as subsidies for green technologies.
This simple sketch illustrates how in a dynamic setting, strategies need to be sequenced appropriately since they can build-off each other. Ill-conceived sequencing can lock-in stalemates. There are many potential sequencing options which depend on initial conditions and feedback dynamics.
Strategies may also be deployed jointly to increase efficacy. For example, appeasement on its own, without complementary measures could lead to inefficiently large pay-outs to CCCM capital-owners. This could also create perverse incentives to falsely project continued operations to secure compensation for "early" closures. Germany's coal exit law stipulates that a total of 4.35 billion Euros in compensation will be paid for planned shutdowns by 2030 (Wettengel 2020). However, legal challenges are imminent as the European Commission questions whether "compensating operators for foregone profits reaching very far into the future corresponds to the minimum required" (European Commission 2021). It is likely that antagonism or institutionalism will be needed as complementary strategies to safeguard public interest and put a reasonable upper bound on compensation to capital-owners. Citizens can leverage institutions designed to protect the environment to file antagonistic lawsuits or alternatively, countervailance could be used to create green industrial clusters, which can lobby the government to enact institutional reforms that threaten the CCCM business model.
Our analysis demonstrates that due to positive feedbacks and mutual reinforcement, each strategy likely has a role to play. Some may initially outperform others due to the institutional context, while others may set the stage for more ambitious action subsequently. Tactics that garner the most success are: (i) appropriate to the actors who carry them out; (ii) appropriate to the institutional setting in which they are applied; and (iii) timely.
Previous literature in the field has suggested solutions that fall within one ambit or the other: for example, Meckling et al. (2017) talk about the importance of green industrial policy as a precursor to carbon pricing. By contrast, Zhao and Alexandroff (2019) focus on appeasement as a key strategy, highlighting Germany's compensation efforts as a way to push forward the transition. We combine these perspectives to illustrate how strategy choice and sequencing depend on the initial conditions and the dynamics of three macrostructural parameters: climate consciousness among the citizenry, green industrial incentives and the level of democratization, and how the deployment of strategies in turn also affects these parameters, forming feedback dynamics. Future work could empirically examine how each of these strategies perform in different institutional contexts and explore questions around the sequencing of strategies.
).The CCCM lobby in the US has swayed politicians through several different tactics. This
includes offering politicians lucrative private sector roles after office (Blanes i Vidal, Draca, and
Fons-Rosen 2012), strategically leveraging tax-free corporate philanthropy (Bertrand et al.
5
2020; Brulle 2018), threatening politicians with competition if they do not acquiesce to
demands (Stokes 2020; Dal Bó and Di Tella 2003; Chamon and Kaplan 2013), influencing
voters through funding advocacy institutions that promote climate skepticism (DellaVigna,
Durante and La Ferarra 2016; Farrell 2016; Farrell 2019), and inserting representatives into
regulatory institutions, such as the Environmental Protection Agency to dilute climate policy
(Leonard 2019).
Table 1 .
1The Sensitivity of Strategies to Initial C onditions Make it an electoral liability to ignore the climate crisis via awareness campaigns and grassroots movements e.g. Fridays for Future, Sunrise Movement, Extinction Rebellion (antagonism)Initial Conditions (If):
Goal (Then): Strategy & Tactic (By):
Citizens are against policy &
citizens have at least as much
bargaining power as businesses
e.g. deindustrialised mining
towns
Increase 1 Financial compensation to coal workers and
regional transition funds (appeasement)
Green business interests are
weak and corporations have
more bargaining power than
citizens.
e.g. US Congress where
CCCM interests exert large
influence
Increase
Incentivize dirty firms to become clean via:
-business model reform and executive
incentives (co-optation);
-tax breaks for clean tech, R&D support,
grants (countervailance)
-financial compensation to capital owners
(appeasement)
Citizens are for policy but
have less bargaining power
than businesses
e.g. Germany where a climate
conscious citizenry contends
with a powerful CCCM lobby
Increase
Increase
Incentivize dirty firms to become clean via:
-climate lawsuits, boycotts, and reputational
damage (antagonism);
-institutional reforms, including carbon
pricing and mandatory disclosure of risks
(institutionalism).
In the case of countries without democratic elections, this can be rephrased as a politician's "ability to retain power".2 Consensus democracies such as those of the Nordic countries, or semi-direct representative democracies such as that of Switzerland, will have a relatively high value of . Where there is a strong revolving door between industry and government, such as in the United States, is lower. In China, where citizens cannot vote but still play a role insofar as they can leverage implicit threats of civil disobedience, is even lower.3 For simplicity we assume there is no neutrality for firms or citizens in relation to how perceived welfare will change in response to climate ambition. This can be modelled but it will not change the core conclusions.
See: https://coal.sierraclub.org/campaign
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Re-appraisal of the global climatic role of natural forests for improved climate projections and policies
Anastassia M Makarieva
Theoretical Physics Division
Petersburg Nuclear Physics Institute
188300Gatchina, St. PetersburgRussia
Institute for Advanced Study
Technical University of Munich
Lichtenbergstraße 2 a85748GarchingGermany
Andrei V Nefiodov
Theoretical Physics Division
Petersburg Nuclear Physics Institute
188300Gatchina, St. PetersburgRussia
Anja Rammig
School of Life Sciences
Technical University of Munich
Hans-Carl-von-Carlowitz-Platz 285354FreisingGermany
Antonio Donato Nobre
Centro de Ciência do Sistema Terrestre INPE
12227-010São José dos Campos, São PauloBrazil
Re-appraisal of the global climatic role of natural forests for improved climate projections and policies
Along with the accumulation of atmospheric carbon dioxide, the loss of primary forests and other natural ecosystems is a major disruption of the Earth system causing global concern. Quantifying planetary warming from carbon emissions, global climate models highlight natural forests' high carbon storage potential supporting conservation policies. However, some model outcomes effectively deprioritize conservation of boreal and temperate forests suggesting that increased albedo upon deforestation could cool the planet. Potential conflict of global cooling versus regional forest conservation could harm environmental policies. Here we present theoretical and observational evidence to demonstrate that, compared to the carbon-related warming, the model skills for assessing climatic impacts of deforestation is low. We argue that deforestation-induced global cooling results from the models' limited capacity to account for the global effect of cooling from evapotranspiration of intact forests. Transpiration of trees can change the greenhouse effect via small modifications of the vertical temperature profile.Due to their convective parameterization (which postulates a certain critical temperature profile), global climate models do not properly capture this effect. This parameterization may lead to underestimation of warming from the loss of evapotranspiration in both high and low latitidues, and therefore, conclusions about deforestation-induced global cooling are not robust. To avoid deepening the environmental crisis, these conclusions should not inform policies of vegetation cover management. Studies are mounting quantifying the stabilizing impact of natural ecosystems evolved to maintain environmental homeostasis. Given the critical state and our limited understanding of both climate and ecosystems, an optimal policy would be a global moratorium on the exploitation of all natural forests.
Hurtt et al., 2020, their Fig. 7
) and increase of atmospheric CO2 (right axis, data downloaded from https://www.eea.europa.eu/data-and-maps/daviz/atmospheric-concentration-of-carbon-dioxide-5).
During the industrial era, primary ecosystems have declined, and CO2 concentration has grown, by approximately one half. (Wilhere, 2021). Proponents of ecosystem preservation often borrow from the decarbonization argumentation and invoke the carbon storage potential of natural forests as a major illustration of their climatic importance. For example, the ground-breaking proforestation initiative in the United States began with emphasizing how much carbon the unexploited forests can remove from the atmosphere if allowed to develop to their full ecological potential (Moomaw et al., 2019).
However, the carbon-storage argument for temperate and boreal forests is undermined by the fact that global climate models suggest that deforestation in these regions could cool the planet. Here increased albedo is estimated to overcome the warming caused by deforestation-induced carbon emissions (Jia et al., 2019, Fig. 2.17), even if the latter can be underestimated (Schepaschenko et al., 2021). These model outcomes have been known for quite a while (e.g, Snyder et al., 2004), but recently these ideas gained prominence approaching implementation. A recent Science commentary warned that regrowing boreal forests would not make the Earth cooler (Pearce, 2022), a conclusion that is purely derived from global climate model simulations (e.g., De Hertog et al., 2022). The World Resources Institute's report "Not just carbon" noted that the increased albedo from deforestation would cool the Earth and emphasized that the positive climate role of boreal forests is only local (Seymour et al., 2022a, b). Accordingly, a recent study in Nature Ecology and Evolution did not include primary boreal forests into Nature's critical assets (Chaplin-Kramer et al., 2022). One of the criteria for an ecoregion to be classified as a critical asset, was its proximity to people -and primary boreal forests are often distant from any human settlements (which is a major reason for why they are still primary). Together, these mainstream messages not only de-emphasize the preservation of natural boreal and, to a lesser degree, temperate forests, but implicitly incentivize their destruction.
In this Perspective, we would like to ring an alarm bell by showing that this potentially biased picture of the role of natural forests, in particular boreal forests, for stabilizing Earth's climate is based on a few model assumptions ruling out important evapotranspiration feedbacks and can result in policies deepening rather than mitigating the climate crisis. We also outline a possible path forward.
2 Global cooling from plant transpiration
Local versus global cooling
We argue that the conclusion of a cooler Earth upon the loss of boreal forests stems from the limited capacity of global climate models to quantify another effect of the opposite sign: global cooling from forest transpiration. That transpiring plants provide local cooling is well-known (e.g., Huryna and Pokorný, 2016;Alkama and Cescatti, 2016;Ellison et al., 2017;Hesslerová et al., 2018, and see Fig. 2). Instead of converting to heat, a certain part of absorbed solar energy is spent to break the intermolecular (hydrogen) bonds between the water molecules during evapotranspiration. As a result, the evaporating surface cools.
When more sunlight is reflected back to space, the planet receives less energy and it is intuitively clear that it must cool. In comparison, although evaporation does cool locally, the captured energy does not disappear but is released upon condensation elsewhere in the Earth system. In contrast with the well developed methodology of explaining the rising planetary temperature with increasing CO 2 (e.g., Benestad, 2017, and references therein), how and whether loss of plant transpiration could warm the planet remains unclear. While the IPCC science does recognize that global cooling from plant transpiration exists (Jia et al., 2019, Fig. 2.17), its description is not to be found in textbooks. However, with the environmental science being inherently transdisciplinary, understanding this effect is important for the broader community of ecosystem researchers and conservationists, as it will enable a critical assessment of model outputs offered to guide large-scale vegetation management.
Conceptual picture
To illustrate the effect, we will use a simple model of energy transfer (Fig. 3). The greenhouse substances are represented by discrete layers that absorb all incoming thermal radiation and radiate all absorbed energy equally up and down. In the absence of absorbers, the Earth's surface emits as much thermal radiation as it receives from the Sun (Fig. 3a). Each layer of the greenhouse substances redirects part of the thermal radiation back to the Earth's surface. As a result, the planetary surface warms, and the more so, the greater the amount of absorbers (cf. Fig. 3b and c).
When a certain part of the incoming solar radiation is absorbed in the upper atmosphere (for example, by aerosols or clouds), it escapes interaction with the absorbers beneath. Accordingly, the planetary surface cools by an amount by which the absorbers would multiply this escaping part if it dissipated to thermal radiation at the surface (cf. Fig. 3c
and d). This illustrates how
where the solar energy dissipates to thermal radiation, with unchanged amount of greenhouse gases and total absorbed solar energy, impacts the planetary surface temperature.
Similarly, in the presence of the non-radiative heat fluxes of sensible and latent heat, the amount of solar energy converted to thermal radiation at the surface diminishes -and so does the amount of thermal radiation redirected by the absorbers back to the surface. Surface thermal radiation and temperature decline (cf. Fig. 3d and e,f). The non-radiative fluxes "hide" a certain part of absorbed solar energy from the greenhouse substances easing its ultimate release to space. Convection, condensation and precipitation "deposit the latent heat removed from the surface above the level of the main water vapor absorbers, whence it is radiated to space" (Bates, 2003). This energy escaping partially from interaction with the absorbers is the cause of global cooling from plant transpiration.
A related process is the atmospheric transport of heat from the equator to higher latitudes, where the water vapor concentration in the colder atmosphere is smaller. This transport likewise "hides" a certain part of solar energy absorbed at the equator from the abundant greenhouse substances (water vapor) in the warm tropical atmosphere. In the result, despite the amount of absorbers does not change, the globally averaged greenhouse effect diminishes and the planetary surface cools (Bates, 1999;Caballero, 2001). Marvel et al. (2013) modeled an idealized atmosphere with two strong circulation cells connecting the equator and the poles. With such a circulation, the Earth's surface became eleven degrees Kelvin cooler than the modern Earth (Marvel et al., 2013, their Fig. 1e and Fig. 3 bottom).
Increasing the non-radiative flux (from zero in (d) to F L > 0 in (e) and (f)) decreases surface thermal radiation F s by a magnitude proportional to F L itself and to the number of absorbing layers ∆τ beneath the height where this flux dissipates to thermal radiation (1 in (e) and 2 in (f)). Historical deforestation affected about 13% of land area (or 3.8% of planetary surface) (Fig. 1). With the global mean latent flux of F L = 80 W m −2 , if deforestation has reduced this flux by thirty per cent (∆F L ∼ −0.3F L ), this could increase the surface radiation by −0.038∆F L ∼ 0.9 W m −2 (cf. Fig. 3d and e) or twice that value (cf. Fig. 3d and f), Table 1. Given an equilibrium climate sensitivity ε ∼ 1 K/(W m −2 ) (Zelinka et al., 2020), the latter case
z e =0 z e = z 1 z e = z 2 (a)
Earth's surface Solar radiation Thermal radiation to space Figure 3. Scheme to illustrate the dependence of the planetary surface temperature on the amount of greenhouse substances (a-c) and on the magnitude and spatial distribution of the non-radiative energy fluxes (d-f). Thickness of each layer of the greenhouse substances corresponds to unit optical depth τ = 1 (one free path of thermal photons -the mean distance between two consecutive acts of absorption and re-emission by the absorber molecules); τs is the total number of layers: τs = 0 in (a), 1 in (b) and 2 in (c-f). A "gray" atmosphere is assumed, where absorption of thermal radiation is the same for all wavelengths (Ramanathan and Coakley Jr., 1978;Makarieva and Gorshkov, 2001;Gorshkov et al., 2002). Thermal radiation of the planetary surface Fs = σT 4 s (W m −2 ) and of the upper radiative layer to space Fe = σT 4 e are related to surface temperature Ts and temperature of the upper radiative layer Te by Stefan-Boltzmann law, where σ = 5.7 × 10 −8 W m −2 K −4 is the Stefan-Boltzmann constant. All energy fluxes are shown in the units of absorbed solar radiation q, which is in the steady-state equal to thermal radiation emitted by the planet (Fe = q); in (d-f), qa = 0.3q is solar energy absorbed by the atmosphere; in (e,f), FL is the non-radiative heat flux accounting for both sensible and latent heat. With q = 239 W m −2 , configuration (f) approximately corresponds to the modern Earth (Trenberth et al., 2009). Thermal radiation is emitted to space from mean height ze:
(b) (c) (d) (e) (f) (a) (b) Greenhouse gases 1 2 1 (c) 1 1 (d) 1 1 (e) 1 1 (f) 1 1 (c) 3 2 2 (d)(a) 1 1 (b) 1 (c) 1 (d) 0.7 0.3 1 (e) 0.7 0.3 1 (f) 0.7 0.3 1 (a) q F e (d) q F e (a) F s = F e = q (b) F s = (τ s +1) q = 2 q (c) F s = (τ s +1) q = 3 q (d) F s = 3 q-τ s q a = 2.4 q q a (e) F L F s = 3 q-2q a -F L (f) F L F s = 3 q-2q a -2F Lwith qa = 78 W m −2 0.3q, Fs = 390 W m −2 1.6q, FL = 97 W m −2 0.4qze = 0 in (a), ze = z1 > 0 in (b) and ze = z2 > z1 in (c-f).
corresponds to a warming of about two degrees Kelvin (Table 1). This should be manifested as an increase in the temperature difference between the surface and the upper radiative layer (the mean temperature lapse rate Γ = (T s − T e )/z e , Fig. 3). If the optical thickness of the atmosphere is greater, the cooling will be proportionally larger. This work (Fig. 3d,f) Historical * * * 13 −30 2 * Tropical forests replaced by deserts in a coupled atmosphere-biosphere model. * * Deforestation of a fully forested planet without changing the albedo; ∆T is the sum of two effects, change in roughness and change in evapotranspiration efficiency as shown in Table 1
Dependence of global transpirational cooling on atmospheric circulation
The higher up convection transports heat, the more pronounced global cooling it exerts as the energy is radiated more directly to space from the upper atmospheric layer (cf. Fig. 3e and f).
Besides the altitude, it matters how rapidly the air ultimately descends. When the air rises and increases its potential energy in the gravitational field, its internal energy accordingly declines, and it cools. As originally evaporation cooled the evaporating surface, the release of latent heat during condensation in the rising air partially offsets this decline of the internal energy of air molecules making the air warmer than it would be without condensation. Radiating this extra thermal energy to space takes time. The more time the air warmed by latent heat release spends in the upper atmosphere (above the main absorbers), the more energy is radiated unimpeded to space and the stronger the global transpirational cooling. With the characteristic radiative cooling rate of the order of 2 K day −1 , it takes about fifteen-thirty days to radiate the latent heat released by tropical moist convection (Goody, 2003).
Therefore, the long-distance moisture transport (including the biotic pump run by forests, Makarieva and Gorshkov, 2007) enhances global transpirational cooling: moist air travels for many days thousands of kilometers from the ocean to land where it ascends and latent heat is released. Then the dry air warmed by latent heat makes the same long way back in the upper atmosphere radiating energy to space (Fig. 4). If, on the contrary, the warmed air descends rapidly and locally, then most heat is brought back to the surface before it is radiated, and the net cooling effect can be nullified. Disruptions in the long-distance moisture transport (e.g., by deforestation) and violent local rains should warm the Earth. In smaller convective clouds up to a quarter of ascending air descends locally at a relatively high vertical velocity (Heus and Jonker, 2008;Katzwinkel et al., 2014). Global climate models do not correctly reproduce either the long-distance ocean-to-land moisture transport or the moisture transport over the ocean (Sohail et al., 2022). For example, the Amazon streamflow is underestimated by up to 50% (Marengo, 2006;Hagemann et al., 2011, their Fig. 5). This corresponds to a 10% error in the global continental streamflow, the latter being of the same order as global continental evaporation. Nor do global climate models correctly reproduce how the local diurnal cycle of convection changes upon deforestation producing extreme low and high temperatures (Lejeune et al., 2017, their Fig. 7). These are indirect indications of the models' limited capacity to reproduce global transpirational cooling.
Global transpirational cooling in global climate models
We have seen that, for a given amount of absorbers, surface temperature is determined by the vertical distribution of the nonradiative heat fluxes (Fig. 3d-f). But these fluxes themselves depend on the vertical temperature gradient: if the air temperature declines with height faster than a certain critical lapse rate 1 , the atmosphere is unstable to convection. The non-radiative heat fluxes originate proportional to the difference between the actual and the critical temperature lapse rates (Ramanathan and Coakley Jr., 1978).
Therefore, strictly speaking, it is not justified to freely vary where and how the non-radiative heat fluxes dissipate to thermal radiation, not paying attention to whether the resulting vertical temperature profile is consistent with their specified values.
However, since the non-radiative (convective) and net radiative energy fluxes in the Earth's atmosphere are of the same order of magnitude (100 and 60 W m −2 , respectively Trenberth et al., 2009), a rough estimate of global transpirational cooling can be obtained from considering the radiative transfer alone as done in Fig. 3d-f. (This would not be possible if the convective fluxes were an order of magnitude higher than the radiative flux). We emphasize that our goal here is not to obtain an accurate estimate of global transpirational cooling, but to present plausible arguments showing that it can be large.
An exact estimate of what happens when the evapotranspiration and the latent heat flux are suppressed on a certain part of land area requires solving the problem simultatenously for the radiative-convective transfer and the temperature profile. This problem is too complicated for modern global climate models, which therefore apply the so-called convective parameterization.
The idea is to postulate the (generally unknown) value of a critical temperature lapse rate instead of solving for it. While the numerical simulation is run, "whenever the radiative equilibrium lapse rate is greater than the critical lapse rate, the lapse rate is set equal to the critical lapse rate" (Ramanathan and Coakley Jr., 1978). Therefore, by construction, global climate models cannot provide any independent information about the climatic effect of evapotranspirational cooling -that should be manifested as the change in the global mean lapse rate -besides what was fed into them a priori via convective parameterization.
Global climate models have been built with a major goal to assess radiative forcing from changing carbon dioxide concentrations. They do have this capacity: this forcing can be approximately estimated assuming an unchanged atmospheric temperature profile. It is under this assumption that Arrhenius (1896) obtained the first ever estimate of global warming from CO 2 doubling 2 . But radiative forcing caused by the suppression of evapotranspiration is a conceptually different problem for which convective parameterization precludes a solution that would be non-zero in the first order. Therefore, in the models, global warming resulting from the loss of transpirational cooling is, for the same deforested area, at least one order of magnitude smaller than our estimate (Table 1). For example, according to global climate models, tropical deforestation on 16% of land area would produce a global warming of 0.2 K (Snyder et al., 2004), while converting most land from forest to grassland (with unchanged albedo) would warm the Earth by about half a degree Kelvin (Davin and de Noblet-Ducoudré, 2010), see Table 1.
As an illustration of the lack of conceptual clarity with regard to global transpirational cooling, one can refer to the conclusion of Davin and de Noblet-Ducoudré (2010, their Table 1) that modeled global warming due to the loss of evapotranspiration is a "non-radiative" forcing as compared to the change of albedo. This conclusion is reached by noting that loss of evapotran- homogenized and quality controlled, integrated sub-daily data set (Willett et al., 2014); ERA5, the fifth generation European Center for Medium-range Weather Forecasts global reanalysis (Hersbach et al., 2020); amip, Atmospheric Model Intercomparison Project, atmosphereonly simulations (without the ocean-atmosphere feedbacks in the climate system) (Gates et al., 1999); cmip, Phase 6 of the Coupled Model
Intercomparison Project (includes amip simulations as an integral part) (Eyring et al., 2016). See Allan et al. (2022) for further details. In
(d-f), d(Ts − T )/dt for AIRS is calculated using HadISDH dTs/dt. Note that altitude z(p) of a given pressure level p increases slightly as the surface temperature grows, but for p < 300 mb it is a minor effect compared to the increase of the temperature difference Ts − T (p).
spiration practically does not change the radiation balance at the top of the atmosphere: ∆F e → 0 such that ∆T /∆F e ε.
However, using this logic, CO 2 increase would not be a radiative forcing either, because, once the planetary temperature equilibrates, CO 2 increase per se (feedbacks absent) does not change the outgoing radiation at the top of the atmosphere. Indeed, Fig. 3 illustrates how the planetary temperature changes due to the radiative forcing from an increased amount of greenhouse substances (a-c) and due to the radiative forcing from changing non-radiative fluxes (d-f). The incoming solar and outgoing longwave radiation remain the same in all cases (F e = q and ∆F e = 0).
In current models, it is assumed that as the planet warms, the temperature lapse rate should slightly diminish following moist adiabat (the so-called lapse rate feedback, Sejas et al., 2021). This robust model feature is not, however, supported by observations (Fig. 5). Satellite data are consistent with an increase in the lapse rate (Fig. 5). The temperature difference between the surface and the upper radiatve layer z e (located between 500 and 400 mb, Benestad, 2017) grows at approximately the same rate as the surface temperature itself. This effect is especially pronounced over land (Fig. 5c,f). This is consistent with a radiative forcing imposed by changing non-radiative fluxes, including those due to the land cover change (Fig. 3d-f).
Discussion and conclusions
For the ecological audience it could be difficult to assess the credibility of our quantitative estimates, so we would like to emphasize two of the more unequivocal points. First, global climate models do indicate that the regional loss of forest evapotranspiration leads to global warming. Eventhough the effect is small (Table 1), it is of the opposite sign compared to the albedo-related cooling from deforestation that is invoked to argue that certain forests are not globally beneficial in the climate change context. Despite this obvious importance for the policy-relevant model outcomes, a conceptual description of how evapotranspiration cools the Earth, and how its loss would lead to global warming, is absent from the meteorological literature.
Conceptual understanding lacking, how can one independently assess whether the models get the effect right?
Second, global warming resulting from the loss of evapotranspiration is to be pronounced as an increase in the vertical lapse rate of air temperature. Due to the convective parameterization, global climate models keep this lapse rate roughly constant as the planet warms (Held and Soden, 2006). However, this robust feature of global climate models does not agree with observations that accommodate a considerable increase in the temperature difference between the surface and the upper radiative layer (Fig. 5).
Policies based on the model outcomes that we have criticized are being shaped right now, and avoiding delays in their re-evaluation is desirable. While the above arguments are percolating the meteorological literature, interested readers can approach their colleagues in the field of meteorology to see how they respond to the above two challenges, and thus get an indirect confirmation (or disproval) of our argumentation.
Our results highlight the importance of a valid concept put in the core of a model. The assumption of an a priori specified critical lapse rate in the convective parameterization yields a negligible global transpirational cooling, which translates into de-emphasizing the preservation of boreal forests. Concepts are powerful; incorrect concepts can be destructive. This brings us to the question, is there a concept that ecology could offer to put in the core of a global climate model, to adequately represent the biosphere?
From our perspective, it is the concept of environmental homeostasis, which is the capacity of natural ecosystems to compensate for environmental disturbances and stabilize a favorable for life environment and climate (Lovelock and Margulis, 1974;Gorshkov, 1995). Recent studies discuss how the biotic control can be evident in the observed dynamics of the Earth's temperature Ball, 2020, 2021;Arnscheidt and Rothman, 2022). When the information about how the natural ecosystem influences environment is lacking, the best guess could be to assume that they provide a stabilising feedback to the disturbance.
There was already a predicament in climate science that could have been facilitated by such an approach. It was the "missing sink" problem: when the rates of carbon accumulation in the atmosphere and the ocean became known with sufficient accuracy, it turned out that a signifcant part of fossil fuel emissions could not be accounted for. The enigmatic "missing sink" was later assigned to the terrestrial biota (Popkin, 2015). While now it is commonly referred to as plant CO 2 fertilization, this is a response at the level of the ecological community as a whole: for there to be a net sink, as the plants synthesize more organic matter, heterotrophs must refrain from decomposing it at a higher rate under the warming conditions (cf. Wieder et al., 2013).
Surprisingly, while the idea that ecological succession proceeds in the direction of the ecosystem attaining increased control of the environment and maximum protection from environmental perturbations was dominant in ecology (Odum, 1969), a community's stabilizing response to the CO 2 disturbance was not predicted but rather opposed by ecologists on the basis that undisturbed ecosystems should have a closed matter cycle 3 (Hampicke, 1980;Amthor, 1995). However, based on the premises of the biotic regulation concept (Gorshkov, 1995;Gorshkov et al., 2000), and long before the missing sink was assigned to the terrestrial biota, Gorshkov (1986, p. 946) predicted that the undisturbed ecosystems should perform a compensatory response to rising atmospheric CO 2 by elevating synthesis of carbohydrates.
Today, climate science faces a new challenge. Global climate models with an improved representation of clouds display a higher sensitivity of the Earth's climate to CO 2 doubling than models with a poorer representation of clouds (Zelinka et al., 2020;Kuma et al., 2022). This implies more dire projections for future climate change, but also poses the problem of how to account for the past temperature changes that are not affected by the model improvements and have been satisfactorily explained assuming a lower climate sensitivity. The concept of the environmental homeostasis and the biotic regulation of the environment provide a possible solution: the climate sensitivity may have been increasing with time -reflecting the decline of natural ecosystems and their global stabilising impact (Fig. 1).
Currently model uncertainties are assessed by comparing outputs from models developed by different research centers (Zelinka et al., 2020). This provides a minimal uncertainty estimate, as the model development may follow universal principles sharing both progress and errors. A distinct approach would be to attempt building a model that departs significantly from the others in its core concept and see if such a model can be plausibly tuned to competitively describe observations. Success of such a model would force the range of model uncertainties to be extended. As global climate models are currently being used to navigate our spacecraft Earth, with its multibillion crew, through the storm of global climate disruption, such a stress test on their performance would not be superfluous.
Such an endeavour requires a plausible alternative concept, and we propose that a global climate model built around the stabilising impact of natural ecosystems can become such an alternative. This will require an interdisciplinary effort and an account of global transpirational cooling, the role of natural ecosystems in the long-distance moisture transport (Makarieva and Gorshkov, 2007;van der Ent et al., 2010;Ellison et al., 2012;Poveda et al., 2014;Molina et al., 2019) and water cycle stabilization (O'Connor et al., 2021;Baudena et al., 2021;Zemp et al., 2017) and the distinct impact of ecosystems at different stages of ecological succession on the surface temperature and fire regime (e.g., Baker and Spracklen, 2019;Aleinikov, 2019;Lindenmayer et al., 2022) and the cloud cover (Cerasoli et al., 2021;Duveiller et al., 2021). Living systems function on the basis of solar energy that under terrestrial conditions can be converted to useful work with a near 100% efficiency. What processes are enacted with use of this energy, is determined by the genetic programs of all the organisms composing the ecological community. Randomly changing the species composition and morphological status of living organisms in the communityfor example, by replacing natural forest with a plantation with maximized productivity or by forcing the forest to remain in the early successional state (Kellett et al., 2023) -disturbs the flow of environmental information and disrupts the ecosystem's capacity to respond to environmental disturbances.
While fundamental science is being advanced, the precautionary principle should be strictly applied. Any control system increases its feedback as the perturbation grows. Therefore, as the climate destabilisation deepens, the remaining natural ecosystems should be exerting an ever increasing compensatory impact per unit area. In other words, the global climate price of losing a hectare of natural forest grows as the climate situation worsens. We call for an urgent global moratorium on the exploitation of the remaining natural ecosystems and a broad application of the proforestation strategy to allow them to restore to their full ecological and climate-regulating potential.
Figure 1 .
1Decline of primary forest and non-forest ecosystems (left axis, data from
Figure 2 .
2Local cooling from plant transpiration. With incoming solar radiation of about 1 kW m −2 , dry area on the deforested plot (left panel) has temperature of 55.3 • C. Young transpiring trees (right panel) lower the surface temperature by almost 30 • C. Distance between the two spots is 1 meter. Measurements and photo credit Jan Pokorný.
FL) is the local reduction of latent heat on the deforested area ∆S (% of land area Sl); ∆T is the change of global surface temperature
Estimated as ∆T ∼ −0.29(∆S/S l )∆F L ∆τ ε, assuming that deforestation reduces latent heat flux by 30% of F L = 80 W m −2(Trenberth et al., 2009) on 13% of land (the area affected by historical deforestation(Fig. 1), 0.29 is the relative global land area) with ∆τ = τs = 2 as optical depth of the atmosphere(Fig. 3d,f); ε ∼ 1 K/(W m −2 ) is the assumed equilibrium climate sensitivity to radiative forcing.
Figure 4 .
4Visualization of the link between transpirational cooling and air circulation. After latent heat is released upon condensation, this energy can be radiated to space while the air travels back to the ocean in the upper troposhere.
Figure 5 .
5Mean trends of the surface temperature Ts (a-c) and of the temperature difference (Ts − T ) between the surface and atmospheric pressure levels (d-f) for the planet as a whole (a,d), ocean (b,e) and land (c,f) over 1988-2014 in models (amip, cmip) versus observations (AIRS, HadISDH, ERA5). In (a-c), whiskers for HadISDH and ERA5 indicate ± one standard deviation, for amip and cmip -the maximum and minimum values. Shading in (d-f) indicates ± one standard deviation. Dashed, solid and dash-dotted model curves in (d-f) were obtained, respectively, by using the maximum, median and minimum values of dTs/dt and dT /dt in the model ensembles (amip and cmip). Data from Fig. S4 of Allan et al. (2022): AIRS, Atmospheric Infrared Sounder satellite data (Tian et al., 2019); HadISDH, The Met Office Hadley Centre
Table 1 .
1Estimates of global warming from the loss of tree transpiration associated with deforestation; ∆FL (% of the global mean value
Lapse rate Γ is the absolute magnitude of the vertical temperature gradient, Γ ≡ −∂T /∂z. 2 If the lapse rate Γ is known, an alternative way to calculate how surface temperature rises with increasing concentration of greenhouse substances is to calculate the change of radiative height ∆ze = z 2 − z 1 (cf.Fig. 3band c) using the hydrostatic equilibrium; then use ∆Ts = Γ∆ze.
This represents what can be called Odum's paradox, who thought that ecological succession culminates in ecosystem's maximum control of the environment(Odum, 1969). But if the ecosystem functions on the basis of closed matter cycles, its environmental impact (and, hence, environmental control) is zero by definition. The biotic regulation concept introduced the notion of directed openness of the matter cycles to compensate for environmental disturbances(Gorshkov, 1995).
AcknowledgmentsThe auhors are grateful to Jan Pokorný, David Ellison, Ugo Bardi, Jon Schull and Zuzana Mulkerin for useful discussions.We thank Richard P. Allan for kindly supplying the data for trends in atmospheric and near surface temperature in numerical
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A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting
April 28, 2023
Reetam Majumder
North Carolina State University
Brian J Reich
North Carolina State University
A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting
April 28, 20231 arXiv:2212.07267v2 [stat.ME] 26 Apr 2023Deep LearningDensity regressionMax-stable pro- cessesGaussian processVecchia approximationClimate change
Extreme streamflow is a key indicator of flood risk, and quantifying the changes in its distribution under non-stationary climate conditions is key to mitigating the impact of flooding events. We propose a non-stationary process mixture model (NPMM) for annual streamflow maxima over the central US (CUS) which uses downscaled climate model precipitation projections to forecast extremal streamflow. Spatial dependence for the model is specified as a convex combination of transformed Gaussian and max-stable processes, indexed by a weight parameter which identifies the asymptotic regime of the process. The weight parameter is modeled as a function of the annual precipitation for each of the two hydrologic regions within the CUS, introducing spatio-temporal non-stationarity within the model. The NPMM is flexible with desirable tail dependence properties, but yields an intractable likelihood. To address this, we embed a neural network within a density regression model which is used to learn a synthetic likelihood function using simulations from the NPMM with different parameter settings. Our model is fitted using observational data for 1972-2021, and inference carried out in a Bayesian framework. The two regions within the CUS are estimated to be in different asymptotic regimes based on the posterior distribution of the weight parameter. Annual streamflow maxima estimates based on global climate models for two representative climate pathway scenarios suggest an overall increase in the frequency and magnitude of extreme streamflow for 2006-2035 compared to the historical period of 1972-2005.
Introduction
The increase in the frequency of hydroclimatic extreme events in the last few decades has caused devastating economic damage and claimed thousands of human lives (Hirabayashi et al., 2013;Winsemius et al., 2018). (Winsemius et al., 2016) predicted an increase in this cost due to sea level rise and extreme precipitation events brought about by climate change. Uncertainty in climate change projections, particularly those associated with precipitation (Bhowmik et al., 2017), also results in significant challenges to the design and maintenance of water infrastructure (e.g., Vahedifard et al., 2017;Kasler and Hecht, 2017). This is further exacerbated by the complexity of flooding events Condon et al., 2015;Kundzewicz et al., 2017;François et al., 2019) as extremal streamflow, which is a key measure of flood risk, shows spatial clustering (Hirsch and Ryberg, 2012;Majumder et al., 2022). There is therefore a need to account for spatial and temporal variability (i.e., non-stationarity) in extremal streamflow due to precipitation when assessing current and future flood risk (Milly et al., 2008;Vogel et al., 2011;Kundzewicz et al., 2014;Salas and Obeysekera, 2014;Milly et al., 2015;Šraj et al., 2016).
A relatively simple approach to projecting flood risk on the basis of extreme streamflow is by the statistical extrapolation of spatiotemporal trends observed in the historical record. Extreme value analysis (EVA) methods have been used to model the relationship between flooding, watershed characteristics, and the weather, using regressions or hierarchical models to account for non-stationarity (Šraj et al., 2016;Dawdy et al., 2012;Lima et al., 2016). However, purely statistical projections of extremal streamflow that do not consider physical variables which are expected to change under climate change (e.g., temperature and precipitation) are likely to be unreliable for long-term projections (Jain and Lall, 2001). Precipitation has a large impact on groundwater flow and is therefore a major driver of extremal streamflow. Like streamflow, it exhibits non-stationarity (Cheng et al., 2014;Kunkel et al., 2020) which needs to be incorporated into any modeling that attempts to provide future projections of extremal streamflow. In this paper, our objective is to build a spatial model relating precipitation and streamflow and use climate model forecasts of future precipitation to understand flood risk under different climate change scenarios.
While climate change is often described in terms of the mean, it will mostly be experienced through extremes. Data for extreme events are by definition sparse, and parametric models must therefore be carefully chosen based on extremal theory to estimate small probabilities. Standard measures of dependence such as correlation and spatial models such as Gaussian processes (GP) do not adequately model extreme events; in order to properly account for spatial dependence while modeling rare event probabilities, we use spatial extreme value analysis (EVA). For modeling block maxima, e.g., the annual maximum of daily streamflow, the commonly used spatial EVA model is the max-stable process (MSP) (De Haan and Ferreira, 2006;Smith, 1990;Tawn, 1990;Schlather, 2002;Kabluchko et al., 2009;Buishand et al., 2008;Wadsworth and Tawn, 2012;Reich and Shaby, 2012). MSPs are a natural asymptotic model for block maxima, but can also be applied to peaks over a threshold using a censored likelihood (e.g., Huser and Davison, 2014;Reich et al., 2013). Exact inference for MSPs is challenging, and commonly used censored likelihood models for MSPs are also computationally intractable for all but a small number of spatial locations (Schlather, 2002;Kabluchko et al., 2009;Wadsworth andTawn, 2012, 2014;Wadsworth, 2015). Further, MSPs enforce asymptotic dependence among spatial locations (Huser and Wadsworth, 2019), an unreasonable assumption for environmental data that often has weakening spatial dependence with increasing extremeness. Alternatives and extensions to MSPs include process mixture models (Huser and Wadsworth, 2019;Majumder et al., 2022; and maxinfinitely divisible process (MIDP) models (Bopp et al., 2021), both of which can accommodate more flexible asymptotic regimes of tail dependence.
Climate-informed flood projections which consider non-stationarity is an ongoing area of research Condon et al., 2015;François et al., 2019;Schlef et al., 2018Schlef et al., , 2021Sankarasubramanian and Lall, 2003;Zhang et al., 2015;Bertola et al., 2019;Awasthi et al., 2022), but flood projections are not commonly studied as a spatial EVA problem. The intractability of common spatial EVA likelihoods pose computational challenges which make it difficult to fit realistic statistical models. For example, in a study of a large geographic region under a changing climate, it is unrealistic to assume stationarity in the degree of extremal dependence between nearby locations. Non-stationarity could appear due to dependence on variables which vary spatio-temporally, or due to physical considerations like topography. Recent work on incorporating non-stationarity in spatial EVA models include Wadsworth and Tawn (2022), which incorporates non-stationarity using the framework of Sampson and Guttorp (1992). They deform the coordinate system into one where the process is stationary; this approach, however, does not use covariates. Huser and Genton (2016) use covariates in the covariance structure of an MSP, extending the work of Paciorek and Schervish (2006). Chevalier et al. (2021) uses multidimensional scaling to capture regional variation in the asymptotic spatial dependence of an MSP, and Zhong et al. (2022) construct an MIDP which include covariates to capture spatiotemporal non-stationarities. Similarly, our work proposes a spatial EVA model that allows extremal dependence to vary over both space and time via climate covariates. While this model is flexible and intuitive, it is difficult to fit using standard computational methods.
Many of the modeling and computational limitations of extreme value theory have been addressed using deep learning. For example, (Cannon, 2010;Vasiliades et al., 2015;Shrestha et al., 2017;Pasche and Engelke, 2022;Richards and Huser, 2022) and the references therein use neural networks to obtain flexible regression frameworks relating covariates to extreme quantities. Similar to the application in this paper, Shrestha et al. (2017) use neural networks to model the dependence of extreme streamflow and precipitation and temperature, and then use these relationships with climate models to project future extreme streamflow events. Recently, Wilson et al. (2022) have used a convolutional neural network to regress spatial fields onto the parameters of an extreme value distribution. Computational limitations due to intractable likelihoods associated with spatial extreme value processes have also been addressed using deep learning. Lenzi et al. (2021); Sainsbury-Dale et al. (2022) replace maximum likelihood estimators with neural networks, while Majumder et al. (2022) develop synthetic likelihood functions by sampling from the spatial extreme value process with different parameter settings, and fitting these simulations with neural networks to learn an approximate likelihood function connecting the data with the model parameters.
In this work, we propose a non-stationary process mixture model (NPMM) for climate-informed estimation of extremal streamflow. We specify a statistical EVA model for annual streamflow maxima within the central US (CUS) region, and use downscaled and bias-corrected precipitation projections obtained from the Multivariate Adaptive Constructed Analogs (MACA) dataset (Abatzoglou and Brown, 2012) as predictors. The NPMM addresses two important aspects of climate-informed EVA modeling. First, the process mixture model allows learning both the type and strength of asymptotic (in)dependence from the data by interpolating between a GP and an MSP. Second, the NPMM introduces non-stationarity by allowing the asymptotic regime of the spatial process to vary spatio-temporally as a function of precipitation for sub-regions within the CUS. Climate models not only consider different distributions of climate variables between historical and future time periods, they also consider multiple future pathways where model outputs diverge considerably as we extend the time horizon. Covariates allow us to accommodate potential changes in the spatial or marginal behavior or both for extreme streamflow under future climate projections which deviate from historical patterns. Inference for the NPMM is separated into density estimation and parameter estimation. The density estimation, used to approximate the intractable likelihood of the spatial process, is carried out using semiparametric quantile regression (SPQR) (Xu and Reich, 2021). The quantile process has a basis function representation, whose weights are estimated using a feed-forward neural network. The NPMM provides a flexible framework for incorporating covariates into the spatial process as well as the marginal distributions at each location, and we use it to project extremal streamflow for 2006-2035 informed by climate model precipitation under two different climate pathways.
The rest of the paper is organized as follows. We introduce the streamflow and precipitation datasets for the CUS region in Section 2. Section 3 presents the NPMM and discusses density estimation, parameter estimation, and tail behavior for the model. Density estimation using SPQR for the CUS locations is carried out in Section 4, and we conduct a simulation study to see how errors in density estimation affect parameter estimates. The analysis of extremal streamflow as a function of precipitation is presented in Section 5, along with future projections of extremal streamflow based on downscaled and bias-corrected climate model precipitation data. Section 6 concludes.
2 Hydroclimatic data for the Central US
Observed streamflow data
The USGS Hydro-Climatic Data Network (HCDN) (Lins, 2012) is a dataset of streamflow records within the United States and its Territories. The HCDN consists of locations that are minimally impacted by anthropogenic activity, making it suitable to study the effects of changing climate on streamflow. The HCDN has been used to study the effect of climatic variables on streamflow (Sankarasubramanian et al., 2001;Oh and Sankarasubrama- nian, 2012) and to study the change in extremal streamflow over time (Majumder et al., 2022). For studying water resources, the USGS divides the US into groups of nested Hydrologic Units, identified by Hydrologic Unit Codes (HUCs). The first level of classification divides the US into 21 regions, referred to as HUC-02 regions. Our study focuses on two specific HUC-02 regions for which we have a complete data record between 1972-2021; the lower half of Region 10, denoted as 10L, and Region 11. Together, they span a region in the Central US (CUS) that consist of 55 gauges spread across South Dakota, Nebraska, Colorado, Wyoming, Kansas, Iowa, Missouri, Arkansas, Oklahoma, New Mexico and Texas. Figure 1 plots the sample 0.99 quantile of annual streamflow maxima (measured in m 3 /s) over the last 50 years at each station. There is spatial variation in these data, with extremal streamflow increasing from west to the east.
Observed precipitation data
The CUS is characterized by severe convective storms (Risser et al., 2019;, and precipitation trends that could potentially influence flooding (Kunkel et al., 2020). (Condon et al., 2015) have used monthly average precipitation as a model predictor to project future floods, while (Awasthi et al., 2022) have used monthly total precipitation as predictors to project flood frequencies under near-term climate change. We refer the reader to (Awasthi et al., 2022) for further references regarding the use of precipitation and temperature as predictors of extremal streamflow. In this study, we use seasonal and annual precipitation means as predictors of annual extremal streamflow. Monthly precipitation data is sourced from the NOAA Monthly US Climate Gridded Dataset (NClimGrid) (Vose et al., 2014), which is based on the Global Historical Climatology Network (GHCN) dataset. NClimGrid data is available on a 5km × 5km grid, and for each of the 55 HCDN stations we use monthly precipitation for all NClimGrid cells for the corresponding basins as outlined in Figure 1.
The NClimGrid data are treated as covariates to estimate both the marginal parameters at each site as well as dependence parameters for the underlying spatial process. For our response variable Y t (s), the extremal streamflow for year t and location s, we consider the corresponding seasonal precipitations as covariates. Following (Awasthi et al., 2022), the seasons correspond to winter (JFM), spring (AMJ), summer (JAS), and autumn (OND), where JFM denotes the months of January-February-March, and so on. Figure 2a plots the mean seasonal precipitation across the 2 HUC-02 regions. Not only is there spatial variability within a season, we also see heterogeneity across seasons. The highest values are observed in the southeast, and lower values seen along the west. We also note that the spring season has the highest precipitation. Figure 2b plots the 0.99 quantile of the seasonal precipitation associated with the HCDN sites for each season. Additionally, we define the covariates Z 1t and Z 2t as the annual precipitation within HUC-02 Regions 10L and 11, respectively, which is computed as the total precipitation for all NClimGrid points for the corresponding region. Figure 3 plots a time series of annual precipitation for the 2 HUC-02 regions from 1972-2021. We note that Region 11, which is located in the southern part of the CUS, has higher precipitation than Region 10L. forcings (1950-2005) as well as future Representative Concentration Pathways (RCPs) RCP 4.5 and RCP 8.5 scenarios (2006-2100) from the native coarse resolution of the GCMs to a higher spatial resolution of 4km. RCP 4.5 assumes that total anthropogenic CO 2 will peak around 2040, and decline till 2080, whereas RCP 8.5 assumes that CO 2 concentrations continue to rise until the end of the century. MACA provides monthly precipitation (pr) as one of its outputs; we obtain both the historical runs for 1972-2005 for calibrating it to NClimGrid output, and use it to estimate extremal streamflow for the CUS from 2006-2035. The quality of the GCM model projections can vary according to variable, climate pathway, geographic region, and time horizon, and (Joyce and Coulson, 2020, page 9) provides criteria for selecting climate models. We choose 6 models for each RCP scenario following on the model rankings provided by Joyce and Coulson (2020); the chosen models are the top three ranked projections in terms of precipitation change (dry, wet) at mid-century (2041-2070) under the 2 scenarios (RCP 4.5, RCP 8.5) at the coterminous US scale. While our study focuses on projections up until 2035, our choice of models ensure that these results can be extended for longer durations, and account for model and scenario uncertainty. The models chosen for RCP 4.5 are IPSL-CM5A-MR, bcc-csm1-1-m, IPSL-CM5A-LR, CSIRO-Mk3-6-0, CNRM-CM5, and MRI-CGCM3; models chosen for RCP 8.5 are IPSL-CM5A-MR, HadGEM2-ES, inmcm4, CNRM-CM5, MRI-CGCM3, and CSIRO-Mk3-6-0. We refer readers to Joyce and Coulson (2020) for further comparisons of all 20 models. Figure 4 contains a schematic of the observational and climate model datasets used in this study, as well as the historical and projection time periods.
The GCM data do not have temporal correspondence; GCM output for the year 2005 is not a representation of the weather in 2005. Rather, GCM data for the historical and future periods are designed to approximate the distribution of the observed or forecast data for similar time periods. The lack of temporal correspondence makes it inappropriate to regress observed stream- flow onto modeled precipitation to estimate the relationship between these variables. However, given a model fit using temporally-correspondent observed precipitation and streamflow, estimates generated using bias-corrected GCM data as covariates can be used to compare the changes in the distribution across different time periods. Figure 5 plots mean seasonal precipitation over the CUS based on the CNRN-CM5 model for the GCM historical period of 1972-2005. This is one of the models projecting a wetter future, and the historical precipitation from this model is higher than the observed NClimGrid data in Figure 2a. The spatial patterns are broadly similar between the two datasets, and the GCM output needs to be calibrated to the observational data before it can be used as a covariate to model extremal streamflow.
The GCM output is calibrated to remove bias compared to the observed precipitation at each location. The GCM log-precipitation outputs during the historical period are calibrated to have the same sample mean and variance as the observed precipitation for the same time period. This log-linear transformation is estimated and applied separately for each HCDN station and each GCM forcing, and applied to the GCM precipitation projections as well. Precipitation for the 2 HCDN regions are also similarly calibrated. It is recommended that averages of the weather over at least 30 years be used to assess the climate. Hence, we consider a historical (baseline) period of 1972-2005 and a future projection period of 2006-2035, and study changes in the extremal quantiles of the distribution of predicted streamflow maxima for these two time periods.
3 Non-stationary Process Mixture Models for Spatial Extremes
The NPMM for block maxima
Let Y t (s) be the extreme observation at time t and spatial location s, for t ∈ {1, . . . , T } and s ∈ {s 1 , . . . , s n }. The observations Y t (s) are defined as block maxima, and are thus assumed to arise from a generalized extreme value (GEV) distribution with location µ t (s), scale σ t (s), and shape ξ t (s):
Y t (s) ∼ GEV{µ t (s), σ t (s), ξ t (s)}, whose cumulative distribution function (CDF) F t,s (y) := P[Y t (s) < y] is P Y t (s) < y = exp − 1 + ξ t (s) y − µ t (s) σ t (s) −1/ξt(s)
.
(1)
The CDF is defined over the set y : 1 + ξ t (s)(y − µ t (s))/σ t (s) > 0 . Denote Z jt , for j = 1, 2 and t = 1, . . . , 50, as the annual precipitation for the two HUC-02 regions (10L and 11) defined in Section 2. We define X 1t (s) as the annual precipitation for the HUC-02 region that location s belongs to, i.e.,
X 1t (s) = I{s ∈ Region 10L}Z 1t + I{s ∈ Region 11}Z 2t ,
where I(·) is the indicator function. Further, denote X it (s), i = 2, . . . , 5 and t = 1, . . . , 50 as the seasonal precipitation for site s at time t for the four seasons as defined in Section 2. We assume the GEV location parameters vary spatially and are dependent on precipitation, while the scale and shape parameters also vary spatially, i.e.,
µ t (s) = µ 0 (s) + 5 i=1 µ i (s)X it (s), σ t (s) = σ(s). ξ t (s) = ξ(s).(2)
The CDF transformed variables U t (s) := F t,s Y t (s) share common uniform marginal distributions but are spatially correlated; this transformation separates residual spatial dependence in U t (s) from the spatial dependence induced by spatial variation in the GEV parameters, which can be modeled using GP priors over s.
A spatial dependence model on U t (s) is obtained via the transformation U t (s) = G t,s V t (s) , such that V t (s) = δ t (s)g R R t (s) + (1 − δ t (s))g W W t (s) ,(3)
where R t (s) is a max-stable process (MSP), W t (s) is a Gaussian process (GP), and g R and g W are transformations to ensure that g R R t (s) and g W W t (s) both follow the standard exponential distribution. Without loss of generality, we assume that R t (s) has a marginal GEV(1, 1, 1) distribution and W t (s) has a marginal N(0, 1) distribution; the corresponding transformations are g R (r) = − log(1 − exp(−1/r)) and g W (w) = − log(1 − Φ(w)) for the standard normal CDF Φ(w). By construction, V t (s) follows a two-parameter hypoexponential distribution marginally, with CDF
G t,s (v) = 1 − 1 − δ t (s) 1 − 2δ t (s) e − 1 (1−δ t (s)) v + δ t (s) 1 − 2δ t (s) e − 1 δ t (s) v .(4)
The parameters δ t (s) ∈ [0, 1] are weight parameters that control the relative contribution of the two spatial processes at every site and time point. The spatial dependence model in (3) was originally introduced in (Majumder et al., 2022) where it assumed a constant value of δ t (s) = δ. In practice, however, it is reasonable to partition the sites into L regions such that sites within each partition share a common value of δ t (s) at any given time point t, with different partitions having potentially different values of δ t (s). Locations can be assigned to partitions based on underlying geophysical characteristics of the data, or clustered according to an appropriate distance metric. For streamflow data, the two HUC-02 regions (10L and 11) are considered partitions of the CUS. Thus L = 2 for our study, and we denote δ 1t and δ 2t as the weight parameters for these 2 partitions, i.e., δ t (s) = I{s ∈ Region 10L}δ 1t + I{s ∈ Region 11}δ 2t .
As with the marginal parameters, we assume δ 1t and δ 2t depend on partitionspecific covariates:
g −1 (δ it ) = β i0 + β i1 Z it , i = 1, 2,(5)
where g(·) is an appropriate link function, and Z it are the annual precipitation for the two HUC-02 regions as defined in Section 2. The variable δ it depends on time through the covariate Z it . Mixing the asymptotically dependent MSP with the asymptotically independent GP provides a rich model for spatial dependence, while the covariates help capture changes in the spatiotemporal dependence.
We model the correlation of the GP W t (s) using the isotropic poweredexponential correlation function
Cor W t (s 1 ), W t (s 2 ) = exp{−(h/ρ W ) α W } with distance h = ||s 1 −s 2 ||, smoothness α W ∈ (0, 2), and range ρ W > 0. The MSP R t (s) is assumed to have isotropic Brown-Resnick spatial dependence defined by the variogram γ(h) = (h/ρ R ) α R for smoothness α R ∈ (0, 2) and range ρ R > 0.
We also incorporate a nugget into the process mixture. We denote the proportion of the variance explained by the spatial process by r, and construct W t (s) and R t (s) as:
Cor W t (s 1 ), W t (s 2 ) = r · exp{−(h/ρ W ) α W } R t (s) = max{r · R 1t (s), (1 − r) · R 2t (s)}, where R 1t (s) is an MSP, and R 2t (s) iid ∼ GEV(1, 1, 1) distributed independently of R 1t (s).
We refer to this model as a non-stationary process mixture model (NPMM), with marginal parameters θ 1 = {µ 0 (s i ), ..., µ 5 (s i ), σ(s i ), ξ(s i ); i = 1 : n} and spatial dependence parameters θ 2 = {β 10 , β 11 , β 20 , β 21 , ρ R , α R , ρ W , α W , r}. Alternative spatial dependence structures are viable under the NPMM; in general, most spatial processes are compatible with the methodology presented in this work. For the purposes of this particular problem, we choose a relatively smooth spatial process, and aim to capture additional complexity using spatio-temporally varying coefficients (STVC) models Gelfand et al.
Asymptotic joint tail behavior for the NPMM
Extremal spatial dependence of the process at sites s 1 and s 2 is often measured using the conditional exceedance probability,
χ u (s 1 , s 2 ) := P{U (s 1 ) > u|U (s 2 ) > u},(6)
where u ∈ (0, 1) is a threshold. The random variables U (s 1 ) and U (s 2 ) are defined as asymptotically dependent if the limit
χ(s 1 , s 2 ) = lim u→1 χ u (s 1 , s 2 )(7)
is positive, and independent if χ(s 1 , s 2 ) = 0. To examine the model in a simpler case, we assume δ 1t to be the same for t = 1, . . . , T , and define δ i := δ it , i = 1, 2. We numerically approximate χ u (s 1 , s 2 ) for various values of u, δ 1 and δ 2 . We scale our region of interest and all 55 sites within it to fall within the unit square, and consider the extremal spatial dependence between a hypothetical pair of sites at a distance of h = 0.12 from each other. The value for h is chosen as the solution to:
h = max i=1:55 ||s i − s i * ||,
where a : b is used as shorthand notation for a, a + 1, . . . , b − 1, b, and s i * is the site closest to s i . In its original scale, this is equivalent to HCDN stations 218 km apart. Figure 6a plots the behavior of χ u (s 1 , s 2 ) for different (δ 1 , δ 2 ) pairs. Assuming an isotropic model, χ u (s 1 , s 2 ) is a function only of the distance h = ||s 1 − s 2 ||, and so we use the notation χ u (h) := χ u (s 1 , s 2 ). While χ u (h) depends on (δ 1 , δ 2 ) in our work, we suppress the dependence for notational convenience and instead use χ u (h) in the remainder of the text. As in (Huser and Wadsworth, 2019), we set the GP to have a correlation of 0.40, which is equivalent to fixing ρ W = 0.134 and ρ R = 0.19ρ W (see Section 4 for a discussion on the choice of ρ W and ρ R ), and computed the conditional exceedance probability for u = 0.9999. When δ 1 = δ 2 = δ, (Majumder et al., 2022) have shown using empirical studies that χ u (h) → 0 if δ < 0.5 and χ u (h) > 0 for δ > 0.5. An analytical result consistent with this finding was also derived for the case of a shared extremal process, i.e., for R(s 1 ) = R(s 2 ) = R, at which point we recovered the similar result from (Huser and Wadsworth, 2019). From Figure 6a, we can also see that χ u (h) → 0 when both δ 1 , δ 2 < 0.5. To understand the tail behavior of the process when δ 1 is high and δ 2 is low (and vice-versa), we consider the case where δ 1 = δ, δ 2 = 1−δ, for δ ∈ (0, 1). We find that χ(h) → 0 in this situation for all values of δ; this is verified empirically in Figure 6b where χ u (h) → 0 for different values of δ 1 and δ 2 . It also corresponds to the diagonal in Figure 6a which is shown to go to 0. This is intuitively reasonable; R(s) and W (s) are independent, and thus asymptotic dependence is only achieved if both sites have large delta and thus both sites allow substantial contribution for the asymptotically dependent process R(s). An analytical derivation of this result for the case of a shared extremal process is provided in A.
Density regression using Deep Learning for the NPMM
Assume the process is observed at n sites s 1 , ..., s n . We partition the parameters into those that affect the marginal distributions in (2), denoted θ 1 , and those that affect the spatial dependence, denoted θ 2 . Denoting Y (s i ) ≡ Y i and U i := F (Y i ; θ 1 ), we can express the joint distribution for all the observations using a change of variables, as:
f y (y 1 , ..., y n ; θ 1 , θ 2 ) = f u (u 1 , ..., u n ;
θ 2 ) n i=1 dF (y i ; θ 1 ) dy i .(8)
Model fitting for the NPMM is challenging due to the way the spatial dependence is specified; the joint distribution of the MSP R(s) is available only for a moderate number of locations, and working with the term f u (u 1 , ..., u n ; θ 2 ) in (8) analytically is not viable. As in (Majumder et al., 2022), the change of variables in (8) sets the process mixture component up for density estimation. The density estimation is carried out on a surrogate likelihood based on a Vecchia decomposition (Vecchia, 1988;Stein et al., 2004;Datta et al., 2016;Katzfuss and Guinness, 2021) of the joint distribution f u (u 1 , ..., u n ; θ 2 ),
f u (u 1 , ..., u n ; θ 2 ) = n i=1 f i (u i |θ 2 , u 1 , ..., u i−1 ) ≈ n i=1 f i (u i |θ 2 , u (i) ),(9)
for
u (i) = {u j ; j ∈ N i } and N i ⊆ {1, . . . , i − 1}.
The set of locations s (i) are analogously defined as s (i) = {s j ; j ∈ N i } and is referred to as the Vecchia neighboring set. The approximation therefore entails truncating the dependence that u i has on all its previous i − 1 ordered sites to instead consider dependence on only up to m sites, i.e., |N i | ≤ m. The first term of the approximation is the marginal density f 1 (u 1 |θ 2 ). The univariate conditional distribution terms on the right hand side of (9) do not have closed-form expressions. Density regression is carried out for each of the n − 1 terms separately using the semi-parametric quantile regression (SPQR) model introduced in (Xu and Reich, 2021):
f i (u i |x i , W) = K k=1 π ik (x i , W i )B k (u i ),(10)
for i = 2 : n, where π ik (x i , W i ) ≥ 0 are probability weights with K k=1 π ik (x i ) = 1 that depend on the parameters W i , and B k (u i ) ≥ 0 are M-spline basis functions that, by definition, satisfy B k (u)du = 1 for all k. The density regression model in (10) treats u (i) and θ 2 as features (covariates), denoted as x i , with u i being the corresponding response variable.
By increasing the number of basis functions K and appropriately selecting the weights π ik (x i ), the mixture distribution in (10) can approximate any continuous density function (e.g., Chui et al., 1980;Abrahamowicz et al., 1992) which makes it suitable for our application. The weights are modeled using a neural network (NN) with H hidden layers and a multinomial logistic (softmax) activation function on its output layer, i.e.,
π ik (x i , W i ) = f N N i (x i , W i ), for i = 2, . . . , n.(11)
Instead of using observational data, the weights are learned from training data generated from the process mixture model with parameters θ 2 ∼ p * , which can then be used to obtain realizations from the process over sites s i and s (i) from the model conditioned on θ 2 . Specifically, we generate data at the observed spatial site with the same Vecchia neighbor sets as the problem at hand. We select the design distribution p * with support covering the range of plausible values for θ 2 . Given these values, we generate U (s) at s ∈ {s i , s (i) }. The feature set x i for modeling u i at site s i thus contains the spatial parameters θ 2 , and process values at the neighboring sites U (s (i) ). Since we can generate arbitrarily large datasets from the design distribution, model fit is not affected by any data scarcity of the observations. This is important since NNs often require large datasets for training.
The NNs have their own hyperparameters which cannot be estimated directly but rather need to be tuned. These include the network architecture -the number of hidden layers (H), the size of each hidden layer (L h ), the number of basis functions (K), the activation function (ψ(·)), etc. They also include NN training parameters like the learning rate, batch size, number of epochs, and early stopping criteria. We have assumed the same network architecture for all the NNs in (11), with the exception of differences due to a smaller Vecchia neighboring set for the first few sites. The model is fit using the R (R Core Team, 2022) package SPQR (Xu and Majumder, 2022) whose inbuilt cross-validation functions can be used to tune the NN hyperparameters. Once the weights have been learned, applying the NN to the approximate likelihood is straightforward, and the Vecchia approximation ensures that the computational burden increases linearly in the number of spatial locations. Algorithm 1 outlines the local SPQR approximation.
Parameter estimation using MCMC for the NPMM
Given the approximate model in (8)-(9) for f y with an SPQR approximation for the spatial dependence f u , a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods is used for parameter estimation. We use Metropolis updates for both θ 1 and θ 2 . For an STVC model with local GEV coefficients for site i, we update parameters {µ t (s i ), σ(s i ), ξ(s i )} as a block sequentially by site, and exploit the Vecchia approximation to use only terms in the likelihood corresponding to sites which appear either as the response variable in the Vecchia approximation or in a Vecchia neighbor set. The coefficients (β i0 , β i1 ) are updated as a block for each i, and the weight parameters δ ti , i = 1, 2 Algorithm 1 Local SPQR approximation Require: sites s 1 , . . . , s n with sets of neighboring locations s (1) , . . . , s (n) Require: Design distribution p * , training sample size (10) using SPQR i ← i + 1 end while are updated as a result of that. All Metropolis updates are tuned to give acceptance probabilities of 0.4, and convergence is diagnosed based on the visual inspection of the trace plots.
N i ← 2 while i ≤ n do j ← 1 while j ≤ N do Draw values of θ 2j ∼ p * Generate U j (s) at s ∈ {s i , s (i) } given θ 2j using (3) Define features x ij = (θ 2j , u (i)j ), where u (i)j = {U j (s); s ∈ s (i) } j ← j + 1 end while solveŴ i ← argmax W N j=1 f i (u ij |x ij , W) for f i (u i |x i , W) defined in
Density Estimation for CUS Sites and Numerical Studies
Density estimation for the NPMM only requires knowledge of the spatial configuration of sites, and a reasonable design distribution. We consider the n = 55 HCDN sites with the domain scaled to the unit square for convenience. Sites are assigned to the two different regions with their own weight parameters based on which HUC-02 region they belong to. Figure 7 plots the distribution of the 55 sites, alongside site 45 and its Vecchia neighboring set of m = 15 neighbors. We assume a common smoothness parameter α R = α W = 1 to put the 2 spatial processes on the same scale. A further assumption is made to improve model identifiability; we parameterize ρ W and ρ R to have the same effective range. We define the effective range as the distance at which the GP correlation reaches 0.05 and the extremal co- efficient χ for the MSP reaches 0.05. In (Majumder et al., 2022), this was achieved by setting ρ = ρ W and ρ R = 0.19ρ.
Local SPQR model architecture: For density estimation, we fit local SPQR models for each site s i , i = 2 : 55. The local SPQR models have identical architectures for each site with 2 hidden layers with 30 and 20 neurons respectively, 15 output nodes, a learning rate of 0.01, and 100 epochs with a batch size of 1000. The model architecture was chosen by comparing the log-likelihood of fitted models with different architectures, and are very similar to those used in (Majumder et al., 2022). The number of output nodes in this case correspond to the number of basis functions used to approximate the true conditional density. While the analytical form of the conditional densities are not available for the NPMM, Majumder et al. (2022) was able to study this for a GP, which is equivalent to setting δ 1t = δ 2t = 0. The conditional densities are univariate Gaussian and analytically available in this case; 10-15 output nodes were found to be sufficient in modeling the conditional density, with higher values leading to random fluctuations in the estimated approximated conditional density. We train the SPQR models with the design distribution p * , generating 2 × 10 6 samples uniformly from for goodness of fit and variable importance plot (right) for the local SPQR model. δ 12 in the variable importance plots is defined as log δ 1 − log δ 2 .
ρ, δ 1t , δ 2t , r ∈ (0, 1) with all parameters independent of each other. Choosing p * ∼ U (0, 1) for each of the parameters allows us to explore the parameter space uniformly within its support. The response u i is a function of exactly one of δ 1t or δ 2t depending on which region s i belongs to. The other weight parameter is relevant for density estimation only if one of the neighbors is in the other region. Thus, some sites require exactly one of δ 1t or δ 2t , while other sites require both. To ensure consistent dimensions of the feature vector across locations as well as identifiability of the weight parameters, we define δ y and δ y to be the weight parameters corresponding to the response and the neighbors respectively. If all neighbors belong to the same region as the response, δ y = δ y . Finally, we define δ (y) = log δ y − log δ y , which is non-zero only if some of the neighbors belong to a different region from the response. Instead of using δ 1t and δ 2t , we use δ y and δ (y) as covariates for density estimation. Algorithm 1 is then used to fit the local SPQR models. Figure 8a plots the probability integral scores for the local SPQR model at site 45; the scores falling along the Y = X line (partially visible, in red) suggests a good model fit. Figure 8b plots the variable importance scores for the two nearest neighbors (denoted as X 1 and X 2 ) as well as the spatial parameters of the process. The neighbors have the highest importance across the quantiles, and the spatial parameters are important covariates for Numerical study for parameter estimation: Before using the density estimates on the observed annual streamflow maxima data, we consider 3 scenarios with different spatial and marginal GEV parameters in order to ascertain how the density-estimation errors propagate to parameter-estimation errors. We assume δ 1t and δ 2t are independent of each other and depend on time by means of a probit link function, i.e.,
Φ −1 (δ it ) = β i0 + β i1 Z it , i = 1, 2.(12)
As covariates, we use Z 1t = (t −t)/10 and Z 2t = Z 1t − 0.05, where t = 1972 + t − 1 andt is the mean of t. For all cases, the location parameters of the GEV are assumed to depend on a covariate as in (2), and we use X t (s) = Z 1t for all sites. Within a scenario, each site is assumed to have the same marginal GEV parameters. Table 1 lists the true parameter values for the 3 scenarios. We generated 60 datasets for each scenario. Each dataset contains 50 independent realizations of the NPMM at the 55 sites shown in Figure 7. For priors, we select µ 0 , µ 1 , log(σ) ∼ Normal(0, 10 2 ), ξ ∼ Normal(0, 0.25 2 ), β 10 , β 11 , β 20 , β 21 ∼ Normal(0, 1), and ρ, r ∼ Uniform(0, 1). We approximate the posterior using MCMC with 11,000 iterations and Metropolis candidate distributions tuned to have an acceptance probability of around 0.4. After discarding the first 1,000 iterations as burn-in, we compute posterior means and 95% confidence intervals for each parameter based on the remaining samples. The posterior distributions of β 10 , β 11 , β 20 , and β 21 are used to evaluate the posterior distributions of the mean of δ 1t and δ 2t . Figure 9 plots the sampling distribution of the posterior mean estimator of model parameters of interest and provides the empirical coverage of 95% posterior intervals at the bottom of each panel. Posterior estimators of the GEV parameters have relatively little bias and nominal coverage. To evaluate the posterior of δ 1t and δ 2t , we plot δ i = 1 50 50 t=1 δ it , for i = 1, 2. Estimation of δ i proves more challenging, likely due to the spatial configuration of the locations, and the relatively low importance of δ y and δ (y) in the SPQR model. While bias and variability are higher for the spatial parameters, but our methods can still distinguish between the asymptotic regimes of δ 1 and δ 2 .
Analysis of Extremal Streamflow in Central US
Model description
We assign an STVC model to each of the marginal GEV parameters. The responses are modeled as
Y t (s) ∼ GEV µ 0 (s) + 5 j=1 µ j (s)X jt (s), σ(s), ξ(s) .(13)
The intercept process µ 0 (s) is assigned a GP prior with nugget effects to allow local heterogeneity:
µ 0 (s) =μ 0 (s) + e 0 (s) e 0 (s) iid ∼ Normal(0, v µ 0 ) µ 0 (s) ∼ GP(β µ 0 , τ 2 µ 0 K(s, s )), where K(s, s ) = exp{−||s − s ||/ρ µ 0 } β µ 0 ∼ Normal(0, 10 2 ), τ 2 µ 0 , v 2 µ 0 iid ∼ IG(0.1, 0.1), log ρ µ 0 ∼ Normal(−2, 1),
where IG(·, ·) is the inverse-Gamma distribution. The slopes µ j (s), j = 1 : 5, the log-scale log σ(s), and the shape ξ(s) are modeled similarly using GPs. The STVC parameters are denoted as θ 3 = {β µ 0 , τ 2 µ 0 , ρ µ 0 , . . . , β ξ , τ 2 ξ , ρ ξ }. For the residual model, we use the process mixture model in Section 3 for spatial dependence and assume independence across years. The simplifying assumptions that we make for the MSP R t (s) and the GP W t (s) in Section 4 are maintained here. The model for the weight parameters δ 1t and δ 2t along with the priors for all parameters in θ 2 are written as:
Φ −1 (δ it ) = β i0 + β i1 Z it , i = 1, 2 β 10 , β 11 , β 20 , β 21 ∼ Normal(0, 1) ρ, r ∼ Uniform(0, 1).
Note that the priors on the spatial ranges are for the scaled domain. In addition, both the streamflow and precipitation data have been rescaled to [0,1] to ensure stable estimates. Figure 10a plots χ u (h) for rank-standardized streamflow data as a function of u for different values of h. The rank standardization ensures a Uniform(0, 1) marginal distribution at each location. The plot suggests an asymptotically independent process. Figure 10b plots the mean of the annual variograms of the streamflow data. It shows a range of over 500 km, as well as the presence of a nugget effect.
Extremal streamflow patterns within the CUS
The local SPQR models from Section 4 are used to compute the density estimates. For parameter estimation, we ran 2 independent MCMC chains for 15,000 iterations each, discarding the first 5,000 of each chain as burn-in. Table 2 lists the posterior means and standard deviations of the spatial parameters based on the 20,000 post-burn-in posterior samples. The posterior mean of r suggests the presence of a nugget effect. For the posterior distribution of δ i , i = 1, 2, we evaluate 1 50 50 t=1 δ it for each posterior MCMC sample of (β i0 , β i1 ) and interpret it as the average value of the weight parameter conditioned on precipitation. The empirical 95% confidence intervals for the slope parameters β i1 are β 11 ∈ (−0.76, 2.56), and β 21 ∈ (−1.18, 2.47); both intervals include zero, suggesting that the weight parameters for the two regions which ascribe the asymptotic regime of extremal streamflow are not associated with the annual regional precipitation. To understand changes in δ it as a function of annual precipitation, we evaluate it for 1972-2021 based on the posterior means of (β i0 , β i1 ). Figure 11 plots the value of the weight parameter for the 2 HUC-02 regions from 1972-2021. Region 11 which corresponds to the lower half of the CUS, has a higher estimate of the weight parameter than region 10L. The sites in region 11 tend to show asymptotic dependence, while the sites in region 10L vary between asymptotic dependence and asymptotic dependence in different years. The estimates are quite different for the 2 regions and vary quite a lot from year to year for region 10L, indicating the appropriateness of the non-stationarity assumption of the spatial process. Figure 12 shows the goodness of fit of the marginal GEV models, based on maximum likelihood estimates (MLE) computed individually at each site in 12a, and estimates derived using the posterior means of the NPMM in 12b. Visual inspection suggests that the NPMM provides overall better fits compared to independent MLE despite having more bias. We compared the standard errors of the GEV parameters based on the MLE with the posterior standard deviation of the GEV parameters based on the NPMM, and found that the latter was always lower; see Table 4 in B.3 for more details. Since extremes data is often scarce by definition, pooling in spatial information across sites is crucial for improving model fits and in turn getting valid inference. The posterior means and standard deviations for the components of θ 3 are also provided in Table 5. Figure 13 shows the posterior means of the slope parameters for each HCDN site. Since each site has 5 slopes corresponding to the annual precipitation as well as 4 seasonal precipitations, we focus on the largest slope parameters for each site, corresponding to the season where precipitation has the most significant effect on streamflow. Figure 13a plots the slope parameter for the most significant season at each site; the colors denote the magnitudes of the slope parameter for the most significant season and the shapes denote the season it corresponds to. We see that most of the points are for spring (AMJ), and exactly one location (in region 11) is affected more by annual precipitation than by seasonal precipitation. To assess the strength of the significance for all seasons, we computed the posterior probability of each slope parameter being greater than 0, i.e., P[µ j (s) > 0] for j = 2 : 5. The slope corresponding to the annual precipitation is not considered in this case, and all 55 sites had at least one seasonal slope with a non-zero probability. we count the number of seasons where P[µ j (s) > 0] > 0.90 for each site; the resulting plot is presented in Figure 13b. The lower values in the plot indicate that precipitation has a large effect on streamflow only in spe- cific seasons, whereas the higher values signify that maximum streamflow is a function of seasonal precipitation from different seasons for different years. We refer the reader to (Awasthi et al., 2022) for further discussion on the seasonal/annual effect of precipitation on streamflow for different regions.
Considering that most of these sites have 3-4 significant seasons as shown in Figure 13b, it is reasonable to conclude that maximum streamflow is affected by the convective storms that occur in the CUS and the associated precipitation. Finally, Figure 14 contains posterior means of the scale and shape parameters of all the watersheds. Both parameters are spatially dependent over the CUS region. We also note that the posterior means of the shape parameter are positive for 54 of the 55 sites.
Annual streamflow maxima projections under RCP 4.5 and RCP 8.5
We used the bias-corrected MACA precipitation data for six RCP 4.5 and six RCP 8.5 models as specified in Section 2.3 to get future projections of streamflow. RCP 4.5, RCP 8.5) and each GCM model listed in Section 2.3, we use seasonal and annual bias-corrected GCM precipitation to generate estimates of annual streamflow maxima using the following steps:
1. Draw 1000 post burn-in samples θ
(1) 1 , . . . , θ from the posterior distribution of the GEV parameters. Repeat steps 2-3 for each sample and each scenario 2. Use bias-corrected GCM precipitation as covariates in (2) to get GEV distribution location, scale, and shape parameter estimates independently for each site 3. Solve for and compute the 0.90 and 0.99 quantiles of the distribution of streamflow maxima over the entire time period.
The quantiles for each site, given the GEV parameters for the entire time period (34 years for the historical period and 30 years for the projection period), can be computed by univariate root-finding algorithms. This gives us 1000 extremal quantile estimates of the distribution of annual streamflow maxima at each of the 55 sites for the historical, RCP 4.5, and RCP 8.5 scenarios. For each of the two RCP scenarios and two extremal quantile levels, we study and report the percent change in annual streamflow maxima compared to the historical period. Figures 15-16 show the mean percentage change in the observed 0.90 and 0.99 quantiles under the RCP 4.5 and RCP 8.5 projections, averaged over the 1000 estimates. The top row of each figure consists of models that project a wetter future, whereas the bottom row consists of models which project a drier future. In both figures, the triangles denote an increase, while the circles denote a decrease in annual streamflow maxima at each location. Four of the six models under each RCP scenario are common to both scenarios -CNRM-CM5, CSIRO-Mk3-6-0, and MRI-CGCM3 which project wetter futures, and IPSL-CM5A-MR, which projects a drier future. The output based on these four models can thus be compared across scenarios and quantile levels. For a particular quantile level, with the exception of CSIRO-Mk3-6-0, the wetter models predict more positive changes under RCP 8.5 than under RCP 4.5 Similarly, IPSL-CM5A-MR predicts more negative changes under RCP 8.5 than under RCP 4.5. CSIRO-Mk3-6-0 shows noticeable differences between RCP 4.5 and RCP 8.5 with several locations that show positive change under one scenario showing negative change under the other and vice versa. We expect further divergences between scenarios if this study is extended to a longer time horizon due on the underlying assumptions of the 2 RCP scenarios.
Looking across quantile levels, we note that the 0.99 quantiles in Figure 16 estimate lower levels of change, ranging from -2.7%-8.4%, compared to the 0.90 quantiles in Figure 15 which show changes between -10.3%-12.3%. However, the number of locations with positive changes are the same or higher when we go from the 0.90 quantile to the 0.99 quantile under both RCP scenarios. Under RCP 4.5, all six models estimate that more than 50% locations have increased flow for both quantile levels, with values ranging from 51% -93%. For RCP 8.5, four out of the six models estimate more than half the locations to have increased streamflow. In this case, the values range from 22% -91%; in all cases, CSIRO-Mk3-6-0 gives the lowest estimates. Table 3 shows the expected number of locations jointly above the threshold for the historical and projection periods based on Monte-Carlo simulations from the fitted spatial model using bias-corrected GCM precipitation data. The values in parentheses correspond to the minimum and maximum of the estimates obtained from the 6 GCM models used. If the probability of exceeding the threshold at all locations were independent, the number of locations above the threshold would follow a Binomial distribution with parameters n = 55 and probability 1 − u, for the two cases of u = 0.90 and u = 0.99. In turn, the expected number of locations above the threshold under the independence assumption would be 5.5 and 0.55 respectively. For both the historical and projection periods, estimates from most of the models are higher than estimates from the independence assumption. In particular, both the mean and median for each of the 8 sets of values are higher than what we would get from an independence assumption. Overall, this suggests that concurrent extremal streamflow at multiple locations is likely to keep occurring into the near future.
Discussion
In this paper, we propose a non-stationary process mixture model for spatial extreme value analysis. The marginal distributions of the process are GEV, while the spatial dependence is specified as an interpolation of a GP and an MSP indexed by a weight parameter which is allowed to vary spatio-temporally, introducing non-stationarity. Similarly, STVC specifications used for the marginal parameters make the model flexible in terms of learning different spatio-temporal patterns present in the data. The model is an extension of the (stationary) process mixture model introduced in Majumder et al. (2022). The intractable joint likelihood for the spatial model is approximated using a Vecchia decomposition, and is learned using the density regression approach of Xu and Reich (2021). The density regression estimates a quantile process for the approximate likelihood whose weights are obtained from a neural network by maximizing the approximate likelihood.
We use the NPMM to provide climate informed near-term projections of annual streamflow maxima for the central US region. The CUS is affected by convective storms and, therefore, any projections of streamflow should take into account seasonal and annual precipitation over the region. The CUS is divided into two HUC-02 regions, and the asymptotic regime for the regions are estimated independently. We used observed NClimGrid precipitation data to fit the model for annual streamflow maxima. The means of the posterior distribution puts Region 11 in the south to be asymptotically dependent for all 50 years, whereas Region 10L in the north is asymptotically dependent for 39 out of the 50 years and asymptotically independent for the rest of the years. Region 10L also has more variability in the posterior mean of asymptotic (in)dependence parameter from year to year. These inter-year differences and differences between the regions justify the appropriateness of the non-stationary assumptions we make about the process. While we find no significant linear relationship between region-wide precipitation and the logit of weight parameter, we note that region 11 has higher precipitation compared to region 10L. Afterwards, bias-corrected GCM precipitation pro-jections are used as covariates to obtain streamflow estimates for the future period of 2006-2035 and compared against the historical period of 1972-2005. Based on our projections, both the magnitude of extremal streamflow as well as the number of locations which are concurrently affected by these extreme events are likely to increase in the near-term future.
Future research will focus on generating long-term climate-informed projections. The current work considers only seasonal precipitation as covariates, as adding too many variables adversely affected MCMC convergence. However, longer-term precipitation as well as temperature can affect streamflow Awasthi et al. (2022), and we would like to incorporate additional covariates in future work. Learning the weight parameter proves more challenging for the NPMM compared to its stationary equivalent; we hope to improve the spatial dependence in the model as well as the estimates obtained from it by incorporating network structure, as has been done for both max-stable (Asadi et al., 2015) and Gaussian (Santos-Fernandez et al., 2022) processes. Relaxing the simplifying assumptions on the smoothness and range parameters would improve the spatial modeling, but could make estimation more difficult as more variables are free to vary. Finally, the synthetic likelihood approach to density estimation for spatial processes using deep learning is not specific to the NPMM, and we would like to explore its performance and properties for other spatial extremes models.
A Derivation of Conditional Exceedance for a Common Spatial Process (Majumder et al., 2022) derived χ(s 1 , s 2 ) for a process mixture model with a common MSP R(s 1 ) = R(s 2 ) = R and W (s 1 ) and W (s 2 ) are independent.
We extend that and focus on a specific case where δ 1 = δ and δ 2 = 1 − δ, where δ 1 , δ 2 are defined as in Section 3.2. This is a convenient case because with this restriction both sites have the same marginal distribution. This case is also interesting because it illustrates the behavior of the process when the two sites are in different asymptotic regimes. We denote (1). Under these conditions, the joint survival probability is as follows:
g W {W (s 1 )} = W * 1 , g W {W (s 2 )} = W * 2 , g R (R) = R * for convenience. By assumption W * 1 , W * 2 , R * iid ∼ ExponentialP r[Y 1 > y, Y 2 > y] = P r[δ 1 R * + (1 − δ 1 )W * 1 > y, δ 2 R * + (1 − δ 2 )W * 2 > y] = E R * P r W * 1 > y − δr 1 − δ P r W * 1 > y − (1 − δ)r δ |R * = r .
Defining r 1 := (y − δr)/(1 − δ) and r 2 := (y − (1 − δ)r)/δ, we get P r[Y 1 > y, Y 2 > y] = E R * P r{W * 1 > r 1 }P r{W * 2 > r 2 }I{r 1 > 0, r 2 > 0} + E R * P r{W * 1 > r 1 }I{r 1 > 0, r 2 < 0} + E R * P r{W * 2 > r 2 }I{r 1 < 0, r 2 > 0} + E R * I{r 1 < 0, r 2 < 0} . (14) Note that:
r 1 > 0, r 2 > 0 =⇒ r < min(y/δ, y/(1 − δ)) r 1 > 0, r 2 < 0 =⇒ (y/(1 − δ) < r < y/δ)I{δ < 0.5} r 1 < 0, r 2 > 0 =⇒ (y/δ < r < y/(1 − δ))I{δ > 0.5} r 1 < 0, r 2 < 0 =⇒ r > max(y/δ, y/(1 − δ))
We first assume that δ < 0.5. Denoting the four terms on the right-hand side of (14) as J 1 , J 2 , J 3 , and J 4 , we first see that J 3 = 0. The remaining three terms are computed individually.
J 1 = exp −y 1 δ + 1 1 − δ y/1−δ 0 exp r δ 1 − δ + 1 − δ δ exp{−r}dr = exp −y 1 δ + 1 1 − δ y/1−δ 0 exp 3δ 2 − 3δ + 1 δ(1 − δ) r dr = k 1 exp −y 1 δ + 1 1 − δ exp 3δ 2 − 3δ + 1 δ(1 − δ) 2 y − 1 = k 1 exp − y 1 − δ exp − 1 − 2δ (1 − δ) 2 y − exp − y δ ,
where k 1 is the appropriate constant arising from the integration.
J 2 = exp − y 1 − δ y/δ y/1−δ exp r δ 1 − δ − 1 dr = k 2 exp − y 1 − δ exp − 1 − 2δ δ(1 − δ) y − exp − 1 − 2δ (1 − δ) 2 y ,
where k 2 is the appropriate constant that arises from the integration. Finally, J 4 = exp{−y/δ}.
The marginal survival probability can be obtained from (4). We denote it as M , where
M = δ 1 − 2δ exp{− y δ } − 1 − δ 1 − 2δ exp{− y 1 − δ }. J 2 M = k 2 exp − 1−2δ δ(1−δ) y − exp − 1−2δ (1−δ) 2 y δ 1−2δ exp −y 1−2δ δ(1−δ) − 1−δ 1−2δ =⇒ lim y→∞ J 2 M = 0
Finally,
J 4 M = exp − y δ δ 1−2δ exp{− y δ } − 1−δ 1−2δ exp{− y 1−δ } = exp −y 1−2δ δ(1−δ) δ 1−2δ exp −y 1−2δ δ(1−δ) − 1−δ 1−2δ =⇒ lim y→∞ J 4 M = 0.
∴ χ(s 1 , s 2 ) = 0.
Next, consider the case of δ > 0.5. We see that the term J 2 in (14) is 0. Like before, we simplify the remaining 3 terms.
J 1 = exp −y 1 δ + 1 1 − δ y/δ 0 exp r δ 1 − δ + 1 − δ δ exp{−r}dr = exp −y 1 δ + 1 1 − δ y/δ 0 exp 3δ 2 − 3δ + 1 δ(1 − δ) r dr = k 3 exp −y 1 δ + 1 1 − δ exp 3δ 2 − 3δ + 1 δ 2 (1 − δ) y − 1 = k 3 exp − y δ exp − 2δ − 1 δ 2 y − exp − y 1 − δ ,
where k 3 is the appropriate constant from the integration. We note the symmetry between J 1 for δ < 0.5 and J 1 computed for δ > 0.5. It is straightforward to show that lim y→∞ J 1 /M = 0 in this case as well. It follows by symmetry that lim y→∞ J 4 /M = 0 for δ > 0.5. Finally, we verify the behavior for J 3 : where k 4 is the appropriate constant for integration. Thus, lim y→∞ J 3 /M = 0 due to its symmetry with J 2 . Therefore, for δ ∈ (0, 0.5) ∪ (0.5, 1), χ(s 1 , s 2 ) = 0.
J 3 = exp − y δ y/1−δ y/δ exp r 1 − δ δ − 1 dr = k 4 exp − y δ exp − 2δ − 1 δ(1 − δ) y − exp − 2δ − 1 δ 2 y ,
B Computational Details
B.1 Asymptotic joint tail behavior Figure 17 depicts the behavior of χ u (0.12) at the 0.9999 quantile for two related models, which relax our current model assumption of ρ R = 0.19ρ W . In Figure 17a, we assume that ρ R = ρ W . This increases the range of χ u (0.12) as more extremal dependence is introduced. In Figure 17b, we replace the MSP with a GEV(1,1,1) distribution, which makes this equivalent to the model presented in Huser and Wadsworth (2019). This has the maximum amount of extremal dependence among this class of models by construction, which is reflected in the high range of χ u (0.12). However, for both cases, the same behavior holds for different values of δ 1 and δ 2 , with asymptotic dependence only if both sites are in an asymptotic dependence regime. Vecchia neighboring set can have up to 15 neighbors. Location 16 is the first location which has all 15 neighbors, and locations 35 and 50 also have all 15 neighbors. For all 4 locations, the nearest neighbor has the highest importance. The importance of the second neighbor varies from location to location. We have found this to be a function of the spatial configurationin particular, how far the second neighbor is from the response site, as well as how close it is to the other neighbors. It could also depend on whether it belongs to the same region or not. The remainder of the neighbors show similar behavior with a steady drop off of their importances, and have thus been omitted for clarity. It is interesting to note the fundamentally different way the neighbors affect the quantiles of the response compared to how the spatial parameters affect them. The neighbors have the largest effect around the median and drop off in importance near the extreme quantiles at both ends. The spatial parameters have the opposite behavior. We also note that δ y is more important to the response compared to δ (y) . This is to be expected since δ y is the mixing parameter that corresponds to the response, while δ (y) can be either 0 or a function of the other mixing parameter that does not directly affect the response. Table 4 provides a comparison of the marginal GEV model fits across locations based on the NPMM, as well as independent MLE estimates of the GEV parameters. The MLE estimates were used as initial values in our MCMC; we computed the standard errors for each variable and averaged it across the 55 sites. For the NPMM estimate, we compute the posterior SD of each parameter based on 20,000 post-burn in samples, and similarly average over all 55 locations. In all cases, the NPMM has lower spread, suggesting a better model fit. Finally, Table 5 provides posterior means and SD of the GP parameters associated with the STVC model for the marginal parameters described in Section 5.1.
B.2 Variable importance plots
B.3 Parameter estimates
Figure 1 :
1HCDN sites in HUC-02 regions 10L and 11: Locations and 0.99 quantiles of annual streamflow maxima (in m 3 /s) at 55 HCDN stations overlaid on an elevation map (in m) of the central United States region bounded by [−107, −90] × [30, 44]. The two large polygons within the figure correspond to regions 10L (top) and 11 (bottom), and the smaller polygons correspond to the HCDN basins that each station measures streamflow for.
quantiles of seasonal precipitation associated with each HCDN site.
Figure 2 :
2Seasonal distribution of NClimGrid precipitation for 1972-2021: Seasons are specified on the top right of each panel and defined as winter (JFM), spring (AMJ), summer (JAS), and autumn (OND).
Figure 3 :
3Time series of annual NClimGrid precipitation (in mm) from 1972-2021 for the 2 HUC-02 regions of the CUS. Values represent an average over all grid cells within the corresponding region. 2.3 Global Climate Model output of future precipitation While Global Climate Models (GCMs) do not produce streamflow estimates, they provide precipitation variables which we use to predict extremal streamflow. The Multivariate Adaptive Constructed Analogs (MACA 1 ) dataset Abatzoglou and Brown (2012) is a statistical downscaling method for GCMs. MACA downscales the model output from 20 GCMs of the Coupled Model Inter-Comparison Project 5 (CMIP5) Taylor et al. (2012) for historical GCM
Figure 4 :
4Datasets used in the study, with periods of availability and usage details.
Figure 5 :
5Mean seasonal precipitation (in mm) over the CUS based on the CNRM-CM5 model for the GCM historical period of 1972-2005. Seasons are specified on the top right of each panel and defined as winter (JFM), spring (AMJ), summer (JAS), and autumn (OND).
(2003);Majumder et al. (2022) on the components of θ 1 . χ u (0.12) for different values of δ with δ 1 = δ and δ 2 = 1 − δ.
Figure 6 :
6Empirical χ u (h) where h = 0.12 for the process mixture model as a function of δ 1 and δ 2 for sites corresponding to the HCDN stations in the CUS.
Figure 7 :
7Sites used to fit SPQR models: Distribution of 55 watershed locations scaled to the unit square. Squares and circles denote the 2 different regions. The blue square corresponds to site 45, and the red squares and circles correspond to its Vecchia neighboring set.
Figure 8 :
8Model diagnostics for local SPQR fit at site 45: Q-Q plot (left)
one of the extremal quantiles. The remaining neighbors have significantly lower importances compared to the first few and have been omitted from the plot for clarity; their exact magnitude often depends on the spatial configuration of the locations. Variable importance plots for additional locations are provided in B.2.
Figure 9 :
9Marginal and spatial parameter estimates: Sampling distribution of the posterior mean for GEV and spatial parameters for the three simulation scenarios. The red dots are the true values, and empirical coverage of the 95% intervals are provided at the bottom of each plot.
variogram for annual maximum streamflow, averaged over 50 years of data.
Figure 10 :
10Spatial behavior of annual maximum streamflow in terms of the conditional exceedance and the variogram.
Figure 11 :
11Posterior means of δ 1 corresponding to region 10L and δ 2 corresponding to region 11, computed annually for 1972-2021.
Figure 12 :
12Goodness of fit for the marginal distributions of annual streamflow maxima: Q-Q plots for MLE computed independently at all sites (left), and based on posterior means from the NPMM (right).
of seasons with for which µ(s) > 0 with high probability.
Figure 13 :
13Posterior means of slope parameters for annual streamflow maxima: Estimates of µ(s) = max(µ j (s)) for i = j(1)4 corresponding to the 4 seasons with shapes denoting the season with the highest slope value (left), and number of seasons (excluding annual) where P[µ(s) > 0] > 0.90 (right).
of shape parameter ξ(s).
Figure 14 :
14Posterior means of scale and shape parameters of annual streamflow maxima.
Future projections for MACA (and CMIP5 data in general) begin from 2005, and we consider the distribution of extremal streamflow forecasts for the period from 2006-2035. Each CMIP5 model also provides historical runs alongside the projections, from which we estimate the distribution of extremal streamflow for 1972-2005. For each scenario (historical, Change in projected streamflow based on RCP 8.5.
Figure 15 :
15Percentage change in observed 0.90 quantile under RCP 4.5 and RCP 8.5 for 2006-2035, compared to the baseline period of 1972-2005. Triangles denote positive values and circles denote negative values. Change in projected streamflow based on RCP 8.5.
Figure 16 :
16Percentage change in observed 0.99 quantile under RCP 4.5 and RCP 8.5 for 2006-2035, compared to the baseline period of 1972-2005. Triangles denote positive values and circles denote negative values.
) χ u (h) when ρ R = ρ W . ) χ u (h) when R t (s) = R.
Figure 17 :
17Empirical χ u (h) for different combinations of δ 1 and δ 2 with threshold u = 0.9999 under two different model specifications.
Figure 18 presents
18variable importance plots for 4 different locations within our study area. Location 11 does not have a full suite of neighbors, as the
Figure 18 :
18Variable importance (VI) plots based on SPQR output for 4 different locations within the CUS.
Table 1 :
1True parameter values for the 3 simulation study scenarios.
Table 2 :
2Posterior means and standard deviations (SD) of spatial parameters of the NPMM based on MCMC.Parameter Mean SD Parameter Mean SD
β 10
-0.15 0.33
ρ
0.25
0.49
β 11
0.92
0.86
r
0.88
0.03
β 20
0.47
0.41
δ 1
0.53
0.10
β 21
0.65
0.94
δ 2
0.71
0.12
1
Table 3 :
3Measure of joint exceedance in projected streamflow maxima:Mean number of locations jointly above the 0.90 and 0.99 quantile thresholds. Values in parentheses represent the minimum and maximum projections from among the 6 models used in each scenario.u = 0.90
u = 0.99
RCP 4.5 RCP 8.5 RCP 4.5 RCP 8.5
1972-2005 (5.49,5.55) (5.49,5.55) (0.54,0.56) (0.54,0.56)
2006-2035 (5.49,5.54) (5.50,5.53) (0.54,0.56) (0.55,0.56)
Table 4 :
4Model fit diagnostics for marginal GEV parameters: Standard errors based on the maximum likelihood estimates of GEV distributions fitted independently at each location (MLE), and posterior standard deviations based on the process mixture model (NPMM). Values represent an average taken over all 55 locations.Parameter MLE NPMM Parameter MLE NPMM
µ 0
0.05
0.03
µ 1
0.17
0.09
µ 2
0.07
0.05
µ 3
0.09
0.06
µ 4
0.08
0.05
µ 5
0.07
0.05
σ
0.20
0.01
ξ
0.22
0.13
Table 5 :
5STVC parameter estimates: Mean and SD for the GP parameters for the marginal GEV parameters.Param. Mean SD Param. Mean SD Param. Mean SDβ µ0
-0.01
0.18
τ 2
µ0
0.19
0.04
ρ µ0
4.52
1.60
β µ1
-0.06
0.25
τ 2
µ1
0.26
0.08
ρ µ1
3.24
1.53
β µ2
0.20
0.29
τ 2
µ2
0.30
0.09
ρ µ2
2.86
1.46
β µ3
0.26
0.32
τ 2
µ3
0.33
0.11
ρ µ3
2.56
1.43
β µ4
0.06
0.24
τ 2
µ4
0.25
0.07
ρ µ4
3.50
1.55
β µ5
0.08
0.22
τ 2
µ5
0.23
0.06
ρ µ5
3.73
1.59
β σ
0.17
2.19
τ 2
σ
0.89
0.48
ρ σ
1.36
1.20
β ξ
0.33
0.69
τ 2
ξ
0.72
0.29
ρ ξ
1.57
1.14
https://www.climatologylab.org/maca.html
AcknowledgmentsThe authors thank Prof. Sankarasubramanian Arumugam of NC State University for discussion of the data and scope of the project.FundingThis work was supported by grants from the Southeast National Synthesis Wildfire and the United States Geological Survey's National Climate Adaptation Science Center (G21AC10045) and the National Science Foundation (DMS2152887, CBET2151651). Part of this research was performed while author Reetam Majumder was visiting the Institute for Mathematical and Statistical Innovation (IMSI), which is supported by the National Science Foundation (Grant No. DMS-1929348).The conditional exceedance probability χ(s 1 , s 2 ) can be expressed as:Each of the limits are evaluated individually:
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Intercomparison of Machine Learning Methods for Statistical Downscaling: The Case of Daily and Extreme Precipitation
13 Feb 2017 February 15, 2017
Thomas Vandal
Sustainability and Data Science Lab
Civil Engineering Dept
Northeastern University
Evan Kodra
risQ Inc
Auroop R Ganguly
Sustainability and Data Science Lab
Civil Engineering Dept
Northeastern University
Intercomparison of Machine Learning Methods for Statistical Downscaling: The Case of Daily and Extreme Precipitation
13 Feb 2017 February 15, 2017
Statistical downscaling of global climate models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in machine learning have not been explored. In this paper, we compare four fundamental statistical methods, Bias Correction Spatial Disaggregation (BCSD), Ordinary Least Squares, Elastic-Net, and Support Vector Machine, with three more advanced machine learning methods, Multi-task Sparse Structure Learning (MSSL), BCSD coupled with MSSL, and Convolutional Neural Networks to downscale daily precipitation in the Northeast United States. Metrics to evaluate of each method's ability to capture daily anomalies, large scale climate shifts, and extremes are analyzed. We find that linear methods, led by BCSD, consistently outperform non-linear approaches. The direct application of stateof-the-art machine learning methods to statistical downscaling does not provide improvements over simpler, longstanding approaches. * vandal.t@husky.neu.edu † evan.kodra@risq.io ‡ a.ganguly@neu.edu limiting models to coarse spatial and temporal scale projections. While the coarse scale projections are useful in understanding climate change at a global and continental level, regional and local understanding is limited. Most often, the critical systems society depends on exist at the regional and local scale, where projections are most limited. Downscaling techniques are applied to provide climate projections at finer spatial scales, exploiting GCMs to build higher resolution outputs. Statistical and dynamical are the two classes of techniques used for downscaling. The statistical downscaling (SD) approach aims to learn a statistical relationship between coarse scale climate variables (ie. GCMs) and high resolution observations. The other approach, dynamical downscaling, joins the coarse grid GCM projections with known local and regional processes to build Regional Climate Models (RCMs). RCMs are unable to generalize from one region to another as the parameters and physical processes are tuned to specific regions. Though RCMs are useful for hypothesis testing, their lack of generality across regions and extensive computational resources required are strong disadvantages.
Introduction
The sustainability of infrastructure, ecosystems, and public health depends on a predictable and stable climate. Key infrastructure allowing society to function, including power plants and transportation systems, are built to sustain specific levels of climate extremes and perform optimally in it's expected climate. Studies have shown that the changing climate has had, and will continue to have, significant impacts on critical infrastructure [13,31]. Furthermore, climate change is having dramatic negative effects to ecosystems, from aquatic species to forests ecosystems, caused by increases in greenhouse gases and temperatures [43,32,20]. Increases in frequency and duration of heat waves, droughts, and flooding is damaging public health [18,12].
Global Circulation Models (GCMs) are used to understand the effects of the changing climate by simulating known physical processes up to two hundred years into the future. The computational resources required to simulate the global climate on a large scale is enormous,
Statistical Downscaling
Statistical downscaling methods are further categorized into three approaches, weather generators, weather typing, and transfer functions. Weather generators are typically used for temporal downscaling, rather than spatial downscaling. Weather typing, also known as the method of analogues, searches for a similar historical coarse resolution climate state that closely represents the current state. Though this method has shown reasonable results [11], in most cases, it is unable to satisfy the non-stationarity assumption in SD. Lastly, transfer functions, or regression methods, are commonly used for SD by learning functional relationships between historical precipitation and climate variables to project high resolution precipitation.
A wide variety of regression methods have been applied to SD, ranging from Bias Correction Techniques to Artificial Neural Networks. Traditional methods include Bias Correction Spatial Disaggregation (BCSD) [46] and Automated Regression Based Downscaling (ASD) [21] and are the most widely used. BSCD assumes that the climate variable being downscaled is well simulated by GCMs, which often is not the case with variables such as precipitation [35]. Rather than relying on projections of the climate variable being downscaled, regression methods can be used to estimate the target variable. For instance, precipitation can be projected using a regression model with variables such as temperature, humidity, and sea level pressure over large spatial grids. High dimensionality of covariates leads to multicollinearity and overfitting in statistical models stemming from a range of climate variables over three dimensional space. ASD improves upon multiple linear regression by selecting covariates implicitly, using covariate selection techniques such as backward stepwise regression and partial correlations. The Least Absolute Shrinkage and Selection Operator (Lasso), a widely used method for high dimensional regression problems through the utilization of a l1 penalty term, is analogous to ASD and has shown superior results in SD [42,19]. Principle component analysis (PCA) is another popular approach to dimensionality reduction in SD [39,14,24], decomposing the features into a lower dimensional space to minimize multicollinearity between covariates. PCA is disadvantaged by the inability to infer which covariates are most relevant to the problem, steering many away from the method. Other methods for SD include Support Vector Machines (SVM) [14], Artificial Neural Networks (ANNs) [40,8], and Bayesian Model Averaging [49].
Many studies have aimed to compare and quantify a subset of the SD models presented above by downscaling averages and/or extremes at a range of temporal scales. For instance, Burger et al. presented an intercomparison on five state-of-the-art methods for downscaling temperature and precipitation at a daily temporal resolution to quantify extreme events [5]. Another recent study by Gutmann et al. presented an intercomparison of methods on daily and monthly aggregated precipitation [17]. These studies present a basis for comparing SD models by downscaling at a daily temporal resolution to estimate higher level climate statistics, such as extreme precipitation and long-term droughts. In this paper we follow this approach to test the applicability of more advanced machine learning models to downscaling.
Multi-task Learning for Statistical Downscaling
Traditionally, SD has focused on downscaling a locations independently without accounting for clear spatial dependencies in the system. Fortunately, numerous machine learning advances may aid SD in exploiting such dependencies. Many of these advancements focus on an approach known as multi-task learning, aiming to learn multiple tasks simultaneously rather than in isolation. A wide variety of studies have shown that exploiting related tasks through multitask learning (MTL) greatly outperforms single-task models, from computer vision [48] to biology [27]. Consider the work presented by [10] in which increasing the number of tasks leads to more significant feature selection and lower test error through the inclusion of task relatedness and regularization terms in the objective function. MTL has also displayed the ability to uncover and exploit structure between task relationships [50,6,2].
Recently Goncalves et al. presented a novel method, Multi-task Sparse Structure Learning (MSSL), [16] and applied it to GCM ensembles in South America. MSSL aims to exploit sparsity in both the set of covariates as well as the structure between tasks, such as set of similar predictands, through alternating optimization of weight and precision (inverse covariance) matrices. The results showed significant improvements in test error over Linear Regression and Multi-model Regression with Spatial Smoothing (a special case of MSSL with a pre-defined precision matrix). Along with a lower error, MSSL captured spatial structure including long range teleconnections between some coastal cities. The ability to harness this spatial structure and task relatedness within a GCM ensembles drives our attention toward MTL in other climate applications.
Consider, in SD, each location in a region as a task with an identical set of possible covariates. These tasks are related through strong unknown spatial dependencies which can be harnessed for SD projections. In the common high dimensional cases of SD, sparse features learned will provide greater significance as presented by [10]. Furthermore, the structure between locations will be learned and may aid projections. MSSL, presented by [16], accounts for sparse feature selection and structure between tasks.
In this study we aim to compare traditional statistical downscaling approaches, BCSD, Multiple Linear Regression, Lasso, and Support Vector Machines, against new approaches in machine learning, Multi-task Sparse Structure Learning and Convolutional Neural Networks (CNNs). During experimentation we apply common training architectures as part of the automated statistical downscaling framework. Results are then analyzed with a variety of metrics including, root mean Square error (RMSE), bias, skill of estimating underlying distributions, correlation, and extreme indices.
Statistical Downscaling Methods
Bias Corrected Spatial Disaggregation
BCSD [46] is widely used in the downscaling community due to its simplicity [1,5,45,30]. Most commonly, GCM data is bias corrected followed by spatial disaggregation on monthly data and then temporally disaggregated to daily projections. Temporal disaggregation is performed by selecting a month at random and adjusting the daily values to reproduce it's statistical distribution, ignoring daily GCM projections. Thrasher et al. presented a process applying BCSD directly to daily projections [41], removing the step of temporal disaggregation. We the following steps with overlapping a reanalysis dataset and gridded observation data.
1) Bias correction of daily projections using observed precipitation. Observed precipitation is first remapped to match the reanalysis grid. For each day of the year values are pooled, ± 15 days, from the reanalysis and observed datasets to build a quantile mapping. With the quantile mapping computed, the reanalysis data points are mapped, bias corrected, to the same distribution as the observed data. When applying this method to daily precipitation detrending the data is not necessary because of the lack of trend and is therefore not applied.
2) Spatial disaggregation of the bias-corrected reanalysis data. Coarse resolution reanalysis is then bilinearly interpolated to the same grid as the observation dataset. To preserve spatial details of the fine-grained observations, the average precipitation of each day of the year is computed from the observation and set as scaling factors. These scaling factors are then multiplied to the daily interpolated GCM projections to provide downscaled GCM projections.
Automated Statistical Downscaling
ASD is a general framework for statistical downscaling incorporating covariate selection and prediction [21]. Downscaling of precipitation using ASD requires two essential steps: 1. Classify rainy/non-rainy days (≥ 1mm), 2. Predict precipitation totals for rainy days. The predicted precipitation can then be written as:
E[Y ] = R * E[Y |R] where R = 0, if P(Rainy) < 0.5 1, otherwise(1)
Formulating R as a binary variable preserves rainy and non-rainy days. We test this framework using five pairs of classification and regression techniques.
Multiple Linear Regression
The simplicity of Multiple Linear Regression (MLR) motivated its use in SD, particularly as part of SDSM [44] and ASD [21]. To provide a baseline relative to the following methods, we apply a variation of MLP using PCA. As discussed previously, PCA is implemented to reduce the dimensionality of a high dimensional feature space by selecting the components that account for a percentage (98% in our implementation) of variance in the data. These principle components, X, are used as inputs to classify and predict precipitation totals. We apply a logistic regression model to classify rainy versus non-rainy days. MLP is then applied to rainy days to predict precipitation amounts,
Y :β = argmin β Y − Xβ(2)
This particular formulation will aid in comparison to [14] where PCA is coupled with an SVM.
Elastic-Net
Covariate selection can be done in a variety of methods, such as backward stepwise regression and partial correlations. Automatic covariate selection through the use of regularization terms, such as the L1/L2 norms in the statistical methods Lasso [42], Ridge [23], and Elastic-Net [51]. Elastic-Net uses a linear combination of L1/L2 norms which we will apply in this intercomparison. Given a set of covariates X and observations Y , Elastic-net is defined as:
β = argmin β Y − Xβ 2 2 +λ1 β 1 +λ2 β 2 2(3)
The L1 norm forces uninformative covariate coefficients to zero while the L2 norm enforces smoothness while allowing correlated covariates to persist. Cross-validation is applied with a grid-search to find the optimal parameter values for λ1 and λ2. High-dimensional Elastic-Net is much less computational than stepwise regression techniques and most often leads to more generalizable models. A similar approach is applied to the classification step by using a logistic regression with an L1 normalization term. Previous studies have considered the use of Lasso for SD [19] but to our knowledge, none have considered Elastic-Net.
Support Vector Machine Regression
Ghosh et al. introduced a coupled approach of PCA and Support Vector Machine Regression (SVR) for statistical downscaling [15,14]. The use of SVR for downscaling aims to capture non-linear effects in the data. As discussed previously, PCA is implemented to reduce the dimensionality of a high dimensional feature space by selecting the components that account for a percentage (98% in our implementation) of variance in the data. Following dimensionality reduction, SVR is used to define the transfer function between the principle components and observed precipitation. Given a set of covariates (the chosen principle components) X ∈ R n×m and Y ∈ R n with d covariates and n samples, the support vector regression is defined as [37]:
f (x) = d i=1 wi × K(xi, x) + b(4)
where K(xi, x) and wi are the kernel functions and their corresponding weights with a bias term b. The support vectors are selected during training by optimizing the number of points from the training data to define the relationship between then predictand (Y ) and predictors (X). Parameters C and ǫ are set during training, which we set to 1.0 and 0.1 respectively, corresponding to regularization and loss sensitivity. A linear kernel function is applied to limit overfitting to the training set. Furthermore, support vector classifier was used for classification of rainy versus non-rainy days.
Multi-task Sparse Structure Learning
Recent work in Multi-task Learning aims to exploit structure in the set of predictands while keeping a sparse feature set. Multi-task Sparse Structure Learning (MSSL) in particular learns the structure between predictands while enforcing sparse feature selection ( [16]). Goncalves et al. presented MSSL's exceptional ability to predict temperature through ensembles of GCMs while learning interesting teleconnections between locations ( [16]). Moreover, the generalized framework of MSSL allows for implementation of classification and regression models. Applying MSSL to downscaling with least squares regression (logistic regression for classification), we denote K as the number of tasks (observed locations), n as the number of samples, and d as the number of covariates with predictor X ∈ R n×d , and predictand Y ∈ R n×K . As proposed in [16], optimization over the precision matrix, Ω, is defined as
min W ,Ω≻0 1 2 K k=1 XW k − Y k 2 2 − K 2 log|Ω| + T r(W ΩW T ) + λ Ω 1 +γ W 1(5)
where W ∈ R d×K is the weight matrix and Ω ∈ R K×k is an inverse precision matrix. The L1 regularization parameters λ and γ enforce sparsity over Ω and W . Ω represents the structure contained between the high resolution observations. Alternating minimization is applied to (5) 1.
Initialize
Ω 0 = I k , W 0 = 0 dXk 2. for t=1,2,3,.. do W t+1 |Ω t = min W 1 2 K k=1 X k W k − Y k 2 2 +T r(W ΩW T ) + γ W 1 (6) Ω t+1 |W t+1 = min Ω T r(W ΩW T ) − K 2 log|Ω| + λ Ω 1(7)
6 and 7 are independently approximated through Alternating Direction Method of Multipliers (ADMM). Furthermore, by assuming the predictors of each task is identical (as it is for SD), 6 is updated using Distributed-ADMM across the feature space [4].
GCM Convolution Convolution Pooling
Pooling Fully Connected Figure 1: Given a set of GCM inputs Y , the first layer extracts a set of feature maps followed by a pooling layer. A second convolution layer is then applied to the reduced feature space and pooled one more time. The second pooling layer is then flattened and fully connected to the high resolution observations.
MSSL enforces similarity between rows of W by learning the structure Ω. For example, two locations which are nearby in space may tend to exhibit similar properties. MSSL will the exploit these properties and impose similarity in their corresponding linear weights. By enforcing similarity in linear weights, we are encouraging smoothness of SD projections between highly correlated locations. L1 regularization over W and Ω jointly encourages sparseness and does not force structure. The parameters encouraging sparseness, γ and λ, are chosen from a validation set using the grid-search technique. These steps are applied for both regression and classification.
Convolutional Neural Networks
Artificial Neural Networks (ANN) have been widely applied to SD with mixed results [40,36,5], to name a few. In the past, ANNs had difficulty converging to a local minimum. Recent progress in deep learning has renewed interested in ANNs and are beginning to have impressive results in many applications, including image classification and speech recognition [29,22,3]. In particular, Convolutional Neural Networks (CNNs) have greatly impacted computer vision applications by extracting, representing, and condensing spatial properties of the image [29]. SD may benefit from CNN advances by learning spatial representations of GCMs. Though CNNs rely on a high number of samples to reduce overfitting, dropout has been shown to be an effective method of reducing overfitting with limited samples [38]. We note that the number of observations available to daily statistical downscaling may cause overfitting.
CNNs rely on two types of layers, a convolution layer and a pooling layer. In the convolution layer, a patch of size 3 × 3 is chosen and slid with a stride of 1 around the image. A non-linear transformation is applied to each patch resulting in 8 filters. Patches of size 2 × 2 are then pooled by selecting the maximum unit with a stride of 2. A second convolution layer with a 3 × 3 patch to 2 filters is followed by a max pooling layer of size 3 × 3 with stride 3. The increase of pooling size decreases the dimensionality further. The last pooling layer is then vectorized and densely connected to each high resolution location. This architecture is presented in Figure 1.
Multiple variables and pressure levels from our reanalysis dataset are represented as channels in the CNN input. Our CNN is trained using the traditional back propagation optimization with a decreasing learning rate. During training, dropout with probability 0.5 is applied the densely connected layer. This method aims to exploit the spatial structure contained in the GCM. A sigmoid function is applied to the output layer for classification. To our knowledge, this is the first application of CNNs to statistical downscaling.
Bias Corrected Spatial Disaggregation with MSSL
To further understand the use of BCSD in Statistical Downscaling, we propose a technique to estimate the errors introduced in BCSD. As presented above, BCSD utilizes a relatively simple quantile mapping approach to statistical downscaling following by interpolation and spatial scaling. Following the BCSD estimates of the observed climate, we compute the presented errors, which may be consistent and have a predictive signal. Modeling such errors using the transfer function approaches above, such as MSSL, may uncover this signal and improve BCSD projections. To apply this technique, the following steps are taken:
1. Apply BCSD to the coarse scale climate variable and compute the errors.
2. Excluding a hold out dataset, use MSSL where they predictand is the computed errors and the predictands are from a different set of climate variables, such as Temperature, Wind, Sea Level Pressure, etc.
3. Subtract the expected errors modeled by step 2 from BCSD projections in step 1.
The transfer function learned in step 2 is then applicable to future observations.
Data
The Northeastern United States endures highly variable season and annual weather patterns. Variable climate and weather patterns combined with diverse topology provides difficulty in regional climate projection. Precipitation in particular varies heavily in frequency and intensity seasonally and annually [26]. We choose this region to provide an in-depth comparison of statistical downscaling techniques for daily precipitation and extremes.
United States Unified Gauge-Based Analysis of Precipitation
High resolution gridded precipitation datasets often provide high uncertainties due to a lack of gauge based observations, poor quality control, and interpolation procedures. Fortunately, precipitation gauge data in the continental United States is dense with high temporal resolution (hourly and daily). The NOAA Climate Prediction Center CPC Unified Gauge-Based Analysis of Precipitation exploits the dense network of rain gauges to provide a quality controlled high resolution (0.25 • by 0.25 • ) gridded daily precipitation dataset from 1948 to the current date. State of the art quality control [7] and interpolation [47] techniques are applied giving us high confidence in the data. We select all locations within the northeastern United States watershed.
NASA Modern-Era Retrospective Analysis for Research and Applications 2 (MERRA-2)
Reanalysis datasets are often used as proxies to GCMs for statistical downscaling when comparing methods due to their low resolution gridded nature with a range of pressure levels and climate variables. Uncertainties and biases occur in each dataset, but state-of-the-art reanalysis datasets attempt to mitigate these issues. NASA's MERRA-2 reanalysis dataset [34] was chosen after consideration of NCEP Reanalysis I/II [25] and ERA-Interm [9] datasets. [28] showed the reduced bias of MERRA and ERA-Interm over NCEP Reanalysis II, which is most often used in SD studies. MERRA-2 provides a significant temporal resolution from 1980 to present with relatively high spatial resolution (0.50 • by 0.625 • ). Satellite data provided by NASA's GEOS-5 project in conjunction with NASA's data assimilation system when producing MERRA-2 [34]. Only variables available from the CCSM4 GCM model are selected as covariates for our SD models. Temperature, vertical wind, horizontal wind, and specific humidity are chosen from pressure levels 500hpa, 700hpa, and 850hpa. At the surface level, temperature, sea level pressure, and specific humidity are chosen as covariates. To most closely resemble CCSM4, each variable is spatially upscaled to 1.00 • to 1.25 • at a daily resolution. A large box centralized around the Northeastern Region ranging from 35 • to 50 • latitude and 270 • to 310 • longitude is used for each variable. When applying the BCSD model, we use a spatially upscaled Land Precipitation MERRA-2 Reanalysis dataset at a daily temporal resolution. Bilinear interpolation is applied over the coast to allow for quantile mapping of coastal locations as needed.
Experiments and Evaluation
In-depth evaluation of downscaling techniques is crucial in testing and understanding their credibility. The implicit assumptions in SD must be clearly understood and tested when applicable. Firstly, SD models assume that the predictors chosen credibly represent the variability in the predictands. This assumption is partially validated through the choice of predictors presented above, which physically represents variability of precipitation. The remainder of the assumption must be tested through experimentation and statistical tests between downscaled projections and observations. The second assumption then requires the statistical attributes of predictands and predictors to be valid outside of the data using for statistical modeling. A hold out set will be used to test the feasibility of this assumption at daily, monthly, and annually temporal resolutions. Third, the climate change signal must be incorporated in the predictands through GCMs. Predictands chosen for this experiment are available through CMIP5 CCSM4 simulations. It is understood that precipitation is not well simulated by GCMs and therefore not used in ASD models [35].
To test these assumptions, we provide in-depth experiments, analysis, and statistical metrics for each method presented above. The years 1980-2004 are used from training and years 2005-2014 are used for testing, taken from the overlapping time period of MERRA-2 and CPC Precipitation. For each method (excluding the special case of BCSD), we chose all covariates from each variable, pressure level, and grid point presented above, totaling 12,781 covariates. Each method applies either dimensionality reduction or regularization techniques to reduce complexity of this high dimensional dataset. Separate models are trained for each season (DJF, MAM, JJA, SON) and used to project the corresponding observations. Analysis and evaluation of downscaled projections aim to cover three themes:
1. Ability to capture daily anomalies.
2. Ability to respond to large scale climate trends on monthly and yearly temporal scales.
3. Ability to capture extreme precipitation events.
Similar evaluation techniques were applied in recent intercomparison studies of SD [5,17].
Evaluation of daily anomalies are tested through comparison of bias (Projected -Observed), Root Mean Square Error (RMSE), correlations, and a skill score [33]. The skill score presented by [33] measures how similar two probability density functions are from a range of 0 to 1 where 1 corresponds to identical distributions. Statistics are presented for winter (DJF), summer (JJA), and annually to understand season credibility. Statistics for spring and fall are computed but not presented in order to minimize overlapping climate states and simply results. Each of the measures are computed independently in space then averaged to a single metric. Large scale climate trends are tested by aggregating daily precipitation to monthly and annual temporal scales. The aggregated projections are then compared using Root Mean Square Error (RMSE), correlations, and a skill score as presented in [33]. Due to the limited number of data points in the monthly and yearly projections, we estimate each measure using the entire set of projections and observations. Climate indices are used for evaluation of SD models' ability to estimate extreme events. Four metrics from ClimDEX (http://www.clim-dex.org), chosen to encompass a range of extremes, will be utilized for evaluation, as presented by Bürger [5]. Metrics will be computed on observations and downscaled estimates followed by annual (or monthly) comparisons. For example, correlating the maximum number of consecutive wet days per year between observations and downscaled estimates measures each SD models' ability to capture yearly anomalies. A skill score will also be utilized to understand abilities of reproducing statistical distributions.
Results
Results presented below are evaluated using a hold-out set, years 2005-2014. Each model's ability to capture daily anomalies, long scale climate trends, and extreme events are presented. Our goal is to understand a SD model's overall ability to provide credible projections rather than one versus one comparisons, therefore statistical significance was not computed when comparing statistics.
Daily Anomalies
Evaluation of daily anomalies depends on a model's ability to estimate daily precipitation given the state of the system. This is equivalent to analyzing the error between projections and observations. Four statistical measures are used to evaluate these errors: bias, Pearson Correlation, skill score, and root mean square error (RMSE), as presented in Figure 2, Figure 3, and Table 1). All daily precipitation measures are computed independently in space and averaged to provide a single value. This approach is taken to summarize the measures as simply as possible. Figure 2 shows the spatial representation of annual bias in Table 1. Overall, methods tend underestimate precipitation annually and seasonally with only PCASVR overestimating. BCSD-MSSL shows the lowest annual and summer bias and second lowest winter bias. BCSD is consistently under projects daily precipitation, but by modeling the possible error with MSSL, bias is reduced. PCAOLS and ELNET are less biased compared to MSSL. CNN has a strong tendency underestimate precipitation. Figure 2 shows consistent negative bias through space for BCSD, ELNET, PCAOLS, MSSL, and CNN while PCASVR shows no discernible pattern.
Correlation measures in Table 1 presents a high linear relationship between projections and observations for the models ELNET (0.64 annually) and MSSL (0.62 annually). We find that BCSD has a lower correlation even in the presence of error correction in BCSD-MSSL. PCASVR provides low correlations, averaging 0.33 annually, but PCAOLS performs substantially better at 0.55.
The skill score is used to measure a model's ability to reproduce the underlying distribution of observed precipitation where a higher value is better between 0 and 1. BCSD, MSSL, and PCASVR have the largest skill scores, 0.93, 0.92, and 0.91 annually. We find that modeling the errors of BCSD decreases the ability to replicate the underlying distribution. The more basic linear models, PCAOLS and ELNET, present lower skill scores. The much more complex CNN model has difficulty replicating the distribution.
RMSE, presented in Figure 3 and Table 1, measures the overall ability of prediction by squaring the absolute errors. The boxplot in Figure 3, where the box present the quartiles and whiskers the remaining distributions with outliers as points, shows the distribution of RMSE annually over space. The regularized models of ELNET and MSSL have similar error distributions and outperform others. CNN, similar to its under performance in bias, shows a poor ability to minimize error. The estimation of error produced by BCSD-MSSL aids in lowering the RMSE of plain BCSD. PCAOLS reasonably minimizes RMSE while PCASVR severely under-performs compared to all other models. Regression models applied minimize error during optimization while BCSD does not. Seasonally, winter is easier to project with summer being a bit more challenging.
Large Climate Trends
Analysis of a SD model's ability to capture large scale climate trends can be done by aggregating daily precipitation to monthly and annual temporal scales. To increase the confidence in our measures, presented in Table II and Figures 4 and 5, we compare all observations and projections in a single computation, rather than separating by location and averaging. Table 2 and Figure 4 show a wide range of RMSE. A clear difficulty in projecting precipitation Table 3: Statistics for ClimDEX Indices: For each model's downscaled estimate we compute four extreme indices, consecutive wet days (CWD), very heavy wet days (R20), maximum 5 day precipitation (RX5day), and daily intensity index (SDII), for each location. We then compare these indices to those extracted from observations to compute correlation and skill metrics.
in the fall, October in particular, is presented by each time-series in Figure 4. The difference in overall predictability relative to RMSE between the models is evident. BCSD and BCSD-MSSL have significantly lower monthly RMSEs compared to the others. Annually, BCSD-MSSL reduced RMSE by 25% compared to plain BCSD. The linear models, ELNET, MSSL, and PCAOLS, have similar predictability while the non-linear models suffer, CNN being considerably worse. The skill scores in Table 2 show more difficulty in estimating the annual distribution versus monthly distribution. On a monthly scale BCSD and BCSD-MSSL skill scores outperform all other models but BCSD suffers slightly on an annual basis. However, BCSD-MSSL does not lose any ability to estimate the annual distribution. PCAOLS annual skill score is remarkably higher than the monthly skill score. Furthermore, the three linear models outperform BCSD on an annual basis. PCASVR's skill score suffers on an annual scale and CNN has no ability to estimate the underlying distribution.
Correlation measures between the models and temporal scales show much of the same. BCSD has the highest correlations in both monthly ( 0.85) and yearly ( 0.64) scales while BCSD-MSSL are slightly lower. CNN correlations fall just behind BCSD and BCSD-MSSL. PCASVR fails with correlation values of 0.22 and 0.18. ELNET has slightly higher correlations in relation to MSSL and PCAOLS.
Extreme Events
A SD model's ability to downscale extremes from reanalysis depends on both the response to observed anomalies and ability to reproduce the underlying distribution. Resulting correlation measures present the response to observed anomalies, shown in Figure 6 and Table 3. We find that BCSD has higher correlations for three metrics, namely consecutive wet days, very heavy wet days, and daily intensity index along with a similar results from 5-day maximum precipitation. Furthermore, modeling BCSD's expected errors with BCSD-MSSL decreases the ability to estimate the chosen extreme indices. Non-linear methods, PCASVR and CNN, suffer greatly in comparison to more basic bias correction and linear approaches. The linear methods, PCAOLS, ELNET, and MSSL, provide similar correlative performance.
A skill score is used to quantify each method's ability to estimate an indices statistical distribution, presented in Table 3. Contrary to correlative results, PCASVR outperforms the other methods on two metrics, very heavy wet days and daily intensity index, with better than average scores on the other two metrics. BCSD also performs reasonably well in terms of skill scores while BCSD-MSSL suffers from the added complexity. MSSL estimates the number of consecutive wet days well but is less skilled on other metrics. The very complex CNN model has little ability to recover such distributions. Figure 6 displays a combination of correlative power and magnitude estimate of the daily intensity index. The SDII metric is computed from total annual precipitation and number of wet days. A low SDII metric corresponds to either a relatively large number of estimated wet days or low annual precipitation. We find that the on average methods underestimate this intensity. Based on Figure 5 we see that CNN severely underestimates annual precipitation, causing a low SDII. In contrast, PCASVR overestimates annual precipitation and intensity.
Inconsistent results of PCASVR and CNN indicates that capturing non-linear relationships is outweighed by overfitting. However, BCSD and linear methods are more consistent throughout each metric.
Discussion and Conclusion
The ability of statistical downscaling methods to produce credible results is necessary for a multitude of applications. Despite numerous studies experimenting with a wide range of models for statistical downscaling, none have clearly outperformed others. In our study, we experiment with the off-the-shelf applicability of machine learning advances to statistical downscaling in comparison to traditional approaches.
Multi-task Sparse Structure learning, an approach that exploits similarity between tasks, was expected to increase accuracy beyond automated statistical downscaling approaches. We find that MSSL does not provide improvements beyond ELNET, an ASD approach. Furthermore, the parameter set, estimated through cross-validation, attributed no structure aiding prediction.
The recent popularity in deep learning along with it's ability to capture spatial information, namely Convolutional Neural Networks, motived us to experiment with basic architectures for statistical downscaling. CNNs benefit greatly by implicitly learning abstract non-linear spatial features based on the target variable. This approach proved to poorly estimate downscaled estimates relative to simpler methods. We hypothesize that implicitly learning abstract features rather than preserving the granular feature spaced caused poor performance. More experimentation with CNNs in a different architecture may still provide valuable results.
BCSD, a popular approach to statistical downscaling, outperformed the more complex models in estimating underlying statistical distributions and climate extremes. In many cases, correcting BCSD's error with MSSL increased daily correlative performance but decreased skill of estimating the distribution. From this result, we can conclude that a signal aiding in prediction was lost during quantile mapping, interpolation, or spatial scaling. Future work may study and improve each step independently to increase overall performance.
Of the seven statistical downscaling approaches studied, the traditional BCSD and ASD methods outperformed non-linear methods, namely Convolutional Neural Network and Support Vector regression, while downscaling daily precipitations. We find that BCSD is skilled at estimating the statistical distribution of daily precipitation, generating better estimates of extreme events. The expectation of CNN and MSSL, two recent machine learning advances which we found most applicable to statistical downscaling, to outperform basic modeled proved false. Improvements and customization of machine learning methods is needed to provide more credible projections.
MERRA-2 climate reanalysis datasets used were provided by the Global Modeling and Assimilation Office at NASA's Goddard Space Flight Center. The CPC Unified Gauge-Based Analysis was provided by NOAA Climate Prediction Center.
Figure 2 :
2Each map presents the spatial bias, or directional error, of the model. White represents no bias produced by the model while red and blue respectively show positive and negative biases.1. CWD -Consecutive wet days ≥ 1mm 2. R20 -Very heavy wet days ≥ 20mm 3. RX5day -Monthly consecutive maximum 5 day precip 4. SDII -Daily intensity index = Annual total / precip days ≥ 1m
Figure 3 :
3Root mean square error (RMSE) is computed for each downscaling location and method. Each boxplot presents the distribution of all RMSEs for the respective method. The box shows the quartiles while the whiskers shows the remaining distribution, with outliers displayed by points.
Figure 4 :
4The average root mean square Error for each month with each line representing a single downscaling model.
Figure 5 :Figure 6 :
56Annual precipitation observed (x-axis) and projected (y-axis) for each model is presented along with the corresponding Pearson Correlation. Each point represents a single location and year. The daily intensity index (Annual Precipitation/Number of Precipitation Days) averaged per year.
Table 1 :
1Daily statistical metrics averaged over space for annual, winter, and summer projections.
Bias measures the directional error from each model. Correlation (larger is better) and RMSE (lower
is better) describe the models ability to capture daily fluxuations in precipitation. The skill score
statistic measure the model's ability to estimate the observed probability distribution.
Table 2 :
2Large Scale Projection Results: After aggregating daily downscaled estimates to monthly
and yearly time scales, RMSE and Skill are computed per location and averaged.
AcknowledgmentsThis work was funded by NSF CISE Expeditions in Computing award 1029711, NSF CyberSEES award 1442728, and NSF BIGDATA award 1447587.
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A convex formulation for learning task relationships in multi-task learning. Yu Zhang, Dit-Yan Yeung, Uncertainty in Artificial Intelligence. Yu Zhang and Dit-Yan Yeung. A convex formulation for learning task relationships in multi-task learning. Uncertainty in Artificial Intelligence, 2012.
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| sample_749 | 0.9517 | arxiv | |
RYTHMES D'ACTIVITE LOCOMOTRICE CHEZ DEUX INSECTES PARASITOIDES SYMPATRIQUES : EUPELMUS ORIENTALIS ET
Hyménoptère, EupelmidaeEupelmus Vuilleti
) A Ndoutoume-Ndong
Ecole Normale Supérieure de Libreville
B.P17009LibrevilleGabon
D Rojas-Rousse
Institut de Recherche sur la Biologie de l'Insecte, UPRESA-CNRS 6035, Faculté des Sciences, Parc de Grandmont
37200Tours
R Allemand
Laboratoire de Biométrie, Génétique et Biologie des populations de Lyon I -Université
RYTHMES D'ACTIVITE LOCOMOTRICE CHEZ DEUX INSECTES PARASITOIDES SYMPATRIQUES : EUPELMUS ORIENTALIS ET
1Eupelmidaeparasitoïdesactivité locomotricerythmevariations journalièresdécalage d'activitéinteractionscohabitation LOCOMOTOR ACTIVITY RHYTHMS IN TWO SYMPTRIC PARASITOID INSECTS : EUPELMUS ORIENTALIS AND EUPELMUS VUILLETI (HyménopteraEupelmudae)
Claude Bernard -43, Bd du 11 novembre 1918, 69622 Villeurbanne.
Mots clés : Eupelmidae, parasitoïdes, activité locomotrice, rythme, variations journalières, décalage d'activité, interactions, cohabitation.
LOCOMOTOR ACTIVITY RHYTHMS IN TWO SYMPTRIC PARASITOID INSECTS : EUPELMUS ORIENTALIS AND EUPELMUS VUILLETI (Hyménoptera, Eupelmudae).
Abstract : With an automatic image analysis device, we studied the temporal distribution of the locomotor activity of E orientalis and E vuilleti during 24 hours, and over several days to know whether the activity rhythms of these two Eupelmidae play a role in their competitive interactions. The analysis of locomotor activity rhythms of E. orientalis and E vuilleti shows that the locomotor activity of both species presents daily cyclic variations. These two
Eupelmidae have similar activity rhythms. Displacements of these parasitoïdes essentially take place during the photophase. But the activity of E vuilleti is earlier because the individuals of this species start their activity on average 4 to 5 hours earlier than those of E orientalis. E vuilleti begins displacements several hours before lighting whereas E orientalis is active only in the presence of the light. This shift of starting activity is thus a factor allowing these concurrent species to minimize their interactions during the cohabitation period in traditional granaries after the harvests of niébé.
Résumé en Anglais:
The biological rhythms are observed in the great majority of alive beings in the expression of molecular, biochemical, physiological or behavioural phenomena. [6,7,8,9], partage des ressources [10, 11, 12,], partage temporel à l'échelle saisonnière [13], hétérogénéité de l'habitat [14], et toute une série de stratégies reproductives décrites dans de nombreuses associations [15,16,17 ].
Au cours de ce travail, nous avons étudié la répartition temporelle de l'activité [20]. Ce paramètre permet de distinguer les individus selon que leur activité est plus ou moins précoce. Na = la durée de l'activité.
Am = activité maximale
Ip varie entre 0 et 1 : il tend vers 0 pour des profils présentant des pics d'activité, il tend vers 1 lorsque le profil est en plateau c'est-à-dire qu'il y a au cours de la journée une augmentation rapide vers un maximum avec une phase d'activité constante plus ou moins longue puis une décroissance rapide. Les résultats que nous obtenons montent que les deux espèces présentent des variations journalières de leur activité locomotrice comme la grande majorité des insectes [18].
2-Résultats a-Mise en évidence des rythmes journaliers d'activité locomotrice
L'existence des rythmes d'activité locomotrice a également été mise évidence chez d'autres hyménoptères parasitoïdes. En effet, chez les hyménoptères parasitoïdes de Drosophiles l'activité locomotrice varie de façon circadienne [1], le même phénomène a été observé chez les Trichogrammes [21]. L'étude des paramètres caractérisant l'activité locomotrice a permis une meilleure description des rythmes d'activité qui est utile notamment dans le cas des variations plus subtiles dues à certains facteurs. La variabilité de l'activité locomotrice observée à différentes échelles résulterait des caractéristiques endogènes différentes [21]. En effet, la différence entre les taux d'activité journalière des mâles et des femelles pourraient provenir de significations différentes de l'activité locomotrice : chez les femelles elle est surtout liée à la recherche du site d'oviposition [ 22,23,1] alors que chez les mâles elle est en relation avec la recherche de partenaires sexuels [24,25].
Résumé : A l'aide d'un système automatique d'analyse d'images, nous avons étudié la répartition temporelle de l'activité locomotrice de E. orientalis et E. vuilleti au cours de 24 heures, et sur plusieurs jours pour savoir si les rythmes d'activité de ces deux Eupelmidae jouent un rôle dans leurs interactions compétitives. L'analyse des rythmes d'activité locomotrice d' E. orientalis et E. vuilleti montre que l'activité locomotrice des deux espèces présente des variations cycliques journalières. Ces deux Eupelmidae ont des rythmes d'activité semblables. Les déplacements de ces parasitoïdes ont lieu essentiellement pendant la photophase. Mais l'activité d'E. vuilleti est plus précoce puisque les individus de cette espèce démarrent leur activité en moyenne 4 à 5 heures plus tôt que ceux d'E. orientalis. E. vuilleti commence les déplacements plusieurs heures avant l'éclairage alors que E. orientalis n'est actif qu'en présence de la lumière. Ce décalage de démarrage d'activité est donc un facteur permettant aux deux espèces concurrentes de minimiser leurs interactions pendant la période de cohabitation dans les greniers après les récoltes du niébé.
-
Indice de profil (Ip) : Cet indice permet de décrire la forme de la courbe d'activité lors d'un cycle de 24 heures. Aj Aj Ip = ⎯⎯⎯ = ⎯⎯ M a × N a A m Aj = l'activité journalière. Ma = le maximum d'activité de la journée.
Dans nos conditions expérimentales, l'activité locomotrice des individus des deux espèces présente des variations cycliques (figure). On remarque que les déplacements ont lieu essentiellement pendant la phase lumineuse. Mais il y a une légère anticipation chez les individus E. vuilleti qui démarrent leur activité avant l'éclairage, cette anticipation est plus importante chez les mâles. Chez les deux espèces, l'activité augmente lentement pendant les toutes premières heures de la photophase puis reste constante à son maximum pendant 3 à 4 heures chez les mâles et commence aussi à décroître lentement jusqu'à l'extinction. Chez les femelles la phase d'activité maximale est encore plus courte et dure entre 2 et 3 heures maximum et la décroissance de l'activité est plus précoce puisqu'elle suit presque immédiatement l'augmentation.
The occurrence of these phenomena is considered as an adaptation to cyclic variations of physical environment. In parasitoïde insects, the circadian rhythms of activity play an important role in the coexistence several species because females are in general unable to recognize an already parasitized host by another species.This study carried out temporal distribution of locomotor activity of two hymenopteraEupelimidae insects (Eupelmus orientalis and Eupelmus vuilleti). These hymenoptera are two close related species encountered in the fields and in stocks after harvest. Those sympatric species are parasitoïdes of bruchidae insects which are leguminous plant pest in tropical Africa. In the fields as in stocks of niebe (Vigna unguiculata), E orientalis and E vuilleti parasitize larvae and nymphs of bruchidae. The coexistence of two species exploiting the same resources is possible only if exists mutual recognition or temporal sharing of resources.This study carried out the existence of rhythms in locomotor activity and the temporal distribution of these parasitoïdes according to daily activity and this activity over several days.Using an automatic system of images analysis, we studied the temporal distribution of the locomotor activity of E orientalis and E vuilleti during 24 hours, and over several days. It is before discovered by E orientalis females. The role of the activity shift in the coexistence of the sympatric species was evoked for several insects associations. In the case of these Eupelmidae it is probable that E vuilleti early activity is an effectiveness factor of hosts search making it possible to compensate lower competitive capacity. The study of search capacity of hosts by these Eupelmidae must be planned in situation of competition in order to understand better the role of the early activity of E vuilleti.an effective tool because allowing an automatic follow-up of several individuals the day like
the night. The automation of the system was not done with precision detriment of the
measurements one combined the quantification of insect trajectory to the temporal follow-up.
The analysis of locomotor activity rhythms of E orientalis and E vuilleti shows that locomotor
activity of both species presents daily cyclic variations. These two Eupelmidae have similar
activity rhythms. Displacements of these parasitoïdes take place early during the photophase.
But E vuilleti activity is early because of this species start their activity on average 4 to 5
hours before E orientalis. E vuilleti begins displacements several hours before lighting
whereas E orientalis is active only in light presence. This starting shift of the activity is thus a
factor making possible two concurrent species to minimize their interactions during the
cohabitation period in the granaries after harvests.
In fields, these Eupelmidae exploit the same hosts, for it they can consider that the activity
shift is a means of reducing the competition intensity. An other study on the competition
between these two species showed that E vuilleti eggs deposited on hosts parasitized by E
orientalis are likely weak to reach the adult stage. That probably constitutes a pressure which
led E vuilleti to start its daily activity earlier in order to parasitize available healthy hosts
INTRODUCTION
En réponse aux variations périodiques des facteurs de l'environnement (alternance
jour/nuit et cycles associés), les êtres vivants ont développé des phases d'activité et de repos
en fonction de leurs exigences physiologiques et écologiques. Les rythmes biologiques sont
observés chez la grande majorité des êtres vivants dans l'expression de phénomènes
moléculaires, biochimiques, physiologiques ou comportementaux. L'expression de ces
phénomènes est considérée comme une adaptation aux variations cycliques de
l'environnement physique [1].
Chez les insectes parasitoïdes, les rythmes circadiens d'activité jouent un rôle
important dans la coexistence des espèces car les femelles sont en général incapables de
reconnaître un hôte déjà parasité par une autre espèce [2, 3, 4, 5]. La plupart des travaux sur la
coexistence d'espèces de parasitoïdes appliquent les mécanismes classiques : spécificité
parasitaire
locomotrice de deux insectes hyménoptères Eupelimidae (Eupelmus orientalis et Eupelmus vuilleti). Ce sont deux espèces sympatriques de parasitoïdes des insectes bruchidae qui sont des ravageurs de légumineuse en Afrique tropicale. Dans les champs comme dans les stocks Dès l'émergence, les mâles et les femelles parasitoïdes sont séparés avant de s'accoupler ; les mâles sont ensuite placés dans une boite de Pétri et les femelles dans une autre. Pour avoir des femelles accouplées, on laisse cinq femelles en présence de cinq mâles âgés de deux jours. Après un seul accouplement, les femelles sont à nouveau isolées dans les boîtes de Pétri et sont prêtes pour les expériences. La mesure des rythmes d'activité a été faite dans deux conditions climatiques : celles qui sont similaires aux conditions climatiques qu'on observe dans la localité d'origine (Niger) de ces espèces pendant la saison des pluies avant la récolte du niébé (32° : 22°C, 50 % : 80 % h. r., L. D. 12 : 12), puis dans les conditions semblables à celles qui règnent dans cette région pendant la saison sèche au début du stockage du niébé (25°: 15°C, 30 % : 60 % h. r., L. D. 12 : 12). b)-Présentation du matériel de mesure d'activité et acquisition des données b.1-Système de mesure Les mesures de l'activité locomotrice ont été réalisées au moyen d'un système automatique d'analyse d'image du Laboratoire de Biométrie et de Génétique des populations de Lyon I. Le système automatique d'analyse d'image est composé d'enceintes de mesure, une caméra, un micro-ordinateur, un moniteur vidéo et une imprimante. La caméra vidéo (Canon CI-20PR) se déplace dans un plan parallèle à celui des enceintes de mesure grâce à deux axes de translation dirigés par des moteurs (Socitec, FDL 603-370-47). Le fonctionnement du moteurs est commandé par le programme de mesure qui assure donc à la fois l'analyse d'images et les mouvements de la caméra. La liaison entre les moteurs et le micro-ordinateur se fait grâce à une carte d'interface (IF1 Socitec).Les images prises par la caméra sont transmises à l'ordinateur au niveau d'une carte vidéo (SECAD) permettant leur numérisation. Les images numérisées sont ensuite analysées par le logiciel. Les données enregistrées à chaque mesure sont stockées dans un fichier dont Afin de limiter les variations de température et d'humidité, et bien que la pièce d'étude soit climatisée, les enceintes de mesure sont placées dans un dispositif en verre[19]. Etant donné que la pièce d'étude n'est pas équipée d'un système de régulation automatique de la Activité journalière : c'est le pourcentage de temps consacré au déplacement en 24 heures. Il peut s'agir d'une moyenne sur plusieurs jours si on travaille sur le jour moyen.de niébé (Vigna unguiculata), Eupelmus orientalis et Eupelmus vuilleti parasitent des larves et
nymphes de bruches. La coexistence de deux espèces exploitant les mêmes ressources n'est
possible que s'il y a reconnaissance mutuelle ou partage temporel de ressources. C'est
pourquoi l'objet de cette étude est de mettre en évidence l'existence de rythmes d'activité
locomotrice et la répartition temporelle de cette activité chez ces parasitoïdes à l'échelle
journalière et sur plusieurs jours.
1-Matériel et méthode de mesure
a)-Matériel biologique
l'analyse en fin d'expérience permet la représentation des variations temporelles. A tout
instant, les opérations d'analyse d'images sont visualisables sur un moniteur de contrôle.
Les cellules de mesure sont éclairées en permanence par transparence par une source
infra rouge (λ > 730 nm), longueurs d'ondes auxquelles les insectes ne sont pas sensibles [18].
L'objectif de la caméra étant muni d'un filtre ayant la même bande passante, la prise d'image
est indépendante des variations de la "lumière du jour" simulée par 2 tubes fluorescents
(lumière blanche, intensité 350-500 lux).
Ce système d'analyse d'image est performant puisqu'il permet le suivi automatique
d'un grand nombre d'individus de jour comme de nuit. L'automatisation du système ne s'est
pas faite au détriment de la précision des mesures puisqu'on a allié la quantification du trajet
de l'insecte au suivi temporel [19]. Ceci permet de considérer plusieurs aspects de l'activité
locomotrice, tant qualitatifs que quantitatifs. De plus le système est adaptable à plusieurs
situations car il permet aussi bien l'étude de l'activité spontanée que celle de l'activité en
présence d'hôte ou celle des rythmes d'émergence.
c-Conditions expérimentales
Pour mesurer l'activité, les insectes sont placées dans les cellules de mesure (diamètre
= 2,8 cm, épaisseur = 1 cm) réalisées dans des plaques de métal maintenues entre deux
plaques de verre par des pinces métalliques. Chaque cellule contient des gouttelettes de miel
dilué en quantité suffisante pour permettre la nutrition d'un individu pendant plusieurs jours.
thermopériode et d'humidité relative, les mesures ont été faites dans des conditions constantes
de 28° C ± 2° C, 75 % h. r. pour les parasitoïdes qui se sont développés à 32° : 22°C, 50 % :
80 % h. r., L. D. 12 : 12. Pour ceux qui se sont développés en conditions 25°: 15°C, 30 % : 60
% h. r., L. D. 12 : 12, les mesures ont été faites à 21° C ± 2° C, 75 % h. r.. Toutes les mesures
sont faites sous une photopériode de L.D. 12 : 12. La photophase commence à 8 heures et
s'arrête à 20 heures, ainsi la scotophase dure de 20 heures à 8 heures.
d-Paramètres calculés
--Heure médiane d'activité (H. M. A.) : c'est le moment de la journée auquel
50 % de l'activité journalière est réalisée
La comparaison des deux espèces a été faite chez les femelles car ce sont elles qui jouent un rôle important dans les phénomènes de compétition interspécifique.Quant au moment de démarrage de l'activité locomotrice, les femelles E. vuilleti sont plus précoces que les femelles E. orientalis. Dans les deux conditions thermiques les femelles E. vuilleti sont actives bien avant le début de l'éclairage (4 à 5 heures avant l'éclairage). Ainsib-Variabilité des paramètres caractérisant les rythmes d'activité
b.1-Variabilité intra spécifique
Dans les deux conditions climatiques la quantité journalière d'activité exprimée par les
femelles est plus importante que celle des mâles (tableau 1). Les taux d'activité journalière
montrent que les femelles consacrent plus de temps au déplacement par rapport aux mâles. La
comparaison des heures médianes d'activité montre que les mâles ont une activité journalière
plus précoce puisqu'ils commencent toujours leur activité 1 heure ou plus avant les femelles
(tableau 1) .
b.2-Variabilité interspécifique
L'enregistrement de l'activité locomotrice a été fait simultanément sur 53 femelles dont 26 E.
orientalis et 27 E. vuilleti. Les taux d'activité et par conséquent les indices de profil (les deux
espèces ayant des profils d'activité similaires) des femelles accouplées des deux espèces ne
sont pas significativement différents en conditions chaudes (Tableau 2). On observe que ce
taux est différent chez les deux espèces à faible température : le temps consacré aux
déplacements au cours d'une journée est plus élevé chez les femelles de E. orientalis (Tableau
2).
les heures médianes d'activité de E. vuilleti sont plus précoces dans toutes les conditions
climatiques (tableaux 2). A 28° C les heures médianes d'activité de E. orientalis et E. vuilleti
sont respectivement 12 h 14 mn ± 19 mn et 12 h 49 mn ± 10 mn, tandis qu'à 21° C ces valeurs
sont respectivement 12 h 24 mn ± 24 mn et 14 h 03mn ± 24 mn. On remarque que l'écart est
beaucoup plus important à basse température.
3-Discussion
E. orientalis et E. vuilleti sont des espèces sympatriques qui exploitent les mêmes hôtes tant
dans les champs que dans les greniers qui sont d'ailleurs un milieu confiné où la compétition
doit être rude. Comment expliquer la coexistence de ces deux Eupelmidae dans les stocks
lorsqu'on sait que les oeufs d' E. vuilleti arrivent difficilement au stade adulte quand ils sont
déposés sur les hôtes préalablement parasités par E. orientalis ? A l'aide d'un système
automatique d'analyse d'images, nous avons étudié l'activité locomotrice des deux espèces en
tenant compte des facteurs climatiques. Comme tout appareillage de laboratoire, notre
système de mesure constitue un environnement artificiel qui est susceptible d'influencer le
comportement des parasitoïdes. Il permet toutefois de limiter la variabilité des conditions
externes et mettre en évidence l'expression endogène de l'activité.
295 .
295hôtes permettant de compenser une capacité compétitive plus faible. L'étude de la capacité de recherche d'hôtes par ces Eupelmidae doit être envisagée en situation de compétition afin de mieux comprendre le rôle de l'activité précoce de E. vuilleti. BIBLIOGRAPHIE [1] FLEURY F., Les rythmes circadiens d'activités chez les Hyménoptères parasitoïdes de Drosophiles. Variabilité, déterminisme génétique, signification écologique, Thèse doctorat, Université de Lyon I, Lyon, 1993.[2] VAN STRIEN-VAN LIEMPT & VAN ALPHEN, The absence of interspecific host discrimination in Asobara tibida Nees and leptopilina heterotoma (Thomson) coexisting larval parasitoïds of Drosophila species, Neth. J. Zool. 33 (1981) 125-163.[3] TURLINGS T. C. J., Van BATENBURG F. D. H. & Van STRIEN-Van LIEMPT W, Why is there no interspecific host discrimination in the two coexisting larval parasitoïds of Drosophila species, Leptopilina heterotoma (Thomson ) and Asobara tibida (Nees ), DIJKERMAN, H. J. & KOENDERS J. T. H., Competition between Trieces tricarinatus and Triclistus yponomeutae in multiparasitized hosts. Entomol. Exp. Appl. 47 (1988). 289-Tableau 1 : Variabilité entre sexes des paramètres caractérisant le rythme d'activité chez E.orientalis dans les conditions "chaudes" (28° C ± 2° C, 75 % r.h., L.D. 12 : 12) et dans les conditions "froides" (21° C ± 2° C, 75 % h. r., L.D.12 : 12). Les valeurs présentées dans le tableau sont des moyennes ± écart-type. La comparaison des moyennes s'est faite par le test t de Student (N. S. = différence non significative).-Activité locomotrice de E. orientalis• Conditions "chaudes".• Conditions "froides".-Activité locomotrice de E. vuilleti• Conditions "chaudes".• Conditions "froides".Tableau 2 : Paramètres caractérisant le rythme d'activité chez les femelles accouplées d'E. orientalis et d'E. vuilleti. Les valeurs présentées dans le tableau sont des moyennes ± écarttype. La Comparaison entre femelles des deux espèces s'est faite pour chaque condition thermopériodique avec le test t de Student (N. S. = différence non significative). Conditions "chaudes". • Conditions "froides". médiane d'activité (H. M. A.) Indice de profil (I. P.)La comparaison de l'activité des deux espèces montre qu'elles ont des taux et des
profils d'activité semblables. Cependant l'heure de démarrage d'activité et l'heure médiane
d'activité sont les paramètres qui différencient nettement les deux Eupelmidae. Les individus
E. vuilleti sont capables d'émerger plusieurs heures avant le signal lumineux alors que les E.
orientalis émergent exclusivement pendant la photophase et leur activité est très dépendante
de la lumière [26]. Cette différence de sensibilité au signal photopériodique a donc pour
conséquence un décalage de démarrage de l'activité au cours de la journée, ce qui permet de
réduire les contacts entre les organismes des deux espèces. Dans la nature, ces Eupelmidae
exploitent les mêmes hôtes, on peut de ce fait considérer que le déphasage d'activité est un
moyen de réduire l'intensité de la compétition. Les études sur l'hyperparasitisme facultatif de
ces parasitoïdes montrent que les oeufs de E. vuilleti déposés sur des hôtes parasités par E.
orientalis ont de faibles chances d'atteindre le stade adulte [27]. Cela constitue probablement
une pression qui a conduit E. vuilleti à démarrer plus tôt son activité journalière afin de
parasiter les hôtes sains disponibles avant qu'ils soient découverts par les femelles de E.
orientalis.
Le rôle du déphasage d'activité dans la coexistence des espèces sympatriques a été évoqué
pour plusieurs types d'associations intéressant les insectes [28]. Dans le cas de ces Eupelmidae
il est probable que l'activité précoce de E. vuilleti soit un facteur d'efficacité de la recherche
d'Oecologia 67 (1985) 352-359.
[4] Taux d'activité journalière
Heure médiane d'activité
(H.M.A.)
Indice de profil (I. P.)
-Femelles
30,43 ± 0,70
n=15
12h58 ± 12mn
n=15
0,38 ± 0,01
n=15
-Mâles
14,22 ± 2,59
n=12
11h48 ± 30mn
n=12
0,53 ± 0,13
n=12
-Valeur de t
22,35
(p < 0,001)
3,47
(p < 0,01)
4,28
(p < 0,001)
Taux d'activité journalière
Heure médiane d'activité
H.M.A.)
Indice de profil (I. P.)
-Femelles
27,95 ± 1
n=13
13h25 ± 18mn
n=13
0,37 ± 0,03
n=13
-Mâles
24,59 ± 2,68
n=13
13h10 ± 8mn
n=13
0,36 ± 0,03
n=13
-Valeur de t
4,09
(p < 0,001)
2,67
(p < 0,002))
0,9
(N. S.)
Taux d'activité journalière
Heure médiane d'activité
H.M.A.)
Indice de profil (I. P.)
-Femelles
25,84 ± 2,07
n=15
12h21 ± 24mn
n=15
0,40 ± 0,02
n=15
-Mâles
13,75 ± 1,18
n=12
11h48 ± 12mn
n=12
0,48 ± 0,11
n=12
-Valeur de t
17,52
(p < 0,001)
4,18
(p < 0,001)
2,66
(p < 0,002)
Taux d'activité journalière
Heure médiane d'activité
H.M.A.)
Indice de profil (I. P.)
-Femelles
31,23 ± 3,82
n=13
11h58 ± 34mn
n=13
0,40 ± 0,02
n=13
-Mâles
27,22 ± 1,15
n=12
12h30 ± 17mn
n=12
0,41 ± 0,02
n=12
-Valeur de t
3,36
(p < 0,002)
2,81
(p < 0,002)
0,9
(N. S.)
• Heure médiane d'activité
(H. M. A.)
Taux d'activité journalière
(%)
Indice de profil (I. P.)
E. orientalis.
12h49 ± 10mn
n=16
22,36±2,11
n=16
0,38±0,05
n=16
E. vuilleti
12h14±19mn
n=18
24,12±3,43
n=18
0,38±0,02
n=18
Test t
6,40
(p < 0,001)
1,72
(N.S.)
0
(N.S.)
Heure Taux d'activité journalière
(%)
E. orientalis.
14h03 ± 24mn
n=10
21,25 ± 3,50
n=10
0,46 ± 0,02
n=10
E. vuilleti
12h24 ± 24mn
n=9
14,51 ± 2,28
n=9
0,34 ± 0,02
n=9
Test t
8,49
(p < 0,001)
4,68
(p < 0,001)
12,35
(p < 0,001)
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| sample_790 | 0.5642 | arxiv | |
Understanding the complex dynamics of climate change in south-west Australia using Machine Learning
Alka Yadav
School of Computational and Integrative Sciences
Jawaharlal Nehru University
New Delhi-110067India
Sourish Das *sourish@cmi.ac.in
Chennai Mathematical Institute
Chennai-603103India
K Shuvo Bakar
School of Public Health
The University of Sydney
2006NSWAustralia
Anirban Chakraborti *anirban.chakraborti@bmu.edu.in
School of Computational and Integrative Sciences
Jawaharlal Nehru University
New Delhi-110067India
School of Engineering and Technology
BML Munjal University
Gurugram-122413India
Understanding the complex dynamics of climate change in south-west Australia using Machine Learning
The Standardized Precipitation Index (SPI) is used to indicate the meteorological drought situation -a negative (or positive) value of SPI would imply a dry (or wet) condition in a region over a time period. The climate system is an excellent example of a "complex system" since there is an interplay and inter-relation of several climate variables. It is not always easy to identify the factors that may influence the SPI, or their inter-relations (including feedback loops). Here, we aim to study the complex dynamics that SPI has with the sea surface temperature (SST), El Niño Southern Oscillation (ENSO) (aka., NINO 3.4) and Indian Ocean Dipole (IOD), using a machine learning approach. Our findings are: (i) IOD was negatively correlated to SPI till 2008; (ii) until 2004, SST was negatively correlated with SPI; (iii) from 2005 to 2014, the SST had swung between negative and positive correlations; (iv) since 2014, we observed that the regression coefficient (δ ) corresponding to SST has always been positive; (v) the SST has an upward trend, and the positive upward trend of δ implied that SPI has been positively correlated with SST in recent years; and finally, (vi) the current value of SPI has a significant positive correlation with a past SPI value with a periodicity of about 7.5 years. Examining the complex dynamics, we used a statistical machine learning approach to construct an inferential network of these climate variables, which revealed that SST and NINO 3.4 directly couples with SPI, whereas IOD indirectly couples with SPI through SST and NINO 3.4. The system also indicated that Nino 3.4 has a significant negative effect on SPI. Interestingly, there seems to be a structural change in the complex dynamics of the four climate variables of NINO 3.4, IOD, SST, and SPI, some time in 2008. Though a simple 12-month moving average of SPI has a negative trend towards drought, the complex dynamics of SPI with other climate variables indicate a wet season for western Australia.
Introduction
Global climate change affects the large-scale atmospheric circulation anomalies, resulting in metrological drought in many parts of the world, including Australia 1, 2 . Agricultural system is highly vulnerable with the extreme volatility of climate variables. In particular, in Western Australia the wheat 3 and broadacre livestock 4 productions are in concern. The agriculture water supplies have decreased quite drastically, which is about 44% reduction in 2010-2018 compared to 2001-2009 5 . According to the Bureau of Meteorology (BoM), the annual mean temperature anomaly is increased with a fluctuation in the early and late years of the millennium 6 . Similar pattern has also been observed for the rainfall anomaly during this time 7 . Understanding the complex dynamics of the drought with respect to climate change and its impacts on the ecosystem is essential, as it severely impacts agriculture, water resources and public health [8][9][10][11] . In this paper, we study the complex dynamics between climate variables, such as sea surface temperature (SST), El Niño Southern Oscillation (ENSO) NINO 3.4, Indian Ocean Dipole (IOD) and their impact on the standard precipitation index (SPI) in south-west Australia using the Machine Learning (ML) based approach. Western Australia contributes 18% (about 10.7 billion AUD) of the total gross agricultural production in Australia 12 , and the grain exports are worth around 4 billion AUD 13 . There are four types of droughts: meteorological, hydrological, agricultural, and socioeconomic 14 . Among them, meteorological droughts are characterized by below-normal precipitation and measured by SPI. It explains the degree of dryness and the duration of the dry period. Usually, low SPI is prone to trigger other types of droughts.
To understand meteorological drought, McKee et al. (1993) developed SPI using rainfall measurements [15][16][17] . Wenhong et.al (2008) showed that the SPI over the southern Amazon region decreased from 1970 through 1999 by 0.32 per decade, indicating an increase in dry conditions 18 . Rengung et. al. (2008) presented their study based on the SPI and analyzed the relationship of summer droughts in the United States 19 . Climatic factors also influence meteorological droughts, such as a brief review that can be found on the ENSO variability and drought risk over Australia 20 . The dynamics of ENSO and IOD cycles with the pattern of occurrence of meteorological drought is reported 21 23 . Lee et al. (2009) showed that when the time lag is 0 or 1 month, the November-February ENSO, SST explains much of the drought signals over eastern Australia 24 . Taschetto et al. (2009) investigated the inter-seasonal impact of ENSO on Australian rainfall using peak SST anomalies 25 , and the correlation between ENSO and the eastern part of the IOD is positive from January to June, and then changes to negative from July to December 26 . Takeshi et al. (2014) showed that the IOD could affect the ENSO state, in addition to the well-known preconditioning by equatorial Pacific warm water volume 27 . It also explored the interdecadal robustness of this result over the 1872 to 2008 27 . SST measurement is an essential factor that influences the Australian rainfall pattern 28 . Nicholls et. al. (1989) presented an ML-based approach using the rotated principal component analysis of Australian winter (June-August) rainfall, which revealed the correlation of precipitation and SST in the Indian and Pacific oceans 28 . Similarly, other studies analyzed the link between SST, SPI, and global vegetation 2,24,29,30 .
There are sparse multivariate approaches to understanding the complex dynamics of drought available in the literature. Most of the studies focused on the pairwise relationship between the NINO 3.4 with SST, or NINO 3.4 with IOD separately, or their pairwise effect on SPI 23,24 . In this paper, we explored the combined teleconnection of SST, NINO 3.4 and IOD on SPI through ML based approach. Here, we developed the Granger causal model to see the causal behaviour of SST, IOD and NINO 3.4 with SPI and then their effect on SPI altogether in south-west Australia.
Data
We used four variables for this study: SPI, SST, NINO 3.4 and IOD indices for the Western Australia region. The NINO 3.4 and IOD data are available from NOAA website 31 . The monthly SPI is calculated from the daily precipitations observed in 194 stations in south-west Australia, which is downloaded from the Bureau of Meteorology (BOM) website 32 . We have extracted the SST data for the Australian region from NOAA 33 . The range of the area we have considered for this study varies from longitude position 113.72 to 137.12 and latitude position -26.70 to -35.73. Figure (1) presents the 194 rainfall gauged locations on the map of Australia. For this study, we have used SPI monthly time series over 58 years . Since SST data is available from 1982, we used SST, IOD and Nino 3.4 monthly averaged data from 1982 to 2018 and performed all our model analyses for this period.
SPI for south-west Australia
The SPI is a popular index to monitor the drought. In 1993, McKee et al. suggested a classification scale for SPI 15,34 . For any given location, SPI values are classified into seven different regimes (from wet to dry), as shown in Table ( From the plots, we see that the signal-to-noise ratio is much higher for SPI 12-month series than for the SPI 1-month series. We checked this for all 194 monitoring stations and saw a similar higher signal-to-noise ratio for the 12-month series. Hence, the rest of the analysis is based on considering the SPI 12-month series. A high signal-to-noise ratio helps reduce the standard error of our analysis 35 .
In south-west Australia, October to March is monsoon time. Hence we observe higher variability of SPI compared to other months. Figure (
Results
We explored the dynamics of SPI with SST, NINO 3.4 and IOD over 1982 to 2018 period. Figures (4) present the time series of SST, NINO 3.4, and IOD respectively. We see that these are mean reversal processes, i.e. the series values return to their means after a certain period. To check whether these series have a long memory or not, we estimated the Hurst exponent, which relates to the autocorrelations of the time series. The Hurst exponent coefficient 36 in Table (2) explains that the variables, including the SPI, have long memory as the values are above 0.5. period with the 12-month moving average (solid black line). A high signal-to-noise ratio helps reduce the standard error of our analysis 35 . We see that the signal-to-noise ratio is much higher for SPI 12-month series than for the SPI 1-month series. We checked this for all 194 monitoring stations and saw a similar higher signal-to-noise ratio for the 12-month series. Hence, we considered the SPI 12-month series for our analysis.
To investigate the dynamics, we considered the cross-correlation functions (CCF) among the time-series of SPI, SST, IOD and NINO 3.4 variables see Figure (5,6). The maximum lag is considered 120 months for this analysis. Figure (5) represents the CCF over 1999-2008, which shows that all the climate variables influence each other. Hence it creates a dense network, which we present in Figure ( We developed a hybrid model that captures SPI's both long-term and short-term memory. The model identifies the long-term memory using Fourier harmonics. The Granger causal model captures the short-term memory and causality among SPI and other variables (NINO 3.4, IOD, and SST ). We also adjust the method by correcting spatial correlation among monitoring locations through the Gaussian process model. From the proposed model we explored the trend in SPI to check if the study-area is becoming more drought-prone or wet prone? Equation (1) estimates trends (β 1 ) for each year based on the past data. For example, Figure ( , it has a negative relationship with SPI. That means, SPI values will be in positive range, which again means there will be more wet conditions in south-west Australia. Figure (8a) tells that SST and SPI are correlated to each other. As SST has increasing trend, SPI values will be in positive range, which means there will be more wet conditions in south-west Australia.
Methodology
To understand the complex dynamics of the climate variables NINO 3.4, IOD and SST with the SPI, we resort to different statistical machine-learning models. The Granger causal model 38 is useful to determine whether one-time series helps to estimate another. It is also helpful in capturing the short-term memory of the system. We developed it to test the causal relationship among SPI, SST, NINO 3.4, and IOD. We used the Fourier series model to investigate the SPI's long-term memory for all rainfall monitoring locations. The Fourier series method used here is a special case of the functional data analysis technique to capture the long-term memory 39 . For each location, we develop a hybrid statistical model, which captures the long-term behaviour with the Fourier series method and the Granger causal model describes the short-term behaviour. We also correct the estimates for spatial correlation among the locations using the Gaussian Process (GP) model. We used the following algorithms to identify the long memory period of each chain.
(i) Calculate autocorrelation function on training time series data.
(ii) Identify period P 1 , P 2 , · · · , P m s , with autocorrelation ρ m > s, where s = 1 M ∑ M m=1 |ρ m −ρ|; ρ m is the m th −lag autocorrelation;ρ is median of all autocorrelation; M is the maximum lag considered in the study. It shows that though the ccf value is small but SPI and SST are correlated to each other. SPI has an effect on IOD but vice versa is not true. SPI and IOD are not that significantly correlated to each other. It is clear that both SPI and NINO 3.4 are significantly correlated to each other. From the figure it is clear that IOD has an effect on NINO 3.4 but reverse is not true. IOD has a small effect on SST but SST has no effect on IOD. We see that both NINO 3.4 and SST are significantly correlated to each other. The cross-correlation coefficient is significant enough to tell that all these indices have significant effect on each other.
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The rest of the data from December 2010 to 2018 were used to test the generalization of the analysis. We propose the following hybrid statistical machine learning model for location s = 1, 2, · · · , S(= 194),
M s : y(t) = β 0 + β 1 t + α(t) + η(t) +W (s) + ε(t),(1)
where β 0 is intercept, β 1 is the coefficient of trend, α(t) models the short-term memory of the process, η(t) models the long term memory of process. The W (s) is the spatial or geographical effect at location s, where W (s) ∼ GP(0, Σ(s, s )), i.e., W (s) follows Gaussian Process with mean zero and covariance function as: Σ(s, s ) = τ 2 exp{−ρ|s − s | 2 }, where we consider an exponential covariance matrix exp{−ρ|s − s | 2 }. The ε(t) is the white noise with E(ε) = 0 and Var(ε) = σ 2 , M s denote the model for location s. We consider four different types of the model, as follows:
• Type I: Long term memory model
η(t) = m s ∑ j=1 K ∑ i=1 β ji sin(i * ω j * t) + K ∑ i=1 γ ji cos(i * ω j * t) ,(2)
where ω j = 2π P j , j = 1, 2, · · · , m s , P j is estimated via the algorithm explained earlier, and m s denote the number of periods for s th location. For the short term memory, i.e. α(t), we considered two different approaches considering Granger causal model:
• Type II: Short term memory model with Nino3.4 and IOD as estimators. Here, y(t − K) denotes as k th lag SPI and X(t) as a estimator's time-series such as NINO 3.4 and IOD.
α(t) = α 0 + α 1 y(t − k) + δ X(t),(3)
• Type III: Short term memory model with the lag effect of Nino3.4 and IOD.
In this model we take lag effect for X(t) (Nino and IOD) such that
α(t) = α 0 + α 1 y(t − k) + δ X(t − k),(4)
where y(t − K) is the k th -lag SPI, X(t − k) is the k th -lag estimator's time-series.
• Type IV: Short term memory model with Nino3.4, IOD and SST.
In this model we take X(t) as a estimator's time-series such as NINO 3.4, SST and IOD.
α(t) = α 0 + α 1 y(t − k) + δ X(t − k),(5)
We implemented the machine learning shrinkage technique the LASSO (least absolute shrinkage and selection operator) selection to find out the best harmonics in the Fourier model 40 . The LASSO technique only picks the harmonics that have a statistically significant effect in reducing the error. We fit the model for location s, with data from {(t − w), · · · , (t − 1)}, where w = 450 months. For estimating y(t) at the location s, we define the estimated value asŷ s (t) for t th month, and apply spatial correction with GP model as
y(t) = Σ(s, s )[Σ(s, s ) + τ 2 I] −1ŷ (t),
where Σ(s, s ) = exp{−ρ|s − s| 2 } as defined in Equation (1).
The LASSO approach for the Fourier model with spatial correction helps improve the model's performance. The SST contributes significantly to improving the accuracy of out-of-sample SPI. For the Fourier model without spatial correction, we see that without a short-term memory, the value of Root Mean Squared Error (RMSE) is 1.26 (Full Model without Spatial correction, Type I). However, when we considered short-term memory, the RMSE was reduced to 0.49 for Type II and 0.51 for Type III. By considering SST as covariate in the Type III, we see that the out-sample RMSE dropped to 0.38. It means that SST has a significant effect in estimating SPI. When we considered the spatial GP correction without LASSO, the RMSE value dropped from 1.26 to 0.96 (Type I), and it decreased from 0.38 to 0.37 when we consider SST as a covariate (Type 1V). Similarly, we see that with GPs spatial correction and Lasso selection for optimal Fourier harmonics, the RMSE value is reduced further to 0.77 (Type I) and the out-sample RMSE is the lowest level of 0.34 for Type III and Type IV. Our analysis shows that the LASSO selection process with spatial correction model can improve the accuracy of the proposed model by many folds as RMSE value is lowest (0.34) in this case.
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Discussion and Summary
We developed the hybrid model and analyzed the relationship of the SPI to SST, NINO 3.4 and IOD. We used the machine learning algorithm including LASSO to select the significant Fourier harmonics to model the long memory. To capture the short term memory of SPI we used lagged estimators like IOD, SST and NINO 3.4 in Granger causal model. We also applied the GP spatial correction in estimating SPI. Our study observed that SPI, SST, NINO 3.4 and IOD have long memory as Hurst exponent values are estimated above 0.5, see Table (2). We have performed a number of validations of the proposed model based on out of sample test data. In validation step, we set aside the month that we want to validate. For example, Figure (10) represents the actual and estimated value in Dec, 2010 on Australia map. Here, we take training data from June, 1973 to Nov, 2010, i.e., 450 months, and we apply the proposed model (1) to estimate the SPI value for Dec, 2010. In Figure(10), we presented the out of the sample estimates and actual SPI. The visual inspection also indicates that the proposed model(1) estimated well for Dec 2010. However, this validation is just for one particular month. To evaluate the performance of the proposed model, we repeat this estimation process from December 2010 to November 2018 (for eight years) and calculate the out-of-sample RMSE of the estimates for 194 locations. The results for the median RMSE are given in Table (3).
Based on the best performing model, we observed an increasing trend in SST attribute change in the characteristics of the SPI's distribution. Figure (8) shows the average regression coefficient value (δ ) corresponding to SST, IOD and Nino 3.4 over the period from 1995 to 2018. It indicates that Nino 3.4 always has a significant negative effect over SPI. IOD was negatively correlated to SPI till the period of 2008 and in between 2009 to 2013 it was in positive range and after that it is significantly negatively correlated to SPI. However, until 2004, SST was always negatively correlated with SPI. During 2005 to 2014, the SST has some swings between negative to a positive correlation. Since 2014, we observe that the regression coefficient (δ ) corresponding to SST is always positive. Overall, we observe an upward trend in the δ corresponding to SST in Figure (8). It means, as we know SST itself has an upward trend, the upward positive trend of δ indicates that SPI is positively correlated with SST in recent years. This implies a more wet season in the study area of Western Australia. Though 12-month moving average of SPI has a negative trend towards drought, see Figure (2b), but the complex dynamics of SPI with other climate variables indicates more wet season for western Australia.
1). The SPI is a unitless index in which negative values indicate drought, where −1 is commonly used as a threshold; positive values mean wet conditions. Figure (2a) presents the SPI 1-month time series over 58 years (from 1961 to 2018) for 194 locations in south-west Australia. Figure (2b) presents the monthly SPI calculated with a 12-month epoch and annual moving average for the site positioned at longitude 113.72 and latitude −26.70.
3a) shows the average SPI for each month over 58 years (from 1961 to 2018) for all 194 sites. Figure (3b) is a correlation matrix among all 194 stations over all 58 years. Visual representation of the correlation matrix of SPI depicts that all the locations are spatially correlated.
Figure 1 .
1(a) Map of Australia with the rainfall gauged locations is superimposed in the study area. (b) A close representation of the 194 gauged locations in the south-west part of Australia. The range of the area considered varies from longitude position 113.72 to 137.12 and latitude position -26.70 to -35.73.
Figure 2 .
2The Standardized Precipitation Index (SPI) (a) one-month and (b) 12-month time series over 58 years
7a). Figure (6) presents the CCF over the period 2009-2018, where Figure (6a) shows that SPI and SST influence each other.Figure (6b) presents the CCF for SPI and IOD; it shows that the IOD does not couple SPI directly. Similarly, fromFigure (6c), we see that NINO 3.4 couples SPI and vice-versa.Figure (6d) and (6e)show that IOD couple SST and NINO 3.4, but the reverse is not foundFigure (6f), we see thatNINO 3.4 and SST couple each other. We present this analysis for 2009-2018 as a network diagram inFigure (7b).
9) presents the β 1 coefficients for Dec 2017 and Dec 2018 of all 194 locations. A location is more likely to see a dry weather if β 1 < 0, whereas, if β 1 > 0 then the location is more likely to see a wet condition. We observe that for both years, some locations show a mild increasing trend in the drought, especially in the inland. We also see that several locations near or close to the coastal area have β 1 ≈ 0, indicating a non significant trend for Dec 2017 and 2018.Based on historical data 37 , analysis presented inFigure (7,8) showed that IOD and SPI were negatively correlated until 2008. Figure (4b) shows a mild increasing trend in IOD. Increasing IOD results in decreasing SPI i.e., south-west Australia have faced more drought conditions around 2008. After 2008, Figure (8c) indicates sharp increase in the regression coefficients of the IOD -in the positive region. It means that in the last decade (2009-2018), we have observed a reversal of relationship between IOD and SPI. If the trend in Figure(8c) continues in the positive direction, then we expect to see a more positive values of SPI, which means less dry and more wet conditions in south-west Australia. Similarly, from Figure (8b) we see that beta values of Nino 3.4 are all negative for all years, i.e.
Figure ( 11 )
11shows the autocorrelation plot for a location (coordinate: longitude 116.45 and latitude -32.85), which has a maximum lag of 400 months. We used 450 months of data, from June 1973 to Nov 2010, to create the autocorrelation function. By implementing the algorithm, we identify four periods: 91, 183, 263, and 289 months. The first three periods indicate that the current value of SPI has a significant positive correlation with a past SPI value with a periodicity of about 7.5 years Detail investigation indicates that for all 194 locations, the period number varies where average Value is around 148 months (approx 12 years) with standard deviation 103.15 months.Figure (11)is a representative figure of one out of 194 locations in the study area. We repeated this process for all 194 locations and identified the long memory periodicity of each location.Figure (12)shows the long-memory period for all 194 locations on the western Australia map. The long memory period ranges from 60 months to 360 months, and clearly, we see a strong spatial correlation. The identification of the period would help us in analyzing the seasonality. For each location, we consider 450 months of data, starting from June 1973 to Nov 2010.
Figure 3 .
3(a) Plot of the average value of Standardized Precipitation Index (SPI) for all months over 58 years (from 1961 to 2018) in each location in south-west Australia. The dark black curve is the average of all 194 curves. (b) Visual representation of the correlation matrix of SPI among 194 locations. This correlation matrix depicts that all the locations are spatially correlated.
Figure 4 .Figure 5 .Figure 6 .
456Time-series plots for (a) Sea Surface Temperature (SST) (b) Indian Ocean Dipole (IOD) and (c) El Niño-Southern Oscillation (ENSO) NINO 3.4 over 37 years (1982-2018) for south-west Australia. The black curve is the three years moving average. For decade: 1999 to 2008; The cross-correlation function (CCF) plots between (a) Standard Precipitation Index (SPI) and Sea Surface Temperature (SST), (b) SPI and Indian Ocean Dipole (IOD), (c) SPI and Nino 3.4, (d) IOD and Nino 3.4, (e) IOD and SST, (f) Nino and SST with a lag of 120. The cross-correlation coefficient is significant enough to tell that all these indices have significant effect on each other. For decade: 2009 to 2018; The cross-correlation function (CCF) plots between (a) Standard Precipitation Index (SPI) and Sea Surface Temperature (SST), (b) SPI and Indian Ocean Dipole (IOD), (c) SPI and Nino 3.4, (d) IOD and Nino 3.4, (e) IOD and SST, (f) Nino and SST with a lag of 400.
Figure 8 .Figure 9 .
89Plots for the average regression coefficient value (δ ) corresponding to NINO 3.4, SST, and IOD over the period 1995 to 2018. The red smooth curve is the three years moving average of δ . It shows that NINO 3.4 always has a significant negative effect over SPI. On the other hand, until 2004, SST was always negatively correlated with SPI. During 2005 to 2104, the δ of SST swings between negative to a positive correlation. IOD was negatively correlated to SPI till the period of 2009 and in between 2009 to 2013 it was in positive range and after that it is significantly negatively correlated to SPI. The trend (β 1 ) coefficient of SPI for Dec 2017 and Dec 2018 for 194 locations in the south-west Australia.
Figure 10 .Figure 11 .
1011estimate of SPI for Dec, 2010 using training data from June 1973 to November 2010. Defined following color scheme: (1) If SPI> 1 : Black (2) If 1 > SPI > 0: Blue; (3) If −1 < SPI < 0: Red, (4) If SPI< −1: Brown The autocorrelation plot with a maximum lag of 400 months for a rainfall gauged location at the longitude 116.45 and latitude -32.86. We used 450 months of data, from June 1973 to Nov 2010, to create the autocorrelation function. There are four significant periods of 91, 183, 263, and 289 months. The first three periods indicate that the current value of SPI has a significant positive correlation with a past SPI value with a periodicity of about 7.5 years.
Figure 12 .
12The plot presents the long-memory period for each of the 194 locations. There is a strong spatial correlation between all locations' long-memory periods. The colour bar shows the length of the period in the number of months.
. The direct impact of ENSO on precipitation was reported by Wen et al. (2015) 22 . Loughran et. al. (2018) investigated how the ENSO couple the mechanisms of heatwaves in Australia 23 . They examine the ENSO large-scale mode of variability that influences the Australian heatwaves using prescribed SST characteristics of El Niño and La Niñ conditions
Table 1 .
1Classification scale for Standardized Precipitation Index (SPI).SPI range
Category
2.00 and above
Extremely wet
1.50 to 1.99
Very wet
1.00 to 1.49
Moderately wet
-0.99 to 0.99
Near normal
-1.00 to -1.49
Moderately dry
-1.50 to -1 . 99
Severely dry
-2.00 and less
Extremely dry
Table 2. This table presents the Hurst exponent value for all index, i.e., SPI, IOD, SST and Nino 3.4. The values indicate that
the system has a long memory.
Index
Hurst Value
Standard Precipitation Index (SPI)
0.71
El Niño Southern Oscillation (ENSO) NINO 3.4
0.66
Indian Ocean Dipole (IOD)
0.69
Sea Surface Temperature (SST)
0.58
3/17
Table 3 .
3The out of sample Root Mean Square Error (RMSE) values for all four types of the model for from December 2010 to November 2018 (8 years). Here, SPI is a target variable. The brief description of all types of the model are as follows: Type I: It captures the long term memory only using Fourier Series methods, Type II: Nino 3.4 and IOD are the covariates, Type III: lag values of Nino 3.4 and IOD are covariates, Type IV: Nino, IOD, and SST are covariates. We see that Type III and Type IV considering LASSO and GP correction are giving 0.34 the lowest (best) RMSE values in estimating SPI.Different Combinations
Type I
Type
II
Type
III
Type
IV
Full Model without Spatial
Correction
1.26
0.49
0.51
0.38
Full Model with Spatial
Correction
0.96
0.45
0.46
0.37
LASSO Selected Model
with Spatial Correction
0.77
0.35
0.34
0.34
AcknowledgementsA.Y. is grateful for the fellowship from JNU and hospitality at CMI funded by AlgoLabs. S.D. acknowledges the partial financial support from Infosys Foundation, TATA Trust, and Bill & Melinda Gates Foundation's grant to CMI.Author contributions statementA.C., S.B., S.D., and A.Y. conceived the research. S.D. and A.Y. developed the methods, analysed the results and prepared the figures. All authors discussed the results, contributed to the writing of the manuscript, and reviewed the manuscript.Ethics declarationsCompeting interests : The authors declare no competing interests.
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| sample_791 | 0.9832 | arxiv | |
Avaliação de Classificadores para Segmentação de Imagens: Aplicações para Inventário Florestal de Eucalipto
28 Mar 2017
Rodrigo M Ferreira
Universidade Federal de Mato Grosso do Sul Sistemas de Informação Câmpus de Três Lagoas -MS
Ricardo M Marcacini
Universidade Federal de Mato Grosso do Sul Sistemas de Informação Câmpus de Três Lagoas -MS
Avaliação de Classificadores para Segmentação de Imagens: Aplicações para Inventário Florestal de Eucalipto
28 Mar 2017
The task of counting eucalyptus trees from aerial images collected by unmanned aerial vehicles (UAVs) has been frequently explored by techniques of estimation of the basal area, i.e, by determining the expected number of trees based on sampling techniques. An alternative is the use of machine learning to identify patterns that represent a tree unit, and then search for the occurrence of these patterns throughout the image. This strategy depends on a supervised image segmentation step to define predefined interest regions. Thus, it is possible to automate the counting of eucalyptus trees in these images, thereby increasing the efficiency of the eucalyptus forest inventory management. In this paper, we evaluated 20 different classifiers for the image segmentation task. A real sample was used to analyze the counting trees task considering a practical environment. The results show that it possible to automate this task with 0.7% counting error, in particular, by using strategies based on a combination of classifiers. Moreover, we present some performance considerations about each classifier that can be useful as a basis for decision-making in future tasks.--Resumo --A tarefa de contagem deárvores (ou mudas) de eucalipto por meio de imagens aéreas coletadas por Veículos Aéreos não Tripulados (VANTs) tem sido frequentemente explorado por meio de técnicas de estimativa daárea basal, ou seja, que determinam o número esperado deárvores com base em amostragem. Uma estratégia alternativaé o uso de aprendizado de máquina para identificar padrões que representam uma unidade arbórea (copa deárvore ou muda), e verificar a ocorrência desses padrões em toda a imagem. Esta estratégia depende de uma etapa de segmentação supervisionada da imagem, queé o processo para identificar regiões de interesse predefinidas. Assim,é possível automatizar a contagem (individualizada) deárvores nestas imagens, aumentando a eficiência da gestão em inventário Este trabalhoé parte dos requisitos para aprovação na disciplina de Trabalho de Conclusão de Curso (2016/2) do discente Rodrigo M. Ferreira, no curso de Bacharelado em Sistemas de Informação. florestal de eucalipto. Neste trabalho foram avaliados 20 classificadores para a tarefa de segmentação de imagens. Foi utilizada uma amostra real, de uma grande empresa naárea de papel e celulose, para analisar o problema de contagem deárvores considerando um ambiente prático. Os resultados indicam que foi possível automatizar esta atividade com erro de 0.7%, em particular, com estratégias baseadas em combinação de classificadores. Ainda,é apresentada uma visão geral do desempenho de cada classificador que pode ser utilizada como base para tomada de decisão em tarefas futuras.I. INTRODUÇÃOO cultivo de eucalipto representa um papel de destaque na economia brasileira[1]. O eucalipto tem uma característica econômica vantajosa relacionadaà sua diversidade, pois pode ser empregado nas indústrias de papel, celulose, madeira industrializada e carvão vegetal. Além disso, tem um efeito importante no controle ambiental no que diz respeito ao seqüestro de CO2, uma vez que um hectare de eucalipto remove 60 toneladas de CO2 da atmosfera [2]. As empresas de setor têm reportados investimentos volumosos para viabilizar a silvicultura de precisão, queé o processo para aumentar o grau de automatização e eficiência com operações envolvendo madeira florestal[3].No sentido de aumentar esta eficiência, noś ultimos anos há um aumento considerável de uso de veículos aéreos não tripulados (VANTs) para apoiar monitoramento do inventário florestal[4]. Dentre os principais objetivos, a detecção de falhas de plantio e contagem deárvores têm sido alvo de diversos estudos; uma vez que são importantes na estimativa de produção das empresas. Além
Abstract-The task of counting eucalyptus trees from aerial images collected by unmanned aerial vehicles (UAVs) has been frequently explored by techniques of estimation of the basal area, i.e, by determining the expected number of trees based on sampling techniques. An alternative is the use of machine learning to identify patterns that represent a tree unit, and then search for the occurrence of these patterns throughout the image. This strategy depends on a supervised image segmentation step to define predefined interest regions. Thus, it is possible to automate the counting of eucalyptus trees in these images, thereby increasing the efficiency of the eucalyptus forest inventory management. In this paper, we evaluated 20 different classifiers for the image segmentation task. A real sample was used to analyze the counting trees task considering a practical environment. The results show that it possible to automate this task with 0.7% counting error, in particular, by using strategies based on a combination of classifiers. Moreover, we present some performance considerations about each classifier that can be useful as a basis for decision-making in future tasks.
--Resumo --A tarefa de contagem deárvores (ou mudas) de eucalipto por meio de imagens aéreas coletadas por Veículos Aéreos não Tripulados (VANTs) tem sido frequentemente explorado por meio de técnicas de estimativa daárea basal, ou seja, que determinam o número esperado deárvores com base em amostragem. Uma estratégia alternativaé o uso de aprendizado de máquina para identificar padrões que representam uma unidade arbórea (copa deárvore ou muda), e verificar a ocorrência desses padrões em toda a imagem. Esta estratégia depende de uma etapa de segmentação supervisionada da imagem, queé o processo para identificar regiões de interesse predefinidas. Assim,é possível automatizar a contagem (individualizada) deárvores nestas imagens, aumentando a eficiência da gestão em inventário Este trabalhoé parte dos requisitos para aprovação na disciplina de Trabalho de Conclusão de Curso (2016/2) do discente Rodrigo M. Ferreira, no curso de Bacharelado em Sistemas de Informação. florestal de eucalipto. Neste trabalho foram avaliados 20 classificadores para a tarefa de segmentação de imagens. Foi utilizada uma amostra real, de uma grande empresa naárea de papel e celulose, para analisar o problema de contagem deárvores considerando um ambiente prático. Os resultados indicam que foi possível automatizar esta atividade com erro de 0.7%, em particular, com estratégias baseadas em combinação de classificadores. Ainda,é apresentada uma visão geral do desempenho de cada classificador que pode ser utilizada como base para tomada de decisão em tarefas futuras.
I. INTRODUÇÃO
O cultivo de eucalipto representa um papel de destaque na economia brasileira [1]. O eucalipto tem uma característica econômica vantajosa relacionadaà sua diversidade, pois pode ser empregado nas indústrias de papel, celulose, madeira industrializada e carvão vegetal. Além disso, tem um efeito importante no controle ambiental no que diz respeito ao seqüestro de CO2, uma vez que um hectare de eucalipto remove 60 toneladas de CO2 da atmosfera [2]. As empresas de setor têm reportados investimentos volumosos para viabilizar a silvicultura de precisão, queé o processo para aumentar o grau de automatização e eficiência com operações envolvendo madeira florestal [3].
No sentido de aumentar esta eficiência, noś ultimos anos há um aumento considerável de uso de veículos aéreos não tripulados (VANTs) para apoiar monitoramento do inventário florestal [4]. Dentre os principais objetivos, a detecção de falhas de plantio e contagem deárvores têm sido alvo de diversos estudos; uma vez que são importantes na estimativa de produção das empresas. Além disso, a visão aérea proporcionada pelos VANTs podem fornecer informações complementaresàs detectadas em solo, bem como coletar dados de grandesáreas em um curto espaço de tempo. Por propocionar baixo custo de coleta de dados quando comparado com alternativas tradicionais (e.g. satélites e veículos tripulados), tal coletaé realizada com maior frequência o que gera uma quantidade maior de dados a serem analisados [4]. Em particular, as imagens aéreas das florestas são um tipo de informação coletada, geralmente em alta resolução, que por serem georreferenciadas são combinadas em imagens maiores por meio de uma técnica denominada "mosaicagem" [5], i.e., a fusão de imagens para recobrimento fotográfico de umaárea de interesse [6].
As imagens coletadas pelos VANTs são recursos importantes para o inventário florestal de eucalipto, em especial, na estimativa de quantidade deárvores. A técnica mais tradicional para esta estimativaé baseada indicadores deárea basal, que são técnicas estatísticas para estimar a densidade florestal de umaárea [7]. A popularidade desta técnicaé baseada na ideia de queé inviável a contagem individual deárvores para o inventário florestal, sendo necessário realizar tal procedimento por técnicas de amostragem. Por outro lado, e reconhecido que a medição porárea basal pode obter resultados insatisfatórios, geralmente devidò a processos imprecisos de amostragem [8].
Com o aumento de recursos computacionais e avanços naárea de aprendizado de máquina, bem como a alta disponibilidade das imagenś areas, diversas pesquisas têm apresentados resultados promissores sobre métodos para contagem individual deárvores [9], [10], [11]. Nesse caso, a ideia principalé identificar padrões nas imagens que representam a copa de umaárvore (ou muda) de eucalipto (unidade arbórea) e contabilizar a ocorrência desses padrões naárea de interesse. Métodos de segmentação de imagens são utilizados para identificar tais padrões com base em dois critérios [12]: (1) uniformidade intra-região, que ocorre quando elementos de uma mesma região da imagem têm alta similaridade de brilho, cor, forma e textura; e (2) contraste inter-região, que ocorre quando elementos em regiões diferentes têm baixa similaridade de brilho, cor, forma e textura. Os métodos de segmentação de imagens em geral são não supervisionados [13], na qual heurísticas baseadas nos dois critérios acima são aplicadas para identificação de bordas ou com base em algoritmos de agrupamento de dados [14]. No entanto, para domínios específicos (como florestas de eucaliptos)é possível realizar segmentação supervisionada de imagens, com apoio de algoritmos de classificação de dados, em que uma amostra de dadosé rotulada (como copa deárvores) para definir previamente o critério de uniformidade intraregião dos elementos de interesse [15].
Em relação ao uso de classificadores para segmentação de imagens, a ideiaé rotular uma amostra em duas classes, "árvores" e "nãó arvores", e então realizar a tarefa de segmentação. A saídaé comumente uma imagem binarizada (e.g. cor preta para classe "árvores" e cor branca para "nãoárvores") e assim um algoritmo de contageḿ e aplicado nessa imagem. Naárea de aprendizado de máquina dezenas de algoritmos de classificação foram propostos, cada um com suas vantagens e desvantagens, sendo necessário um procedimento experimental para escolha do classificador [16].
Neste trabalhoé apresentada uma avaliação de classificadores para segmentação de imagens, em particular, na tarefa de automatização de contagem deárvores em florestas de eucalipto. O trabalhó e motivado por uma constatação de que não há um algoritmo de classificação queé eficaz em todos os tipos de imagens, sendo importante um procedimento de avaliação e seleção de classificadores. Até mesmo para um domínio específico (como imagensáreas das copas de eucalipto) há variações importantes na coleta das imagens, como luminosidade do dia (e.g. ensolarado ou nublado), altura e angulação das fotos, características da região da plantação, bem como possíveis problemas na técnica de mosaicagem. As principais contribuições deste trabalho são destacadas a seguir:
•É apresentada uma avaliação empírica de 20 algoritmos de classificação para segmentação de imagens, em que o critério de avaliaçãó e a taxa de erro na contagem deárvores de eucalipto. Embora tal resultado não possa ser generalizado para outras imagens, são discutidas as características dos algoritmos com melhor desempenho que podem serúteis para apoiar a seleção de classificadores em aplicações futuras. • Tambémé analisado o uso de restrições de domínio na contagem deárvores, após o processo de segmentação, com base na distância esperada entreárvores para melhorar o processo de contagem. Esta técnica obtém melhores resultados do que as técnicas convencionais baseadas na contagem de segmentos com formatos predefinidos; que são elipses no caso de copas de eucaliptos. O restante deste texto está organizado da seguinte maneira. Na seção II são apresentados os fundamentos deste trabalho, descrevendo pocesso de extração de características das imagens e algoritmos de classificação utilizados na tarefa de segmentação supervisionada. Na Seção IIIé apresentado o procedimento de avaliação de classificadores para segmentação de imagens com foco no inventário de florestas de eucalipto. Os resultados experimentais são discutidos na Seção IV. Por fim, limitações do trabalho e direção para trabalhos futuros são apresentados na Seção V.
II. FUNDAMENTOS BÁSICOS O processo de segmentação supervisionada de imagens depende inicialmente em representar a imagem em um formato adequado para a tarefa de classificação [15]. Tal representação contém as características extraídas das imagens. Assim, uma imagemé representada no modelo espaço-vetorial, em que cada possível segmento s da imagemé um vetor m-dimensional s = (f 1 , f 2 , ..., f m ) e f i indica a relevância da característica i no segmento s. Além disso, caso o segmento s seja rotulado pelo usuário na classe "árvore" ou "nãoárvore", então fará parte do conjunto de treinamento para aprendizado do classificador.
Nas próximas seçõesé apresentado em mais detalhes o processo de extração de características, bem como uma breve descrição dos classificadores utilizados neste trabalho na tarefa de segmentação de imagens.
A. Extração de Características das Imagens
Uma imagem digital pode ser definida como uma matriz M (x, y) de pixels com valores de intensidade, luminosidade e cor, associados a cada pixel. Para o processo de extração de características de uma imagem ou de um fragmento dela,é comum o uso de histogramas de cor, qué e a representação numérica das características da imagem. A principal vantagem do uso de histogramasé a representação compacta das características da imagem [15].
Um histograma geralmenteé representado por um vetor contendo as variações de cores contidas na imagem, dadas em porcentagem, sendo invariante as transformações geométricas (escala, rotação e translação). As cores têm grande significância na indexação e recuperação de imagens. Podem ser representadas por diferentes padrões tais como RGB (red, green, blue) e HSI (hue, saturation, intensity); esseúltimo mais próximo da percepção de cores da visão humana. Histogramas não possuem representatividade espacial dos pixels, sendo assimé possível que imagens diferentes possuam histogramas iguais ou próximos. Embora a cor possa ser facilmente utilizada como característica, há casos em que ela não pode sozinha representar característica, dado a isso os sistemas mais bem difundidos se utilizam de múltiplas características [17].
A texturaé outro tipo de característica que pode ser suscintamente definida como a representação de padrões repetitivos em uma imagem de forma equânime. Podem ser analisadas por procedimento dentro de uma janela, denominada de análise estatística, ou se for feito no elemento da texturá e denominado de analise estrutural. Analise estrutural se aplica a elementos claramente identificáveis, enquanto análise estatística a elementos mais pequenos e difíceis de identificar [18]. A análise da texturaé baseada em formatos e regras descrevendo o posicionamento dos elementos relativos aos demais, como vizinhança e conexidade. Também são usadas regras sobre densidade de elementos por unidade espacial, regularidade e homogeneidade. A segmentação baseada em textura determina as regiões que possuem textura uniforme, em que após identificação da textura um retângulo envolventeé usado para criar uma indexação do tipo R-Tree [19].
Além da cor e textura, tambémé possível caracterizar imagens com base nas formas dos seus elementos internos.É uma das tecnicas mais difíceis para extração de características devidoà dificuldade em identificar tais formas, limitando a extração de características baseada em poucos objetos claramente identificados [15]. Em geral, abrange o pré-processamento da imagem para encontrar os objetos e detectar bordas podendo ser dificultado pela oclusão parcial de objetos e ruídos ou sombras. Há domínios que não apresentam formas pré-definidas, tais como tumores e mancha de pragas em folhas. Por outro lado temos domínios com formas geométricas definidas, por exemplo, localizar uma placa em um carro.
As características podem ser combinadas em umúnico vetor m-dimensional ou serem utilizadas separadamente para o treinamento do classificador. Trabalhos recentes na literatura indicam que uma combinação de características produz resultados mais satisfatórios do que o uso de apenas um tipo de característica [17].
B. Métodos de Classificação
A seguir são apresentados os métodos de classificação utilizados neste trabalho para apoiar a segmentação de imagens visando a contagem deárvores de eucalipto. Para cada métodó e apresentada uma breve descrição com base na documentação apresentada na ferramenta Weka [20] e FIJI-ImageJ [21], a qual contém referências para uma leitura mais detalhada desses algoritmos.
• NaiveBayes: fornece uma abordagem simples de aprendizado probabilístico, baseado no teorema de Bayes. Uma limitação do algoritmoé assumir que todas as características são independentes entre si durante a indução do classificador.
• Naive Bayes Updatable:é uma versão incremental do NaiveBayes queéútil para grandes conjuntos de treinamento.
• Naive Bayes Multinonomial: desenvolvido para dados com representações de alta dimensão, geralmente baseado em frequência de ocorrência das características, e com grande esparsidade (muitos elementos nulos ou zeros), como textos. O modelo multinomial captura informações de frequência de ocorrência, criando um vocabulário. Também permite realizar o aprendizado de forma incremental, sendoútil para grandes conjuntos de treinamento.
• SimpleLogistic: constrói modelos de regressão logística linear. Para problemas de classificação, utiliza-se um limiar para definir a classe após o treinamento do regressor.
• Logistic: constrói um modelo de regressão logística multinomial. Para problemas de classificação, utiliza-se um limiar para definir a classe após o treinamento do regressor.
• VotedPerceptron: um classificador baseado em uma lista de Perceptrons que, durante o treinamento, recebem pesos conforme a quantidade de objetos que conseguem classificador corretamente. Os pesos são utilizados, na etapa de teste, em uma estratégia de votação de cada Perceptron para a classificação final.
• MultilayerPerceptron: MultilayerPerceptroné um tipo de Rede Neural que usa o algoritmo backpropagation para classificar instâncias. Na implementação utilizada, os nós nessa rede usam a função sigmóide.
• RBFClassifier: classificação usando redes de função de base radial, treinadas de forma totalmente supervisionada com minimização de erro quadrático. Na implementação utilizada, todos os atributos são normalizados na escala [0,1]. Os centros iniciais para as funções de base radial gaussianas são encontrados usando uma execução do algoritmo k-means.
• SMO: representa o algoritmo para Máquinas de Vetores de Suporte, baseado na teoria do aprendizado estatístico. Na implementação utilizada, todos os atributos são normalizados por padrão. Tambémé utilizado um kernel polinomial, o que permite o aprendizado de classificadores não lineares.
• SMO LibLinear: SMO LibLinearé uma biblioteca open source para classificação linear em larga escala. Utiliza como classificador base máquinas de vetores de suporte linear. .
• FLDA: constrói um função Discriminante Linear de Fisher. O limiaré selecionado de modo que o separador esteja a meio caminho entre os centróides das classes.
• IB1: classificação com a técnica de vizinho mais próximo. Usa a distância euclidiana para encontrar a instância de treinamento mais próximà a instância de teste fornecida e prediz a mesma classe dessa instância de treinamento. Se várias instâncias tiverem a mesma (menor) distância para a instância de teste, a primeira encontrada será utilizada.
• RandomCommittee: constroi um conjunto de classificadores base e a predição finalé uma média linear das previsões geradas pelos classificadores base individuais. O classificador base comumente utilizadoé o DecisionStump.
• RandomSubSpace: constrói um classificador que consiste em váriasárvores construídas sistema-ticamente por seleção pseudo-aleatória de subconjuntos de características, istoé,árvores construídas em subespaços escolhidos aleatoriamente.
• RandomForest:é um comitê deárvores de decisão (floresta), em que cadaárvoreé construída por meio de subconjunto de atributos e de instâncias. A classificação finalé a moda da classificação de todas asárvores. Tal proposta tem a vantagem de evitar um modelo de classificação que faz um super ajuste nos dados, ou seja, melhora a tarefa de generalização.
• FastRandomForest:é uma versão otimizada da RandomForest no sentido de uso de memória. Dentre as otimizações, utiliza processamento paralelo via threads. Assim como a RandomForest, o resultado de classificação pode ser diferente em cada execução conforme a semente pseudoaleatória.
• PART: contrói uma lista de regras de decisão com base em umaárvore de decisão, na qual em cada iteração a "melhor folha" atualé transformada em uma regra.
• DecisionStump:é umaárvore de decisão com apenas um nível. Em geral, cada atributo gera uma regra caso sua entropia seja baixa, ou seja, caso o atributo seja discriminativo para as classes. Por ser simples e rápido, os algoritmos baseados em comitês usualmente utilizam por padrão este classificador como base.
• J48:é uma implementação baseada no algoritmo C4.5 para construção deárvore de decisão, com base em ganho de informação. Aárvore de decisão pode ser podada ou não.
• LMT: classificador para a construção de "árvores de modelo logístico", que sãoárvores de classificação com funções de regressão logística nas folhas.
III. AVALIAÇÃO DE CLASSIFICADORES PARA SEGMENTAÇÃO DE IMAGENS
Conforme comentado anteriormente, aplicações para apoiar o inventário florestal têm recebido grande atenção em empresas do ramo de papel e celulose. Neste processo, aumentar a precisão na contagem deárvores de eucaliptoé fundamental, pois permite melhorar a estimativa da produção futura. O desenvolvimento deste trabalho visa apoiar a metodologia adotada em uma das principais empresas brasileiras no setor, localizada na região de Três Lagoas -MS. Na Figura 1 são ilustrados os passos da metodologia utilizada para apoiar o processo de inventário florestal de eucalipto.
O processoé iniciado por meio da coleta de imagens por VANTs. O processo de fusão de imagensé aplicado ao final da coleta, gerando um mosaico (imagem unificada) daárea de interesse. Em seguida, os técnicos daárea de inventário florestal realizam recortes na imagem para (i) remover plantações que estão na borda daárea de interesse e (ii) definir uma amostra para o processo de segmentação de imagens. Este trabalho apoia diretamente a etapa de seleção do classificador apropriado para a segmentação, considerando a imagem coletada. A imagem segmentadaé utilizada como entrada para algoritmos que realizam o processamento da imagem e contagem deárvores, disponíveis na ferramenta FIJI-ImageJ. A ideia desses algoritmosé identificar segmentos similares a elipses, que possuem maiores chances de serem copas (ou mudas) de eucalipto. Essas informações são tabuladas em uma planilha indicando a posição na imagem em que cada unidade arbórea foi contabilizada. Por fim,é proposto neste trabalho o uso de um filtro de restrições de domínio, que remove contagens inválidas. Nesse caso, informações predefinidas sobre a distância mínima entreárvores (ou mudas) são utilizadas como restrições. Enfim, a eficácia desta metodologia depende da integração de vários softwares utilizados no processo:
• QGIS: sistema de informação geográfica que permite analisar imagens georreferenciadas coletadas pelos VANTs; • FIJI-ImageJ: ambiente para processamento de imagens que auxilia tanto na etapa de extração de características das imagens quanto na contagem deárvores após a segmentação; e • Weka: ambiente de aprendizado de máquina com dezenas de algoritmos de classificação e utilitários para avaliação de classificadores.
Para melhor compreensão desta metodologia, a seguir são ilustrados os passos principais. Na Figura 2,é ilustrada a etapa em que o usuário deve identificar quais regiões das imagens representam as classes de interesse. Na prática, o usuário seleciona na própria imagem as regiões que representam mudas (ou copas) de eucalipto para formar a classe de interesse e outras regiões da imagem para representar a classe "outros (ou nãoárvore)". O usuário também deve identificar quais as técnicas de processamento de imagem serão utilizadas para extração das características, geralmente baseada em cores e texturas. Por fim, o classificador para segmentação supervisionada, bem como seus parâmetros devem ser definidos. A ferramenta apresenta os parâmetros melhor avaliados na literatura como padrão.
Considere uma imagem com mudas de eucalipto conforme ilustrado na Figura 3. Na Figura 4é ilustrada esta imagem segmentada por meio de um classificador. Note que a classe de interesseé apresentada por elipses, que visa futuramente facilitar o processo de contagem deárvores. Para finalizar esse processo, aindaé necessário transformar a imagem para um formato binário. Em seguida, aplicam-se os filtros denominados "Fill Holes" e "Watershed". O primeiro tem o objetivo de realçar formas de elipses, preenchendo seu conteúdo com pixels preto. O segundo permite realçar as bordas de divisão entre as elipses identificadas. A imagem resultanteé ilustrada na Figura 5.
Para finalizar o processo aplica-se um algoritmo para contagem deárvores propriamente dito, queé baseado na análise de particulas. A ideiaé buscar agrupamentos de pixels, em formato de elipses, definindo como parâmetro um raio mínimo (nesse trabalho o mininoé 50px). Assim, obtemos uma imagem com a eliminação dos grupos de pixels fora do limite especificado para o domínio, como ilustrado na Figura 6. As informações relacionadas a contagem dasárvores são apresentadas de forma tabulada, contendo um identificador e as coordenadas do centro de cada agrupamento de pixels identificados como a classe de interesse.
Por fim, neste trabalho,é proposto o uso de regras com restrições de domínio (como a distância mínima conhecida entreárvores) podem ser empregadas nesses dados tabulados, a fim de remover possíveis contagens inválidas. Nesse caso, o usuário deve informar restrições do domínio previamente. O algoritmo de filtro verifica, para cadaárvore, se (i) o raio da copa (ou muda) satisfaz as restrições; se (ii) existemárvores vizinhas a uma distância menor do que a permitida; e se (iii) existe trêsárvores consecutivas formam possuem uma tendência linear devido ao estilo de plantação. Tais restrições permitem identificar ruídos que foram incorretamente consideradas comoárvores. E importante ressaltar que a saída desse processoé uma planilha tabulada que pode ser importada novamente para o sistema de informação geográfica e, assim, realçar aos usuários asárvores contabilizadas naárea de interesse.
IV. AVALIAÇÃO EXPERIMENTAL
A avaliação experimental consiste em analisar o erro obtido em relaçãoà contagem deárvores no final do processo, variando-se o classificador utilizado para segmentação da imagem.
Um problema crítico para este tipo de avaliaçãó e a obtenção de uma imagem já contabilizada e validada por humanos para ser utilizada como referência (conjunto verdade). Conforme comentado anteriormente, o processo manual de contagem deárvoresé inviável. Uma alternativa comumente utilizada por outros trabalhosé comparar a contabilização obtida via segmentação de imagens com a contabilização obtida via amostragem porárea basal. No entanto, acreditamos que essa comparação poderia levar a erros, uma vez que o conjunto de referência seria obtido por uma estratégia não confiável. Desse modo, neste trabalho optou-se por contabilizar (de fato) manualmente aś arvores de uma região de interesse para construir um conjunto de referência. Embora a amostra para a avaliação experimental seja reduzida, há a vantagem de que a análise dos resultadosé mais próxima de uma aplicação real.
Todos os classificadores descritos na Seção II foram utilizados nesta avaliação. Adotou-se os parâmetros definidos como padrão de cada classificador, que usualmente obtém bons resultados conforme descrito na documentação das ferramentas (FIJI-ImageJ integrado ao Weka).
A imagem de referência contém 412 mudas de eucalipto. Foram analisados dois aspectos durante a avaliação: taxa de erro na contagem e tempo em segundos (treinamento e teste) da segmentação. O computador utilizado para os experimentos possui quatro núcleos de 3Ghz e 8GB de memória RAM.
Na Tabela Por fim, no Apêndice A são apresentadas imagens segmentadas obtidas por cada classificador para possibilitar uma análise visual dos resultados.
V. CONSIDERAÇÕES FINAIS
A avaliação experimental para escolha de classificadores na segmentação de imagensé uma etapa importante para a contagem deárvores, uma vez que não há um método de classificação que será promissor em todas as variações de imagem. Nesse sentido, destaca-se o uso de métodos baseados em combinação de classificadores, que se mostraram competitivos quando comparados com classificadores usualmente utilizados naárea, como Redes MLP e Máquinas de Vetores de Suporte.
Uma limitação deste trabalhoé o uso de uma amostra reduzida para treinamento dos modelos, dada a reconhecida dificuldade em contabilizar manualmente grandesáreas de florestas de eucalipto. No entanto, a imagem de referência escolhidaé representativa para aárea, e será disponibilizada para outros trabalhos.
Como direção para trabalho futuro, espera-se incluir classificadores baseado em aprendizado profundo (Deep Learning) na tarefa de contagem dé arvores, uma vez que tem obtidos resultados interessantes em aprendizado de máquina envolvendo imagens.
VI. AGRADECIMENTOS
Fig. 1 .
1Passos da metodologia utilizada para o processo de inventário florestal de eucalipto, em que a etapa de contagem deárvoresé apoiada por técnicas de segmentação de imagem via métodos de classificação.
Fig. 2 .
2Interface do FIJI-ImageJ integrado ao Weka. O usuário seleciona um conjunto de técnicas para extração de características da imagem. Em seguida, seleciona regiões da imagem que farão parte amostra anotada (classes). Por fim, o algoritmo de classificação e seus parâmetros são selecionados para iniciar a etapa de segmentação supervisionada da imagem.Fig. 3. Imagemárea com plantação de mudas de eucalipto.Fig. 4. Imagem resultante da segmentação supervisionada.
Fig. 5 .
5Binazariação da imagem segmentada e aplicação de filtros de realce de elipses para apoiar a contagem deárvores.
Fig. 6 .
6Imagem resultante do processo de contagem deárvores. Essas informações também são apresentadas em dados tabulados para serem importados pelos sistemas de informações geográficas.
Ié apresentado um resumo geral da avaliação experimental. Os tempos de treinamento, classificação, e total são fornecidos em segundos. O erro de contagemé a diferença entre o número real de mudas e o número deárvores identificadas com base na imagem segmentada, sem a aplicação de filtro com restrição de domínio. Quandoé contabilizado um número maior deárvores do que o real, então o erroé precedido pelo sinal de +. Caso contrário,é precedido pelo sinal de −.Cada classificador foi ordenado conforme o erro
de contagem, do menor para o maior.
Uma análise dos principais pontos dos resulta-
dos experimentaisé listada abaixo:
• Embora o classificador DecisionStump tenha
obtido o menor erro, apresenta um efeito
indesejado queé subestimar o número dé
arvores. Isso significa que o filtro de restrições
de domínio para eliminação de ruídos contabi-
lizado comoárvore não terá o efeito desejado
quando for aplicado.
• O classificador RBFClassifier obeve resulta-
TABLE I
IVISÃO GERAL DA AVALIAÇÃO DOS CLASSIFICADORES PARA SEGMENTAÇÃO DE IMAGEM. O ERRO DE CONTAGEMÉ A DIFERENÇ A ENTRE O NÚMERO DE MUDAS E O NÚMERO DEÁRVORES IDENTIFICADAS COM BASE NA IMAGEM SEGMENTADA, SEM A APLICAÇÃO DE FILTRO COM RESTRIÇÃO DE DOMÍNIO. OS TEMPOS SÃO DADOS EM SEGUNDOS. realiza um ajuste dessa segmentação utilizando a minimização do erro quadrático nas classes fornecidas. • Estratégias baseados na combinação de vários classificadores obtiveram resultados satisfatórios, como FastRandomForest, Random-Forest, RandomCommittee e RandomSubSpace. Tal resultadoé baseado em dois fatores: (i) aumento da capacidade de generalização por utilizar subconjuntos de instâncias e atributos e (ii) maior chance em explorar de forma independente cada tipo de característica extraída das imagens (cores e texturas) ao selecionar subconjuntos de características. • Estratégias baseadas em aprendizado estatístico (SMO) e redes MLP apresentaram um erro significativo. No entanto, existe uma grande combinação de parâmetros (e topolo-gias no caso de MLP) que poderiam ser testadas para minimizar o erro. Do ponto de vista dos autores deste trabalho, estratégias livres de parâmetros ou que determinam automaticamente os parâmetros são potencialmente maiś uteis em cenários com grande diversidade de imagens. • Estratégias baseadas em regressão logística não apresentaram resultados satisfatórios para segmentação de imagens, principalmente devidoà alta dimensionalidade deste tipo de problema. • Estratégias baseadas em vizinhos mais próximos (IB1) são ineficientes no quesito de tempo e também não apresentaram resultados satisfatórios. As imagens em alta resolução e a dificuldade em definir uma medida de distância apropriada inviabiliza seu uso prático. • Vale destacar os resultados negativos do classificador Naive Bayes Multinomial. Esse resultadoé esperado uma vez que as características para representação do problema não são esparsas, fazendo com que o modelo multinomial não compute corretamente as probabilidades das classes. Após esta etapa da avaliação, foram selecionados os três melhores classificadores, conforme o erro de contagem, para aplicação do filtro com restrições de domínio. Nesse caso, o erro do classificador DecisionStump aumentou para 5.6%, após a remoção de 11árvores incorretamente contabilizadas. Já o erro do classificador RBFClassifier foi reduzido para 1.9% após remoção de 23árvores incorretamente contabilizadas. Por fim, o erro do classificador FastRandomForest foi reduzido para 0.7% após remoção de 18árvores incorretamente contabilizadas. Assim, considerando os resultados experimentais, o classificador FastRandomForesté uma opção promissora, tanto em relaçãoà capacidade de segmentação (principalmente na presença de diferentes tipos de característica de imagens) quanto em relação ao custo computacional.Classificador
Tempo de Treino Tempo da Segmentação Tempo Total Erro Erro(%)
Decision Stump
0.2
0.2
0.4
-12
2.9%
RBFClassifier
14.7
1.3
16.0
+15
3.6%
FastRandomForest
5.6
39.9
45.4
+21
5.1%
RandomCommittee
42.3
34.0
76.3
+57
13.8%
LibLINEAR
12.9
1.3
14.2
+63
15.3%
RandomForest
13.8
10.2
24.0
+66
16.0%
RandomSubSpace
5.8
1.9
7.8
+107
26.0%
Naive Bayes
0.3
10.4
10.7
+135
32.8%
Naive Bayes Updatable
0.2
10.2
10.4
+135
32.8%
SMO
55.5
1.1
56.6
143
34.7%
MultilayerPerceptron
498.6
6.0
504.6
+151
36.7%
FLDA
0.2
1.1
1.3
+156
37.9%
IB1
0.0
7033.0
7033.0
+166
40.3%
PART
9.8
0.6
10.4
+170
41.3%
SimpleLogistic
31.8
1.2
33.0
+177
43.0%
LMT
188.8
0.8
189.6
+178
43.2%
VotedPerceptron
13.4
604.1
617.5
+188
45.6%
Logistic
3.0
1.1
4.1
+200
48.5%
J48
3.8
0.3
4.1
+294
71.4%
Naive Bayes Multinomial
0.0
1.8
1.9
+430
104.4%
dos promissores. Uma possível explicaçãoé
relacionadaà sua estratégia de inicialização
de parâmetros, baseado em uma execução
do algoritmo k-means. No contexto da
segmentação, o k-means permite identificar
grupos com regiões uniformes, ou seja,é um
processo de segmentação não supervisionada.
A rede neural RBF, então, durante seu trei-
namento basicamente
Os autores agradecemà valiosa contribuição de Luiz Henrique Terezan (Supervisor de Qualidade Florestal na Eldorado Brasil Celulose S/A) para o desenvolvimento deste trabalho.Apêndice A
NaiveBayes
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
10703
NaiveBayes Updatable
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
10437
NaiveBayes Multinomial
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
1877
DECISIONSTUMP
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
FastRandomForest
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
45445
FLDA
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
1285
IB1
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
7032997
J48
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms) LibLINEAR
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
14190
LMT
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
189586
Logistic
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
4082
MultilayerPerceptron
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
PART
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
10372
RandomCommittee
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
76296
RandomForest
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
23965
RandomSubSpace
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
RBFClassifier
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
15987
SimpleLogistic
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
33028
SMO
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
56563
VotedPerceptron
Imagem Segmentada
Imagem Binária
Contagem de Árvores
Tempo Total (ms)
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| sample_801 | 0.8669 | arxiv | |
Enabling Heterogeneous Catalysis to Achieve Carbon Neutrality: Directional Catalytic Conversion of CO2 into Carboxylic Acids
xxxXiaofei Zhang
KAUST Catalysis Center (KCC)
King Abdullah University of Science and Technology (KAUST)
23955-6900ThuwalSaudi Arabia
Huabin Zhang huabin.zhang@kaust.edu.sa
KAUST Catalysis Center (KCC)
King Abdullah University of Science and Technology (KAUST)
23955-6900ThuwalSaudi Arabia
DrX Zhang
KAUST Catalysis Center (KCC)
King Abdullah University of Science and Technology (KAUST)
23955-6900ThuwalSaudi Arabia
ProfH Zhang
KAUST Catalysis Center (KCC)
King Abdullah University of Science and Technology (KAUST)
23955-6900ThuwalSaudi Arabia
Enabling Heterogeneous Catalysis to Achieve Carbon Neutrality: Directional Catalytic Conversion of CO2 into Carboxylic Acids
1
The increase in anthropogenic carbon dioxide (CO2) emissions has exacerbated the deterioration of the global environment, which should be controlled to achieve carbon neutrality. Central to the core goal of achieving carbon neutrality is the utilization of CO2 under economic and sustainable conditions. Recently, the strong need for carbon neutrality has led to a proliferation of studies on the direct conversion of CO2 into carboxylic acids, which could effectively alleviate CO2 emissions and create high-value chemicals. The purpose of this review is to present the application prospects of carboxylic acids and the basic principles of CO2 conversion into carboxylic acids through photo-, electric-, and thermal catalysis. Special attention is focused on the regulation strategy of the activity of abundant catalysts at the molecular level, inspiring the preparation of high-performance catalysts. In addition, theoretical calculation, advanced technologies, and numerous typical examples are introduced to elaborate on the corresponding process and influencing factors of catalytic activity. Finally, 2 challenges and prospects are provided for the future development of this field. It is hoped that this review contributes to a deeper understanding of the conversion of CO2 into carboxylic acids and inspires more innovative breakthroughs. a fuel and is a vital chemical compound for producing long-chain hydrocarbons(15). Similarly, methane is an important storage fuel with the advantage of low-cost storage(16). Produced olefins, such as ethylene and propylene, are key chemicals in fabricating plastics, medicines, and paints(17). Although CH3OH, CH4, and olefin have obvious economic value, their production processes undergo multiple electron transfers, leading to poor conversion efficiency and unsatisfactory product selectivity(18). In contrast to these products, carboxylic acids occupy a unique position due to the great breakthroughs made in recent years and their commercial value and apparent advantages, such as low toxicity, high density, and high value per kWh of electrical energy input, over other products.Despite the great progress achieved in the conversion and utilization of CO2 in the past few decades, the extreme stability of CO2 creates considerable challenges in its activation to participate in synthesizing carboxylic acids via specific intermediates and control the selectivity of carboxylic acids due to competitive reactions. This daunting challenge has prompted the development of outstanding heterogeneous catalysts to efficiently convert CO2 into carboxylic acids under mild conditions. Currently, the reported emerging nano-materials, including clusters, metal oxide, porous materials, organic-inorganic hybrid materials and alloys, have proved efficient heterogeneous catalysts presenting superior catalytic activity to homogeneous catalysts in producing carboxylic acids(19,20). More effort should be made to discern the decisive factors in producing carboxylic acids through advanced characterization techniques and theoretical calculations to develop ideal catalysts based on an accurate understanding of the mechanical process to realize large-scale, efficient production of carboxylic acids with CO2.
Introduction
General Background
With the intensification of the global energy crisis and environmental deterioration caused by the warming climate, aiming for carbon-neutral recycling is in imminent demand regardless of environmental protection or economic development(1, 2). The effective conversion of carbon dioxide (CO2) into fine chemicals has undoubtedly emerged as a powerful strategy to achieve carbon-neutral recycling due to its low cost and potentially low energy consumption (3)(4)(5). Extensive cost-effective conversion paths have been explored to realize such conversion practicably (5)(6)(7)(8). To date, various methods and strategies, including biological transformation, photocatalytic reduction, electrocatalytic reduction, organic transformation, dry reforming, and others, have been explored to convert CO2 into valuable chemicals based on continuing indepth studies over the past two decades (9)(10)(11).
In general, CO2 can be converted into numerous chemicals, such as CO, carboxylic acids, CH3OH, CH4, olefin, and so on, under the drivers of light, electricity, and heat (12,13). A large volume of CO2 emissions in the atmosphere is regarded as exhaust gas and the root cause of environmental deterioration, whereas these products could become valuable raw chemical materials with wide application value through catalytic conversion. A well-known application of CO is the synthesis of aldehydes through hydroformylation reaction, and high toxicity also poses challenges for its use and storage (14). Another product, CH3OH, can be widely used as
Introduction of Carboxylic Acid Compounds
Carboxylic acids encompassing formic, acetic, benzoic, acetylenic, amino, lactic, and other acids are essential components in fine chemicals and are regarded as core compounds in the natural carbon cycle (21). These chemicals have great application value in synthesizing chemical compounds and energy conversion. In all these carboxylic acids, formic acid has the smallest molecular formula and can be obtained in high yield with clean water or hydrogen as a reactant to react with CO2 over numerous heterogeneous catalysts (22). In addition, it is also regarded as a safe and convenient hydrogen storage carrier due to its high volumetric capacity of 53 g H2/L, which can be converted into clean electricity in direct formic acid fuel cells with appealing advantages, such as easy transportation and storage and high theoretical open-circuit voltage (23). Furthermore, it is an important chemical intermediate, which can be widely used in the leather, pesticide, antibacterial agent, medicine, livestock feed, dyestuff, and rubber industries (24). Moreover, other multi-carbon carboxylic acids have equivalent application prospects and economic value to formic acid. For example, they have been widely used as preservatives in pharmaceutical, cosmetic, agriculture, and polymer industries and are recognized as valuable platform chemicals for a growing nonfossil industry (25).
The industrial production of carboxylic acids has undergone a cumbersome and ineffective process that generates more energy consumption and threatens the current environment. For instance, one adopted route to synthesize formic acid undergoes the direct carboxylation of methanol and subsequent hydrolysis of methyl formate, which has evident shortcomings, such as high cost and low production efficiency (26). Another developed synthesis route using lignocellulosic biomass to produce formic acid still suffers from 5 complicated steps, such as acid hydrolysis, wet oxidation, and catalytic oxidation, leading to ultra-low biomass utilization and poor selectivity (27). Recently, the direct conversion of CO2 into formic acid has become widely appealing due to the drive for carbon neutrality and the economics of the synthetic route. The high yield and selectivity of formic acid are expected under a low energy consumption, profiting from a one-step synthesis path and well-developed heterogeneous CO2 activation process.
Likewise, the synthesis of other carboxylic acids, such as benzoic, acetylenic, amino, and lactic acids, faces vigorous challenges in activating inert CO2 and C-H bonds of organic substrates, leading to excessive energy consumption and possible impure products from competitive reactions (28). This outcome is evident in the synthesis of benzoic acid by the partial oxidation of toluene using a cobalt-manganese catalyst under high temperature.
Benzaldehyde forms as a side product, and the conversion rates of toluene are far from satisfactory. Another case is the preparation of acetylenic acid, where metal-organic reagents that are sensitive to water and air are often needed and operated under anhydrous and oxygenfree conditions, increasing the production cost and creating challenges for industrialized operations (29). In the case of producing amino and lactic acids, the original organic reactants containing multiple functional groups have the possibility of side reactions. The transformation of functional groups that may produce undesired products should be avoided.
The central goal is to prepare various carboxylic acids with CO2 with a high conversion rate and selectivity under mild conditions to overcome the above challenges and minimize carbon emissions. Thus far, significant progress has been reached in producing numerous kinds of carboxylic acids through photocatalytic reduction, electrocatalytic reduction, and thermally 6 driven organic transformation (Figure 1) (30)(31)(32). Despite the great achievements, the unsatisfactory utilization rate of catalytic sites, competitive side reactions, and unclear reaction mechanism pathways should still be addressed by developing efficient heterogeneous catalysts and revealing the inner relationship between the structure and activity.
Scope of this Review
The increasing literatures recognize the urgency of reducing CO2 emissions to achieve carbon neutrality. Most published reviews are focused on the specific materials and characterization techniques in catalyzing CO2 conversion or are limited to preparing formic acid from CO2 (33)(34)(35)(36). However, few reviews have systematically summarized the progress and challenges in producing carboxylic acids using CO2. A systematic understanding of how the catalyst structure contributes to the yield or selectivity of products is still lacking, and it is not clear which factors primarily contribute to the conversion efficiency and product selectivity.
Therefore, an opportune overview of construction strategies for advanced catalysts and an elaboration of the mechanical process in converting CO2 into carboxylic acids through the drivers of light, electricity, and heat are highly desirable and may provide important insight into advancing the development of practical strategies in mitigating carbon emissions and producing more high-value chemicals, such as carboxylic acids.
This review starts with a general introduction of the basic principles of catalyzing CO2 into various carboxylic acids through photocatalysis, electrocatalysis, and thermal catalysis.
Then, we highlight the adopted strategies, including composite catalysts, heteroatom doping, morphology control, and surface functionalization in rationally engineering heterogeneous catalysts to boost the conversion of CO2 into carboxylic acids. Furthermore, recent experimental and theoretical progress has revealed the reaction mechanism and presented rich examples to reveal the achievements in converting CO2 to carboxylic acids. Finally, the key challenges and prospects are presented for guiding the rationale design of heterogeneous catalysts and the improvement in the conversion efficiency of CO2 to carboxylic acids. We aim to illustrate the important relationship between the structure of the designed catalysts and reaction activity by discussing vital influencing parameters in the reaction process and providing fundamental principles and strategies for further developing superior heterogeneous catalysts.
Fundamentals of Catalyzing CO2 into Carboxylic Acid
Photocatalytic CO2 Conversion Process
Photocatalytic reduction of CO2 into highly valuable chemicals has been attracting considerable attention due to the economy of solar energy, which is expected to replace fossil fuels, and the utilization of CO2 with minimal carbon emissions ( Figure 2A). In this process, well-designed photocatalysts with specific bandgap sizes and positions of the conduction band (CB) and valence band (VB) occupy a core position in enhancing solar energy utilization due to their ability to harvest light and drive the following redox reactions (37,38). Typically, the photocatalytic CO2 reduction to carboxylic acids includes the following three steps: (1) lightharvesting, (2) generation and separation of a photogenerated charge carrier, and (3) surface redox reactions ( Figure 2B). The corresponding photocatalytic process involves harvesting the incident photons by generating photoexcited electrons (e -) and holes (h + ) over the traditional semiconductors. Light-harvesting determines the utilization rate of solar energy and facilitates the following CO2 photoreduction step. Considering that visible light and near-infrared (IR) 8 light account for more than 95% of natural light, many attempts have been made to enhance light-harvesting photocatalysts (39). For example, the visible-light absorption of graphitic carbon nitride can be increased due to the produced nitrogen vacancies and modified electron structure through polymerization of dicyandiamide using tartaric acid (40). Furthermore, another example demonstrates that the enhanced photocatalysis performance can be realized in Ti-doped SnS2 by forming an intermediate bond to extend the absorption of IR light (41).
In the second step, the formed electron and hole (e-h) pairs migrate to the surface of the designed catalysts. The photogenerated charge separation process is accompanied by recombination, and only a few photogenerated electrons participate in the following CO2involved reaction. Numerous strategies have been developed to suppress the recombination of charge carriers to overcome the inefficient utilization of photogenerated electrons. For instance, the photocatalytic activity of Bi2WO6 increased greatly by reducing the bulk Bi2WO6 into Bi2WO6 nanosheets (NSs) due to the minimized charge transport pathway, leading to the rapid migration of photoexcited electrons and holes to the surface of photocatalysts (42). In addition, combining the semiconductor photocatalyst with carbon-based materials to form composite catalysts efficiently boosts the carrier separation efficiency due to the improved conductivity with the aid of support. Composite catalysts, such as CdS@biomass porous carbons, can be used as electron reservoirs to boost the separation of charge carriers and the transportation of electrons owing to good conductivity, leading to excellent activity in CO2 photoreduction under visible irradiation (43).
After the charge migrates to the catalyst surface, it reacts with the CO2 adsorbed around the active site. Engineering active sites can stimulate the occurrence of surface redox reaction 9 and effectively regulate the activation energy barrier of the intermediates to produce carboxylic acids, leading to the desired products with high activity and selectivity (44,45). For instance, the selectivity of formic acid can be tuned by installing different metal active centers with variable electron structures into covalent organic frameworks (COF). The metal sites, as a poor π-donor, prefer to enhance the C-O bonding force of CO2, producing formic acid, whereas metal sites with an electron-rich coordination environment tend to weaken and break the C-O bond to form CO (46).
In the past few years, great progress has been made in boosting the conversion efficiency of CO2 into carboxylic acids through photocatalysis by optimizing the structure and composition of photocatalysts, such as adjusting the band structure and allowing the electron pumps to accelerate the surface charge separation and transfer (47). Numerous highly valuable carboxylic acids can be obtained through the photocatalytic conversion path with CO2 ( Figure 2C). Nevertheless, the process of producing carboxylic acids is often accompanied by producing a diverse range of products via proton-coupled multi-electron transfer processes with thermodynamic potentials between about -0.20 and -0.70 V. For instance, formic acid is produced through two electron transfer processes with a potential of -0.61 V, which faces competitive reactions, such as the hydrogen evolution reaction with a potential of -0.42 V, reduction of CO2 into CH4 with a potential of -0.24 V, and reduction of CO2 into CO with a potential of -0.52 V(48).
The unfavorable energy barrier for producing formic acid should be reduced by introducing efficient catalysts to enhance the reaction kinetics. Furthermore, some effective strategies, such as enhancing the hydrophobicity of the catalyst surface to inhibit the hydrogen evolution reaction and controlling the composition of the catalyst to suppress the occurrence of multiple electron transfer processes, should be considered to improve the selectivity of formic acid.
Electrocatalytic CO2 Conversion Process
Electrocatalytic CO2 reduction to valuable fuels represents an appealing way to make full use of CO2 as a C1 resource, driven by electricity generated through renewable energy sources, such as wind and hydropower ( Figure 2D) (49). As a result of the significant decline in the cost of electricity, electrocatalytic CO2 reduction exhibits great potential for future practical and large-scale industrial applications. The appealing advantages in this process include the highly selective preparation of chemicals, satisfactory electric-power utilization efficiency, and environmentally friendly reaction medium. Therefore, researchers are enthusiastic about exploring advanced devices, efficient catalysts, and green additives to realize high-efficiency electrocatalytic CO2.
The design of heterogeneous catalysts for electrocatalytic conversion of CO2 into formic acid with superior performance depends on the accurate understanding of the mechanical process ( Figure 2E) (50)(51)(52). It is generally accepted that, in the initial stage, CO2 is adsorbed on the catalyst surface to form CO2*, where * indicates a binding site at the catalyst surface.
The adsorption and desorption of CO2 on the catalyst surface can be precisely regulated by introducing defects and tuning the catalyst structures to improve formic acid production. Duan et al. reported that Bi/CeOx has excellent CO2 adsorption capacity due to the intrinsically enhanced ability to absorb CO2 with Bi and the inherent heterogeneity of amorphous CeOx (53).
The formation of CO2* with a reduced energy barrier in Bi/CeOx facilitated the subsequent 11 conversion into formic acid products.
In the following step, the formed CO2* obtains one electron to produce *CO2· − , which is the rate-determining step of the electrocatalytic conversion of CO2 into HCOOH/HCOO − .
The corresponding process faces the problem of a kinetically sluggish and excessive energy barrier. The formed *CO2· − is further protonated to generate *OCHO, which can finally be reduced to generate HCOO − by obtaining one electron. Different reaction pathways may occur due to multiple electron and proton transfer processes. Variable intermediate species, such as *COOH, *CO, *COH, and *CHO, could exist in the reaction system, leading to undesired products, such as CO, CH3OH, CH4, and multi-carbon products ( Figure 2F) (54). Therefore, promoting the formation of intermediates to obtain formic acid and avoiding the production of C-C bonds are necessary to eradicate the barrier from efficient conversion in practical applications. For instance, pure Sn and Bi usually have an unfavorable binding energy of the intermediate for producing formic acid, which can be solved to form Bi-Sn aerogel(55). The synthesized Bi-Sn can inhibit the formation of *COOH, which tends to transform into CO, and suppress the hydrogen evolution reaction with less H2 than pure Bi.
Thus far, great achievements have been made in electrocatalytic CO2 reduction into formic acid (56). The selectivity of formic acid production can reach more than 90% through variable heterogeneous catalysts, demonstrating considerable potential for commercialization.
Although great progress has been achieved, some challenges still exist and should be overcome to meet the criteria for practical applications. For example, the efficient preparation of formic acid is often achieved under alkaline conditions, which helps to form intermediates that tend to generate formic acid and accelerate electron transfers. In contrast, the produced formic acid often exists in the form of formate in an alkaline environment, leading to the need for further acidification treatment with more energy consumption. Therefore, exploring the efficient synthesis of formic acid under acidic conditions is meaningful, paving the way to an efficient one-step synthesis. Furthermore, the hydrogen evolution reaction should be suppressed due to water as the solvent competing with CO2 to participate in the reduction reaction.
Electrocatalytic CO2 reduction and hydrogen evolution reactions involve hydrogen transfer, adsorption, and desorption. By regulating the active sites of the catalyst to inhibit the occurrence of the hydrogen evolution reaction, the yield and selectivity of formic acid can be effectively improved. In addition, the reports on the formation of other carboxylic acids, such as acetic and aromatic carboxylic acid, are still rare due to the difficulty of controlling multiple electron transfers (that tend to have side reactions) and the inertness of C-H in organic reactants.
Fortunately, these challenges can be overcome by developing high-efficiency catalysts to accelerate the hydrogen transfer, reducing the activation energy required to form intermediates, *OCHO, and strengthening the ability to activate CO2 and promote the reaction with inert organic reactants.
Thermocatalytic CO2 Conversion Process
Recently, thermocatalytic CO2 conversion into carboxylic acids has been fully developed as an alternative strategy for using the CO2 molecule ( Figure 2G) (57,58). It is a relatively practical route to convert inert CO2 compared to the photocatalytic or electrocatalytic path. It has apparent advantages and feasibility in preparing carboxylic acids, such as benzoic, acetylenic, amino, and lactic acids, with higher commercial values and wider application prospects. However, the participation of CO2 in the reaction should usually be carried out under 13 high temperature and pressure due to the nature of its remarkable kinetic and thermodynamic stability (59). Thus, higher energy consumption is often required in thermocatalytic CO2 conversion into carboxylic acids, and the harsh reaction conditions could introduce great challenges in ensuring the purity of the products. As a result of recent extensive and in-depth research on the thermocatalytic conversion of CO2 to carboxylic acids, powerful strategies, such as improved atomic utilization and a regulated coordination environment, electronic structure, and space chemical environment of active sites, have been developed to drive the inert CO2 to participate in the reaction under relatively mild conditions. According to different reactants reacting with CO2, the reaction types of thermocatalytic CO2 into carboxylic acids primarily include the hydrogenation of CO2, Friedel-Crafts -acylation reaction, and carboxylation of terminal alkynes. Hydrogenation of CO2 to produce formic acid has been regarded as a mature and promising route to ensure the effective utilization of CO2 and economic viability (60). However, it is not thermodynamically favorable with the free energy change (ΔG 0 ) of 33.0 kJ mol −1 (CO2(g) + H2(g)/HCOOH(l)). The inherent thermodynamic obstacles could be overcome by reacting in an aqueous solution to make the conversion of CO2 into formate more likely (61). When the hydrogenation of CO2 occurs in the liquid phase, the reaction (CO2(aq) + H2(aq)/HCOOH(aq)) is more prone to occur with the decline in free energy (ΔG θ = −4 kJ mol −1 ). However, the conversion efficiency is still far from satisfactory if no catalyst is involved. The utilization of heterogeneous catalysts has been emphasized to accelerate CO2 conversion by enabling CO2 capture and facilitating the formation of specific intermediates, such as carbonate and bicarbonate, according to the possible mechanism process. In a typical CO2 hydrogenation process, it is widely accepted that H2 is first dissociated into a hydride species and proton through a heterolytic process ( Figure 2H) (62,63). The formed hydride species becomes an intermediate of metal-bound formate by undergoing a nucleophilic attack on the carbon atom of CO2 via metal-hydride bonds, which is usually regarded as the rate-determining step in the CO2 hydrogenation process. Then, formate is formed by reducing the produced intermediate using hydride, instantly recovering the surface of active sites.
Although CO2 hydrogenation can produce formic acid, some other challenging issues still exist and should be solved. For instance, organic amine bases, such as ethanolamine, are added to the reaction system to overcome unfavorable free energy, leading to increased costs and difficulty in separation and purification. Furthermore, the reaction of CO2 hydrogenation involves a gas-liquid-solid multi-phase, and this complex reaction system causes obstacles in exploring the mechanisms for the activation and transformation of H2 or CO2 on the surface of selected catalysts. Fortunately, abundant heterogeneous catalysts with different chemical environments and clear structures have been developed to obtain satisfactory performance and deeply investigate the inner origin of catalytic activity. In future studies, more research should explore efficient non-noble heterogeneous catalysts, understand the factors affecting H2 adsorption/activation on non-noble metal sites, and search reasonable methods to tune the microenvironments of the active sites to activate H2 and CO2.
The preparation of multi-carbon carboxylic acid products via carboxylation of terminal alkynes and Friedel-Crafts acylation reactions exhibit outstanding advantages that include a satisfactory yield and green reagents over other synthetic routes, such as the acid-mediated hydrolysis of nitriles (64), carbonylation of organic halides with toxic and odorless CO(65), and 15 oxidation of primary alcohols ( Figure 2I) (66). In the carboxylation of terminal alkynes with CO2, unsaturated terminal alkynes are deprotonated using an inorganic base and are coordinated onto the surface of metal sites. Then, the captured electrophilic CO2 is further inserted into the C≡C-metal bond to provide the intermediate, regarded as the rate-determining step for the entire process. Finally, the product, acetylenic acid anion, is released from the catalyst surface. However, heterogeneous catalysts containing Ag, Au, or Cu have been reported to catalyze the conversion of terminal alkynes into carboxylic acids with relatively good activity (67). Some difficulties include the need for an additional strong base and the inertness of weakly nucleophilic terminal alkynes that have difficulty attacking CO2. These problems lead to the need for acidification to obtain carboxylic acids, posing a serious challenge to the catalyst stability and poor conversion efficiency. Based on years of exploration, some practical strategies, such as enhancing the ability to capture CO2, controlling the electronic state of metal sites, and optimizing the utilization of active metal centers, have been adopted to overcome existing challenges. It is expected to develop novel heterogeneous catalysts that can activate alkynes and CO2 under acidic conditions and reduce the activation energy of forming acetylenic acid, achieving enhanced efficiency in carboxylic acid production.
The Friedel-Crafts acylation reaction to prepare aromatic carboxylic acids dates to the Al2Cl6/Al catalytic system created by Olah et al (68). The accepted pathway involves an initial complexation between CO2 and metal sites to form a CO2-metal complex (69). The produced electrophilic complex reacts with arene, turning into carboxylate coordinated on the catalyst surface and is identified as the rate-determination step. Subsequently, the final product, aromatic carboxylic acids, can be obtained via deprotonation and proton transfer. However, 16 various homogeneous systems, such as TiCl4, FeCl3, Ga(OTf)3, and CF3SO3H, and heterogeneous systems, including metal nanoparticles (NPs), metal-organic frameworks (MOFs), and others, have been explored to boost the reaction occurrence. They still have limited ability to activate C-H bonds in the benzene ring and inert CO2 and exhibit poor regioselectivity or stereoselectivity for aromatic substrates with the ortho or meta position to participate in the carboxylation reaction. Benefiting from the increased improvement in material characterization methods and increased maturity of preparation methods, the design of heterogeneous catalysts with a controllable spatial environment or surface confinement effect could effectively determine product selectivity by affecting the kinetic behavior, activation energy, and intermediate types.
Engineering Active Sites to Accelerate CO2 Conversion
Highly active heterogeneous catalysts play a decisive role in converting CO2 to carboxylic acids. Practical strategies can improve the activity, such as maximizing exposed active sites by constructing composite catalysts or tuning the catalyst morphology and increasing the intrinsic activity of the active site via doping heteroatoms and surface functionalization to enhance the activity of traditional catalysts (70). These strategies can sometimes work together in the same catalytic system to realize great improvements in activity and selectivity. In the following section, these strategies have been well explained, whereas the corresponding relationships between the structure and catalytic property for each strategy are briefly discussed.
Composite Structure
The composite catalysts primarily refer to the combination of different materials to form supported heterogeneous catalysts, enriching the structure types and delicately enhancing catalytic properties compared with single-component catalysts ( Figure 3A) (71)(72)(73)(74)(75).
Specifically, the components containing metal sites, such as metal nitride, metal complexes, oxides, noble metals, and metal clusters, are often loaded onto functional carriers with auxiliary catalytic functions (76)(77)(78). The reported functional emerging carriers include traditional metal oxide or metal hydroxide and involve emerging support ranging from carbon-based materials (graphene oxide, carbon nanotubes, carbon nitride, and carbon foam) to porous materials (MOFs, COFs, conjugated microporous polymer, and zeolite) (79)(80)(81)(82)(83).
In the early stages of the development of composite catalysts for accelerating CO2 conversion, traditional carriers, such as metal oxide, are often used to support noble metals or immobilize homogeneous metal complexes (84,85). The catalytic activity of this type of composite catalyst can be further improved by introducing defects, increasing the loading of active species, and other methods. As a result of the weak interaction between the active constituent and carrier, the stability of synthesized composite catalysts should be guaranteed by introducing composites with strong interactions. Recently, based on an elaborate design, a multiple-composite system composed of Cu2O-Pt/SiC/IrOx proved to be an efficient artificial photosynthetic catalyst for converting CO2 into formic acid due to the greatly prolonged lifetime of photogenerated electrons and holes ( Figure 3B-D) (86). This study realizes the separate operation of CO2 reduction and H2O oxidation, facilitating the suppression of the backward reaction of products and promoting whole conversion efficiency.
Another promising composite catalyst to enhance the intrinsic activity of active centers is selecting carbon-based materials as functional carriers. Among these carbon-based materials, graphene, carbon nanotubes, and carbon foam are regarded as appealing carriers due to their good electrical conductivity and nanostructure, conducive to enhancing the material transfer rate (87,88). The inherent activity of the active center is improved by ameliorating the poor electron conductivity and inefficient electron transfer, and the turnover number and turnover frequency of the composite catalysts increase greatly by fully exposing and dispersing the active center. Lou et al. reported that an emerging composite heterogeneous catalyst composed of Bi2O3 NSs and a conductive multi-channel carbon matrix could catalyze the CO2 reduction into formic acid with high activity ( Figure 3E-G) (89). This superior performance can be attributed to the synergistic effects of the composite matrix, facilitating electron transfer and enhancing CO2 by producing pyrrolic-N and pyridinic-N. Furthermore, another carbon-based material, carbon nitride, has a good ability to absorb light, and the abundant nitrogen sites are beneficial to capture CO2 and improve the turnover frequency of the active centers (90).
Compared with carbon-based composite catalysts, porous material-based composite catalysts have unparalleled advantages due to their ultrahigh specific surface area, adjustable pore environment, and abundant acid or basic sites (91). The porous structure can enhance the catalytic efficiency of the active site by capturing CO2 around the active site and increasing the substance transfer rate. Furthermore, the introduced basic sites and Lewis acid sites in the support are beneficial to activate the CO2 in a nonlinear configuration, which promotes the declination of the activation energy required for the rate-determining step of the reaction. In addition, some conjugated porous materials, such as MOFs, with the ability to capture and activate CO2 molecules are used to construct sandwich-shaped composite catalysts to produce alkynoic acid with CO2 ( Figure 3H-J) (92). Another type of porous material, COFs, can combine active centers to realize the efficient photocatalytic reduction of CO2 to formic acid upon visible-light irradiation due to the excellent visible-light harvesting ability and extended life of photogenerated charge carriers via accelerating the electron transfer(93).
Heteroatom Doping
Heteroatom doping is another effective strategy to enhance the activity of heterogeneous catalysts in converting CO2 into carboxylic acids, which can be widely used to form metaldoped oxides, metal alloys, intermetallic compounds, multiple metals with porous materials, and multi-metal complexes ( Figure 4A) (94)(95)(96)(97)(98)(99)(100). In addition, some nonmetal-doped heterogeneous catalysts, including doping nonmetal elements, such as N, P, S, and B, into carbon-based materials or metal-containing materials are designed to boost the catalytic conversion of CO2 (101)(102)(103). Benefiting from the introduction of doped elements, the electronic structure, coordination environment, and geometric configuration of pristine active sites change significantly, leading to enhanced catalytic activity compared with the original state.
Based on the low costs of preparation, nonmetal-doped heterogeneous catalysts have aroused enthusiasm in promoting the preparation of carboxylic acids from CO2. Doping heteroatoms can endow pristine catalysts with improved electrical conductivity and abundant catalytic active centers(104). For instance, nonmetal-doped heterogeneous catalysts, such as boron-doped graphene, can catalyze CO2 into formic acid with higher Faradaic efficiency than that of pure graphene (105). The enhanced catalytic performance can be attributed to the stronger adsorption of activated CO2 resulting from the high spin density of the introduced boron element. As nonmetal atoms have a weaker activation effect on CO2 than metal atoms, the increase in the inherent activity of the material itself is limited.
Given the limited activity of nonmetal catalytic systems, more attempts have been made 20 to dope heteroatoms on heterogeneous catalysts containing metal atoms (106)(107)(108)(109)(110). Doping sulfur into indium catalysts has been reported to catalyze the electrocatalytic CO2 reduction to formic acid with excellent catalytic performance due to the strong ability of sulfur to activate water to form hydrogen species, which can further react with CO2 to produce formate ( Figure 4B-D) (111). Theoretical calculations reveal that doping sulfur into indium significantly decreases the Gibbs free energies (ΔG) for forming HCOO* and HCOOH* in the pathway of The multi-metal-doped catalytic system is usually regarded as a more effective strategy to tune the inherent activity of the active center than the mentioned strategies due to the significant change in the electronic state and coordination environment, which can have a decisive influence on activating the CO2 and stabilizing intermediates(55, [112][113][114][115][116][117][118].
Morphology Control
Tuning the morphology of the heterogeneous catalysts effectively improves the insufficient utilization of catalytic sites of inherent catalysts (122)(123)(124). In general, the categories of morphology for the designed heterogeneous catalysts can be divided into hollow structures, one-dimensional nanowires, two-dimensional (2D) NSs, quantum dots, and hierarchical porous structures ( Figure 5A) (125)(126)(127)(128). The changes in catalyst morphology have positive effects on the specific surface area, exposed active site, dispersibility in solution, and transfer rate of reactants and can thus endow additional defects, grain boundaries, unsaturated sites, and improved conductivity, which are beneficial for enhancing activity compared with the unprocessed morphology(129-132).
22
The solid bulk nature of conventional heterogeneous catalysts leads to only a small amount of metal sites on the surface participating in the reaction with a low turnover and poor mass transfer rate. In contrast, the catalytic activity of these heterogeneous catalysts can be enhanced via elaborate morphology control. For instance, hollow heterogeneous catalysts, such as CuInS2, have been approved as excellent electrocatalysts to produce formic acid by facilitating the electron transfer and interaction between the reactant and active site and enriching the CO2 local concentration in the void of heterogeneous catalysts (133). Furthermore, a hollow photocatalyst can exhibit higher activity in photocatalytic CO2 reduction than that of its bulk counterpart due to the promoted light absorption ability, abundant active sites, and mass transfer channels. In addition, SnO2 quantum wires with grain boundaries have proved to be efficient catalysts to drive the conversion of CO2 into formic acid and exhibit better catalytic activity than SnO2 NPs ( Figure 5B-D) (134). The enhanced activity could be attributed to more
Surface Functionalization
Surface functionalization can effectively combine the merits of organic and inorganic components and greatly improve the catalytic activity of the inherent catalytic centers for converting CO2 into carboxylic acids ( Figure 6A) (137)(138)(139). The common organic units, including amide, Schiff base, amine, hydroxyl, pyridine, azazole, and light-adsorbing organic ligands, can be flexibly modified using chemical bonds on the surface of typical heterogeneous catalysts to meet the need to improve catalytic activity (140)(141)(142). Surface functionalization is suitable for a wide range of traditional heterogeneous catalysts, such as metal oxide, metal clusters, metal NPs, porous materials, and others (143)(144)(145). Moreover, some metal-containing organic molecules, such as porphyrin, phthalocyanine, and the Schiff base complex, can be grafted onto the surface of the original catalysts to boost catalytic performance (146,147).
Functionalization of organic groups on the surface of the active constituent allows many positive facilitators, such as an improved charge transfer rate, strong light-responsive ability, enhanced capture of CO2, and stabilization of intermediates (148). For instance, the semiconductor functionalized with an organic linker can obtain higher selectivity in photocatalytic CO2 reduction to formic acid than an untreated one (149). The introduced organic constituents could smoothly allow efficient hole and electron migration on the catalyst surface, 24 leading to the enhanced conversion efficiency of CO2. Furthermore, some organic groups with enhanced CO2 capture capacity, such as amide linkages and tris-N-heterocyclic carbene, can be introduced in heterogeneous catalysts to realize the selective electrocatalytic CO2 reduction to formic acid by enhancing the concentration of CO2 around the active site and suppressing the formation of intermediates to produce CO ( Figure 6B-D) (150). The theoretical calculations have found that the tris-N-heterocyclic carbene group on the surface of Pd favored the formation of COOH* and the hydrogenation of COOH* into HCOOH with a lower energy barrier than that of the pure Pd catalyst.
Recent studies have noted the importance of surface functionalization in enhancing the stability of the original heterogeneous catalyst and auxiliarily activating the reaction substrate.
For instance, a bipyridine-based covalent triazine framework with an Ru active center has been reported in catalyzing CO2 hydrogenation with high activity. However, the bond between the metal and bipyridine is not strong enough, and the active center could dissociate into the reaction solvent, leading to poor stability of the designed catalyst ( Figure 6E-G) (151,152). An oxyanionic ligand is a well-established approach in stabilizing the active species by avoiding the dissociation of metal sites from bipyridine. Moreover, the introduced oxyanionic ligand could assist in the heterolysis of H2, which is the rate-determining step for this conversion, leading to highly efficient conversion.
Organic functional groups can form specific intermediates to promote the reaction rate due to the reduced activation energy of the rate-determining step. For instance, different organic amines can be flexibly grafted onto the surface of noble metals, such as Au NPs, to catalyze CO2 hydrogenation, which can stabilize noble metals to avoid aggregation and enhance CO2 concentration (153). More importantly, these grafted organic amines can help activate CO2 through a nonbicarbonate route with negative free energies for adsorption of CO2 and can benefit from forming the zwitterion intermediate, which is regarded as beneficial for producing formic acid ( Figure 6H-J). The density functional theory (DFT) calculation has revealed that the added Schiff base plays a vital role in the activated CO2, which can be further hydrogenated by the activated H to form an HCO2 intermediate and become HCOOH with the assistance of another H atom.
Advanced Characterization Techniques and Theoretical Calculations
Although great progress has been achieved in the catalytic conversion of CO2 into carboxylic acids, previous studies have suffered from a lack of clarity in revealing the dynamic process of the CO2 transformation. Considering that the catalytic reaction and product selectivity are dominated by the evolution of the catalyst structure in the reaction process and the interaction between the active sites and reactants or intermediates, it is crucial to distinguish the true active centers and their dynamic evolution in the reaction process (154). However, identifying real active sites and monitoring the evolution of the catalysts or involved reactants has been vigorously challenged by dynamic changes in the catalyst structure during the reaction (155). In addition, difficulties exist in distinguishing complex intermediates due to multi-step reaction paths in converting CO2 into carboxylic acids (156). Thus, these obstacles preclude the recognition of real active sites and reveal the reaction mechanisms of CO2 conversion. As a result of developing numerous emerging in situ characterization instruments, we can approach observing the true state of the catalysts in the reaction process via operando techniques at the molecular level.
Parallel to the characterization technique development, the theoretical calculation should improve the fundamental understanding of the mechanical process in converting CO2 to carboxylic acids. The ongoing development of the DFT has led to significant progress in preparing the catalyst from a blind attempt to accurately predict using computer-aided prediction. Importantly, the reactivity origin of the designed heterogeneous catalysts could be uncovered by analyzing the effect of changes in the electronic state in metal sites, exposed crystal faces, and coordination environment based on DFT calculations. The following section introduces advanced in situ techniques and significant progress in theoretical calculations in converting CO2 into carboxylic acids.
In situ Characterization Techniques
Moreover, X-ray absorption spectroscopy (XAS) has become an essential characterization technique to detect the structural evolution of catalysts during CO2-involved reactions ( Figure 7A) (157). The specific elements, catalyst coordination environment, and chemical valence changes that affect the conversion efficiency of the CO2 and product selectivity can be determined using XAS ( Figure 7B). In addition, XAS can be divided into the extended x-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) spectra based on different origins. The XANES spectrum provides fingerprint information on the geometric structure, oxidation state, and electronic structure of the detected metal sites. Furthermore, the EXAFS spectrum identifies the atomistic structure/configuration and coordination geometry of reactive centers combined with a fitting analysis. Recently, Li et al.
have analyzed the EXAFS results by building reasonable models, revealing abundant defects in reduced Bi2O3 in the CO2 reduction process through a model-based quantitative analysis (158). In addition, the authors have testified that the changes in chemical valences in bismuth could affect the electrocatalytic reduction of CO2 into formate with in situ XAS ( Figure 7C). to the symmetric stretching adsorption of CO3 2is more obvious over the S-doped Cu-based catalyst than the undoped one, manifesting that S doping can enhance the adsorption ability of carbonate intermediates ( Figure 7I)(160).
28
Compared with the above-mentioned techniques, in situ IR spectroscopy has advantages in detecting the intermediates formed on active sites during the reaction, benefiting from its high sensitivity to the vibration mode of the adsorbed molecules ( Figure 7J). The IR absorption peak position is the characteristic signal of the adsorbed molecule, reflecting the structural composition and chemical groups in the reaction process ( Figure 7K). For example, Gong et al. have investigated the active species in CO2 reduction over SnOX as a catalyst using in situ attenuated total reflection surface-enhanced IR absorption spectroscopy (161). The signals of the HCOO* can be identified by analyzing the characteristic peaks when the potential is applied to the surface of Sn-OH branches. In addition, the intensity of HCOO* can be quantitatively analyzed to evaluate the content of produced intermediates, assessing the influence of different hydroxyl content on catalytic activity ( Figure 7L).
Theoretical Calculations
Extraordinary progress in theoretical calculation has created enormous opportunities in evaluating the energy required for the adsorption, activation, and conversion of reactants in the catalytic reaction process, allowing the design of highly efficient heterogeneous catalysts (162)(163)(164)(165). (Figure 8D-F). The latter step is regarded as the rate-determining step for the overall reaction. By comparing the energy of the rate-determining step of different spin-state COF-367-Co catalysts, the spin-state transition of Co can be disclosed as the decisive factor in forming formic acid with CO2. Furthermore, product selectivity in converting CO2 can be explained by evaluating the energy superiority of various products for the designed catalysts. For example, the process of electrocatalytic conversion of CO2 into formic acid is often accompanied by producing CO. By comparing the Gibbs free energies of electrochemical CO2 reduction into the corresponding products, the generation of CO via a CO* intermediate or production of HCOOH(g) via the COOH* intermediate can be predicted over synthesized catalysts (169). In addition to explaining the fundamental reasons for product selectivity, the occurrence of competing reactions on the surface of catalysts can be inhibited by optimizing the catalyst structure.
With the development of machine learning and theoretical calculation methods, more efficient heterogeneous catalysts are predicted and synthesized to boost the conversion of CO2involved reactions (170). For instance, Guo et al. have successfully used machine learning to electro-catalyze CO2 into formic acid with high yield by discovering and optimizing additives in Cu-based catalysts ( Figure 8G) (171). In the initial step, they select combinations from the collected additive library, including different metal salts and water-soluble organic molecules, to tune the morphology and surface structure of Cu catalysts ( Figure 8H). Then, through the screening of machine learning, the experiment is guided using Sn containing metal salts and organic ligands containing aliphatic amino and carboxyl groups to obtain high selectivity of formic acid (FEHCOOH = 65%) ( Figure 8I). In the future, machine learning is expected to play a more important role in achieving efficient conversion and preparation of a variety of high-value carboxylic acids.
Frontier Progress of Conversion of CO2 into Carboxylic Acid
Photoreduction of CO2 into Carboxylic Acid
31
The synthesis of multi-carbon carboxylic acids with a high conversion rate is challenging due to the transfer of more electrons involved in the photoelectric conversion process. Some breakthroughs have been made in preparing multi-carbon carboxylic acids, such as acetic acid, through photocatalytic CO2 reduction (172). Wang Figure 9F).
In addition, a great breakthrough has been made in promoting CO2 to participate in the photocatalytic organic reaction to produce carboxylic acids ( Figure 9G). Some organic carboxylic acids with important application values, such as trans-cinnamic acid and diaryl αamino acids, can be obtained under blue-light excitation or sunlight. For instance, Schmalzbauer et al. have reported that a redox-neutral C-H carboxylation of arenes and styrenes can be realized by reacting with CO2 to afford carboxylic acids using an anthrolate anion photocatalyst under the blue-light excitation ( Figure 9H) (175). Then, they have proposed a possible reaction mechanism for the photocatalytic C-H carboxylation of the heterocycle. In the initial step, the catalyst, 2,3,6,7-tetramethoxyanthracen-9(10H)-one (TMAH), is deprotonated to form an anionic species with the aid of a base. Next, the excited anion TMA* is formed under visible light (455 nm) and is quenched by the organic substrate (arene) to produce the radical TMA and radical arene anion. Afterward, CO2 attacks the radical arene anion to generate a radical carboxylate intermediate that is deprotonated immediately to produce a carboxylic anion in the presence of the base ( Figure 9I). The final products are 33 obtained by further treatment with hydrochloric acid. This work presents new opportunities for an atom-economic and energy-efficient utilization of CO2 in producing aromatic carboxylic acids and drug intermediates.
Electroreduction of CO2 into Carboxylic Acid
Selective production of formic acid from CO2 electroreduction over abundant catalysts has achieved ideal activity of over 90% Faradaic efficiency. However, the neglected challenge concerning mixed products in an alkaline aqueous system should be overcome to satisfy the practical applications of electrocatalytic preparation of renewable formic acid. The generated formic acid in the conventional H-cell or flow-cell reactors is formate ions mixed with other ion impurities, such as K + and HCO3 − . This problem can be overcome by improving the reaction device. For instance, Xia et al. have developed an efficient strategy to resolve this challenge by decoupling the ionic conduction and allowing product collection (176).
Specifically, a porous solid electrolyte (PSE) layer is used to replace the traditional liquid electrolytes, promoting fast ionic transportation and recombining the generated formate and proton to form pure formic acid ( Figure 10A). The selected insoluble solid electrolyte provides a proper platform to collect the formic acid efficiently by flowing the deionized water through the PSE layer. Furthermore, they have synthesized an ultrathin 2D Bi catalyst to catalyze CO2 into formic acid using the new H + -conducting solid electrolytes. A high FEHCOOH of 93.1% is achieved, and negligible amounts of other ion impurities have been detected using inductively coupled plasma atomic emission spectroscopy ( Figure 10B).
Although it has been demonstrated that pure formic acid can be obtained with solid electrolytes, the formic acid concentration is limited due to the need for a significant amount 34 of water. Recently, Fan et al. have realized continuous generation of high-purity and highconcentration formic acid using an all-solid-state electrochemical device in which the generated formic acid can be efficiently collected via an N2 stream flowing through the PSE layer ( Figure 10C) (177). High activity (maximal Faradaic efficiency ~97%) and ultrahigh concentrations of pure formic acid solutions (up to nearly 100%) can be obtained over the Bi catalyst with an abundant grain boundary ( Figure 10D). This emerging system is expected to be suitable for modular and high-pressure systems, which have exciting potential in future large-scale production of formic acid. Future research should develop highly stable and active catalysts and solid electrolytes with excellent performance and efficient ion-exchange membranes to realize low energy consumption to convert CO2 into formic acid.
In addition to the preparation of high-concentration pure formic acid, there are numerous attempts for further progress in producing multi-carbon carboxylic acids via the electrocatalysis of CO2 (178,179). For instance, Genovese et al. have reported that the selectivity to acetic acid (61%) could be reached in the three-electrode cell over nanostructured ferrihydrite-like (Fh-FeOOH)/nitrogen-doped carbon ( Figure 10E) (180). This high activity for acetic acid production can be attributed to the formed nitrogen-coordinated iron (II) sites at the interface between iron oxyhydroxide and the support, demonstrated by operando x-ray spectroscopy techniques ( Figure 10F). Compared to producing formic acid from CO2, the selectivity is far from satisfactory due to possible competitive reactions. More effort should be made to design effective catalysts to enable C-C coupling.
Thermocatalytic Conversion of CO2 into Carboxylic Acid
In the thermocatalytic conversion of CO2 into carboxylic acids, the carboxylic acid yield should be improved, and the product selectivity, including regioselectivity, stereoselectivity, and chemoselectivity, should also be controlled by the desired catalysts. Great achievements have been made in recent years, profiting from long-term efforts and exploration (181). For instance, Martin et al. have reported that a host of unactivated alkyl chlorides can react with CO2 to produce carboxylic acids with a high conversion rate over catalysts containing Ni ( Figure 11A) (182). Moreover, an anti-carbometalation product has obtained with high selectivity based on this designed catalytic system. The high selectivity of the anti-product in converting secondary alkyl bromides may be attributed to forming rapid isomerization of vinyl radical species, which would undergo recombination to produce a different configuration of the Ni(I)BrLn species ( Figure 11B). This work realizes exquisite chemoselectivity and a high conversion rate for carboxylic acid production with unactivated alkyl chlorides and CO2.
Ling et al. have exploited the interface of Ag@MOF to provide a pseudo microenvironment with high CO2 pressure to enhance the direct C-H carboxylation at ambient conditions ( Figure 11C) (183). Specifically, the interface of Ag@MOF comprised an array of Ag nanocubes has been grafted with mercaptophenol as reaction substrates. XPS has been used to characterize the interaction between the substrate and MOFs, confirming the existence of Zn-O bonds between phenoxide and MOF, which cannot be found in methylbenzenethiol functionalized Ag nanocubes without MOF ( Figure 11D). As a result of the activation and confinement effects of MOF on reaction substrates, the direct C-H carboxylation of arene occurs at the NP@MOF interface under ambient pressure at 25°C. More importantly, an unprecedented meta-carboxylated arene is generated rather than a traditional orthocarboxylated product ( Figure 11E). This work introduces new opportunities to synthesize high-value products that cannot be obtained under common conditions and provides new inspiration for improving the selectivity of carboxylic acids.
Recently, Xiong et al. have reported that the hydrocarboxylation of alkynes with CO2 can be catalyzed to form a wide array of α-acrylic acids with high regioselectivity through the combination of Pd(PPh3)4 and 2,2′-bis(diphenylphosphino)-1,1′-binaphthalene (binap) under mild conditions (184). For example, for phenylacetylene, the product of α-acrylic acids can be obtained with a 70% isolated yield in high selectivity by adding 0.5 mol% Pd(PPh3)4 and 0.5 mol% binap ( Figure 11F). DFT studies have further revealed that alkynes react with CO2 via the cyclopalladation process, generating a five-membered palladalactone intermediate, and undergo a σ bond metathesis step regarded as the rate-determining step of the entire process.
The calculated results have demonstrated that the Markovnikov adducts, α-acrylic acids, are the main products with a more favorable free-energy barrier than the anti-Markovnikov product ( Figure 11G). This work reveals that the designed catalyst is a powerful tool to use CO2 to produce complex molecules with high selectivity.
Conclusions and Prospects
In the past few decades, the exhaustion of fossil fuels and the deterioration of the environment have necessitated carbon neutrality, and prior studies have noted the importance of consuming the emission of CO2 via a stainable and green approach. Accordingly, the direct conversion of CO2 into chemical compounds accomplishes both goals. Climate warming can be slowed, and fine chemicals can be produced in an economically and environmentally friendly way. Considering the wide application prospects and social needs concerning carboxylic acids, the direct conversion of CO2 into carboxylic acids has attracted considerable attention in fundamental research and industrial applications. Given the importance and social needs regarding this field, a systematic and in-depth review of the selective conversion of CO2 into carboxylic acids is urgently needed.
The process of CO2 conversion requires a controllable catalytic system to accelerate the conversion of reactants; thus, recent developments and feasible tuning strategies on designing heterogeneous catalysts are systematically summarized in this review. The past few years have witnessed numerous breakthroughs involving the conversion of CO2 into carboxylic acids, benefiting from the advancements in characterization techniques and the understanding of the mechanical process. However, many issues should still be addressed to achieve large-scale production of carboxylic acid compounds with a high conversion rate and satisfactory selectivity. Second, although remarkable progress has been made in photo-catalyzing CO2 into carboxylic acids, several challenging issues should be considered and solved. The use of near IR light and visible light is far from satisfactory, and low quantum efficiency hinders the widespread practical application of photocatalysis. Increasing the efficiency of photocatalytic CO2 conversion and making the most of natural light by constructing stable heterogeneous catalysts with sufficient activity and a strong ability to harvest broad-spectrum light are highly desired. In addition, the introduction of sacrificial agents or cocatalysts to guarantee conversion efficiency may create additional problems, such as high production costs and poor catalyst stability. The appealing solution is to develop heterogeneous catalysts with multiple functions to improve light utilization and produce synergistic effects between the active sites and cocatalysts and thus to get rid of the usage of sacrificial agents.
Third, electrocatalytic conversion of CO2 into high-value-added products, such as formic acid, is expected to reach the goal of actual production based on the continued development of efficient catalysts and facile reactors. However, the generation of multi-carbon carboxylic acids with high selectivity still has a long way to go due to the competition of multiple side reaction paths. Regulating the active catalytic sites via the electronic state, coordination environment, and chemical components is feasible to inhibit undesired products. Furthermore, the research on disclosing the reconstruction of the catalyst in the electrolyte process is still in its infancy, leading to a poor understanding of the relationship between structure and activity. More attention should be focused on revealing the changes in composition and structure that have occurred in the reaction process, reducing the over-potential required for CO2 reduction and inhibiting the occurrence of competitive reactions under the premise of ensuring the efficiency of carboxylic acid products.
Fourth, the conversion efficiency of the thermo-catalytic conversion of CO2 can be improved under harsh reaction conditions, such as high temperature and high pressure, but introduces substantial challenges to the selectivity of products due to the byproducts caused by the high energy. Especially for carboxylic acid compounds involving organic substrates, the regioselectivity, stereoselectivity, and chemoselectivity of products determine the purity and produce specific chemicals with different values and applications. Highly selective carboxylic acids can be synthesized under relatively mild conditions only by accurately constructing a steric hindrance environment, using the pore restriction effect and regulating the strength of the Lewis acidity and alkalinity.
Fifth, relatively high energy consumption with high temperature and pressure is usually required to obtain satisfactory yields of carboxylic acids, especially for preparing multi-carbon carboxylic acids. The accompanying process poses great challenges to the reaction devices and the stability of catalysts. More efficient strategies are urgently needed to promote the conversion of CO2 under green, environmentally friendly, and mild conditions. It has been demonstrated that seeking strategies to realize photoelectric conversion or electrothermal conversion could improve the efficiency of the input energy and create new opportunities to reduce carbon emissions and significantly decrease production costs.
Sixth, theoretical algorithms play a vital role in the deeper understanding of the reaction mechanisms and correlations between catalytic performance and structure. However, the 40 inherent limitations of theoretical models and the narrow applicability of theoretical methods greatly compromise the guiding role of theoretical calculation. Machine learning and artificial intelligence are highly desirable for the design of experiments, optimization of catalysts, understanding of the mechanism. By analyzing the available fundamental data and basic theory with machine learning, the discovery of efficient catalysts can be accelerated with an accurate guide rather than tedious trial-and-error investigations.
forming HCOOH compared with the undoped element. Similarly, doping a heteroatom, such as N, in Sn or Bi containing heterogeneous catalysts can enhance the inherent activity of the initial active sites for the electrocatalytic conversion of CO2 into formic acid. The introduced N element, accompanied by the generation of abundant oxygen vacancies, facilitates the declination of the reaction free energy of HCOO* protonation to form HCOOand weakened H* adsorption energy to suppress the hydrogen evolution reaction. In addition, doping heteroatoms into metal oxides can cause configuration distortions, enhancing activity in the hydrogenation of CO2 into formic acid by facilitating the process of H2 dissociation and accelerating the following rate-determining step for forming the HCOO* intermediate with a declined energy barrier compared with the undoped state.
For instance, doping metals to form alloys has been widely used to boost the hydrogenation of CO2 into formic acid (Figure 4E-G)(119). The reaction process is initially provoked by the dissociation of H2 to afford a metal-hydride species and undergoes the formation of the formate intermediate as the rate-determining step for the entire process. Benefiting from doping another metal atom with the electron donation effect, the electron-rich formed metal-hydride species more easily forms formate intermediate through a nucleophilic attack, leading to a decreased energy barrier of the intermediate and corresponding enhanced yields of formic acid(120). Usually, Cu-based catalysts produce hydrocarbons in electrochemical CO2 reduction, exhibiting limited selectivity toward a specific product. Doping single-atom Pb to form a Pb1Cu catalyst can exclusively catalyze CO2 into formate with high selectivity with over 95% Faradaic efficiency(121). Theoretical calculations have revealed that the Pb1Cu electrocatalyst could facilitate forming HCOO* rather than the COOH* path, leading to formate as the main product (Figure 4H-J).
inherent active sites created by the grain boundary-enhanced effect. The transformation of layered materials into 2D NSs with a single layer or a few layers can have enhanced and novel properties, such as enhanced conductivity and the facile diffusion of photogenerated charge carriers. The low coordinated atomic sites at the edges of NSs and abundant defects caused by morphological changes can afford significantly enhanced catalyticproperties. This result is exemplified in work with NSs containing Bi with abundant defects widely used in CO2 electroreduction to formic acid, benefiting from a fast interfacial charge transfer and facile desorption of products(135). The theoretical calculation illustrates that the Gibbs free energy of the rate-determining step forming *OCHO in Bi NSs is lower than that of the pristine counterpart, implying that defective active centers in NSs have a stronger ability to 23 stabilize intermediates (Figure 5E-G). Recently, hierarchically mesoporous SnO2 NSs can be obtained by adjusting the hydrophobic chain length of surfactants and exhibits a higher Faraday efficiency in the CO2 electroreduction reaction than mesoporous SnO2 NPs due to the surface mesoscopic structure with increasing surface area, exposure of more active sites, and facile interfacial charge transfer (Figure 5H-J)(136).
Compared to XAS, the X-ray photoelectron spectroscopy (XPS) technique could reveal the chemical composition, oxidation states, and electron transfer of designed catalysts with the characteristics of surface sensitivity (Figure 7D). With the development of reaction cells and simplification of operating conditions, the in situ ambient pressure XPS (AP-XPS) technique has been exploited to monitor the dynamic changes in the electronic state and structural evolution in the reaction process (Figure 7E). For instance, Yoshinobu et al. have investigated the reaction process of CO2 hydrogenation with Zn/Cu alloy using AP-XPS, which reveals that the CO2 can be activated on the surface of the Zn/Cu to form the carbonate species under reaction conditions (Figure 7F)(159). In situ Raman spectroscopy is another valid characterization technology that complements IR spectroscopy to detect catalyst evolution and possible intermediates in a liquid solution (Figure 7G). The intrinsic vibration and rotation energy levels of catalysts in the Raman spectrum can reflect their intrinsic properties and are expected to probe the mechanism process for the corresponding catalytic systems (Figure 7H). Song et al. have used in situ Raman spectroscopy to probe the transition of intermediate adsorption states in electrochemical CO2 reduction over S-doped Cu-based catalysts. The intensity of peak at 1080 cm −1 corresponding
For instance, by analyzing the adsorption free energy of CO2 and other reactants on the surface of various catalysts, we can determine whether the adsorption and desorption behavior of reactant molecules affects the conversion efficiency of the entire reaction process and preliminarily assess the catalytic performance of the designed catalysts. Zhang et al. have used theoretical calculations to reveal that the grafted amide bond on the graphene oxide substrate with a lower CO2 adsorption energy of -6.94 kcal/mol demonstrates a stronger CO2 capacity than the original graphene oxide with the CO2 adsorption energy of -4.56 kcal/mol(166). 29 Intermediates are often difficult to capture during experimentation; thus, theoretical calculations introduce substantial possibilities for identifying true intermediates and the optimal configuration on the catalyst surface, which provide essential information for disclosing the entire reaction paths. For instance, Johnson et al. have reported that frustrated Lewis pairs functionalized MOFs (UiO-66-P-BF2) can effectively catalyze the hydrogenation of CO2 (Figure 8A-B)(167). They further identified the desirable reaction path for CO2 hydrogenation over UiO-66-P-BF2 by comparing the energy barrier of two possible reaction pathways. The corresponding theoretical calculation results demonstrated that the reaction between physically-adsorbed CO2 and chemisorbed 2H* with an energy barrier of 0.47 eV is more favorable than the process of reacting between physically-adsorbed H2 and CO2* with an evident higher barrier of 2.65 eV, verifying the possible mechanism proceeded by H2 heterolytic dissociation, followed by the CO2 reaction with the adsorbed H atoms (Figure 8C). Moreover, the rate-determining step in the corresponding process can be distinguished by comparing the energy barrier in the formation and transfer of reactants, the intermediate state, and products on the catalyst surface. For instance, theoretical calculations have revealed that photocatalytic conversion of CO2 into formic acid over COF-367-Co with a tunable spin state undergoes two primary transition states(168). These states form an O-H bond between the oxygen in CO2 and the hydrogen with an energy barrier of 0.13 eV and the formation of HCOOH* via another transition state with an energy barrier of 0.68 eV
et al. have realized the efficient preparation of acetic acid by constructing a hybrid photosynthetic system comprising semiconductors and bacteria(173). Perylene diimide derivative (PDI) and poly(fluorene-co-phenylene) (PFP) are selected to coat the bacterial surface as photosensitizers to form a p-n heterojunction layer, enhancing the efficiency of the hole/electron separation (Figure 9A). The designed conjugated molecules/bacteria could exhibit a higher amount of the acetic acid under illumination than only bacteria in the light or conjugated molecules/bacteria in the dark. The acetic acid yield for PDI/PFP/bacteria and PDI/bacteria is 0.63 and 0.25 mM, respectively, which has great potential to further achieve higher activity by optimizing the structure and composition (Figure 9B-C). This work presents the advantages of combining biological bacteria and semiconductors in photocatalytic carboxylic acid production. Furthermore, Sun et al. have developed an artificial photocatalytic system to produce acetic acid by constructing abundant exposed surface oxygen vacancies in ultrathin WO3·0.33H2O nanotubes (Figure 9D)(174). The acetic acid yield over synthesized WO3·0.33H2O with high oxygen vacancies can reach 94 μmol/g after 10 h and is much higher than samples with low oxygen vacancies and commercial WO3, testifying the important role of oxygen vacancies in the CO2 reduction process (Figure 9E). In situ diffuse reflectance IR Fourier-transform spectroscopy has been further used to explore the role of oxygen vacancies in promoting the conversion of CO2 into acetic acid. The results reveal that the HCO3 species is an important intermediate for producing acetic acid, which can be transformed into the COOH intermediate under light irradiation. Specifically, the C=O bond of the CO2 is activated by the W-OH group in WO3 upon light irradiation and is transferred into the O=Ċ-OH radical intermediate after obtaining photogenerated electrons. The corresponding HCO3 bicarbonate species can be formed at the place of oxygen vacancies by undergoing a proton-coupled electron transfer and further reaction with the adjacent ·COOH radicals to form C-C bonds by departing from the oxygen vacancy. After a few steps of proton-coupled electron transfer under light irradiation, acetic acids have been produced with a high yield (
First
, the capture or identification of intermediates and transition states in the reaction process is at the center of understanding the mechanism of conversion efficiency of CO2 into carboxylic acids. Ultra-short lifetimes of transition states and the instability of the intermediate under characterization conditions have accentuated the problem of the lack of in-depth investigation of intermediates at the molecular level. An appropriate transition state can only be inferred indirectly from some seemingly reasonable in situ characterization techniques. An effective solution is achieving catalytic conversion of CO2 under relatively mild or atmospheric conditions via the design of high-efficiency catalysts, allowing the accurate detection of the transition state of the reaction with the existing in situ characterization techniques. In addition, advanced in situ characterization techniques and a combination of multiple in situ technologies 38 should be strongly developed to track the evolution of reactants, including C-O bond breakage, the formation of C-H or C-C bonds, and possible intermediates.
Figure 1 .
1Schematic diagram of conversion of carbon dioxide into carboxylic acids.
Figure 2 .
2Conversion of CO2 into carboxylic acids under the drivers of light, electricity, and heat. (A-C) Photocatalytic conversion of carbon dioxide (CO2) into carboxylic acids: (A) schematic diagram of photocatalytic conversion of carbon dioxide (CO2) into carboxylic acids, (B) mechanism of photo-catalyzing CO2 into formic acid, (C) reaction paths of the photocatalytic process for producing different carboxylic acids. (D-F) Electrocatalytic conversion of CO2 into carboxylic acids: (D) schematic diagram of electrocatalytic conversion of CO2 into carboxylic acids, (E) possible mechanism of electro-catalyzing CO2 into formic acid, (F) reaction paths of the electrocatalytic process for producing different chemicals. (G-I) Thermo-catalytic conversion of CO2 into carboxylic acids: (G) Schematic diagram of the thermo-catalytic conversion of CO2 into carboxylic acids, (H) possible mechanism of hydrogenation of CO2 into formic acid, (I) reaction paths of the thermo-catalytic process for producing carboxylic acids.
Figure 3 .
3Conversion of CO2 into carboxylic acids by composite structure. (A) Schematic diagram of loading active sites onto different supports to form the composite catalyst. (B-D) Photocatalytic conversion of carbon dioxide (CO2) into formic acid by Cu2O-Pt/SiC/IrOx catalyst: (B) Schematic diagram and TEM images of the Cu2O-Pt/SiC/IrOx catalyst, (C) schematic diagram of the efficient CO2 reduction and O2 evolution mechanism, (D) HCOOH evolution with Cu2O-Pt/SiC/IrOx as the photocatalyst [(A-C), adapted with permission from Wang et al. (86)]. (E-G) Electrocatalytic conversion of carbon dioxide (CO2) into formic acid by Bi2O3 nanosheets (NSs)/multichannel carbon matrix (Bi2O3@MCCM): (E) Schematic 43 diagram of Bi2O3@MCCM. (F) FE of all products over the Bi2O3NSs@MCCM. (G) FE of HCOOH of different catalysts [(E-G), adapted with permission from Liu et al. (89)]. (H-J) Thermo-catalytic conversion of carbon dioxide (CO2) into acetylenic acid by ZIF-8@Au25@ZIF-67[tkn] and ZIF-8@Au25@ZIF-8[tkn] [tkn = Thickness of Shell]: (H) Synthetic route for the sandwich structures and TEM images of ZIF-8@Au25@ZIF-67[tkn] and ZIF-8@Au25@ZIF-8[tkn], (I) catalytic activity of various catalysts for the carboxylation of phenylacetylene and the stability of various catalysts for the carboxylation of phenylacetylene, (J) proposed catalytic mechanism of the reaction between terminal alkynes and CO2 over ZIF-8@Au25@ZIF-67[tkn] [(H-J), adapted with permission from Yun et al. (92)].
Figure 4 .
4Conversion of CO2 into carboxylic acids by doping heteroatom. A) Schematic diagram of forming the doped catalyst. (B-D) Electrocatalytic conversion of carbon dioxide (CO2) into formate by sulfur-doped indium catalysts: (B) Schematic illustration of the role of S 2in promoting water dissociation and H* formation for the reduction of CO2 to formate, (C) plot of FE of formate vs. the current density for the S 2-In catalyst and some typically reported catalysts, (D) Gibbs free-energy diagrams for CO2RR to HCOOH on S-In (101) and S-In (101) surfaces [(B-D), adapted with permission from Ma et al. (111)]. (E-G) Thermocatalytic conversion of carbon dioxide (CO2) into formic acid by PdAg+PEI@HMOS catalyst: (E) 45 Schematic illustration of CO2 hydrogenation to produce formate with the PdAg+PEI@HMOS catalyst, (F) reusability tests of PdAg+PEI@HMOS for CO2 hydrogenation, (G) plausible reaction mechanism for the CO2 hydrogenation to produce formate over PdAg+PEI@HMOS catalyst [(E-G), adapted with permission from Kuwahara et al. (119)]. (H-J) Electrocatalytic conversion of CO2 into formate by Pd1Cu catalyst: (H) schematic illustration of CO2 conversion into HCOOH over a Pb1Cu catalyst, (I) FEs of all CO2RR products at different current densities and the corresponding j-V curve of Pb1Cu catalyst, (J) theoretical calculation of adsorption free energies for HCOO* and COOH* and free-energy diagrams for the competition between CO2RR producing formate or CO and the HER reaction [(H-J), adapted with permission from Zheng et al. (121)].
Figure 5 .
5Conversion of CO2 into carboxylic acids by morphology control. (A) Schematic diagram of tuning the catalytic activity of catalysts using morphology control. (B-D) Electrocatalytic conversion of CO2 into formate with SnO2 QWs: (B) Illustration of the structure of ultrathin SnO2 QWs, (C) TEM image of SnO2 QWs, (D) FE of HCOOH over the ultrathin SnO2 QWs and SnO2 nanoparticles [(B-D), adapted with permission from Liu et al. (134)]. (E-G) Electrocatalytic conversion of CO2 into formate with Bi nanosheets (NSs): (E) Schematic diagram of the synthesis of Bi NSs and illustration of the structure of Bi NSs, (F) 47 TEM image of Bi NSs, (G) FEs and cathodic energetic efficiency (CEE) of formic acid over two electrocatalysts in 1 m of KOH [(E-G), adapted with permission from Yang et al. (135)]. H-J) Electrocatalytic conversion of CO2 into formate with porous SnO2 NSs: (H) Schematic diagram of the synthesis of porous SnO2 NSs and illustration of the structure of porous SnO2 NSs, (I) SEM image of porous SnO2 NSs, (J) Faradaic efficiencies of HCOOH over different catalysts [(H-J), adapted with permission from Wei et al. (136)].
Figure 6 .
6Conversion of CO2 into carboxylic acids by surface functionalization. (A)Schematic diagram of tuning catalytic activity via surface functionalization.(B-D) Electrocatalytic conversion of CO2 into formate with tripodal N-heterocyclic carbene functionalized palladium: (B) Synthetic scheme of tripodal N-heterocyclic carbene functionalized palladium, (C) FEs of formate generation using Pd-timtmb R electrodes, (D) Free-energy diagrams of CO2 reduction to HCOOH on Pd(111) and Pd(111)-timtmb Me [(B-D),
Figure 7 .
7In situ characterization techniques. (A) Schematics of the x-ray absorption spectra (XAS), adapted with permission from Long et al. (157). (B) Schematic diagram of operando XAS cell, adapted with permission from Zheng et al. (185). (C) Operando Bi L-edge XANES spectra of Bi2O3 nanotubes and NTD-Bi at -0.24 V compared to Bi or Bi2O3 standards (inset plot: partially enlarged spectra), adapted with permission from Gong et al. (158)) (D) Schematic diagram of the XPS principle. (E) Schematic diagram of operando XPS cell, et al. (159). (G) Schematic diagram of the Raman spectrum principle. (H) Schematic diagram of the operando Raman cell, adapted with permission from Geisler et al. (187). (I) in situ Raman spectra with a static scanning subsection of the S-doped catalyst, adapted with permission from Pan et al. (160). (J) Schematic diagram of Fourier-transform infrared (FTIR) spectroscopy principle. (K) Schematic diagram of an in situ FTIR spectroscopy cell, adapted with permission from Ajjan et al. (188). (L) In situ attenuated total reflection surface-enhanced infrared absorption spectroscopy on Sn-OH-5.9, adapted with permission from Deng et al. (161).
Figure 8 .
8Theoretical calculations. (A-C) CO2) hydrogenation over UiO-66-P-BF2: (A) Schematic diagram of CO2 hydrogenation over UiO-66-P-BF2, (B) schematic diagram of the structure of UiO-66-P-BF2, (C) relative potential energy surfaces for two CO2 hydrogenation pathways in UiO-66-P-BF2 and the involved configuration in the process of CO2 hydrogenation [(A-C), adapted with permission from Ye et al. (167)]. (D-F) Photocatalytic conversion of CO2 into formic acid over COF-367-Co: (D) Schematic diagram of photocatalytic conversion of CO2 into formic acid over COF-367-Co, (E) schematic diagram of COF-367-Co featuring different spin states of Co ions toward photocatalytic CO2 reduction, (F) calculated potential energy profile of CO2 reduction reaction to HCOOH catalyzed by COF-367-Co II and COF-367-Co III [(D-F), adapted with permission from Gong et al. (168)]. (G-I) Machine-learning-53 guided discovery and optimization of additives in preparing Cu catalysts for CO2 reduction: (G) Schematic diagram of combinations of metal salts and additives, (H) schematic diagram of the process of high-performance catalysts under the guide of machine learning, (I) Additives screened out by machine learning [(G-I), adapted with permission from Guo et al. (171)].
Figure 9 . 56 Figure 10 . 58 Figure 11 .
956105811Frontier progress of photoreduction of CO2 into carboxylic acid. (A-C) Photocatalytic conversion of CO2 into acetic acid: (A) Schematic diagram of the photosynthetic production of acetic acid by conjugated molecules/M. thermoacetica, (B) produced acetic acid amount of PDI/PFP/M. thermoacetica in an alternating light-dark cycle of 12 h each, (C) energy-level diagram of PDI/PFP and the representation of the electron transfer mechanism to the bacterial membrane [(A-C), adapted with permission from Gai et al. (173)]. (D-E) Photocatalytic conversion of CO2 into acetic acid over WO3·0.33H2O: (D) Schematic diagram of photocatalytic conversion of CO2 into acetic acid over WO3·0.33H2O, (E) catalytic results with irradiation time over different catalysts, (F) photocatalytic conversion of CO2 with WO3·0.33H2O [(D-F), adapted with permission from Sun et al. (174)]. (G-I) Redox-neutral 55 photocatalytic C-H carboxylation with CO2: (G) Schematic diagram of photocatalytic carboxylation, (H) catalytic results of various substrates using photocatalytic conversion, (I) proposed mechanism for the C-H carboxylation of (hetero)arenes [(D-F), adapted with permission from Schmalzbauer et al. (175)]. Frontier progress of electroreduction of CO2 into carboxylic acid. (A-B) Electrocatalytic conversion of carbon dioxide (CO2) into formic acid with solid electrolytes: (A) Schematic illustration of the CO2 reduction cell with solid electrolytes, (B) corresponding FEs of the resultant reduction products [(A-B), adapted with permission from Xia et al. (176)]. (C-D) Electrochemical CO2 reduction to a high concentration of pure formic acid solutions in an all-solid-state reactor: (C) Schematic illustration of the all-solid-state electrochemical CO2RR to the formic acid reactor (AEM: anion exchange membrane, CEM: cation exchange membrane, GDL: gas diffusion layer, PSE: porous solid electrolyte), (D) corresponding FEs of 57 formic acid vapor under different cell voltages [(C-D), adapted with permission from Fan et al. (177)]. (E-F) Operando spectroscopy study of CO2 electroreduction by iron species on nitrogen-doped carbon: (E) Schematic drawing of the experimental cell with details of electrodes, charge pathways, and electrolytes, (F) in situ normalized Fe k-edge spectra of Fe/N-C [(E-F), adapted with permission from Genovese et al. (180)]. Frontier progress of thermo-catalytic conversion CO2 into carboxylic acid. (A-B) Ni-catalyzed divergent cyclization/carboxylation of unactivated primary and secondary alkyl halides with carbon dioxide (CO2): (A) Schematic diagram of bond formation via electrophile couplings and cyclization/functionalization of alkyl halides, (B) mechanism of catalytic cyclization/carboxylation of unactivated secondary alkyl halides [(A-B), adapted with permission from Wang et al. (182)]. (C-E) Production of carboxylic acids using Kolbe-Schmitt (KS) reactions: (C) Proposed molecular configuration at the Ag-MP@ZIF interface and Zn 2p XPS spectra of Ag-MP@ZIF and Ag-MBT@ZIF, (D) schematic depicting the importance of 59 the NP@MOF interface to activate an inert KS reaction and in situ monitor its unconventional regioselectivity, E) proposed mechanism for how NP@MOF activates a chemical reaction that is otherwise inert at ambient operating conditions [(C-E), adapted with permission from Lee et al. (183)]. (F-G) Pd-catalyzed highly regioselective hydrocarboxylation of alkynes with CO2: (F) Schematic diagram and mechanism of hydrocarboxylation of alkynes with CO2, (G) calculated relative Gibbs free energies of catalytic species through the cyclopalladation pathway [(F-G), adapted with permission from Xiong et al. (184)].
Cao, bpy-CTF-Hydrogenation of CO2 with. with permission from Cao et al. (150)]. (E-G) Hydrogenation of CO2 with [bpy-CTF-
) Schematic diagram of [bpy-CTF-Ru(Ic)2]Cl synthesis, (F) reusability tests of [bpy-CTF-Ru(acac)2]Cl for CO2 hydrogenation, (G) proposed mechanism for hydrogenating CO2 into formate. Ru, acac)2]Cl: (E. adapted with permission from Gunasekar et al. (151)]. (H-JRu(acac)2]Cl: (E) Schematic diagram of [bpy-CTF-Ru(Ic)2]Cl synthesis, (F) reusability tests of [bpy-CTF-Ru(acac)2]Cl for CO2 hydrogenation, (G) proposed mechanism for hydrogenating CO2 into formate [(E-G), adapted with permission from Gunasekar et al. (151)]. (H-J)
Hydrogenation of CO2 with a Schiff-base-modified gold nanocatalyst: (H) Schematic diagram of the Au/SiO2-Schiff structure (insert: quantum mechanics calculation of NMR shifts), I) initial reaction rates in H2 and CO2 pressure-dependent conditions over Au/SiO2-Schiff. Hydrogenation of CO2 with a Schiff-base-modified gold nanocatalyst: (H) Schematic diagram of the Au/SiO2-Schiff structure (insert: quantum mechanics calculation of NMR shifts), I) initial reaction rates in H2 and CO2 pressure-dependent conditions over Au/SiO2-Schiff, (J)
Free-energy diagram of CO2 hydrogenation over a Au/SiO2-Schiff catalyst. adapted withFree-energy diagram of CO2 hydrogenation over a Au/SiO2-Schiff catalyst [(H-J), adapted with
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| sample_822 | 0.6705 | arxiv | |
Leveraging policy instruments and financial incentives to reduce embodied carbon in energy retrofits
Haonan Zhang
School of Engineering
Faculty of Applied Science
The University of British Columbia
V1V1V7KelownaBCCanada
Leveraging policy instruments and financial incentives to reduce embodied carbon in energy retrofits
The existing buildings and building construction sectors together are responsible for over one-third of the total global energy consumption and nearly 40% of total greenhouse gas (GHG) emissions. GHG emissions from the building sector are made up of embodied emissions and operational emissions. Recognizing the importance of reducing energy use and emissions associated with the building sector, governments have introduced policies, standards, and design guidelines to improve building energy performance and reduce GHG emissions associated with operating buildings. However, policy initiatives that reduce embodied emissions of the existing building sector are lacking. This research aims to develop policy strategies to reduce embodied carbon emissions in retrofits. In order to achieve this goal, this research conducted a literature review and identification of policies and financial incentives in British Columbia (BC) for reducing overall GHG emissions from the existing building sector. Then, this research analyzed worldwide policies and incentives that reduce embodied carbon emissions in the existing building sector. After reviewing the two categories of retrofit policies, the author identified links and opportunities between existing BC strategies, tools, and incentives, and global embodied emission strategies. Finally, this research compiled key findings from all resources and provided policy recommendations for reducing embodied carbon emissions in retrofits in BC.
Introduction
Energy use is a main factor influencing the environmental sustainability of the building sector, and has received much attention with the ongoing climate action initiatives [2]. The existing buildings and building construction sectors together are responsible for over one-third of the total global energy consumption and nearly 40% of total direct and indirect greenhouse gas (GHG) emissions as per the International Energy Agency (IEA). The energy consumption and associated GHG emissions in the building sector may double and even triple by 2050. [3]. Poor energy performance of aging buildings in many countries makes a major contribution towards the said emissions. For example, according to the data from European Parliament, around 75% of existing buildings in Europe are energy inefficient [2]. In Canada, over 50% of Canadian residential buildings aged more than 30 years, and over 20% aged 50 years or more [4]. Old buildings mainly use nonrenewable energy options and undergo material and component deterioration [5][6][7]. Thus, this older building stock consumes more energy and consequently emits more GHGs as compared to new construction [8,9]. Moreover, most of aging buildings do not comply with the latest energyefficiency requirements [10,11].
However, the energy-efficient retrofit rates still remain low across the world. For example, retrofit rate is at an average of 1% in Germany [12], 1.0-3.0% in the UK [13], and 0.4-1.2% in Europe per annum [14]. In order to meet the target of emission reductions and the requirements of the latest energy-efficiency codes, immediate actions need to be taken to reduce the environmental impacts of the aging building stock [15]. As such, retrofits that involve modifications to envelope components and energy systems of existing buildings have garnered more attention in many countries [16].
With buildings becoming more energy-efficient, embodied carbon emissions play an increasing essential impact on achieving the goal of carbon reductions and climate changes. Embodied emissions can even become the primary source of carbon emissions in the building sector [17]. Implementing energy retrofits that can most reduce operational carbon emissions may not produce the benefit of life cycle carbon reductions because of higher embodied carbon emissions. According to the literature, the average share of embodied GHG emissions from buildings following current energy performance regulations is approximately 20-25% of life cycle GHG emissions. This figure can increase to 45-50% for highly energy-efficient buildings and surpasses 90% in extreme cases [1]. As such, it is important to mitigate the influence of embodied emissions when implementing energy retrofits.
Government-administered policy instruments are necessary to support the reduction of energy consumption and GHG emissions in the building sector [18]. In reality, retrofitting is an activity that involves multiple stakeholders, making it necessary to streamline and coordinate this process via regulation and policies [19,20]. Renovators and homeowners are mainly responsible for implementing retrofit measures for residential buildings, and there is a possibility of obtaining positive outcomes through retrofits. However, the various economic, environmental, and social issues associated with the entire process have to be addressed by the local or federal governments [21]. Homeowners might not embark on retrofitting without external economic support, especially when they plan to lease or sell their homes [22,23]. Furthermore, selecting the best retrofit options for a given context can vary significantly due to many factors, such as retrofit objectives, building types, climate contexts, technical issues, and stakeholder interests [24]. The benefits of retrofit policies in addressing the above issues are highlighted by literature [25][26][27][28].For example, building assessment and certification policies can assist householders in understanding the energy performance of their homes and the retrofit benefits to their homes. In addition, financial incentives can reduce economic burdens on homeowners and encourage them to start retrofits [29][30][31][32].
This research aims to leverage existing policies to reduce embodied carbon in retrofits in BC. Firstly, this research conducted a literature review and identification of BC policies and incentives for reducing overall GHG emissions from the existing building sector. Then, this research analyzed worldwide policies and incentives that reduce embodied carbon emissions. After reviewing the two categories of retrofit policies, the authors identified links and opportunities between existing BC strategies, tools, and incentives, and global embodied emission strategies. Finally, this research compiled key findings from all resources and provided policy recommendations for reducing embodied carbon emissions in retrofits in BC.
Classification framework for retrofit policies
According to [33], policy instruments focus on stakeholders' main concerns and can be important nexus between policy objectives and application market. These instruments have been recognized as primary channels for administrations to develop social and economic guidelines. Retrofit Policy Instruments (RPIs) represent a set of policy measures, such as requirements, ordinance, certifications, and financial supports, to achieve desired targets (e.g. increase of retrofit rate) set by governments [34]. It has been proved that RPIs have great potential to be studied [21,28,35,36]. Therefore, to reflect the general characteristics of the RPIs, this paper presents a classification framework for the collected RPIs. By using this framework, the collected RPIs provided by governments, utility companies, and other relevant institutions are distributed into four categories: direction and command (DC), assessment and disclosure (AD), research and service (RS), and financial incentives (FI). The descriptions of the DC, AD, RS, and FI instruments are shown in Table 1.
Analysis of retrofit policies
Municipalities have made great efforts to enforce a mix of different RPIs. These instruments can assist in improving stakeholders' retrofit awareness, knowledge, and skills and provide retrofit guidelines and supports for them [21,55].
Direction and command (DC) policies
When governments initiate RPIs, DC instruments, including direction and directive-based instruments, are their main choice, since the instruments have regarded as important interventions for retrofits at the initial stage [21]. The policies set overall retrofit strategies, targets, and requirements to assist stakeholders in better understanding basic knowledge, benefits, and the overall future direction for energy retrofits. Efforts have been made while considering stakeholders' interests and providing them with detailed retrofit guidelines. The efforts provide a clear framework for retrofit implementation, thereby overcoming retrofit implementation barriers and increasing market acceptance.
In response to climate change, the Clean BC Roadmap to 2030 has been proposed in British Columbia [56]. In the building sector, this plan includes the following important actions: achieving zero-carbon new construction by 2030, developing highest efficiency standards for new space and water heating equipment, enhancing energy efficiency programs, introducing home energy labelling, and using more low carbon building materials. This plan provides an overall direction for stakeholders to improve building energy efficiency and reduce GHG emissions in the building sector.
For existing buildings, the government of Canada has introduced three levels of retrofit measures, including minor retrofits, major retrofits, and deep retrofits [57]:
• Minor retrofits refer to modifications that are low-cost, easy to implement and that offer good value for the money and effort invested, such as upgrading lighting systems and adding insulation. • Major retrofits generally take a more holistic approach to upgrade buildings, including replacing window glazing and doors, updating inefficient heating and cooling systems, installing low-flow faucets with sensors, automatic shut-offs, and sub-metering. • Deep retrofits undertake an extensive overhaul of building's systems that can save up to 60 percent in energy costs, such as replacing the roof and replacing the heating, ventilation and air-conditioning system with a renewable technology like a ground-source heat pump. However, deep retrofits can be disruptive to building's occupants. Therefore, it is recommended to take the measures with tenant turnover or other major changes to occupancy.
DC instruments can play an important role in promoting retrofits by providing an overall development direction, retrofit requirements, and recommendations at the early stage of a retrofit project. With this kind of instrument, the stakeholders can be aware of long-term retrofit strategies, retrofit benefits, minimal retrofit requirements, and applicable retrofit measures. However, the compliance of DC instruments requires sufficient technological and financial support from welltrained retrofit practitioners, such as retrofit training courses, energy auditing data, and rebates for retrofit activities. In this regard, DC instruments should be combined with AD, RS, and FI instruments to improve the effectiveness of policy implementation.
Assessment and disclosure (AD) policies
AD instruments serve as an important tool for benchmarking building energy consumption, recognizing operational issues of systems, and identifying retrofit opportunities [58], [59]. This kind of instrument can help homeowners understand the operational energy use conditions and encourage energy retrofits. The related institutes provide energy audits for owners, including an examination of utility bills and comprehensive checks of targeted homes to identify energy-waste locations, and householders can solicit expert advice on retrofit options based on the auditing results. Furthermore, assessors can assist in ensuring that the energy saving goals are achieved after retrofitting.
The EnerGuide Rating System has been implemented across Canada to help Canadians improve the energy efficiency of their houses [60]. An EnerGuide rating is a standard measure of a home's energy performance. The home's energy efficiency level is rated on a consumption-based rating scale using gigajoules per year (GJ/year). The energy label also presents the breakdown of rated annual energy consumption, including space heating, space cooling, water heating, ventilation, lights and appliances, and other electrical energy consumption. Based on its energy efficiency, a home will receive an EnerGuide rating. Ratings are calculated by Registered Energy Advisors who analyze building plans, provide upgrade recommendations to improve energy efficiency, and complete a blower door test to confirm the air tightness of the home.
However, previous studies have indicated that the energy-efficiency labels might not be an essential consideration for landlords when they decide to rent or buy a property. Furthermore, the decisions are highly dependent on the disclosure of energy use data [61]. Therefore, disclosure policies have been introduced with the objectives of making occupants understand their energy use, arousing their environmental awareness, and encouraging them to upgrade the buildings with low energy efficiency through transparent information sharing [62]. Homeowners are required to report their energy uses periodically or when the buildings are put on the market [63]. However, it is recommended that multi-family and affordable buildings be excluded from the disclosure policies because of stakeholder perceptions that compliance would increase rent prices [64].
In addition, AD instruments can be used as effective tools to evaluate the differences between estimated and actual energy savings achieved from retrofits. Previous studies have proved that the discrepancy between expected energy use evaluated by energy modelling software and actual energy use is significant due to occupant behavior influences and inaccurate energy modelling, leading to unreliable paybacks for energy retrofit projects [65][66][67]. Developing simple occupantbased energy models that better address different occupant types and their impacts on energy use has been proven essential for improving modelling accuracy [68]. As such, AD instruments can help retrofit professionals understand why estimated and actual energy use are inconsistent and tune pre-retrofit energy modelling. After completing retrofits, energy savings can be recorded to test the accuracy of the developed energy model. However, the effective enforcement of AD instruments relies on financial supports and specialized retrofit professionals [28]. Therefore, FI and DS instruments should be developed to support the implementation of AD instruments. Furthermore, previous research has shown that it is not cost-effective to monitor energy data in a great level of detail [21]. Thus, striking a balance between building energy monitoring and modelling is essential.
Research and service (RS) policies
RS instruments, including research-related instruments and public service-related instruments, are used to increase occupants' awareness of energy retrofits and provided technological supports for retrofit practitioners.
Many efforts have been devoted to developing innovative research-related instruments, such as state-of-the-art retrofit technologies and innovative retrofit plans. The effectiveness of new technologies is mainly dependent on technological means, costs, climate conditions, and social contexts. In this regard, governments have launched research and development (R&D) programs to apply renewable energy systems to transfer the existing buildings to be a net-zero ready state.
Governments have provided many public services for stakeholders, such as establishing retrofit professional associations and developing training programs and retrofit support tools. Diverse institutions, departments, organizations, and workgroups, which can assist with coordinating among stakeholders and organizing retrofit activities, contribute to the adequate promotion, supervision, and service of home retrofit markets. A lack of practitioners with rich retrofit knowledge and skills is a big challenge that hinders the implementation of energy retrofits [69,70]. Training programs and support tools can strengthen practitioners' knowledge and skills associated with energy retrofits and provide convenience for them to initiate retrofitting and avoid troubles [24], [94]- [99]. Targeted training audiences generally involve occupants and professionals.
Hargreaves et al. [77] suggested that occupants' energy-saving behaviors depend considerably on their inclination towards reducing energy consumption, information exchange, and skills to handle energy-efficient technical systems. The training programs for occupants are conductive to improve their awareness of upgrading their homes and increase their knowledge and skills on manipulating home appliances through an energy-efficient way [78]. In addition, retrofit practitioners' skills can also be enhanced through trainings. Previous practice has indicated that energy assessors trained in building science are more easily to gain homeowners' commitments to conduct retrofits than contractors trained in sales [37].
In terms of retrofit support tools, the EfficiencyBC program has been provided by the Province of British Columbia to assist occupants and business in accessing updated information about incentives and support to reduce energy use and GHG emissions in existing buildings [79]. The supports from this program include:
• Easy to use incentive search tools for residential and commercial renovations.
• Single application for EfficiencyBC, BC Hydro, FortisBC, and local government residential renovation incentives. • Information and answers to frequently asked questions on energy efficiency upgrades. • Free Energy Coaching Services for homeowners and businesses undertaking renovations, including a phone and email hotline staffed by energy coaching specialists. • Search tool to find registered EnerGuide Rating System energy advisors for residential renovations. • Contractor directories to find registered contractors in BC.
Clean BC Better Homes, which is an online rebate search tool, can assist homeowners in finding rebates according to their locations and building heating systems for residential buildings [80]. The heating systems consist of the following items: electricity (baseboard, furnace), natural gas or propane (furnace, boiler, fireplace), oil (furnace, boiler), wood (stove, fireplace), district energy (locally created energy), and heat pump. This program also provides a free coaching service for building owners and managers in BC. Energy Coaches are trained energy efficiency specialists who provide building-science based information about the options and opportunities to improve building energy efficiency. They are available to answer questions at all stages of energy retrofits project. The service, which can provide occupants with general advice about rebate programs and upgrade options, is described as follows:
• Access to Energy Coaches via a toll-free hotline and e-mail • Information and general advice about energy efficiency upgrades and rebates • Directing homeowners to appropriate program representatives In addition, Clean BC Better Buildings, another online platform, can provide information and financial support for commercial buildings [81]. One of the custom programs under this sector is CleanBC Commercial Express Program, which guides and supports building operators and provides electrification opportunities across the commercial and institutional buildings [82]. They offer a free energy coaching service through fuel switching and other electrification measures. Program offers capital incentives based on age, location, square footage, hours of operation, and the type of equipment up to a maximum of $100,000 per project.
To conclude, RS instruments mainly rely on supports from local governments. These instruments also help stakeholders to explore new retrofit technologies and more easily access retrofit information and technical supports to address practical retrofit problems. In this sense, this type of policy can provide reliable supports for DC and AD instruments and disseminate the benefits brought by FI instruments, and thus, arouse stakeholders' awareness and improve their work efficiency.
Financial incentive (FI) policies
Financial incentives have been recognized as essential instruments for implementing retrofits in the residential buildings [83]. From the examinations of the practice of the surveyed policies in this paper, a multitude of financial incentives can be distributed into four groups: grants, rebates, loans, and tax credits.
In Canada, FI instruments are mainly provided by utility providers and local governments. A number of grant and rebate programs have been launched to encourage homeowners to upgrade building envelopes and energy systems.These programs can alleviate homeowners' concerns about high upfront costs of retrofits and reduce economic burdens on them [70,84]. For example, Natural Resources Canada (NRCan) provides grants for the combined cost of the pre-and post-retrofit evaluations up to a maximum of $600, which can assist occupants in evaluating retrofit outcomes. In addition, NRCan also provides direct grants for different retrofit measures as follows:
• Home insulation: Upgrade eligible attic, cathedral ceiling, flat roof, exterior wall, exposed floor, basement and crawl space (up to $5,000). • Air-sealing: Perform air sealing to improve the building airtightness to achieve the airchange rate target (up to $1,000). • Windows and doors: Replace doors, windows or sliding glass doors with ENERGY STAR® certified models (up to $5,000). • Thermostat: Add a smart thermostat to help improve occupants' comfort and save money on energy bill (must be combined with another energy efficiency retrofit, up to $50).
• Space and water heating: Make the switch to more energy-efficient space heating or water heating equipment to save on utility bill and reduce carbon footprint (up to $5,000). • Renewable energy: Install a solar photovoltaic system to convert sunlight energy into electricity (up to $5,000). • Resiliency measures: Implement measures to protect home from environmental damages (must be combined with another energy efficiency retrofit, up to $2,625).
In British Columbia, Fortis BC provides rebates for purchasing energy-efficient HVAC equipment and appliances and replace old ones [85]. The product rebates include boilers, clothes dryers and washers, combination system, fireplaces, furnaces, heat pumps, natural gas heating system, refrigerators, thermostats, and water heaters. In the same vein, BC Hydro also offer rebates for energy-efficiency upgrades, including windows and doors (up to $3,000), insulation (up to $5,500), heat pumps (up to $2,000), and heat pump water heaters (up to $1,000) [86]. Furthermore, the Energy Efficiency Retrofit Program provided by BC Housing offers stakeholders additional funding to complete small-scale, energy saving retrofits of items such as light fixtures and boilers. Using all incentives together, stakeholders can undertake their retrofit projects and retain a portion of the ongoing energy savings [87].
Space heating has been recognized as the largest use of energy in homes. A properly installed heat pump is two to three times more efficient than other alternatives and can provide occupants with both comfortable heating in the winter and cooling for today's hot summers [88]. Thus, Clean BC Better Homes Low-interest Financing program has been introduced, which provides loans with interest rates as low as 0% for switching from a fossil fuel (oil, propane or natural gas) heating system to a heat pump [88]. Furthermore, the Canadian government has also implemented special programs to help low-income householders and senior citizens to live more comfortable, such as the "Healthy Homes Renovation Tax Credit" program and the "Energy Efficiency Retrofit Program for Low-Income Households" program.
As most of retrofit activities require economic supports, FI instruments have garnered much attention. These economic supports mainly come from government capitals, bank loans, utility provider rebates, and commercial institution grants. These instruments can address stakeholders' main concerns on economic issues related to retrofit projects, such as high initial cost, long payback period, and uncertainty of return on investment, and thus, improve their willingness and aspiration to upgrade buildings. In this regard, it is important to provide FI instruments to support the enforcement of DC, AD, and RS instruments. However, FI instruments might impose a heavy financial burden on governments, especially for local governments in a long run. Therefore, the level of investment depends on each governments' economic situation [89]. In addition, the confusing mix of FI instruments provided by different governments and utility companies as well as a lack of monitoring departments for financing retrofit projects also pose challenges to the effectiveness of FI instruments [90].
Analysis of global policies to reduce embodied emissions
The official energy efficiency departments in many countries have enforced a mix of different policies to reduce embodied emissions in the building sector. Different categories of policies are illustrated in the following sections.
Building regulations
Construction materials efficiency declaration
This policy requires declaration of key material mass per m 2 / square foot of building to be filed for the planning permit process at the occupancy permit application stage for buildings. As such, retrofit professionals can establish a benchmark database on building materials use and make stakeholders understand cash savings via saving material.
Expedited permitting for low carbon projects
This policy requires projects that meet given embodied carbon criteria should be given expedited or reduced fee processing. Examples of embodied carbon criteria may include life cycle assessment requirements or other requirements. For example, the City of Seattle's Priority Green Expedited program sets thresholds for energy efficiency, water conservation, waste reduction, and indoor air quality. Municipalities provide building owners who meet the requirements a single point of contact in the Department of Construction & Inspections with priority in scheduling an intake appointment, faster initial review of construction plans, and faster permit processing.
Prohibiting extremely high emitting materials
This policy prohibits the use of specific building materials associated with extremely high GHG emissions, such as spray foams with hydrofluorocarbon blowing agents used in insulation.
Governments can implement different measures to ban the use of extremely high GHG-emitting building materials as follows:
• Ban the sale or purchase of the identified materials.
• Require designers or builders to specify defined low GHG-emitting alternative materials in order the permit to be approved. This policy requires all projects to calculate and report their life cycle carbon emissions using a standardized measure, separating embodied and operational carbon.
Procurement policies
Carbon limits for building materials procurement
This policy set carbon intensity limits for key materials for construction materials used for retrofit projects and implement in public procurement. These can be demonstrated using Environmental Product Declarations (EPDs). For example, in Norway, the City of Trondheim requires the following from materials procurement:
• Concrete, both ready-mix and elements must meet low carbon class A • Massive wood carbon limit 70 kg CO2/m 3 -CLT and glulam carbon limit 100 kg CO2/m 3 • Reinforcement steel shall be 100 % recycled, or emissions for other products shall be correspondingly lower • Leveling screed on top of wooden floors must be B10, low carbon class A • Non load bearing internal walls avg. emissions: max 10 kg CO2/m 3
The data used to demonstrate compliance should be EPDs in compliance with EN 15804, and EPDs must be demonstrated for at least 15 products used in the building.
Requirement of recycled aggregates
This policy sets a minimum level of recycled or reused aggregates and soils in projects, if available within a predefined sourcing radius. For example, in Denmark, the government of Copenhagen requires in their Sustainability in Construction and Civil Works that "Road-building works must use crushed builders" rubble as a substitute for base gravel, provided that this is technically or economically sustainable. The crushed rubble must not contain any bricks, tiles or concrete that could be reused instead. In addition, France has established a target to achieve a 50 % share of reused or recycled building waste materials in road construction for materials bought by authorities in 2017, increasing to 60 % by 2020. This can help in having a market for most of the recycled aggregates processed from construction and demolition waste.
Require use of certified wood products
This policy requires the use of certified wood products when appropriate in projects for which municipal procurement guidelines apply. The required certification system should be determined by the governments and should have standards that have been demonstrated to produce wood with a lower embodied carbon footprint.
Circular materials purchasing strategy
This policy implements a strategy to define procurement in a manner which ensures that the market will either certainly or very likely deliver a circular solution in response. Procurement can be designed to focus on materials efficiency, circularity, maintainability, repairability and end of life opportunities.
Waste and circularity policies
Mandatory pre-demolition audits and data sharing
This policy requires all demolition and larger project permit applications to include a detailed predemolition audit. Municipalities make those pre-demolition audits public and allow a waiting time during which materials salvaging operators can recover what materials they commercially agree to recover from the building owner as opposed to instant demolition. For example, in Europe, the guidelines for the waste audits before demolition and retrofit works of buildings is a voluntary European protocol for pre-demolition audits of buildings that intend to help ensure recovery of recyclable material streams. It supports achieving high quality separated waste fractions.
Information on adaptability and waste reduction
This policy can provide designers, builders, and developers with information on financial benefits to be gained from reducing waste and information on converting existing buildings for adaptive reuse projects by selecting, procuring, and building with low-embodied carbon materials, and designing with later adaptation and reuse of buildings and materials. This can be accomplished through technical assistance, including educational workshops and trainings, through dissemination of financial analyses for low-embodied carbon project precedents, cost charts, as well as information on available tax incentives for donations of salvaged material or through the establishment of an office, internal resource center, or coordinator position to connect builders with information and expertise.
Materials longevity policy
This policy sets prescriptive requirements for the long-lasting design and use of long-lasting building materials. Further research must be conducted by the enforcing jurisdiction to determine the exact requirements, balancing the expected life span of a given material with its initial embodied carbon footprint, its potential for later reuse or recycling, and also the cost, availability, and local needs. For example, PVC windows have a significantly shorter lifetime than woodaluminum windows. This policy should not apply to any buildings with planned short life-time.
Financial incentives
Provide tax rebates for low carbon development
Governments can offer an annual property tax rebate of up to 100% for a set number of years to property owners who opt for low-carbon renovation rather than new construction. The amount of the rebate can be based on a quantification of the embodied carbon reduction, so that projects with greater relative embodied carbon reductions are eligible for larger rebates.
Link land use fees to project life cycle carbon
Municipalities often charge land use fees from projects. These fees could be indexed to project embodied carbon. The charge structure could also be set up so that very low carbon projects would not pay fees at all or be possibly eligible for cash refunds.
Land use fees assessed for projects shall be established based on project life-cycle carbon intensity per square meter relative to building type benchmark. Project life-cycle carbon intensity per square meter is assessed using methodology and scope defined by the city. The life-cycle carbon intensity for project shall be verified by a competent verifier.
Provide Carbon performance grants for projects
Governments can set aside funds to award performance-conditioned grants for projects that achieve a clearly above market embodied carbon performance. Grants can be applied for during planning permission application, but they would be paid out only once project is completed, and performance achieved is possible to verify and audit.
Include embodied carbon in climate action plan
This program requires all future climate action plans or updates to existing climate action plans, to include an assessment of embodied carbon emissions from building and infrastructure construction, transportation, and land use. Also, to include a timeline and strategies for meeting reduction targets for embodied carbon in conjunction with timelines for reducing operational emissions.
Increase demolition permitting fees
Municipalities can increase demolition permitting fees for property owners applying to demolish buildings. Such increases could be applied conditionally, depending on building age, building size, predominant materials, carbon efficiency of the proposed replacement project, suitability of the building to deconstruction or other variables.
Create incentives for manufacturers to reduce carbon
This policy would create incentives for manufacturers located in the region of the jurisdiction to reduce embodied carbon in their products. Possible pathways include:
• Property/council tax rebates for manufacturers within the jurisdiction that demonstrate and quantify significant embodied carbon reductions in their main products.
• Property/council tax rebates for manufacturers within the jurisdiction who meet a Zero Net
Carbon standard for the operation of their facilities, either by generating enough renewable, non-GHG emitting energy on-site to power their manufacturing processes, or procuring renewable, non-GHG emitting energy generated off-site. • Direct grants/rebates for manufacturers for completing facility upgrades that significantly reduce carbon emissions, such as switching from a material or emissions intensive manufacturing process to a less material or emission-intensive alternative, or installing onsite renewable, non-GHG emitting energy generation.
Dedication of government resources and/or staff time to building relationships and facilitating the development of networks of manufacturers to support industrial symbiosis.
Establish landfill tax on construction and demolition waste
This policy establishes a requirement for taxing all landfilled construction and demolition waste. Landfill tax will provide a broad financial incentive to avoid final disposal of all types of material streams. To have impact on construction and demolition waste, this must also be levied on aggregates.
Recommendations for reducing embodied carbon in retrofits in British Columbia
After reviewing existing retrofit polices in British Columbia (BC) and polices that reduce embodied emissions across different countries, the following recommendations for building retrofit policies to reduce embodied emissions in British Columbia can be made.
Providing embodied carbon in retrofits related knowledge and information to the public
Knowledge and information associated with embodied carbon emissions play an essential role in the promotion of energy retrofits in the existing building sector. The knowledge on how retrofit technologies work can increase confidence of occupants in building energy retrofits. It is helpful to promote energy retrofits by providing information (e.g., potential benefits) to the public. From the perspective of energy retrofit investors, it is important for them to know the economic benefits of energy retrofits and what financial support is available. More importantly, such knowledge and information have a positive impact for enhancing occupants' willingness to performing energy retrofits. In British Columbia, as less knowledge and information are provided to the public, their awareness of building energy retrofits and building embodied emissions is at a low level, which lead to a low willingness to implementing energy retrofits. The situation poses a huge challenge to reduce embodied carbon emissions in retrofits in BC. In this regard, knowledge and information polices on building energy retrofits and building embodied emissions should be formulated in BC to increase public awareness.
In addition, it is essential for people to be able to obtain embodied emissions in retrofits related knowledge and information easily. For example, it is recommended that the public media (e.g., broadcast and TV) be used to disseminate knowledge and information of energy retrofits and building embodied emissions. Second, it is recommended that pilot retrofit projects be implemented. The carbon emission reduction data can be shared with the public so that the public can see the real benefits of building energy retrofits. Third, because of the fragmentation of relevant information, it is essential to establish a one-stop-shop information website where the public can easily obtain relevant knowledge and information at a low cost (in terms of effort and time).
Advantages Disadvantages
• It is a cost-effective way to improve occupants' awareness to implement energy retrofits for their homes. • It can have an essential impact on reducing carbon emissions through retrofits.
• It can be time-consuming to implement this strategy. • It cannot achieve direct carbon emission reductions. • It may require special financial supports from governments or utility providers.
Enhancement of building material performance
It is suggested that replace existing conventional construction materials with lower carbon and carbon sequestering materials. In addition, reducing overall material use by modifying the fabrication of individual building components and designing for material efficiency at the whole building scale is another effective way to reduce embodied carbon emissions. Building professionals can conduct analysis of building stock to identify low embodied carbon materials available in BC as alternatives to the current high embodied emission materials. (e.g., hempcrete and straw bale insulation can replace XPS foam). They can also conduct a cost-benefit analysis to estimate the potential of reducing embodied emissions in district buildings. Additional strategies for reducing embodied carbon include:
• Selecting natural products or those with low energy manufacturing processes. For example, timber or materials with natural fibers come from renewal sources and can be used with low processing. However, adding finishes to protect these materials increases their overall impact. Some varnishes for wood can limit its recyclability and lead to its use as energy source. • Specifying durable materials suitable for the climatic context of BC. For example, the façade and roof are under constant wear from natural elements that can lead to frequent repairs and maintenance. By using durable materials, occupants can reduce the cost and frequency of refurbishment and the use of material replacement and its associated carbon footprint. • Minimizing manufacturing and construction waste through comprehensive design (e.g., prefabricated panel manufacturing). The embodied carbon of a building element includes its material footprint and the waste that was generated during its construction. Prefabrication under controlled conditions allows reduction of waste and its associated carbon emissions. Similarly, modular elements permit the efficient use of materials and facilitate the industrialization/prefabrication of these elements. • Selecting salvaged and recycled materials, materials that sequester carbon (e.g., using carbon capturing technology), and sourcing local supplies to avoid transportation emissions. • Designing for end-of-life deconstruction and material reuse or recycling, as well as reducing material usage.
In terms of building material choice, insulation choice is among the most substantive opportunities for building retrofit planners to influence a building's life cycle emissions. Some insulating materials like straw bale, hempcrete, and wool store (sequester) carbon and have negative emissions, while others like extruded polystyrene (XPS) are made with blowing agents that have high global warming potentials (GWP). Compared with rigid insulation and spray foams, blownin fibreglass and cellulose insulation have much lower carbon impacts. In addition, refrigerant choices also have material impacts on the carbon emissions associated with a building. HFC-134a is commonly used in air-conditioning systems; it has a GWP of 3,830 over a 20-year time horizon and GWP of 1,430 over 100 years. Some naturally occurring compounds that can be used as refrigerants, such as ammonia or propane, have much lower GWP. Refrigerant leakage rate is another important element that needs to be factored in when designing and selecting HVAC systems as it can have major impacts on a building's life cycle carbon emissions.
Advantages Disadvantages
• The most direct and easiest way to reduce embodied carbon emissions in the existing building sector. • This strategy can produce life cycle cost benefits.
• It may be a strategy with high upfront cost and long payback period.
Engaging with energy retrofit professionals and organizations
As a lack of highly skilled retrofit professionals might undermine the effectiveness of retrofit schemes, increasing industry capacity is also essential. For example, recruiting newly qualified renovators by examining contractors who have work experience with old house retrofit or new energy-efficient dwelling construction should garner more attention. Practitioners could be encouraged to document their work qualifications and corroborate their eligibility for participation. Furthermore, there is a need to provide training programs for professionals to improve their skills and increase retrofit workforce capacity, which can play an essential role in addressing homeowners' concerns on technical problems.
Providing a bridge between homeowners and professionals can help in removing regulatory barriers and streamline the overall retrofitting process. For instance, establishing a central coordinator and consultant center can assist homeowners in evaluating retrofit opportunities, calculating retrofit costs, submitting rebate applications, verifying the retrofit quality, and conducting a post-retrofit survey. Meanwhile, developing a user-friendly tool (e.g., mobile app) can provide convenience for homeowners to explore retrofit packages and financial incentives most applicable to their homes.
In addition, the engagement of various stakeholders is also important for promoting energy retrofits. Therefore, it is recommended that social participation be encouraged by the inclusion of professionals and building owners in the working groups. Meanwhile, an organization, which functions as a mediator between the government and house owners, can coordinate various stakeholders and organize various activities to promote building renovation. In response to this situation, it is proposed that the participation of industry associations and non-profit organizations be increased in the energy retrofit process in BC, and that their roles be clearly defined, and for support to be given to them. With respect to working groups and industry associations, they should clearly define their relationships to avoid overlapping responsibilities.
Advantages Disadvantages
• It can help in increasing the industry capacity and implementing more retrofit projects at the same time. • It can help in streamlining the retrofit process and improving work efficiency.
• It is time-consuming to be implemented.
• It cannot produce the direct benefit of embodied emission reductions. • It requires extra financial supports from governments or utility providers.
Establishment of an assessment and certification system for building embodied emissions
The establishment of an assessment and certification system is an effective way of dealing with the lack of building embodied emission data in energy retrofit projects. Furthermore, building performance certification (e.g., label, star, rating) systems can be used to improve the quality control of energy retrofit projects. Meanwhile, the data collected can be stored in a building material embodied emissions database for future usage. The assessment and certification system can provide real data support to regulation-based policies and financial support policies for building energy retrofits.
Life cycle carbon calculation and reporting
It is recommended that all retrofit projects calculate and report their life cycle carbon emissions using a standardized measure, separating embodied and operational carbon emissions. As such, stakeholders can understand the share of embodied emissions and operational emissions and which building types have the greatest carbon emission saving potentials, and thus develop optimal plans to reduce carbon emissions in retrofits. The retrofit industry should identify a standardized embodied emissions reporting tool (e.g., BEAM calculator for Part 9 buildings and Athena Impact Estimator for Part 3 buildings). At the same time, retrofit professionals should consider the fees associated with using the tool and collect input from industry stakeholders and develop guidelines for the selected tool to support the industry.
However, a lack of a comprehensive embodied emission database in BC poses a big challenge to calculate life cycle carbon emissions in retrofits. For example, the embodied emissions of many building insulation materials are still missing. While retrofit professionals can refer to other databases in the US and European countries, the embodied emission data may not be reliable due to different climate conditions, manufacturing methods, transportation systems, and landfill places.
Environmental Product Declaration (EPD)
Environmental product declaration (EPD) is a good example of reliable material information as EPD records data directly from manufacturers and companies, and it is developed strictly following ISO 21931 and EN 15643 at the building level. The overall goal of EPDs is to promote the supply of building products that are more environmentally friendly by communicating verifiable and accurate information, and to increase the potential of continuous environmental improvement. Based on ISO 14025, the detailed objectives of EPDs are as follows: 1) To provide LCA-based information and additional information on the environmental performance of products; 2) To help users and purchasers making informed comparisons between products; 3) To encourage improvement of environmental performance; 4) To provide information for evaluating the environmental impacts of products over their life cycle.
In particular, EPDs can provide embodied carbon emission data for building materials. A EPD materials database contains different construction materials environmental impact profiles for different products, technologies, suppliers and products. EPDs can be divided into three types based on system boundaries: cradle-to-gate, cradle-to-gate with options, and cradle-to-grave. A cradle-to-gate EPD only covers minimum information from the product stage. Cradle-to-gate with options EPD covers the information from the product stage, plus additional information from other stages. A cradle-to-grave type EPD covers all the life cycle stages as a minimum, and some benefits or loads beyond the system boundary might be included as well. As of May 2013, 556 PCR and 3614 EPD documents were published worldwide . Italy and Sweden have the highest number of products with EPDs, followed by Spain and Switzerland. It is recommended that BC industry develop EPDs for building construction and insulation materials and energy equipment commonly used in Canadian buildings. With a comprehensive EPD database, retrofit professionals can easily calculate life cycle carbon emissions of existing buildings and identify the buildings with highest emission reduction potential through energy retrofits.
Advantages Disadvantages
• It can provide direct information associated with embodied emissions of various building materials and help retrofit planners compare different building materials and select the best one in in terms of the carbon and economic performance.
• Establishing a comprehensive EPD database will be time-consuming and requires multiple building stakeholders to work together. • It requires extra efforts and time to complete life cycle carbon emission calculation and reporting. • It may increase the upfront cost of a retrofit project.
Development of a comprehensive financial support system for retrofits
Financial incentives can effectively moderate stakeholders' concerns on economic issues such as high upfront cost, payback period, and return on investment. In this regard, it is necessary to provide financial support bundles for them. The bundles may comprise multiple forms of economic supports, such as subsidies, tax credits, and low-interest loans on conducting specific retrofit measures and rebates for purchasing energy-efficient equipment (e.g., heat pump). Furthermore, utility on-bill financing is also recommended, which can effectively address the concern of upfront cost. It is important to keep low administrative burden and interest cost and ensure that administrative and compliance systems can readily adapt to the new billing requirements. In order to assist homeowners in understanding the total actual costs of retrofit options, all available financial choices should be involved in retrofit costs shown to homeowners. While there are a few financial supports for energy retrofits from BC government and utility providers, such as Fortis BC and BC Hydro, further incentives need to be provided to reduce embodied emissions in the existing building sector.
Develop circular economy strategies
It is recommended that develop circular economy strategies to avoid embodied carbon by reducing resource extraction and repurposing materials already in circulation. In the building sector, circular economy strategies consist of salvaging and reusing building materials as well as re-using the core and shell of existing buildings. Developing a comprehensive circular economy strategy requires a huge shift from disposability to durability in the building sector, such as reducing the building area per occupant, prioritizing efficient occupancy of existing buildings, and removing provisions for private transportation [91].
Tax rebates for low carbon development
Governments can offer an annual property tax rebate for a set number of years to property owners who opt for low-carbon renovation rather than new construction. The amount of the rebate can be based on a quantification of the embodied carbon reduction, so that energy retrofit projects with greater relative embodied carbon reductions are eligible for larger rebates.
Carbon performance grants for retrofit projects
Municipalities can set special funds to award performance-conditioned grants for energy retrofit projects that achieve a clearly above market embodied carbon performance. Grants can be applied for during energy retrofit planning permission application, but they would be paid out only once project is completed, and performance achieved is possible to verify and audit.
Increase demolition permitting fees
Municipalities can increase demolition permitting fees for property owners applying to demolish buildings. The increases could be applied conditionally, according to building types, age, size, materials, carbon efficiency of the proposed replacement project, suitability of the building to deconstruction.
Incentives for manufacturers to reduce carbon
This strategy creates incentives for manufacturers in BC to reduce embodied carbon in their products. Possible pathways include:
• Property tax rebates for manufacturers in BC that demonstrate and quantify significant embodied carbon reductions in their main products. • Property tax rebates for manufacturers in BC who meet a zero net carbon standard for the operation of their facilities, either by generating enough renewable, non-GHG emitting energy on-site to power their manufacturing processes, or procuring renewable, non-GHG emitting energy generated off-site. • Direct grants for manufacturers for completing facility upgrades that significantly reduce carbon emissions, such as switching from a material or emissions intensive manufacturing process to a less material or emission-intensive alternative, or installing on-site renewable, non-GHG emitting energy generation.
Rebates for heavy-duty zero-emission vehicles
Governments can provide rebates for heavy-duty zero-emission vehicles to reduce embodied emissions in retrofits due to transportations. For example, the BC transportation department can provide rebates up to 100% of the price difference between an electric heavy-duty vehicle and a traditional gas-power heavy-duty vehicle. This strategy can encourage transport companies to purchase more zero-emissions vehicles and thereby reduce embodied emissions caused by the transportation of building materials and components.
Landfill tax on construction and demolition waste
It is recommended that government establishes a requirement for taxing all landfilled construction and demolition waste. Landfill tax will provide a broad financial incentive to avoid final disposal of all types of material streams. To have impact on construction and demolition waste, this tax should also be levied on aggregates.
Establishment of a comprehensive energy retrofit supply chain
A supply chain is a network between a company and its suppliers to produce and distribute a specific product or service. The entities in the supply chain include producers, vendors, warehouses, transportation companies, distribution centers, and retailers. Energy retrofits supply chain (ERSC) can be defined as a functional chain structure that includes the participants involved in each phase of the energy retrofit project life cycle. The participants in an energy retrofit project, such as the developer, contractor, materials manufacturer and supplier, are linked by cash, information and materials flow. In ERSC, the raw materials production and transportation phase may contribute the most carbon emissions. Regarding the carbon emissions of different ERSCs, the differences in the materials and component production, transportation and construction phases can be significant. Therefore, it is recommended that BC governments establish a comprehensive supply chain for implementing energy retrofits in BC, building relationships and facilitating the development of networks of manufacturers to support industrial symbiosis. A comprehensive supply chain can assist retrofit professionals in reducing unnecessary works, simplifying energy retrofit steps, optimizing building material manufacturing and transportation systems, and thereby decreasing embodied carbon emissions. At the same time, research and development (R&D) for the development of advanced ERSC should be supported by the governments or utility providers (e.g., Fortis BC and BC hydro) through special funds.
Advantages Disadvantages
• It can assist retrofit professionals in reducing unnecessary works, simplifying energy retrofit steps, optimizing building material manufacturing and transportation systems. • It can have a significant impact on reducing embodied emissions in energy retrofits.
• It is complex and time-consuming to establish a supply chain since it requires multiple stakeholders work together, including academic researchers and industry people. • It requires aside financial supports from the BC government and utility companies (e.g., Fortis BC and BC Hydro)
Conclusion and recommendations
This research conducted a literature review and identification of BC policies and incentives for reduce overall GHG emissions from the existing building sector. Then, this research analyzed worldwide policies and incentives that reduce embodied carbon emissions in the existing building sector. After reviewing the two categories of retrofit policies, the author identified links and opportunities between existing BC strategies, tools, and incentives, and global embodied emission strategies. Finally, this research compiled key findings from all resources and provided policy recommendations for reducing embodied carbon emissions in retrofits in BC. The recommendations are as follows:
1. Provide embodied carbon in retrofits related knowledge and information to the public: Employ broadcast and internet and establish one-stop website to disseminate knowledge and information of embodied carbon emissions in energy retrofits. This can help in improving the public awareness of implementing energy retrofits to reduce carbon emissions in the existing building sector.
2. Enhance building material emission performance: Selecting salvaged and recycled materials, materials that sequester carbon, or materials that are manufactured and processed using low-carbon energy, and sourcing local supplies to avoid transportation emissions are effective and direct ways to reduce embodied carbon emissions in energy retrofits.
Engage with energy retrofit professionals and organizations:
Engage with energy retrofit professionals and product manufacturers to learn what incentives would be most attractive to reduce embodied emissions in retrofits. Provide a bridge between homeowners and professionals can help in removing regulatory barriers and streamline the overall retrofitting process.
Establish an assessment and certification system for building embodied emissions in retrofits:
Establishing an assessment and certification system is an effective way of dealing with the lack of building embodied emission data in energy retrofit projects. Furthermore, building performance certification (e.g., label, star, rating) systems can be used to improve the quality control of energy retrofit projects. Meanwhile, the data collected can be stored in a database associated with building material embodied emissions for future usage. A well-developed assessment and certification system can provide real data support for building energy retrofits.
5.
Develop a comprehensive financial support system for retrofits: Explore financial incentives such as circular economy strategies, tax rebates for low carbon development, carbon performance grants, demolition permitting fees, incentives for manufacturers, rebates for heavy-duty zero-emission vehicles, and landfill tax on construction and demolition waste.
6. Establish a comprehensive energy retrofit supply chain: An energy retrofit supply chain is a functional chain structure that includes the participants involved in each phase of the energy retrofit project life cycle. Participants in an energy retrofit project, such as developers, contractors, material manufacturers and suppliers, are linked by cash, information and materials flow. A comprehensive supply chain can assist retrofit professionals in reducing unnecessary works, simplifying energy retrofit steps, optimizing building material manufacturing and transportation systems, and thereby decreasing embodied carbon emissions in retrofits.
•
Financially penalize the use of high GHG-emitting materials and incentivize the use of low GHG-emitting alternative materials. 4. Life cycle carbon calculation and reporting.
Table 1
1Clusters of retrofit policy instrumentsInstruments
Descriptions
List of global Policies that reduce Embodied Emissions adapted to existing buildingsBuilding Regulations
Procurement
Waste & Circularity
Financial Policies
Construction materials
efficiency declaration
Carbon limits for
building
materials
procurement
Design for disassembly
and
adaptability
criteria
Tax rebates for low
carbon development
Expedited permitting
for low carbon project
Requirement
of
recycled aggregates
Mandatory
pre-
demolition audits and
data sharing
Link land use fees to
project
life
cycle
carbon
Prohibiting extremely
high emitting materials
Require use of certified
wood products
Mandatory
material
takeback program
Carbon performance
grants for projects
Life cycle carbon
calculation
and
reporting
Circular
materials
purchasing strategy
Soil coordination for
mass storage and reuse
Include
embodied
carbon in climate
action plan
Information
on
adaptability and waste
reduction
Increase
demolition
permitting fees
Materials
longevity
policy
Incentives
or
manufacturers
to
reduce carbon
Landfill
tax
on
construction
and
demolition waste
AppendixList of BC policies and incentives
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| sample_823 | 0.9838 | arxiv | |
Diverse response of surface ozone to COVID-19 lockdown in China
Yiming Liu
Department of Civil and Environmental Engineering
The Hong Kong Polytechnic University
Hong KongChina
Now in School of Atmospheric Science
Sun Yat-sen University
ZhuhaiChina
Tao Wang
Department of Civil and Environmental Engineering
The Hong Kong Polytechnic University
Hong KongChina
Trissevgeni Stavrakou
Royal Belgian Institute for Space Aeronomy
BrusselsBelgium
Nellie Elguindi
Laboratoire d'Aérologie
ToulouseFrance
Thierno Doumbia
Laboratoire d'Aérologie
ToulouseFrance
Claire Granier
Laboratoire d'Aérologie
ToulouseFrance
NOAA Chemical Sciences Laboratory and CIRES
University of Colorado
BoulderCOUSA
Idir Bouarar
Max Planck Institute for Meteorology
Environmental Modeling Group
HamburgGermany
Benjamin Gaubert
Atmospheric Chemistry Observations and Modeling Laboratory
National Center for Atmospheric Research
BoulderCOUSA
Guy P Brasseur
Department of Civil and Environmental Engineering
The Hong Kong Polytechnic University
Hong KongChina
Max Planck Institute for Meteorology
Environmental Modeling Group
HamburgGermany
Atmospheric Chemistry Observations and Modeling Laboratory
National Center for Atmospheric Research
BoulderCOUSA
Diverse response of surface ozone to COVID-19 lockdown in China
1 * Correspondence to: Tao Wang (cetwang@polyu.edu.hk) and Yiming Liu ( 2Surface ozonemeteorological conditionemission reductionCOVID-19
Ozone (O3) is a key oxidant and pollutant in the lower atmosphere. Significant increases in surface O3 have been reported in many cities during the COVID-19 lockdown. Here we conduct comprehensive observation and modeling analyses of surface O3 across China for periods before and during the lockdown. We find that daytime O3 decreased in the subtropical south, in contrast to increases in most other regions. Meteorological changes and emission reductions both contributed to the O3 changes, with a larger impact from the former especially in central China. The plunge in nitrogen oxide (NOx) emission contributed to O3 increases in populated regions, whereas the reduction in volatile organic compounds (VOC) contributed to O3 decreases across the country. Due to a decreasing level of NOx saturation from north to south, the emission reduction in NOx (46%) and VOC (32%) contributed to net O3 increases in north China; the opposite effects of NOx decrease (49%) and VOC decrease (24%) balanced out in central China, whereas the comparable decreases (45-55%) in these two precursors contributed to net O3 declines in south China. Our study highlights the complex dependence of O3 on its precursors and the importance of meteorology in the short-term O3 variability.
Introduction
The outbreak of coronavirus disease 2019 has severely threatened public health worldwide, leading to millions of deaths (WHO, 2020). China, where the first case of COVID-19 was reported in the city of Wuhan, imposed country-wide measures from 23 January to 13 February 2020 to prevent the spread of the disease, including social distancing, teleworking, and closure of non-essential businesses (Chinazzi et al., 2020;. These restrictions drastically reduced anthropogenic activities, resulting in a sharp decrease in emissions of air pollutants (Doumbia et al., 2020;Huang et al., 2020;Wang et al., 2020a).
The huge and large-scale emission reductions during the COVID-19 lockdown can be treated as a natural outdoor experiment to improve our understanding of the air pollutant's response to emission control. According to satellite and surface observations, compared with the period before the lockdown, nitrogen dioxide (NO2) concentrations decreased by over 50% in China during the lockdown period (Bauwens et al., 2020;Liu et al., 2020;Shi and Brasseur, 2020;Zhang et al., 2020). The concentrations of other pollutants, including SO2, particulate matter with an aerodynamic diameter less than 2.5 μm (PM2.5), particulate matter with an aerodynamic diameter less than 10 μm (PM10), and carbon monoxide (CO), also declined in a large area of China (Miyazaki et al., 2020;Wang et al., 2020b). However, surface ozone (O3) concentrations in northern and central China increased by over 100% (Lian et al., 2020;Shi and Brasseur, 2020). Similar O3 increases have been reported in southern Europe, India, and Brazil despite the large decrease in other pollutants (Sharma et al., 2020;Sicard et al., 2020;Siciliano et al., 2020).
However, the underlying factors driving the O3 changes during the city lockdowns remain unclear. Surface O3 is produced by photochemical reactions of ozone precursors, NOx, volatile organic compounds (VOCs), and carbon monoxide (CO) and can also be transported from higher levels of the atmosphere and from outside regions (Akimoto et al., 2015;Liu and Wang, 2020a;Roelofs and Lelieveld, 1997). It is well known that O3 has a non-linear dependence on its precursors and that NOx can either decrease or increase O3 depending on the relative abundance of NOx to VOCs (Atkinson, 2000;Wang et al., 2017a). In general, the O3 production in urban areas with high NOx/VOCs ratios is VOCs limited, and reducing NOx emissions can increase O3 due to decreased titration of O3 and radicals. In addition to the two precursors, particulate matters can influence ozone by altering the solar irradiance and chemical reactions on aerosol surfaces (Li et al., 2019b;Liu and Wang, 2020b;Stadtler et al., 2018). Meteorological factors affect surface ozone by changing transport pattern, wet and dry depositions, chemical reaction rates, and natural emissions (Liu and Wang, 2020a;Lu et al., 2019).
The responses of ozone (and other air pollutants) to short-term emission reductions have been previously studied for a number of public and political events in China, such as the Beijing Summer Olympic Games (August 2008), the Asia-Pacific Economic Cooperation (APEC) meeting in Beijing (November 2014), and the G20 summit in Hangzhou (September 2016). During these events, various emission-reducing measures were implemented in the cities concerned and their surrounding areas. Whereas atmospheric concentrations of primary air pollutants (NOx, CO, primary PM, and SO2) in the concerned cities generally decreased in response to the temporary control measures, the O3 concentrations showed mixed responses. O3 decreased after emission reductions for some events (Huang et al., 2017;Wang et al., 2017b) but increased in others (Wang et al., 2010;Wang et al., 2015;Wu et al., 2019). The different O3 responses have been qualitatively attributed to differences in the meteorological conditions (including regional transport of air masses) and to different control measures implemented by the local governments.
Compared with the previously studied situations, the COVID-19 lockdown is unique in that emissions decreased across the whole country (and later worldwide) as opposed to a specific city or region, and the decreases were also much more drastic than those due to transportation restrictions alone. Moreover, the COVID-19 lockdown took place in winter, whereas the previous interventions occurred in summer and autumn, when meteorology and atmospheric chemistry are different from winter. The present study analyzes surface O3 data across China before and during the COVID-19 lockdown. We find that O3 decreased in southern China while increasing in most other regions during the lockdown. Using a regional chemistry transport model, we isolate the impacts of meteorological changes and anthropogenic emission reductions on O3. Our results highlight the importance of meteorological influences on the short-term O3 changes and the diverse response of O3 to the emission reductions of its precursors in different climate and emission-mix regions.
Materials and Methods
Surface measurement data
We obtained the observed concentrations of surface O3 and other pollutants (PM2.5, PM10, SO2, CO, NO2) at 1643 stations from the China National Environmental Monitoring Center (http: //106.37.208.233:20035/). Data quality control was conducted for the measurement data in accordance with previous studies (Lu et al., 2018;Song et al., 2017). Fig. 1 shows the locations of these environmental monitoring sites.
The country-wide measures to control the spread of COVID-19 were implemented starting from 23 January 2020 (the exact date varies for different cities), just before the Chinese New Year. All enterprises remained closed until no earlier than 13 February, except those required for essential public services, epidemic prevention and control, and residential life needs. We focused on the period during the COVID-19 lockdown from 23 January to 12 February 2020 (hereafter referred to as the CLD period), 3 weeks in total. We derived the changes in O3 and other pollutants by comparing the CLD period with the 3 weeks before the COVID-19 outbreak, from 2 to 22 January 2020 (hereafter referred to as the pre-CLD period). We focused on three where the megacities of Guangzhou and Shenzhen are situated, is the most developed region in southern China.
Numerical modeling
The CMAQ model (Community Multiscale Air Quality model, v5.2.1) was applied to simulate the O3 mixing ratios over China from 2 January to 12 February 2020. The WRF model (Weather Research and Forecasting model, v3.5.1) was driven by the dataset of the National Center for Environmental Prediction (NCEP) FNL Operational Model Global Tropospheric Analyses with a horizontal resolution of 1° × 1° and provided meteorological inputs for the CMAQ model. The CMAQ target domain covered the continental China at a horizontal resolution of 36 km × 36 km. SAPRC07TIC (Carter, 2010;Hutzell et al., 2012) and AERO6i Pye et al., 2017) were adopted as the gas-phase chemical mechanism and aerosol mechanism, respectively. The CMAQ model has been improved with updated heterogeneous reactions to better predict the O3 concentration; details can be found in Liu and Wang (2020a). Although the WRF-CMAQ model was run in offline mode, the CMAQ model employs an in-line method that uses the concentrations of particles and O3 predicted within a simulation to calculate the solar radiation and photolysis rates (Binkowski et al., 2007). As a result, the effect of aerosol on O3 concentrations via changing the photolysis rates were also considered in the simulation. Two experiments were conducted to investigate the impacts of meteorological changes and emission reductions on O3 during the CLD period. The first (baseline) used the same anthropogenic emissions for the pre-CLD and CLD periods, and the second (Reduction case) used emission reductions of 70%, 40% and 30% for transportation, industry and power generation, respectively, and a 10% increase of residential emission during the CLD period. These emission reductions for the whole country were estimated according to the previous literature (Doumbia et al., 2020;Huang et al., 2020;Wang et al., 2020a). Comparing these two model simulations, the O3 changes during the CLD period relative to the pre-CLD period for the Reduction Case were considered to be entirely due to the meteorological changes and emission reductions. The impacts of the meteorological changes (including the changes in chemical boundary conditions) were quantified by subtracting the O3 mixing ratios of the pre-CLD period from those of the CLD period for the baseline experiment, while the impacts of emission reduction were estimated by comparing the O3 mixing ratio during the CLD period between the Reduction Case and the baseline experiment. Furthermore, we individually reduced the emissions of nitrogen oxide (NOx), VOCs, CO, PM (particulate matter, including PM10, PM2.5, black carbon, and organic carbon), and SO2 during the CLD period to elucidate the response of O3 to each pollutant reduction.
The performance of the CMAQ model in simulating the O3, NO2, PM2.5, SO2, and CO concentrations for the Reduction Case was evaluated ( Fig. S1 and Table S2), showing reasonable agreements with the respective surface observations. Details of the emission estimation and the model evaluation are presented in Supplementary Information. and 71% in the NC and CC regions (Fig. 2d). In the SC region, most stations displayed a decrease in O3 during daytime, leading to a regional average O3 drop of 14%. During nighttime, the O3 mixing ratio increased significantly across China (Fig. 2e), by 154%, 77%, and 18% in NC, CC, and SC, respectively (Fig. 2f). These results reveal the diverse response of O3 during the lockdown in different regions, especially for the daytime. The changes in the Ox (NO2+O3) concentration (Fig. 3a), which takes into account the NO titration, also varied in different regions. The daytime average Ox levels increased by 4% in NC and by 11% in CC, and decreased by 29% in SC. These results suggest that the NO titration effect was not the only cause of the O3 increase in northern and central China, as Ox would have decreased with sharply reduced NOx emissions.
Results
Observed O3 changes in different parts of China
Contribution of meteorological changes and emission reductions to O3
Ground-level O3 is influenced by both chemical reactions of O3 precursors and meteorology. In this study, we used the WRF-CMAQ model to separate the impacts of meteorological changes and emission reductions on the changes in O3 across China ( Fig. S2), which reveals significant contributions of both meteoroglgy (over most of contrinental China) and emissions (mainly in populated areas of eastern China) . Fig. 4 shows the more detailed results for the NC, CC, and SC regions for both daytime and nighttime and Fig. S3 presents the meteorological impact and emission impact in terms of percent change. The observed O3 changes in these regions were reasonably captured by the simulations. For the daytime average, the O3 increase in NC was attributed to the comparable contributions from both meteorological changes (58%) and emission reductions (42%) (Fig. 4a).
In CC (Fig. 4b), the meteorological change (98%) was the primary cause of the O3 increase, whereas the contribution of emission reduction was much lower (2%). In SC (Fig. 4c), the meteorological changes (73%) and emission reductions (27%) both contributed to the O3 decrease. During nighttime, the emission reduction increased O3 in all three regions (including SC), and its impact was stronger; the effect of meteorological changes weakened at night (Fig. S3).
Impacts of meteorological changes on O3
The impacts of meteorological changes on O3 for the NC, CC, and SC regions can be explained by the changes in the weather pattern and specific meteorological factors. In winter, continental China is generally controlled by a cold high-pressure system (Fig. 5). During our study period, the center of this high-pressure system was located in northern China, moving southward from the pre-CLD to the CLD period, with weakening strength. The high-pressure system therefore became increasingly dominant in southern China, and the strengthened southward winds brought colder air masses from the north (Fig. 6c), which decreased the temperature locally (Fig. 6a). In contrast, in central and northern China, the winds shifted to a more northward direction, transporting warmer air masses from the south (Fig. 6c), which increased the temperature (Fig. 6a). During daytime, the decrease (increase) in temperature in the SC region (CC and NC regions) weakened (enhanced) the surface O3 chemical production. Biogenic emission is an important source of VOCs and thereby contributes to O3 formation in China (Wu et al., 2020). The temperature changes led to an increase (decrease) of biogenic emissions in the CC (SC) region (Fig. S4). Thus, the temperature changes increased (decreased) O3 in the CC (SC) region by influencing chemical reaction rates directly (Fu et al., 2015;Steiner et al., 2010) and altering biogenic emissions indirectly (Im et al., 2011;Liu and Wang, 2020a).
The changes in the weather pattern also resulted in less clouds and precipitation in northern and central China, but more clouds and precipitation in southern China (Fig. 6e and f). Clouds can reduce the amount of solar radiation reaching the surface and thus the chemical production of O3(Lelieveld and Crutzen, 1990), while precipitation can also reduce O3 through the scavenging of its precursors (Seinfeld and Pandis, 2006;Shan et al., 2008). The cloud and precipitation patterns therefore contributed to O3 increases in CC and NC and decreases in SC. Furthermore, in NC and CC, the significant increase in the planetary boundary layer height during the lockdown (Fig. 6d) might promote the transport of O3 from the upper air to the surface, contributing to the O3 increase in these regions Sun et al., 2009). The increase (decrease) in specific humidity in NC and CC (SC) might also have contributed to the decrease (increase) in O3 mixing ratios in those regions (Li et al., 2019c;Ma et al., 2019) (Fig. 6b). During nighttime, the changes in meteorological factors were similar to those in daytime ( Fig. S5) but exerted smaller impacts on O3 changes due to the decreasing effects of temperature and cloud cover (negligible biogenic emissions and solar radiation).
Response of O3 to emission reductions
We further investigated the impact of multi-pollutant reductions on the O3 changes. Because transportation and industrial activities were reduced significantly during the lockdown and they are the major sources of NOx (>80%) and VOCs (>60%) (Fig. 7), the estimated reductions of NOx and VOC emissions were more significant than those for CO, particulate matter (PM), and SO2 (Fig. 8a, c, e). The NOx emission reductions were 46%, 49%, and 55% in the NC, CC, and SC regions, respectively, while the respective reductions for VOC emissions were 32%, 24%, and 45%. The relationship between O3 and the emissions of its precursors is non-linear. We used the ratio of production rates between H2O2 and HNO3 (PH2O2/PHNO3) (Gaubert et al., 2021;Tonnesen and Dennis, 2000) to identify the O3 formation regime in China for the periods before and during the lockdown ( Fig. 9). PH2O2/PHNO3<0.06 is VOC-limited region; PH2O2/PHNO3≥0.2 is NOx-limited region, and 0.06≤PH2O2/PHNO3<0.2 is the transition zone. For the pre-CLD period, during daytime, the VOC-limited (or NOx-saturated) regions included North China Plain and other urban areas, while NOx-limited regions located in southern China and other rural areas (Fig. 9a). During nighttime, most regions are VOC-limited (Fig. 9c).
The O3 formation regime determines the response of O3 to the NOx reduction during the CLD period. During daytime, NOx reduction increased O3 in NOx-saturated regions, but decreased it in NOx-limited regions (Fig. 10b). We also found that although the daytime O3 formation regime in most regions shifted from the VOC-limited regime to the NOx-limited regime after the emission reductions during the CLD period, the daytime O3 formation in the North China Plain was still controlled by the VOC level (Fig. 9b), which suggests that the NOx level is still high in this region. During nighttime, the reduction of NOx emission contributed increased O3 due to the NO titration effect in a large areas (Fig. 10c). The reduction of VOC emission decreased O3 across China (Fig. 10d-f). As an O3 precursor, the reduction of CO emission also contributed to a small decrease in the O3 mixing ratio (Fig. 10g-i); in contrast, the PM and SO2 emissions reductions increased O3 (Fig. 10j-o) through the weakening of aerosol effects (Li et al., 2019a;Liu and Wang, 2020b), but their impacts were much smaller and were insignificant (< 1 ppbv) due to the smaller reductions, compared with NOx and VOCs.
The response of O3 to the emission reductions in different regions depended on the levels of NOx and VOC reductions. For the daytime average, in the NOx-saturated NC region, the O3 increase by the NOx reduction counteracted the O3 decrease by the VOC emission reduction, leading to the decrease in increased O3 production rates (Fig. 11) and a substantial net O3 increase (Fig. 8b). In CC, the contributions of the NOx and VOC reductions were comparable in magnitude, and their opposing impacts resulted in only a slight change in O3 (Fig. 8d). In the NOx-limited SC region, the impact of the NOx reduction on O3 was smaller than that of the reduction of VOCs, leading to the decrease in O3 production rates (Fig. 11), and a net decrease in O3 (Fig. 8f). During nighttime, the effect of the VOC reduction was weakened due to the lower rate of degradation of VOCs by radicals compared with daytime, and the O3 level increased in all three regions due to decreases in the NO titration effect (Fig. 11). The impacts of emission reductions on whole-day average O3 were similar to those during daytime.
The above modeling results show that the contribution of NOx reductions (by 46%-55%) to the rise of O3 decreased from NC to CC and to SC, reflecting the decreasing level of NOx saturation from north to south. In contrast, the impact of the estimated VOC reduction on O3 increased from north to south, which can in part be attributed to the regional variation of VOC reductions.
In the SC region, transportation and industry are the predominant sources of VOCs (97%, compared with 85% and 60% in NC and CC, respectively) (Fig. 7). During the CLD period, the reduction of VOC emission in SC (45%) was significant and comparable with the NOx reduction (55%). In contrast, the VOC reductions in the NC (32%) and CC (24%) regions were much lower (Fig. 8a, c) and could not offset the impact of NOx reduction on O3. The residential sector (mainly household coal burning) is an important source of VOC emission in the NC and CC regions, whereas its contribution is smaller in SC. The residential emissions increased during the CLD period because many migrant workers came back for the Chinese New Year holiday and were stranded there due to the lockdown Wang et al., 2020b).
Conclusion
The first country-wide lockdown during the COVID-19 outbreak in China drastically reduced transportation and industrial activities, leading to sharp declines in air pollutant emissions from these sectors. Surface O3 in urban areas of China responded differently in the northern (increase) and southern regions (decrease) compared to the three-week period before the lockdown, which can be explained by changes in meteorology and differences in the O3 chemistry regimes and the magnitudes of precursor reductions in these regions. The model simulated contributions of meteorology to daytime O3 changes were larger or comparable to most regions. The extent of VOC reduction, which suppressed O3 formation, was insufficient to offset the large NO titration effect during daytime in northern China, and that larger reductions of VOCs (e.g., from residential sectors) would have been needed to reduce the O3 concentration in the northern and central China. The rising O3 concentration in northern China during the COVID-19 lockdown and in recent winters should receive greater attention because O3 boosts the atmospheric oxidative capacity and therefore production of secondary aerosols Huang et al., 2020;Zhu et al., 2020), which are important components of winter haze in northern China. Our findings in China are relevant to untangling the underlying factors driving the O3 changes in other parts of the world during their COVID-19 lockdowns.
Data availability
The codes and data used in this study are available upon request from Yiming Liu (liuym88@mail.sysu.edu.cn) and Tao Wang (cetwang@polyu.edu.hk).
Acknowledgements
Competing interests
The authors declare that they have no conflict of interest.
Materials & Correspondence
Correspondence and requests for materials should be addressed to T.W. or Y.M.L.
Additional information
Supplementary information is available for this paper. suggested reasonable estimations of the anthropogenic emissions for the year 2020 and during the lockdown.
As we focused on the O3 changes in NC, CC, and SC regions, we futher evaluated the modeling performace in simulating the variations of O3 and NO2 for these regions. Fig. S1 shows the time series of simulated and observed O3 and NO2 mixing ratios. The magnitude and variation of the observed NO2 mixing ratios for these three regions were all well captured by the CMAQ model. The observed O3 mixing ratios for three regions were also reasonably reproduced. Both the simulation and observation showed an O3 increase in NC and CC but a decrease in SC (also shown in Fig. 4). However, the O3 mixing ratio in NC during the lockdown was underestimated, probably due to the uncertainties in meteorological simulation. The O3 mixing ratio in SC was generally overestimated during the simulation period, which might be attributed to the influence of the overestimated O3 concentrations on the ocean. Nevertheless, the model was able to faithfully capture the observed O3 variations in these three regions.
Overall, despite some uncertainties, the CMAQ model performance is acceptable and can support further analysis of O3 changes during the COVID-19 city lockdowns. Figure S1: Time series of observed (black points) and simulated (red lines) mixing ratios of maximum daily average 8h (MDA8) O3 and NO2 in North China, Central China, and South China from 2 January to 12 February 2020. The solid lines are the simulated average value and the shaded areas mark the standard deviations. The observed NO2 data were adjusted based on the method proposed by Zhang et al. (2017) and Fu et al. (2019):
! #$% = ! #$% & × '# ! #$% '# ! #$% ('# & #$% ('# ' #$% ( , where ! #$% &
is the measured NO2 data by the catalytic conversion technique, ! %)* , + %)* , and , %)* are the simulated data of NO2, NOz, and particulate nitrate, respectively, using the WRF-CMAQ model. Figure S5: Model simulated changes in nighttime temperature at 2 m height, specific humidity at 2 m height, wind field at 10 m height, planetary boundary layer (PBL) height, cloud fraction, and precipitation during CLD period relative to pre-CLD period. In panel (c), the shaded color and vector represent the wind speed and wind direction, respectively. are the simulated data of NO2, NOz, and particulate nitrate, respectively, using the WRF-CMAQ model.
typical regions in China (Fig. 1): north China (NC, 35-41.5°N, 113-119°E, including Beijing, Tianjin, Hebei, and western Shandong), central China (CC, 28.8-33°N, 108-117°E, including Hubei province, where Wuhan is situated, and the surrounding regions), and south China (SC, 21.5-24°N, 111-116°E, including the Pearl River Delta and the surrounding regions). The NC region is situated in the North China Plain, which is known to suffer from severe haze in winter; CC was the original epicenter of the COVID-19 outbreak in China and is an important economic hub for the central regions of China; the Pearl River Delta,
The chemical boundary conditions were provided by the results of Whole Atmosphere Community Climate Model (WACCM, https://www.acom.ucar.edu/waccm/download). The anthropogenic emissions in China were obtained from the Multi-resolution Emission Inventory for China (MEIC) in 2017 (http://www.meicmodel.org) with scaling factors to the year 2020 (Table S1, see text in Supplementary Information), which were estimated based on the Three-Year Action Plan (2018-2020) issued by the government and the changes in the multipollutant emissions of different sectors in recent years (Zheng et al., 2018). The emission adjustments during the lockdown period are based on recent publications (see text in Supplementary Information). Emissions from the other countries were derived from the MIX emission inventory (Li et al., 2017). International shipping emissions were taken from the Hemispheric Transport Atmospheric Pollution (HTAP) emission version 2.2 dataset for 2010(Janssens-Maenhout et al., 2015). Biogenic emissions were calculated by the Model of Emissions of Gas and Aerosols from Nature (MEGAN) version 2.1(Guenther et al., 2012) with meteorological inputs from the WRF model.
Figures 2
2and 3 present the changes in observed concentrations of O3 and other pollutants during the CLD period compared with pre-CLD. The concentrations of most pollutants (SO2, CO, PM2.5, PM10) that partially or fully originated from the direct emissions declined in China during the lockdown. NO2, a precursor of O3, decreased by about 50% across the entire continental China, and by similar amounts in all regions(Fig. 3b). However, the O3 mixing ratio exhibited varying changes in different regions(Fig. 2a). In NC and CC, the daily average O3 increased significantly, by 112% and 73%, respectively(Fig. 2b); in contrast, it remained almost unchanged in SC. The O3 changes also varied between daytime (8:00-20:00 LST) and nighttime (20:00-8:00 LST). During daytime, the O3 increase in most parts of China was smaller than the daily average(Fig. 2c), 92%
This work was supported by the Hong Kong Research Grants Council (T24-504/17-N and A-PolyU502/16) and the National Natural Science Foundation of China (91844301). B.G. acknowledges support by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under cooperative agreement no. 1852977. We would like to thank Prof. Qiang Zhang from Tsinghua University for providing the emission inventory. Author contributions T.W. initiated the research. Y.M.L. and T.W. designed the research framework. C.G., and T.D. estimated the emission changes. Y.M.L. performed model simulations and drew the figures. T.W. and Y.M.L. analyzed the results. T.W. and Y.M.L wrote the paper with the contributions from all the authors.
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Figure 1 :
1Location of 1643 environmental monitoring stations (red "+" symbols) operated by the Ministory of Ecology and Environmental Protection of China. The blue boxes denote the regions of north China, central China, and south China designated for further analysis.
Figure 2 :
2Observed changes in O3 mixing ratios across mainland China before and during the COVID-19 lockdown period. (a, c, e) The spatial distribution of O3 changes for all-day average, daytime average, and nighttime average during the CLD period compared with the pre-CLD period. The black boxes in (a) show the locations of north China (NC, 184 sites), central China (CC, 108 sites), and south China (SC, 77 sites). (b) The variations of all-day average O3 mixing ratios during the study period for the NC, CC, and SC regions. (d) The same with (b) but for daytime average O3. (f) The same with (b) but for nighttime average O3.
Figure 3 :
3Percentage change of (a) observed daytime average Ox (NO2+O3), whole-day average (b) NO2, (c) CO, (d) SO2, (e) PM2.5, and (f) PM10 concentrations during the CLD period relative to the pre-CLD period.
Figure 4 :
4Changes in O3 mixing ratios during the COVID-19 lockdown period and contributions from meteorological changes and emission reductions for three typical regions. (a) Observed and simulated changes in O3 mixing ratios and the contributions from meteorological changes and emission reductions during the CLD period compared with the pre-CLD period in north China (NC). The O3 changes for the all-day average, daytime average, and nighttime average are presented. (b) The same with (a) but for central China (CC). (c) The same with (a) but for south China (SC). The locations of these three regions are shown in Fig. 1. Note that the error bars mark the standard deviations within the region.
Figure 5 :
5Averaged sea-level pressure during the pre-CLD and CLD periods. Data are from the National Center for Environmental Prediction (NCEP) FNL Operational Model Global Tropospheric Analyses dataset.
Figure 6 :
6Model simulated changes in daytime temperature at 2 m height, specific humidity at 2 m height, wind field at 10 m height, planetary boundary layer (PBL) height, cloud fraction, and precipitation during CLD period relative to pre-CLD period. In panel (c), the shaded color and vector represent the wind speed and wind direction, respectively.
Figure 7 :
7Percentage contribution to NOx, VOCs, CO, PM, and SO2 emissions from industrial (IND), power plant (POW), residential (RES), and transportation (TRA) sectors in (a) north China, (b) central China, and (c) south China. Emission data are from 2017 MEIC (http://meicmodel.org) with estimated scaling factors from 2017 to 2020.
Figure 8 :
8The estimated reductions of multi-pollutant emissions due to the COVID-19 lockdown and their impacts on the O3 changes for three regions. (a, c, e) The estimated reductions of NOx, VOC, CO, PM, and SO2 emissions during the CLD period compared with the pre-CLD period for north China, central China, and south China. (b, d, f) The impacts of different pollutant emission reductions due to the lockdown on O3 changes for the three regions. The O3 changes for all-day average, daytime average, and nighttime average are presented. The error bars are the standard deviations.
Figure 9 :
9Ozone formation regime in the daytime and nighttime before and during the lockdown periods estimated by the ratio of the production rates of hydrogen peroxide to nitric acid (PH2O2/PHNO3). VOC-limited region: PH2O2/PHNO3<0.06; NOx-limited region: PH2O2/PHNO3 ≥0.2, Transition zone: 0.06≤PH2O2/PHNO3<0.2. The production rates of H2O2 and HNO3 were calculated by the integrated reaction rate (IRR) diagnose tool in the CMAQ model.
Figure 10 :
10Model simulated changes in O3 mixing ratios for all-day average, daytime average, and nighttime average due to the reductions of NOx, VOC, CO, PM, and SO2 emissions during the CLD period compared with the pre-CLD period.
Figure 11 :
11O3 chemical production rates before and after the anthropogenic emission reductions and the changes during the COVID-19 lockdown period. The chemical production rates were calculated by the process analysis method in the CMAQ model.
Fig. S2 :
S2Simulated changes in O3 mixing ratios across China during the COVID-19 lockdown period and contributions from meteorological changes and emission reductions. (a, d, g) The simulated total O3 changes for all-day average, daytime average, and nighttime average during the CLD period relative to the pre-CLD period. (b, e, h) Contribution of meteorological changes to O3 for all-day average, daytime average, and nighttime average. (c, f, i) The same with (b, e, h), respectively, but for contribution of emission reductions.
Figure S3 Figure S4 :
S3S4The contributions of meteorological changes and emission reduction to the changes in daytime and nighttime O3 concentrations during the CLD period compared with the pre-CLD period. (a) North China; (b) Central China; Biogenic isoprene emissions during the pre-CLD and CLD periods and their difference (CLD minus pre-CLD).
were adjusted based on the method proposed by Zhang et al. (2017) and Fu et al. (2019):
Supplementary Information for "Diverse response of surface ozone to COVID-19 lockdown in China" Yiming Liu a,*# , Tao Wang a,* , Trissevgeni Stavrakou b , Nellie Elguindi c , Thierno Doumbia c , Claire Granier c,d , Idir Bouarar e , Benjamin Gaubert f , Guy P. Brasseur a,e,f a Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China; b Royal Belgian Institute for Space Aeronomy, Brussels, Belgium; c Laboratoire d'Aérologie, Toulouse, France; d NOAA Chemical Sciences Laboratory and CIRES/University of Colorado, Boulder, CO, USA; e Environmental Modeling Group, Max Planck Institute for Meteorology, Hamburg, Germany; f Atmospheric Chemistry Observations and Modeling Laboratory, National Center for Atmospheric Research, Boulder, CO, USA; *Correspondence to: Tao Wang (cetwang@polyu.edu.hk) and Yiming Liu (liuym88@mail.sysu.edu.cn) # Now in School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai, China This file includes Supplementary text, and Supplementary Figures S1-S5, Supplementary Table S1-S2.
Table S1 :
S1Scaling factors applied to different economic sectors in order to estimate the anthropogenic emissions of China for the year 2020 based on the 2017 MEIC emission inventory.Emitted species
Power plants
Industry
Residence
Transportation
NOx
-35%
-
-
-
SO2
-40%
-40%
-25%
-
PM
-
-20%
-30%
-
Table S2 :
S2Evaluation results of the air pollutants across China for the pre-CLD (2-22 January 2020) and CLD (23 January-12 February 2020) periods. OBS is mean observation; SIM is mean simulation; MB is mean bias; MAGE is mean absolute gross error; RMSE is root mean square error; IOA is index of agreement; r is correlation coefficient; OBS, SIM, MB, MAGE, and RMSE have the same units as given in the first column, while IOA and r have no unit.Species
Period
OBS
SIM
MB
MAGE RMSE IOA
r
SO2 (ppbv)
Pre-CLD
4.9
5.4
0.5
3.8
4.5
0.79
0.35
CLD
4.1
4.1
0.0
3.1
3.8
0.77
0.33
NO2 a (ppbv)
Pre-CLD
14.7
12.5
-2.2
5.1
6.0
0.90
0.49
CLD
6.6
6.7
0.1
3.1
3.7
0.89
0.58
CO (ppmv)
Pre-CLD
0.94
0.66
-0.28 0.42
0.48
0.88
0.40
CLD
0.75
0.51
-0.24 0.34
0.40
0.88
0.40
MDA8 O3 (ppbv) Pre-CLD
26.2
30.1
3.9
10.5
13.0
0.94
0.35
CLD
36.0
37.6
1.6
10.5
12.9
0.97
0.38
PM2.5 (μg/m 3 )
Pre-CLD
69.3
71.8
2.4
33.0
41.6
0.90
0.51
CLD
55.3
52.7
-2.6
25.9
34.2
0.90
0.55
a The observed NO2 data
Supplementary textEstimation of anthropogenic emissions in 2020We estimated the anthropogenic emission for China in 2020 based on the MEIC 2017 (http://www.meicmodel.org) according to the control plan established by the Chinese government and the emission trends in recents years. From 2013 to 2017, the Chinese government launched the to Air Pollution Prevention and Control Action Plan to mitigate haze events. compiled the trends of anthropogenic emissions during this period and demonstrated that the SO2, NOx, and PM (particulate matter, including PM10, PM2.5, and its components) emissions have been reduced significantly. In 2018, the Chinese government issued a Three-Year Action Plan (2018-2020) to further reduce the SO2, NOx, and PM emissions (http://www.gov.cn/zhengce/content/2018-07/03/content_5303158.htm). Previous control measures were implemented and the emissions were thought to continue decreasing after 2017. As the most recent available data on China's anthropogenic emissions are from 2017, we estimated the emissions for 2020 based on the MEIC 2017 according to the trends of these emissions in recent years .Table S1shows the scaling factors from 2017 to 2020 for NO2, PM, and SO2 in the power plant, industry, transportation, and residential sectors. The VOC emission was assumed to be unchanged from 2017 to 2020 because it increased by only 2% from 2013 to 2017 . The NO2, PM, and SO2 emissions from transportation were also assumed constant from 2017 to 2020, considering that they had changed little during 2015-2017. The NOx emission in the residential and industrial sectors was assumed to be the same in 2020 as in 2017 in view of its flat trend in recent years. Because the NOx emission from power plants decreased by ~47% from 2013 to 2017 (11.7% per year), we assumed it to further decrease by 35% from 2017 to 2020. The same approaches were applied to the reductions of the PM and SO2 emissions from 2017 to 2020. With these adjustments, we derived an estimated anthropogenic emission inventory for China in 2020. The modelsimulated pollutant concentrations using this inventory showed a reasonable agreement with the surface measurement data during the period before the COVID-19 lockdown(Table S2, also see the Model evaluation section below), which suggested the estimated emission inventory was reasonable.Estimated reduction of anthropogenic emissions during the CLD periodWe estimated the emission reductions during the COVID-19 lockdown period according to the recent literature(Doumbia et al., 2021;Wang et al., 2020;Huang et al., 2020). For the transportation sector, the decrease in national traffic volume was estimated at 70% during the lockdown according to transportation index data. The industry emissions were assumed to decrease by 40% across China. The emissions of power plants were estimated to decrease by 30% due to the less consumption of electricity. The emissions of residential activities were assumed to increase by 10% due to more coal combustion and cooking. We kept the emissions from agriculture unchanged because they were less affected by the city lockdowns.Fig. 8presents the reductions of NOx, VOCs, CO, PM, and SO2 emissions due to the changes in anthropogenic activities during the lockdown, which generally match the estimation byHuang et al. (2020). The observed pollutant concentrations during the lockdown period could faithfully captured by the CMAQ model using this estimated reduced emissions(Table S2, also see the Model evaluation section below), which suggested the estimated reductions of anthropogenic emissions were acceptable.Model evaluationStatistical parameters were calculated to validate the model performance in simulating the air pollutant concentrations from January 2 to February 12, 2020, including the mean observation (OBS), mean simulation (SIM), mean bias (MB), mean absolute gross error (MAGE), root mean square error (RMSE), index of agreement (IOA), and correlation coefficient (r). The equations of these statistical parameters can be found inFan et al. (2013).Table S2shows the evaluation results of the simulated concentrations of SO2, NO2, CO, O3 and PM2.5 in China for the periods before and during the COVID-19 lockdown, respectively. As the measured NO2 by the catalytic conversion method in the national network overestimates the NO2(Xu et al., 2013), we adjusted the observed NO2 data following the method proposed byZhang et al. (2017)andFu et al. (2019). Generally, the CMAQ model faithfully reproduced the observed concentrations of NO2, SO2, CO, PM2.5 and O3 with low biases during both peirods. The evaluation results
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| sample_893 | 0.9004 | arxiv | |
Multistability in a Coupled Ocean-Atmosphere Reduced Order Model: Non-linear Temperature Equations
Oisín Hamilton oisin.hamilton@meteo.be
Climate Dynamics
Royal Meterological Institute of Belgium
BrusselsBelgium
Earth and Life Institute
Université catholique de Louvain
Louvain-la-Neuve
Climate Dynamics
Belgium Correspondence Oisín Hamilton
Royal Meterological Institute of Belgium
1180Uccle, BrusselsBelgium
Jonathan Demaeyer
Climate Dynamics
Royal Meterological Institute of Belgium
BrusselsBelgium
Stéphane Vannitsem
Climate Dynamics
Royal Meterological Institute of Belgium
BrusselsBelgium
| Michel Crucifix
Earth and Life Institute
Université catholique de Louvain
Louvain-la-Neuve
Climate Dynamics
Belgium Correspondence Oisín Hamilton
Royal Meterological Institute of Belgium
1180Uccle, BrusselsBelgium
Multistability in a Coupled Ocean-Atmosphere Reduced Order Model: Non-linear Temperature Equations
R E S E A R C H A R T I C L E Q u a r t e r l y J o u r n a l o f t h e R o y a l M e t e r o l o g i c a l S o c i e t yAbbreviations: LFV, Low Frequency VariabilityAMOC, Atlantic Meridional Overturning CirculationNAO, North Atlantic OsciliationMAOOAM, Modular Arbitrarty Order Ocean Atmosphere Model
Funding informationEuropean Union Horizon 2020, Marie Sklodowska-Curie grant agreement No.956170 Multistabilities were found in the ocean-atmosphere flow, in a reduced order ocean-atmosphere coupled model, when the non-linear temperature equations were solved numerically. In this paper we explain how the full non-linear Stefan-Bolzmann law was numerically implemented, and the resulting change to the system dynamics compared to the original model where these terms were linearised. Multiple stable solutions were found that display distinct oceanatmosphere flows, as well as different Lyapunov stabilityproperties. In addition, distinct Low Frequency Variability (LFV) behaviour was observed in stable attractors. We investigated the impact on these solutions of changing the magnitude of the ocean-atmospheric coupling, as well as the atmospheric emissivity to simulate an increasing greenhouse effect. Where multistabilities exist for fixed parameters, the possibility for tipping between solutions was investigated, but tipping did not occur in this version of the model where there is a constant solar forcing. This study was undertaken using a reduced-order quasi-geostrophic ocean-atmosphere model, consisting of two atmosphere layers, and one ocean layer, implemented in the Python pro-
One source of non-linearity in the model equations comes from the long wave radiation emitted from the ocean and atmosphere, and modelled using the Stefan-Boltzmann law (σ B T 4 , where σ B is the Stefan Bolzmann constant).
In the MAOOAM model, the quartic radiation terms are linearised to simplify the projection of the equations onto a truncated Fourier expansion. This linearisation is justified by the fact that the perturbations in temperature are small in relation to the climatological reference temperatures (De Cruz et al., 2016). However, this linearisation removes the possibilities of non-linear interactions from the temperature terms. For this reason, this study investigates the impact on the LFV in the model, and the potential for multi-stabilities or bifurcations, when the temperature equations are not linearised.
We will show that removing the linearisation leads to multiple stable flow patterns in the atmosphere and ocean, for certain levels of ocean-atmosphere coupling and atmosphere emissivity. These flow patterns are qualitatively distinct and result in multiple average temperatures, for the same model parameters. They also present different cycle lengths and different dominant modes.
Section 2 describes the reduced order model used in this study, and Section 2.3 describes the modifications made to remove the requirement of linearising the temperature equations. This section also gives a description of the model configurations used in this study. The results are split into two sections, where we first look at the results from altering the ocean-atmosphere coupling (Section 3.1), and then the impact of atmospheric emissivity (Section 3.2). In each of the two results sections, we look at the impact of altering the given parameters on the stability and predictability of the system. Section 4 summarises the main results and discusses the general implications of these findings.
| QGS MODEL
| Model Description
The qgs model (Demaeyer et al., 2020) is a reduced-order midlatitude climate model, with many different model configurations available. In the present work, we use the ocean-atmosphere model version where the atmospheric flow is obtained from a two-layer quasi-geostrophic flow defined on a β plane (Reinhold and Pierrehumbert, 1982). Similarly, the ocean streamfunctions are modelled using a quasi-geostrophic shallow-water model with a rigid lid (Pierini, 2011). The thermodynamic equation for the atmosphere and ocean temperatures are derived using an energy balance scheme proposed by Barsugli and Battisti (1998). The coupled ocean-atmosphere scheme used here was first introduced by Vannitsem et al. . The atmosphercic variables are coupled through wind stress to the oceanic ones, driving the ocean circulation, which transports heat in the ocean. The ocean transfers heat with the atmosphere through radiative and direct heat coupling, which in turn impacts the atmospheric flow.
In this study we imposed a closed ocean basis (no-flux boundary conditions on all boundaries), and a channel atmosphere (no-flux boundary conditions on the north and south boundaries, and periodic boundary conditions at the west and east). We describe how these boundary conditions are implemented in Section 2.2. This version of the model with a closed ocean basin coupled to an atmosphere is called the Modular Arbitrary Order Ocean Atmosphere Model (MAOOAM) (De Cruz et al., 2016).
The governing partial differential equations (PDEs) for the atmosphere barotropic ψ a and baroclinic θ a streamfunctions and ocean streamfunctions ψ o are given as:
∂ ∂t 2 ψ a + J ψ a , 2 ψ a + J θ a , 2 θ a + β ∂ψ a ∂x = − k d 2 2 (ψ a − θ a − ψ o ) (1) ∂ ∂t 2 θ a + J ψ a , 2 θ a + J θ a , 2 ψ a + β ∂θ a ∂x = −2k d 2 θ a + k d 2 2 (ψ a − θ a − ψ o ) + f 0 ∆p ω (2) ∂ ∂t 2 ψ o − ψ o L 2 R + J ψ o , 2 ψ o + β ∂ψ o ∂x = −r 2 ψ o + d 2 (ψ a − θ a − ψ o ) ,(3)
where ψ a and ψ o are the atmosphere and ocean barotropic streamfunctions, and θ a are the atmosphere baroclinic streamfunctions. Vertical velocities are given by ω.
The ocean and atmosphere temperatures are derived from an energy balance model:
γ a ∂T a ∂t + J (ψ a , T a ) − σω p R = −λ (T a − T o ) + εσ B T 4 o − εσ B T 4 a + R a (4) γ o ∂T o ∂t + J (ψ o , T o ) = −λ (T o − T a ) − σ B T 4 o + εσ B T 4 a + R o ,(5)
where T a and T o are the atmosphere and ocean temperatures, γ a and γ o are the heat capacities of the atmosphere and ocean, σ is the static stability of the atmosphere (assumed constant), σ B is the Stefan-Boltzmann constant, R a and R o are the incoming solar radiation absorbed by the atmosphere and ocean, and ε is the atmospheric emissivity.
To reduce the number of variables, the atmosphere temperature variable T a is related to the baroclinic streamfunctions using the hydrostatic balance in pressure coordinates and the ideal gas law, providing the relationship T a = 2f 0 θ a /R .
| Numerical Solution
The differential equations are projected onto basis modes, a procedure also known as Galerkin expansion. The basis modes are chosen to ensure that the boundary conditions described in the previous section are satisfied. This is done by stipulating that φ i (x, y ) = 0 for points (x, y ) on the boundary, and ∂F i (x,y ) ∂x = 0 for x on the boundary and F i (x, y ) = 0 for y on the boundary. In this study we use 10 basis modes for the atmosphere and 8 for the ocean, as in Vannitsem (2017
K −1 ) σ B 5.67 × 10 −8 Stefan-Boltzmann constant (Jm −2 s −1 K −4 )
The key model parameters used in this study. Here C is a variable that we alter to investigate the impact of the ocean-atmosphere coupling. As in Charney and Straus (1980) we assume k = k d and as in Vannitsem (2015) that gravity g = 10ms −2 .
F 1 = √ 2 cos(y ) F 2 = 2 cos(nx ) sin(y ) F 3 = 2 sin(nx ) sin(y ) F 4 = √ 2 cos(2y ) F 5 = 2 cos(nx ) sin(2y ) F 6 = 2 sin(nx ) sin(2y ) F 7 = 2 cos(2nx ) sin(y ) F 8 = 2 sin(2nx ) sin(y ) F 9 = 2 cos(2nx ) sin(2y ) F 10 = 2 sin(2nx ) sin(2y ) φ 1 = 2 sin(nx /2) sin(y ) φ 2 = 2 sin(nx /2) sin(2y ) φ 3 = 2 sin(nx /2) sin(3y ) φ 4 = 2 sin(nx /2) sin(4y ) φ 5 = 2 sin(nx ) sin(y ) φ 6 = 2 sin(nx ) sin(2y ) φ 7 = 2 sin(nx ) sin(3y ) φ 8 = 2 sin(nx ) sin(4y )(6)
Three basis modes are of particular interest as they have real world analogies:
• F 1 (x, y ) = √ 2 cos(y ) represents the solar insolation imbalance between the north and south.
• φ 1 (x, y ) = 2 sin(x /2) sin(y ) represents average temperature fluctuations in the ocean.
• φ 2 (x, y ) = 2 sin(x /2) sin(2y ) is the double gyre, orientated so the peak is either to the north or south of the tough.
This loosely approximates the NAO, which is defined by the difference in surface pressure anomalies between northern and southern locations (often the Azores and Iceland) (Hurrell et al., 2003). The prevailing clockwise winds around the Azores high, and the counter clockwise winds around the northern low pressure can be broadly simulated by projecting the atmospheric streamfunction anomalies on this mode, thus simulating the impact on the wind and heat transport caused by the NAO.
The model variables are expanded using the basis modes. In previous studies using such energy balance models the temperature variables in the model are linearised around a fixed in time equilibria temperature: T (t , x, y ) = T 0 + δT (t , x, y ) to remove the quartic terms σ B T 4 . This resulted in the temperatures being expressed as:
T a (t , x, y ) = T a,0 + δT a (t , x, y ) = T a,0 + 10 i =1 δT a,i (t )F i (x, y ) T o (t , x, y ) = T o,0 + δT o (t , x, y ) = T o,0 + 8 i =1 δT o,i (t )φ i (x, y ).(7)
The PDEs introduced in Equations (4, 5) are then projected onto these basis modes, using the inner product:
f , g = n 2π 2 ∫ π 0 ∫ 2π/n 0 f (x, y )g (x, y )dx dy(8)
This leads to 20 ordinary differential equations (ODEs) for the atmospheric streamfunctions, 10 for the barotropic and 10 for the baroclinic streamfunctions. In addition there are 16 ODEs in the ocean, 8 for the barotropic streamfunctions and 8 for the temperature anomaly. This leads to a total of 36 ODEs describing the model.
| Non-linear radiation terms
This study focuses on the change in the system dynamics caused by not linearising the radiation terms in the temperature equations of the MAOOAM model. This requires the reference temperature T a,0 and T o,0 to be time-varying quantities in the expansions shown in Equation 7. Therefore, to allow the average temperature across the atmosphere and ocean to change dynamically with time, we introduced two new basis modes, corresponding to constant spatial modes: F 0 (x, y ) = 1 and φ 0 (x, y ) = 1. These modes were added to the list of basis modes that were introduced in Section 2.2:
F 0 = 1 F 1 = √ 2 cos(y ) F 2 = 2 cos(nx ) sin(y )
. . .
φ 0 = 1 φ 1 = 2 sin(nx /2) sin(y ) φ 2 = 2 sin(nx /2) sin(2y )
. . .
These additional basis modes now allow the expansions, shown in Equation 7, to be given as
T o (t , x, y ) = 8 i =0 T o,i (t )φ (x, y )
, and similarly for the atmosphere.
Only the temperature equations are projected onto these additional basis modes, as these are the variables linearised in the original MAOOAM model. This means that we still have 10 ODEs for the atmospheric barotropic streamfunctions, and 8 ODEs for the oceanic barotropic streamfunctions. We obtain an additional ODE for the atmospheric baroclinic streamfunction (as this variable replaces the atmospheric temperature variables) and for the ocean temperature. This increases the total number of ODEs describing the system to 38.
We now introduce the two modified versions of the model that are used in the current study:
Dynamic Equilibria: this version of the model includes the same linearisation as the Linearised version of the model, but the equilibrium temperature is dependant on time: T (t , x, y ) = T 0 (t ) + δT (t , x, y ). We will refer to this version as DE.
Non-Linear T4: This version does not involve the linearisation of the Stefan-Boltzmann law terms and the equa-
tions are projected directly onto the basis modes. This retains the quartic radiation terms. We will refer to this version of the model as T4.
This results in three model versions:
• Linear Model (LM) • Dynamic Equilibria (DE) • Non-Linear (T4)
More information about how these modifications were made can be found in the model manual (Demaeyer et al., 2022). See also the Supporting Information.
F I G U R E 1
The Temperature-C diagrams for the averaged atmosphere (left), and ocean (right) temperatures for the DE model (crosses), and the T4 mode (dots), of the stable attractors. The branches were colour coded by qualitatively investigating the behaviour of each attractor. The attractors are projected onto the planes (ψ o,1 , T o,1 ) (left) and (ψ o,2 , T o,2 ) (right), to display how the behaviour differs between the three stable attractors. The projection of the orange attractor is shown for C = 0.009kgm −2 s −1 and the other two projections (blue and pink) of the attractors are shown for C = 0.0125kgm −2 s −1 .
| RESULTS
The results section is split into two main parts. We first describe the system dynamics when the ocean atmosphere coupling is altered, and second we alter the atmospheric emissivity. We focus on values of these parameters that result in multiple distinct ocean-atmosphere flows, which are described by distinct attractors. Multiple stable attractors, for given parameter values, provide the possibility for model solutions to transition from one attractor to another, provided appropriate forcing is imposed. Such transitions between attractors could represent tipping points or abrupt changes or switching in flows. We are particularly interested in flows that present LFV, generated by the coupling between ocean and atmosphere variables, due to the increased predictability of the system dynamics that these solutions provide.
| Ocean-Atmosphere Coupling
This section presents the results where the magnitude of ocean-atmosphere coupling is varied for the three model versions. Increasing the ocean-atmosphere coupling has the effect of increasing the heat transfer between the ocean and atmosphere. This reduces the ocean temperature (which has a higher equilibria temperature than the atmosphere) and
increases the atmospheric temperature, which has an impact on the baroclinic streamfunctions. The ocean temperature anomalies cause uneven temperature exchanges in the atmosphere that require the heat energy to be transported by atmospheric winds. At the same time, increasing the ocean-atmosphere coupling increases the friction felt by the atmosphere from the surface wind stresses with the ocean. In turn, this causes the atmospheric wind to have a greater impact on the movement of the sea temperature anomalies. Together, this reduces the fast moving timescales of the atmosphere through coupling to the ocean, which has a slower timescale relative to the atmosphere.
We alter the ocean-atmosphere coupling C by altering the following parameters: the strength of the oceanatmosphere coupling d , the ocean-atmosphere friction k d , the internal atmosphere friction k d , and the direct heat
F I G U R E 2
The distinct attractors for the T4 runs are projected onto (ψ a,1 , ψ o,1 , T o,1 ) (left) and (ψ a,1 , ψ o,2 , T o,2 ) (right), to present the level of ocean-atmosphere coupling. The orange attractor is shown for C = 0.009kgm −2 s −1 and the other two attractors are shown for C = 0.0125kgm −2 s −1 . Here we only present the T4 runs as the dynamics over these three variables are identical between the T4 and DE model runs.
transfer between the ocean and atmosphere λ (Vannitsem, 2015). These parameters are controlled using a single friction coefficient C , where the relationship between C and the above parameters is given in Table 1. In this study we focus on values of C that are deemed to be within a realistic range (C ∈ [0.008kgm −2 s −1 , 0.02kgm −2 s −1 ]) for the real world coupling of the ocean and atmosphere (Houghton, 1986;Nese and Dutton, 1993;Vannitsem, 2017).
| State Space Probing
The effect of the ocean-atmosphere coupling on the system dynamics was investigated by fixing the coupling value C and running many trajectories with random initial conditions. Once these trajectories had appeared to settle onto an attractor, the initial transient section of the trajectories was discarded and we continued to run the trajectories for long run times (1 × 10 7 model days). This was done to ensure that the attractors remain stable and trajectories remain on the attractor. For these experiments, the atmosphere emissivity was set to ε = 0.7 as the model default (De Cruz et al., 2016). This process was repeated for different values of C .
The average temperatures of the ocean and atmosphere were calculated by projecting the trajectories, that were embedded within an attractor, onto the basis modes to obtain the temperature profiles for each time step. We then took the average across the spatial domain to obtain a single average temperature for each time step. Finally we took the average across time to obtain a single temperature, which represents the average temperature associated with a given attractor. This process is shown for the temperature of the ocean, with a similar process taken to calculate the average atmospheric temperatures:
T o (t ) space, time = 1 n τ n x n y nτ τ=0 nx i =0 n y j =0 no k =0 T o,k (t τ )φ k (x i , y j )
Where n o are the number of ocean modes, n x and n y are the number of spatial grid points being averaged across, and n τ is the number of time steps in the numerical solution.
| Multistabilies in Temperature -C
The average spatial and temporal temperatures are presented on a Temperature-C diagram. These diagrams are not bifurcation diagrams, as we only have information about the stable branches that we could find using the de-
C ∈ [0.008kgm −2 s −1 , 0.009kgm −2 s −1 ] and C ∈ [0.012kgm −2 s −1 , 0.0127kgm −2 s −1 ]
. These figures also show that there exists a single stable branch that bridges the two intervals (shown in blue). We plot the results of the dynamic equilibria (DE) and non-linear (T4) model runs on the same plot.
We found two differences between the T4 and DE runs. The first is that the difference in average temperatures between the stable branches in the DE runs are smaller than in the T4 runs. The small temperature differences between the attractors in the DE runs occurs due to the zeroth order temperature equations controlling the equilibria temperature (T a,0 , T o,0 ) having only one real stable solution. This means that the difference in average temperatures in each stable equilibrium is caused by only higher order terms. In the T4 model, there are additional terms in the zeroth order temperature equations that result in larger differences between the zeroth order temperatures. This difference in the equations occurs in the non-linear longwave radiation terms, and is sketched below for the ocean temperature equation. In the below expressions we introduce the tensor v i ,j ,k ,l ,m = F i , φ j , φ k , φ l , φ m . and (ψ a,1 , ψ o,2 , T o,2 ) to visualise the degree of ocean-atmosphere coupling in the attractors. In Figure 2 we show all three attractors, for the same values of C as before. In each image there is one attractor that stabilises around an unstable orbit that varies across all three variables over a decadal time scale. The image displaying (ψ a,1 , ψ o,2 , T o,2 ) shows that the attractor coloured in pink presents the same oscillating behaviour over the three variables as the attractor found in Vannitsem (2017). In addition, we also recover the attractor found by Vannitsem that does not present LFV (blue). The novel result here is that we have found an additional attractor (orange), for lower values of C , that also displays LFV in the coupled ocean-atmosphere system, but across the ocean-atmosphere modes (ψ a,1 , ψ o,1 , T o,1 ).
To
| Lyapunov Stability -C
To analyse the stability properties of the attractors that were found we calculated the Lyapunov properties of the We present the largest Lyapunov exponents (LLE) in Figure 3 (a), as a function of C , where again there is a multistability present in the two intervals identified. We have used the same colour coding as in Section 3.1.2 to display which Lyapunov exponent is associated with which attractor. Approximately, the midlatitudes have a synoptic forecast time scale of less than two week (Lorenz, 1982), with larger scale process having a larger forecasting time (Lorenz, 1969).
At the synoptic scale, this would correspond to LLE of approximately 0.2-0.3 days −1 . In the MAOOAM model there is a general decrease in the magnitude of the LLEs as C increases due to the increase in coupling between the ocean and atmosphere, resulting in the flow instabilities from the atmospheric dynamics being reduced (Vannitsem, 2017). However, it is clear that the orange branch displays significantly smaller LLEs than the other two branches, for relatively small values of C . Other studies have shown that for low values of C the magnitude of LLEs do decrease (Vannitsem, 2017), however this was observed for values C ≤ 0.0015kgm −2 s −1 , and we did not carry out runs for values of C this low due to these ocean-atmospheric coupling values being unrealistic in the real earth system.
In Figure 4 that the rate of divergence of initial conditions will be much greater in the blue attractor. The novel attractor found in this study (orange), presents significantly smaller magnitude positive Lyapunov exponents than the other attractors, and has a lower number of near zero Lyapunov exponents, implying that the attractor exists on a lower dimensional chaotic manifold than the other attractors. The smaller positive magnitude Lyapunov exponents for two of the three attractors occurs due to these attractors existing around unstable periodic orbits that produce the LFV on decadal timescales and therefore increases the predictability.
F I G U R E 5
The variance of the CLVs (shown on a log 10 scale), for each of the three distinct attractors shown in Figure 1. The attractors are designated by the colour of their title, which corresponds to the previous sections. The orange attractor CLVs are calculated for ε = 0.7, and C = 0.009kgm −2 s −1 , and the other two attractors' CLVs are calculated with ε = 0.7 and C = 0.0125kgm −2 s −1 .
The extent to which coupling between the ocean and atmosphere is responsible for the LFV can be visualised using the variance of Covariant Lyapunov Vectors (CLVs) (Vannitsem and Lucarini, 2016). The CLVs provide a covariant basis of the tangent linear space of the system. In other words, the CLVs are vectors that form a basis and remain covariant with the flow, unlike forwards or backwards Lyapunov vectors (Kuptsov and Parlitz, 2012 other. Therefore variables that are coupled with one another will present higher variance for the same CLV index (horizontal rows on the diagram). This allows us to visualise which variables are coupled and have a greater impact on the system dynamics. In Figure 5 we present a heatmap of the variance (log 10 scale) for the three distinct attractors.
These plots show the CLV index on the y-axis, and the model variables on the x-axis. The variables are ordered as:
• Atmospheric barotropic streamfunctions ψ a (Index: 1-10)
• Atmospheric baroclinic streamfunctions θ a (Index: 11-21)
• Ocean barotropic streamfunctions ψ o (Index: 22-29)
• Ocean temperature T o (Index: 30-38)
As expected, the majority of the variance is seen in the atmosphere as these variables are the components that contribute to the fast timescale dynamics of the system. All three attractors present coupling for CLV indices 13-22,
where the ocean temperature variables present similar variability to the atmosphere variables. The near zero Lyapunov exponents (CLV index 4-22) in general have a larger projection on the ocean variables (columns 22-38). All three attractors present similar dynamics for the indicies greater than 22, where the ocean components have low projection on the dynamics, implying that the large magnitude negative Lyapunov exponents are predominantly caused by the atmosphere dynamics. However, the attractors that present LFV have higher variance for the indices 1-12, implying F I G U R E 6 Temperature-ε diagrams showing the averaged atmosphere (left) and ocean (right) temperatures. The different colours represent stable branches that present qualitatively different attractors. Here we only present the T4 model run results as the DE results produce the same results, and the temperature differences between the three branches of the DE runs are too small to be visible on these graphs. As in Figure 1, the attractors are projected onto the plane of ocean variables with the single gyre (left) and double gyre (right) for ε = 0.9.
that in these attractors the ocean temperature is having a stabilising impact on the atmosphere dynamics, and that there is a greater level of coupling between the ocean and atmosphere. In addition, the orange attractor (heat map on the left hand side) shows greater coupling between all four components of the model, as the ocean streamfunctions show higher variance for the indices 1-10. This explains the low magnitude of the positive Lyapunov exponents for this attractor as the unstable atmosphere components present high levels of coupling with the stable ocean.
| Emissivity
To simulate the impact of climate change on the ocean-atmosphere dynamics in the MAOOAM model, the emissivity ε is increased. Rising the emissivity acts as a proxy for rising levels of greenhouse gases, causing the atmosphere to 'trap' a larger proportion of the outgoing longwave radiation, thus increasing the average ocean and atmosphere temperatures. We picked a single value of ocean-atmosphere coupling C = 0.01175kgm −2 s −1 to investigate. In the previous section this value of C resulted in a single stable attractor, for ε = 0.7.
| Multistabilities in Temperatureε
By using Temperature-ε diagrams, shown in Figure 6, that present the average spatial and temporal temperatures of stable attractors found numerically, we can see that as the emissivity increases bifurcations occur at two values, leading to an additional two stable branches. We have coloured the stable branches to display the attractors that present qualitatively distinct behaviour. On these images we only present the results from the T4 model runs as each of the T4 and DE model runs presented the similar trajectory behaviour, but the resulting average temperature of the three distinct branches in the DE runs were too close to be visible on the graph. This is because of the higher order non-linear terms being removed in the linearised version, as explained in Section 3.1.2.
We have taken the three stable attractors that we found at ε = 0.9 and projected these onto the planes (ψ o,1 , T o,1 )
and (ψ o,2 , T o,2 ), and these are also shown in Figure 6. We can see that two of the attractors (shown in pink and blue)
F I G U R E 7
The three distinct attractors found at C = 0.01175kgm −2 s −1 and ε = 0.9 are projected onto (ψ a,1 , ψ o,1 , T o,1 ) and (ψ a,1 , ψ o,2 , T o,2 ), left and right respectively. The attractors are coloured to match the diagrams shown in Figure 6.
present the same behaviour as seen in Section 3.1, in addition, the highest temperature branch (shown in orange) qualitatively appears to have similarities with the attractor that showed a periodic behaviour with respect to (ψ o,1 , T o,1 ) that we also saw in the previous section. Therefore, increasing the value of ε appears to have the impact of providing stability to unstable branches. Figure 6 shows that the average temperatures in the atmosphere and ocean rise quickly as ε is increased, but in addition there are multistabilies that are separated by up to 1 • K for the same emissivity values.
As in Section 3.1, we visualise the level of ocean-atmosphere coupling by projecting the three stable attractors onto the first atmosphere mode, and the single and double gyre ocean modes. As with this previous section, we see that the orange attractor displays an oscillatory behaviour, coupling the barotropic streamfunctions and the single gyre variables, and the pink attractor displays LFV with the double gyre variables. Again, we see two distinct flows where there exists coupling between the ocean and atmosphere, over decadal time periods. These results show that in the MAOOAM model, rising emissivity leads to multistabilies in the ocean-atmosphere system, that were not present at low levels of emissivity. From our model runs we have not found examples of trajectories switching between the stable branches, however all of our model runs were undertaken using a constant solar forcing. To understand the robustness of the attractors to forcing, further model runs will have to be undertaken. Similar to Section 3.1.2, we have produced videos to show the resulting ocean streamfunction and temperature behaviour given the attractors. These videos can be found in supplementary materials. The qualitative behaviour of each of the attractors identified in this section is similar to that of the corresponding attractors (those sharing the same colours) in Section 3.1.2. One minor difference in the results between the ocean-atmosphere coupling model runs and the emissivity model runs is that the LFV in the orange attractor over the first ocean mode φ o,1 is more clearly defined. This is shown by the projection of the attractor on the plane (ψ o,1 , T o,1 ), where the oscillating behaviour over these variables contains less noise and variation. This change in the orange attractor could be caused by the increase in ocean-atmosphere coupling between the two runs, where we used the value of C = 0.009kgm −2 s −1 in Section 3.1.2, and C = 0.01175kgm −2 s −1 in this section.
| Lyapunov Stabilityε
Following the format of Section 3.1.3, we present the LLEs in Figure 3 (b), where ε is varied, and we fix the oceanatmosphere coupling at C = 0.01175kgm −2 s −1 . As the value of ε is increased we see additional stable attractors appear, however the value of the LLEs on each stable branch does not alter with emissivity. This is because the emissivity has the impact of increasing the temperature of the layers evenly in space. The atmospheric layers in the model are driven from the meridional gradient in solar insolation, leading to baroclinic instability. In the current model set up the emissivity has no impact on this temperature gradient. To more closely model the expected outcomes of global heating, model runs should be undertaken where the rising emissivity reduces the temperature gradient between the Arctic and the equator (Francis and Vavrus, 2012;Rantanen et al., 2022).
We have presented the Lyapunov spectra of the three attractors at ε = 0.9, for C = 0.01175kgm −2 s −1 in Figure 4 (b). Interestingly, the orange attractor, with the lowest magnitude LLE, shows a significantly lower number of near zero Lyapunov exponents, compared to the other two attractors and also the orange attractor presented in Section 3.1.3. There is a clear drop in the magnitude of the Lyapunov exponents at the index 18. This is an interesting result as it implies that the Lyapunov dimension of this attractor is significantly lower than the other attractors. This difference between the Lyapunov spectra of the orange attractors in Figure 4 Two of the distinct attractors present low frequency variability (LFV) behaviour. One of the attractors, which displays LFV over the second ocean mode φ 2 , has been identified in the linear model. In this study we found an additional attractor that displays LFV over the first ocean mode φ 1 , which has not been identified in the linear model. This attractor has a longer time scale (∼ 80 − 100 years) compared with the first attractor (which displays a timescale of approximately 70 years). In addition the two attractors display marked differences in the ocean and atmosphere flows.
With one attractor producing the double gyre behaviour, similar to what is observed over the North Atlantic, and the other attractor displaying a more complex flow, where the main relationships are with the first ocean mode φ 1 and the fifth ocean mode φ 5 . This attractor displayed the greatest degree of coupling between the ocean and atmosphere, comparing with the other stable attractors, where all four variables are coupled. This leads to significantly lower positive Lyapunov exponents, which implies that this attractor would have a longer forecasting window. Further studies will need to be done to find if this attractor describes a real-world ocean-atmosphere flow.
A key reason for undertaking this study, and not linearising the longwave radiation terms, was to investigate the potential of tipping between multistabilities. While we found cases of distinct attractors for the same parameter values, we could not produce trajectories that switched intermittently between the stable branches, though it is not possible to rule out the possibility of such trajectories existing. However, in the current model setup all external forcings are stable with respect to time. To test the robustness of the stability of each attractor model runs could be undertaken, where stochastic forcing or perturbations are included, to see if there is the potential for noise induced tipping between the stable branches. Another potential source of tipping could come from periodic cycles, such as the annual solar cycle as implemented in a similar linearised model (Vannitsem, 2017).
With rising global temperatures, investigating the possibility and impact of tipping points in the climate is of great importance. Understanding how rising temperatures could impact existing multi-decadal patterns in the climate could lead to a better understanding of how established climate patterns may look in the future. Or if there is the possibility of abrupt transitions from one regime to another. This paper has introduced a modified model that produces both multistabilities, as well as attractors that present LFV, that become stable for rising emissivity. These properties are of interest as it facilitates the study of attractors that allow forecasting well beyond the atmospheric Lyapunov time, as well as the potential of tipping from one attractor to the other. These aspects will be investigated in the future.
code availability
The code used to obtain the results is a new version (v0.2.6) of qgs (Demaeyer, De Cruz and Vannitsem, 2020) that was recently released on GitHub: https://github.com/Climdyn/qgs and Zenodo (Demaeyer, De Cruz and Hamilton, 2022
conflict of interest
The authors declare no conflict of interest.
supporting information
The documentation manual of the new qgs version associated with the new temperature scheme is provided as a supplementary material to this article.
The videos discussed in Section 3.
GRAPHICAL ABSTRACT
The climate system contains numerous non-linear interactions that produce chaotic behaviour and provides the possibility of multiple stationary solutions as well as tipping between solutions. This study investigates the impact of implementing the non-linear Stefan-Bolzmann law in a reduced order model. This model produces multiple stationary oscillating solutions. These solutions are a potential method of extending forecasts of the weather, which is limited due to sensitivity to initial conditions.
scribed method. The resulting figures for the average atmosphere and ocean temperatures, where the value of the ocean-atmosphere coupling is altered, are shown in Figure 1. In these figures, the branches are colour coded depending on the qualitative behaviour of the attractor. The figures show there are two intervals of C where there are multistabilies in the temperature. These intervals are approximately
k ,l ,m=0 v i ,j ,k ,l ,m T o,j T o,k T o,l T o,m T 4 o,0 + no j ,k ,l ,m=1 v 0,j ,k ,l ,m T o,j T o,k T o,l T o,mThe second difference between the model runs is that the T4 runs show a wider region of multistability in the interval C ∈ [0.012kgm −2 s −1 , 0.0127kgm −2 s −1 ]. This is again assumed to be a result of higher order terms interacting in the T4 model equations, when compared to the DE runs, where the linearisation removes the higher order terms.To investigate the properties of the attractors in the regions of multiple stability, the attractors were projected onto the ocean variables (ψ o,1 , T o,1 ) and (ψ o,2 , T o,2 ) to visualise the behaviour. Looking at these projections we can see that there are three qualitatively distinct attractor behaviours, which correspond to three distinct flow behaviours in the ocean. We project all three attractors onto the same figure for comparison, shown inFigure 1, with the orange attractor shown for C = 0.009kgm −2 s −1 , and the other two attractors shown for C = 0.0125kgm −2 s −1 . In the intervalC ∈ [0.008kgm −2 s −1 , 0.009kgm −2 s −1 ],there exists two attractors, where the attractor shown in orange displays LFV with respect to the variables (ψ o,1 , T o,1 ). The orange attractor becomes unstable when C > 0.009kgm −2 s −1 . This multistability has not been found in other studies using the linear MAOOAM model. The LFV in the first ocean modes suggests that the variability in the ocean temperature and streamfunctions is prominently impacted by the single gyre oscillation in this case. The pink attractor, which becomes stable for values C > 0.012kgm −2 s −1 , presents LFV over the variables (ψ o,2 , T o,2 ), (a) LLE of the DE and T4 model runs, for varying C and ε = 0.7. (b) LLE of the DE and T4 model runs, for C = 0.01175kgm −2 s −1 and varying ε. F I G U R E 3 The Largest Lyapunov Exponents (LLE), shown in days −1 , where the results are colour coded based on the attractor behaviour, as described in Sections 3.1.2 and 3.2.1. signifying that the dynamics of the flow are impacted by the double gyre dynamics. The other attractor (blue) present does not show LFV with any of the modes and this signifies that flows associated with this attractor do not present the same LFV or the same ocean dynamics as the other two attractors. The blue attractor becomes unstable for values C > 0.01275kgm −2 s −1 . This second bifurcation was found in Vannitsem (2017) using the linear version of the model,however the region of multistability in this interval was not found using the linear model. We have conducted long model runs to ensure the stability of both attractors in this interval and found that both attractors remain stable for at least 3 × 10 7 model days. This region of multistability was found in both the T4 and DE model runs, however it was found that the region of multistability is extended in the T4 model, when compared with the DE model.Following the analysis of Vannitsem et al.(Vannitsem, 2017), we project the attractors onto the variables (ψ a,1 , ψ o,1 , T o,1 )
visualise the resulting flow in the ocean, given the attractor behaviour, we have created videos showing the ocean streamfunction and temperature profiles, given the location in the projected 2D state-space, which can be found in the supplementary materials. The videos are named based on the colour coding used in the above plots. The attractor coloured in blue shows a persistent positive value for the T o,2 variable, leading to a persistent double gyre temperature anomaly in the ocean temperature. In addition no clear LFV is present in the videos. The pink attractor shows oscillating behaviour over the variables T o,2 and ψ o,2 with timescales of approximately 70 model years, leading to transitions between a double and quadruple gyre temperature anomaly in the ocean. Similarly, a clear oscillation is seen in the ocean streamfunction where the most prominent variables oscillate between ψ o,2 and ψ o,6 over the same time period. Lastly, in the case of the orange attractor, no clear double gyre appears in the ocean temperature profile, and the LFV instead manifests in the first ocean mode φ o,1 . This leads to LFV with a timescale of 80-100 model years over the temperature variables T o,1 , T o,5 , and T o,7 . (a) Lyapunov spectra where the orange attractor is shown for C = 0.009kgm −2 s −1 , and the other two for C = 0.0125kgm −2 s −1 , where ε = 0.7.(b) Lyapunov spectra for ε = 0.85 and C = 0.01175kgm −2 s −1 F I G U R E 4 The Lyapunov spectra, shown in days −1 , for the three distinct attractors found are plotted to compare the magnitude of the largest Lyapunov exponent λ 1 , and the number of near zero Lyapunov exponents.
stable attractors, focusing on values of C identified in the previous section where multiple stable attractors exist. For more details on calculating Lyapunov properties in coupled ocean-atmosphere models see Vannitsem and Lucarini (2016); Vannitsem (2017); Vannitsem et al. (2019); Vannitsem and Duan (2020).
(a) we present the Lyapunov spectra of the three distinct attractors identified while varying the level of ocean-atmosphere coupling. The figure shows that the two attractors at C = 0.0125kgm −2 s −1 (blue and pink), both have 18 near zero Lyapunov exponents, 17 negative exponents, and three positive exponents. However the positive Lyapunov exponents are approximately double in one of the attractors compared with the other, showing
(a) and (b) could be caused by the increase in ocean-atmosphere coupling between the two model runs, from C = 0.009kgm −2 s −1 to C = 0.0175kgm −2 s −1 in this section.4 | DISCUSSIONWe have described the novel multistabilities found in a reduced order atmosphere-ocean model, resulting from not linearising the longwave radiation terms. The modifications made to the MAOOAM model have resulted in several features that were not present in the original linearised version with fixed reference temperature. This study intro-duced two new versions of the model (the dynamic equilibria and non-linear versions), and compared the results of these versions with the existing linear model. The properties of the new attractor found, as well as the region of multistability, were analysed qualitatively and by using the Lyapunov properties of the attractors.We have demonstrated in the reduced order ocean-atmosphere model, MAOOAM, that by modifying the linearisation of the longwave radiation terms we can obtain three qualitatively distinct stable attractors, with intervals of multistability for certain parameters. Interestingly, the dynamic equilibria version of the model, which includes the same linearisation as the original model but allows the zeroth order equilibria temperature to change with time, presents similar dynamics as the fully non-linear version for most parameter values. All three distinct attractors can be obtained in the dynamic equilibria (DE) version, where there are two attractors that present LFV while representing largely different coupled ocean-atmosphere flows. In addition, the DE version of the model can be run in the same length of time as the fixed reference temperature version, which is almost an order of magnitude faster than the non-linear version of the model.
). These are set on a domain of x ∈ [0, 2π ], y ∈ [0, π ]. The atmosphere F i and ocean φ i modesare given below:
TA B L E 1 MAOOAM Model Parameters
Parameter
Value
Description (units)
β
1.62 × 10 −11
The meridional gradient of the Coriolis parameter at a given latitude (m −1 s −1 )
f 0
1.032 × 10 4
Coriolis parameter (s −1 )
k d
gC /∆p
Atmosphere-surface friction (s −1 )
k d
gC /∆p
Internal atmosphere friction (s −1 )
r
1 × 10 −7
Ocean bottom Rayleigh friction (s −1 )
L R
1.9934 × 10 4
Reduced Rossby deformation radius
h
136.5 Depth of the ocean layer (m)
d
C /(ρ o h)
Coefficient of mechanical ocean-atmosphere coupling (s −1 )
γ a
1 × 10 7
Specific heat capacity of the atmosphere (Jm −2 K)
γ o
5.46 × 10 8
Specific heat capacity of the ocean (Jm −2 K −1 )
σ
0.2 Static stability of the atmosphere
λ
1004C
Sensible and turbulent heat exchange between ocean and atmosphere (Wm −2 K −1 )
R
287.058 Gas constant in dry air (Jkg −1
). Each covariant Lyapunov vector is stretched by the system dynamics by the corresponding local Lyapunov exponent. Each CLV is made up of 38 components, one for every variable of the system. The CLVs were calculated at each time step, and we took the variance of each of the 38 vector components across time, for each of the 38 vectors. The variance measures the variability of the CLV component in the direction of a given variable. Variables from the atmosphere and ocean that both have high variance for the same CLV index implies that these variables are interacting, or influencing each
). This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.956170. MC was funded as Research Director with the Belgian National Fund of Scientific Research.acknowledgements
1.2 and 3.2.1 can be accessed in the below table. https://doi.org/10.5446/60104 C = 0.009kgm −2 s −1 ε = 0.7 Orange https://doi.org/10.5446/60105 C = 0.0125kgm −2 s −1 ε = 0.7 Blue https://doi.org/10.5446/60106 C = 0.0125kgm −2 s −1 ε = 0.7 Pink https://doi.org/10.5446/60107 C = 0.01175kgm −2 s −1Video list
Link
C value
ε value
Attractor colour
ε = 0.9
Blue
https://doi.org/10.5446/60108
C = 0.01175kgm −2 s −1
ε = 0.9
Orange
https://doi.org/10.5446/60109
C = 0.01175kgm −2 s −1
ε = 0.9
Pink
Further developed byCharney and Straus (Charney and Straus, 1980) and again byReinhold and Pierrehumbert (Reinhold and Pierrehumbert, 1982).
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| sample_914 | 0.5813 | arxiv | |
Interannual observations and quantification of summertime H 2 O ice deposition on the Martian CO 2 ice south polar cap Observations of the H 2 O ice cycle on summertime Martian south polar cap
~
Adrian J Brown abrown@seti.org
SETI Institute
189 Bernardo Ave94043Mountain ViewCAUSA
Sylvain Piqueux
SETI Institute
189 Bernardo Ave94043Mountain ViewCAUSA
Jet Propulsion Laboratory
California Institute of Technology
4800 Oak Grove Drive91109PasadenaCAUSA
Timothy N Titus
Jet Propulsion Laboratory
California Institute of Technology
4800 Oak Grove Drive91109PasadenaCAUSA
U.S. Geological Survey
Astrogeology Science Center
86001FlagstaffAZUSA
SETI Institute
189 Bernardo Ave, Mountain View94043CA
~
Adrian Brown .abrown@seti.org
Interannual observations and quantification of summertime H 2 O ice deposition on the Martian CO 2 ice south polar cap Observations of the H 2 O ice cycle on summertime Martian south polar cap
Corresponding author:
The spectral signature of water ice was observed on Martian south polar cap in 2004 by the Observatoire pour l'Mineralogie, l'Eau les Glaces et l'Activite (OMEGA)(Bibring et al., 2004). Three years later, the OMEGA instrument was used to discover water ice deposited during southern summer on the polar cap(Langevin et al., 2007). However, temporal and spatial variations of these water ice signatures have remained unexplored, and the origins of these water deposits remains an important scientific question. To investigate this question, we have used observations from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) instrument on the Mars Reconnaissance Orbiter (MRO) spacecraft of the southern cap during austral summer over four Martian years to search for variations in the amount of water ice.We report below that for each year we have observed the cap, the magnitude of the H 2 O ice signature on the southern cap has risen steadily throughout summer, particularly on the west end of the cap. The spatial extent of deposition is in disagreement with the current best simulations of deposition of water ice on the south polar cap(Montmessin et al., 2007).This increase in water ice signatures is most likely caused by deposition of atmospheric H 2 O ice and a set of unusual conditions makes the quantification of this transport flux using CRISM close to ideal. We calculate a 'minimum apparent' amount of deposition corresponding to a thin H 2 O ice layer of 0.2mm (with 70% porosity). This amount of H 2 O ice deposition is 0.6-6% of the total Martian atmospheric water budget. We compare our 'minimal apparent' quantification with previous estimates.This deposition process may also have implications for the formation and stability of the southern CO 2 ice cap, and therefore play a significant role in the climate budget of modern day Mars.Highlights• We report on the H 2 O ice depositional cycle on the Martian CO 2 ice residual south polar cap • We use data from the CRISM instrument obtained over the past four Martian summer periods • Potential models: 1) cold trapping 2) sublimation 3) entrained H 2 O ice in sublimation flow • The 'minimal apparent' amount of water ice deposited corresponds to a layer 0.2mm thick. Brown et al. ~ 3 ~ • This amounts to over 0.6-6% of the total Martian atmospheric water budget. Observations of the H 2 O ice cycle on summertime Martian south polar cap ~ 4 ~
Introduction
The Martian north polar ice cap has long been understood as the most important exposed source and sink of water on modern day Mars (Farmer et al., 1976). In contrast, the south seasonal cap was thought to be essentially composed of CO 2 ice following surface temperature measurements using the Viking Infrared Thermal Mapper (IRTM) (Kieffer, 1979). In the late 1990s, the Mars Global Surveyor Thermal Emission Spectrometer (TES) also confirmed CO 2 ice temperatures in the south pole residual cap (SPRC) during the austral summer (Kieffer et al., 2000) and found "no significant presence" of H 2 O ice. Soon after this observation, Nye et al. (2000) published an influential theoretical paper showing that a pure CO 2 ice south polar cap would collapse under its own weight, and suggested dirty H 2 O ice as the principle ice cap constituent. In 2004, the OMEGA instrument on Mars Express was used for one Earth month to observe the Martian south polar region from L s =335-348 and reported observations of H 2 O ice mixed with CO 2 ice in the residual south polar cap and polar layered deposits (Bibring et al., 2004). Doute et al. (2006) used OMEGA to examine the water and dust content of the south polar cap during late summer. Langevin et al. (2007) mapped the springtime retreat and summer evolution of the south polar cap and were the first to note the deposition of water ice on the south polar cap.
Further complicating this cap compositional picture, large deposits of CO 2 ice have recently been discovered in the subsurface of the south polar layered deposits (Phillips et al., 2011).
Observations of the H 2 O ice cycle on summertime Martian south polar cap ~ 6 ~ Viking IRTM and TES temperature observations show that CO 2 ice is the predominating ice in the surface/near surface in the residual cap during summer (Kieffer, 1979;Titus et al., 2008). Mars Global Surveyor Mars Orbiter Camera (MOC) images of the south polar cap were used to discover 'Swiss cheese features' (Malin et al., 2001) which were successfully modeled as a meters-thick layer of CO 2 ice underlain by H 2 O ice (Byrne and Ingersoll, 2003). Mars Odyssey Thermal Imaging Spectrometer (THEMIS) temperature observations of the south polar cap have been used to infer that H 2 O ice becomes exposed at the periphery of the residual cap during late summer (Piqueux et al., 2008), and Titus et al. (2003) used thermal and visual observations, combined with subpixel mixing models, to identify a possible H 2 O ice lag at the edge of the gullies and trenches in the SPRC that were exposed as the edge of the retreating seasonal CO 2 ice cap moved poleward during summer. However, THEMIS and TES do not have spectral coverage of near-infrared (NIR 1.0-2.5 µm) region of the electromagnetic (EM) spectrum where several CO 2 and H 2 O ice absorption bands are available to CRISM.
CRISM is very sensitive to water ice deposited on the surface of Mars. For example, CRISM data were recently used to observe an unexpected asymmetric springtime retreat of CO 2 ice observed in the north polar cap, potentially due to H 2 O ice sourced from the north polar cap outliers (Brown et al., 2012). CRISM has also been used to examine Rayleigh scattering in the Martian atmosphere ~ 7 ~ (Brown, 2014) and to discriminate water and CO 2 ice deposited in halos around Swiss-cheese deposits (Becerra et al., 2014 Placing limits on the modern day deposition rate of water ice on the SPRC will allow us to better understand the modern-day stability of the southern polar cap (Byrne, 2009) and perhaps even shed light on the formation processes on the south polar cap (Montmessin et al., 2007). Many simulations of the Martian water cycle have investigated the question of cold-trapped water ice on the exposed CO 2 ice (Jakosky, 1983;Haberle and Jakosky, 1990;Houben et al., 1997;Richardson and Wilson, 2002;Montmessin et al., 2004;Montmessin et al., 2007) and we conclude the paper by comparing their predictions with our multiyear CRISM measurements. We produced mosaics of all the CRISM mapping data available for each twoweek period (equivalent to the time of an MRO planning cycle and also a useful cadence for investigating seasonal change in the Martian polar regions). Each mosaic is in polar-stereographic projection. Figure 1 shows the residual south polar ice cap region as a mosaic of CRISM images of the SPRC during the summer of MY28.
Methods
Our
<insert Figure 1 here> Water ice can be mapped on the surface using these near infrared mosaics by exploiting the 1.5 µm water ice absorption band. In Figure 2 we display a mosaic ~ 9 ~ map for early and late summer from MY 28, showing the presence of H 2 O and CO 2 ice. We use a H 2 O ice index first used by Langevin et al. (2007) and adjusted for use with CRISM by Brown et al. (2010a). The formula for this index is:
! H 2 Oindex = 1 " R(1.500) R(1.394) 0.7 R(1.750) 0.3(1)
Where R(λ) indicates the reflectance at the wavelength λ in µm. The index is high when the 1.5 µm water ice band is present and low when it is not, and it increases as larger grain water ice is present (Warren, 1982).
<insert Figure 2 here>
Results
Residual ice cap mosaics
The first line of evidence for H 2 O ice deposition is the residual cap ice identification maps in Figure 2. Following previous studies (Brown et al., 2010a;Brown et al., 2012) we use a H 2 O index threshold of 0.125 to indicate that surficial H 2 O is present. CO 2 ice is detected using a band analysis routine described (Brown, 2006) and successfully applied by Brown et al. (Brown et al., 2008b;Brown et al., 2010b). As in previous studies (Brown et al., 2010a;Brown et al., 2012), positive identification of CO 2 ice is indicated by a threshold 1.435 µm band depth of 0.16. detected small but significant increases in the 1.5 H 2 O µm band. As can be seen from the CRISM mosaics in Figure 2, the effect is confined sharply to the south polar cap, and does not extend beyond the SPRC edge.
<insert Figure 3 here>
CRISM Reflectance Spectra
Our second line of evidence is taken from spectra extracted from a point within these maps. Figure 3 shows a set of individual CRISM MSP spectra (no averaging or binning has been done) prior to H 2 O ice deposition (starting at L s =261) and throughout summertime (finishing at L s =337) from 265.5°E, 86.1°S
(marked as Point A on Figure 1). The spectra show a marked decrease in the 1.5 µm band that causes a decrease in the shoulder of the CO 2 ice absorption band at 1.4 µm. As in previous studies (Brown et al., 2008a;Brown et al., 2010a;Brown et al., 2012) we attribute this change in band depth to the presence of increasing amounts of H 2 O ice through the summer season.
<insert Figure 4 here>
Point observations at Point A and B
~ 11 ~ Our third line of evidence comes from mapping observations taken by the CRISM instrument for MY28-31. In order to establish that this process is cyclic, we have extracted individual spectra from regions close to Point A and have plotted the H 2 O ice and CO 2 ice index and also to the 1.2 µm albedo for these spectra in <insert Figure 5 here>
Radiative Transfer Model and Quantification of Water Ice Deposited
In order to quantify the amount of H 2 O ice deposited on the south polar cap, we developed a radiative transfer model to reproduce the broad characteristics of a number of CRISM MSP spectra taken at Point A (see Figure 1). The CRISM spectra taken at L s =337 (in late summer, after H 2 O ice deposition) in MY28 and radiative transfer model spectra are shown in Figure 5. We carried out the radiative transfer modeling using the model proposed by Shkuratov et al.(1999) which is a simplified 1-dimensional model that allows us to interpret the effect of H 2 O ice as a contaminant in a CO 2 ice snowpack. As in past research (Brown et al., 2010a), we used a three component model (optical constants of CO 2 ice (Hansen, 2005), H 2 O ice (Warren, 1984) and palagonite (Roush et al., 1991) as a Martian dust simulant) and attempted to fit the overall albedo and key band strengths of CO 2 ice and H 2 O ice in the spectrum.
We carried out two modeling approaches in order attempt to place physical bounds on the amount of water ice deposited on the south polar cap. The two models adopted are:
1.) 'minimum apparent' model, and
2.) 'extrapolated' model
The 'minimum apparent' model attempts to find the smallest amount of water ice that could explain the observed water ice band, and as discussed in previous work (Brown et al., 2010a;Brown et al., 2012) this is the most robust way to interpret the observed CRISM spectra. The 'extrapolated' model makes additional assumptions in an effort to provide a reasonable best approximation to the depth of the H 2 O ice deposits.
'Minimum apparent' model. To carry out the 'minimum apparent' interpretation, we used a newly developed iterative band-fitting routine based on previous band fitting algorithms (Brown, 2006) For the late summer spectrum in Figure 5, we found that the best spectral match was obtained for CO 2 ice grain size of ~4.25mm, (C CO2 =85.7% by volume) H 2 O ice grain size of ~ 0.2mm (C H20 =5.1%) and palagonite of ~0.35 mm (C dust =9.2% by volume). We used a porosity (q-factor) of q=0.3, corresponding to 70% pores and 30% ice/dust. These results are summarized in Table 1 Roush et al. (1991) 354.9 0.092 Table 1 -Details of the best fit parameters for the CRISM spectrum in Figure 5. The fit was applied over the spectral range from 1.02-2.5 microns. In this range, using wavelengths from the CRISM MSP range, there are 42 bands. Over this range, the average absolute fitting error per band is 0.01659 for this best fit. The porosity was constrained to be 0.3 (30% ice, 70% vacant).
In order to estimate the 'minimum apparent' amount of water ice deposited, we make the simplest assumption that the thickness of the water ice layer is a minimum of the derived grain size diameter (D H2O =0.2mm or 2x10 -7 km) from the radiative transfer calculation. The physical justification for this is that the water ice must be optically detectable, and therefore at least one optical pathlength should be available for the passage of vertically propagating photons. The true situation will be far more complex. We make the obviously simplified assumptions that: With these three assumptions, the minimal amount of water ice observed would be determined by the following linear relationship:
! volume H 2 O = A cap C H 2 O D H 2 O q (2)
therefore volume H2O-minimal apparent =2x10 5 *0.05*2x10 -7 *0.3=6x10 -4 km 3 .
We regard this as a 'minimum apparent' estimate because it is likely that the deposit could be as thick as 10 grain diameters (10.D H2O ).
Extrapolated estimate. The 'extrapolated' approach assumes that the water ice observed by CRISM is the top layer of a deeper deposit that extends ten grain diameters, which is a reasonable situation for this type of deposit. In this case, using:
! volume H 2 O "extrapolated = A cap C H 2 O 10D H 2 O q(3)
we find volume H2O-extrapolated =2x10 5 *0.15*6x10 -8 *0.3=6x10 -3 km 3 .
These rather firm sounding numbers must be balanced with the fact that we have assumed that the entire SPRC is covered by the same amount of water ice,
Brown et al.
~ 15 ~ whereas we know from observations that the western part of the polar cap is covered in more ice than the eastern part of the cap (Figure 2).
Nevertheless, assuming a Martian atmospheric H 2 O ice budget of ~0.1 km 3 (Christensen, 2006), the amount of water ice participating in this process will make up as much as 0.6% (at minimum, for 0.2mm thick ice deposit) to 6% (at maximum, for 2mm thick ice deposit) of the atmospheric Martian water budget.
Note that we are not stating that 0.6-6% of the atmospheric water ice is being deposited on the cap, because we cannot be sure of the immediate source of the process. However, if the water ice is to be completely sourced from the atmosphere, then it would make up 0.6-6% of the current Martian atmospheric water budget.
Discussion
Comparison with previous hydrological models
Reference Annual Water loss rate to south polar cap in grams Total Annual Water loss rate to south polar cap in microns Transport flux to southern polar cap Jakosky and Farmer (1982) 4x10 14 g (maximum) Jakosky (1983) We compare this estimate with previous Martian hydrological cycle models in Table 2. Jakosky and Farmer (1982) Our estimates are smaller than the estimates of all GCM models, which may be due to the conservative approach taken to interpretation of our spectra. We consider this a first order estimate that will be refined as future observations are made of the summer south polar cap. Figure 4. We have looked for evidence of larger amounts of H 2 O ice being deposited each year but the evidence is inconclusive thus far.
Interannual differences
Seasonal changes
The data presented in Figure 2 suggest that the depositional process is gradual and lasts all summer long, rather than being due to isolated or singular
Deposition or Exposure of H 2 O ice?
It should be noted that the spectra in Figure 3 (Titus et al., 2003;Piqueux et al., 2008) and the spectral signature of water ice was also observed by Bibring et al., (2004), on the SPRC mixed with CO 2 ice. Titus (2005) pointed out that it is also possible that H 2 O ice might be deposited on top of the CO 2 ice cap during summertime, thus obscuring a large region of the CO 2 ice on the cap. Potential support for this interpretation is the observation that the water ice index is higher in the western regions of the cap, close to where H 2 O ice is exposed in the sides of gullies (Titus, 2005).
Option 2 (sublimation) is considered less favorable since the weight of GCM modeling suggests that conditions are right for cold trapping of water vapor at this time. The truth may lie between these extremes -water ice may be exposed by CO 2 ice sublimation, and then transported to nearby cold trap locations (e.g.
tops of 'Swiss-cheese' mesas) where it obscures the underlying CO 2 ice. This process may play a role in the burial of large amounts of CO 2 ice, which has been a key scientific question arising from the recent SHARAD radar sounder
Observations of the H 2 O ice cycle on summertime Martian south polar cap
~ 20 ~ findings of large amounts of CO 2 ice beneath the polar layered deposits (PLD) (Phillips et al., 2011).
Option 3 (atmospheric condensation) suggests that CRISM is collecting observations of a sublimation flow from the CO 2 polar cap during the height of summer, and that small H 2 O crystals are forming within the sublimation flow as it evaporates off the ice pack. We consider this option less likely because of the increasing strength of the H 2 O ice signature right through to fall -even as conditions begin to cool in late summer.
Atmospheric effects
For this study we have made no effort to remove atmospheric effects from the CRISM data. As mentioned above, a global dust storm was present in MY28 which affected the absorption band depths (Vincendon et al., 2008), however as can be seen in Figure 4, the H 2 O cycle continued to operate in a similar manner to the following three Martian years. In addition, the water ice signatures appear only on the CO 2 ice cap (unlike the behavior of a cloud). We therefore infer that the H 2 O ice cycle is present on the surface, and not due to an atmospheric event (Langevin et al., 2007). If the cycle is a depositional effect, (controlled by on-cap winds), stronger winds may play a role in the SPRC H 2 O ice cycle, and this question invites future mesoscale climate modeling of the south polar region.
Conclusions
Brown et al.
~ 21 ~
The source for the water ice reported here is unclear and we hope this study initiates new avenues of research for the Martian community. These findings impose an important constraint upon models of Martian water ice dynamics while opening a new front in the battle to understand the impoverished but vital Martian water ice cycle.
Stability of the SPRC
The operation of the H 2 O ice cycle we have reported may have implications for the stability of the thin veneer of CO 2 ice that covers the residual south polar cap. Jakosky and Haberle (1990) suggested that the current CO 2 ice south polar residual cap is unstable and could 'flip' quickly to being covered by H 2 O ice if water ice from the north polar cap makes its way to the southern cap, which acts as a cold trap in their model. As part of this cycle, and to explain observations of atmospheric H 2 O observed above the south pole in 1969 (Barker et al., 1970), these authors suggested that the entire perennial CO 2 cap may have disappeared in the summer of 1969 (MY 8) and started to recondense shortly after. However, countering this suggestion, Thomas et al. (2005) Figure 3 showing decreasing near infrared albedo of the cap as H 2 O index increases), causing more heating of the ice, and therefore more sublimation during the hottest part of the Martian orbital cycle.
CO 2 -H 2 O cycle is shown to be steady over 4 Mars years
It should be pointed out that as seen in Figure 4, for each Martian year observed, the CO 2 residual cap has been 're-coated' during winter with CO 2 ice. This may have taken place by direct condensation or snowfall during the austral winter (Forget et al., 1998;Hayne et al., 2012;Hu et al., 2012;Hayne et al., 2013). We find 'relatively pure' CO 2 ice at the start of each austral summer in our CRISM mosaics ( Figure 2). This shows that this 're-coating' process is cyclic and at least stable on observable time scales .
The fact that 'relatively pure' seasonal CO 2 ice is present all over the cap indicates that the H 2 O ice we see deposited each summertime is entirely interned, and presumably becomes a permanent thin layer within the southern CO 2 ice cap. This process may have played a role in forming the south polar layered deposits (SPLD) if they formed at a time when the SPRC was larger.
~ 23 ~
5.3: Varying emissivity of the South Perennial Cap
The albedo and emissivity of the south cap are two critically important parameters determining its stability in the current climate (Wood and Paige, 1992;Blackburn et al., 2009;Guo et al., 2010). A stable cap (able to survive the short but relatively warm southern Martian summers) is difficult to model and previous studies have used various combinations of CO 2 ice/dust albedo and emissivities (James and North, 1982;Warren et al., 1990;Hansen, 1999;Doute et al., 2006;Bonev et al., 2008;Kahre and Haberle, 2010;Pilorget et al., 2011;Pommerol et al., 2011;Kieffer, 2013). However, we have shown that the optical properties of the cap transition from "covered by CO 2 ice" to "CO 2 and H 2 O ice mixture" in the course of the Martian austral summer, and future models of the cap albedo and emissivity can now take this variability into account.
The southern cap as a sink for the Martian water cycle
The Martian water cycle is crucial to the understanding of geodynamics of the atmosphere, surface and sub-surface (Clifford, 1993) 1.) Non-local origin (e.g. transport from the north polar cap) 2.) Local aeolian origin (e.g. exposed water ice around the edges of the cap being blown into the interior and exposed water ice in 'Swiss-cheese' moats (Titus, 2005)).
3.) Local solid-state origin (e.g. sublimation of H 2 O ice around the cap periphery or regolith and recondensation over the cold cap (the so-called 'Houben process' in springtime in the north pole (Houben et al., 1997;Brown et al., 2012)).
These three possibilities may all be part of the eventual explanation for this intriguing, widespread and repeatable Martian polar phenomenon. Table 1 for details of the fit.
The CRISM spectra is sourced from Point A (see Figure 1) and was acquired in image MSP 86FC_01 on MY28 L s =337.0 (26 Oct 2007).
SUPPLEMENTARY INFORMATION
In the course of this investigation, we used CRISM I/F data that had been processed by the CRISM team at JHU/APL to the TRR3 release level. Figure 3.
Error bars on Figure 4a-f
Error bars are plotted as constant for the plots of 1267nm, CO 2 and H 2 O ice index ( Fig. 4a-f) as +/-0.015, based on the CRISM signal to noise (~100, based on data in Murchie et al. (Murchie et al., 2007)) for the 1.2-1.5 µm region.
The ice identification maps show almost complete coverage of the residual cap in CO 2 ice (shown in red) and little to no H 2 O ice in the early summer period (L s =310). On the right ofFigure 2, we have superposed the CRISM observations in the L s =310-330 time period. These show strips of cyan where CRISM has
Figure 4a -
4ac. Coverage in MY 29-31 is not quite as comprehensive, however in Figure 4d-f we show the same data for Point B, which is on the other side of the
made the first upper estimate of the water that might be transported to the south polar cap by measuring the water vapor above the north polar cap using the MAWD instrument on the Viking orbiters.Jakosky (1983) developed a simplified circulation model that reproduced observations of the MAWD instrument and included a loss of water ice to the south polar cap and a regolith sink.Haberle and Jakosky (1990) used a simulation of the Martian north pole in the light of MAWD measurements to suggest that regolith was necessary in keeping the north polar cap stable. They provided an estimate of 0.1-0.8 mm of loss of water ice from the north polar water ice cap, which they used to put upper bounds on the amount deposited on the south polar cap.Houben et al. (1997) developed a simplified 3D climate model of the Martian water cycle which included transport between atmosphere and regolith.Richardson and Wilson (2002) reported the first use of a Martian GCM with a water ice cycle, with water ice treated as a trace component, andMontmessin et al. (2004) carried out a similar study including water ice clouds (with varying size distributions) with the LMD GCM.
Figure 18 -
18Montmessin et al. (2007) carried out a similar GCM-based simulation of the amount of water ice deposited on the south polar cap on current-day Mars and compared this to a model of water ice deposition during reversed perihelion.They suggested the water ice at the base of the SPRC was emplaced during reversed perihelion conditions.Montmessin et al. (2007) used a symmetric model of the south polar cap and predicted that water ice deposition would correlate with latitude -hence greatest deposition is at the pole and smaller amounts of H 2 O ice would be deposited at the edge of the cap. This is contrary to the CRISM observations reported here of deposition favoring the warmer western part of the cap, a trend which is also apparent in the OMEGA H 2 O ice maps presented by Langevin et al. (2007) (their 19). These observational versus simulation discrepancies indicate to us that future mesoscale modeling of this season is required. At the very least, higher resolution hydrological simulations with a realistic cap orientation should be used to help interpret the observed western depositional pattern on the south polar cap under modern Martian conditions.
Figure 1 -Figure 2 -
12CRISM mosaic of south polar residual cap (SPRC) in Mars Year 28, compiled during aerocentric longitude L s =304-319 (mid summer) using three CRISM L channel bands (Red: 1.467, Green: 1.427 and Blue: 1.276 m). The locations of Point A (265.5°E, 86.1°S) and Point B (1.0°E, 87.0°S) are shown. Observations of the H 2 O ice cycle on summertime Martian south polar cap Martian Year 28 southern summer ice identification mosaics. On left is the mosaic containing images from L s =304-311. Note almost complete coverage by CO 2 ice (in red). On right is the mosaic constructed images spanning L s =320-342. Note appearance of H 2 O ice mixed with CO 2 ice in most recent images.
Figure 3 -
3CRISM summertime MSP spectra (from Point A in Figure 1) showing increase in H 2 O ice absorption band for Mars Year 28 in late summer (pixels are ~180m across). The spectra were all taken close to Point A (265.5°E, 86.1°S; see Figure 1). Note overall decreasing albedo and increase in strength of H2O absorption band at 1.5 µm throughout summertime.
Figure 4a -
4aCRISM H 2 O ice index taken from points close to Point A from MY 28-31 during L s =275-360 (austral summer). Note the increasing H 2 O index during austral summer (from L s =275-360) across all Mars years where data is available.
Figure 4b -Figure 1 Figure 5 -
4b15c -CRISM CO 2 ice index and CRISM 1.267 µm albedo at Point A during MY 28-31 during austral summer. Figure 4d-f -CRISM H 2 O index, CO 2 index and 1.267 µm albedo for MY28-31 at Point B, located at (1°E, 87.0°S -see Shkuratov reflectance models of CO 2 , H 2 O ice and palagonite mixture compared to CRISM L channel MSP spectra. See
). Here we present CRISM observations of the south polar cap over four Martian years that show that surficial H 2 O ice reappears each year on a repeatable and cyclic basis on the residual CO 2 ice cap throughout the austral summer. The increases in H 2 O deposition occur across the entire SPRC but not in dusty or regolith-dominated regions beyond it.
primary means of monitoring the SPRC H 2 O ice cycle comes from mosaics and spectra constructed of the CRISM global mapping data during Mars Year (MY) 28-31. The Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) is a visible to near-infrared spectrometer on Mars Reconnaissance Orbiter (MRO) spacecraft that is sensitive to near infrared (NIR) light from ~0.39 to ~3.9 µm and is operated by the Applied Physics Laboratory at Johns Hopkins University. We used the multispectral (MSP and HSP) TRR3 I/F data that are available from the Planetary Data System (PDS).In CRISM mapping mode 10x on-instrument binning is employed in the crosstrack direction. Consequently the mapping swathes we use are 60 pixels across, covering approximately 10.8 km on the surface(Murchie et al., 2007) with a down and cross track resolution of ~182 m. The length of each swathe is controlled by exposure time and is variable depending on commands sent to MRO.Observations of the H 2 O ice cycle on summertime Martian south polar cap
~ 8 ~
to generate a three-component mixture of CO 2 , H 2 O ice and dust that matched three components: 1.) the NIR albedo, 2.) the CO 2 ice band depths at 1.435 µm, and 3.) the doublet near 2.2 µm and H 2 O ice band at 1.5 µm.Brown et al.
~ 13 ~
.Component
Reference
Best fit
grain size
(microns)
Best fit
concentration
CO 2 ice
Hansen (2005)
4252.7
0.857
H 2 O ice
Warren (1984)
200.1
0.051
Palagonite (soil)
Observations of the H 2 O ice cycle on summertime Martian south polar cap ~ 14 ~ 1.) the residual SPRC has an approximate area of A cap =2x10 5 sq. km(Brown et al., 2010a), 2.) the SPRC is uniformly covered in summertime by a water ice layer, and 3.) that the H 2 O ice is distributed in a 'checkerboard' fashion and occupies C H2O .q= 0.05 * 0.3 = 0.015 or 1.5% of this area.
Table 2 -
2Comparison of GCM model water loss to south polar cap amounts with the results of this study. For the purposed of calculating the transport flux, the estimated total atmosphericwater content is estimated at 1-2 x10
15 g.
During MY28 there was a global dust storm(James et al., 2010) that induced a decrease in the albedo of the polar ice and subdued the H 2 O and CO 2 ice signatures across the SPRC. This explains the relatively low MY28 index values seen inObservations of the H 2 O ice cycle on summertime Martian south polar cap
~ 18 ~
show CO 2 ice and weak H 2 O ice signatures mixed together in the same pixel. The mixing might be 'checkerboard'linear mixing or intimate mixing where CO 2 ice and H 2 O ice grains are
encountered by a single photon traversing the Martian snowpack. Therefore, it is
not possible for us to tell definitively whether the observed H 2 O ice cycle is a
process of:
1.) deposition of H 2 O ice on top of the SPRC (cold trapping)
Brown et al.
~ 19 ~
2.) sublimation of CO 2 ice, revealing stratigraphically older H 2 O ice mixed within
the CO 2 snowpack.
3.) atmospheric condensation of H 2 O ice particles within a sublimation flow
above the CO 2 snowpack.
Option 1 (deposition) is our favored explanation for the observations reported
here. Thermally thick (e.g. decimeter to meter thick) water ice units have been
observed at the periphery and immediate vicinity of the SPRC during the summer
following the sublimation of the last seasonal CO 2 ice
of the planet. The results of this study show there is an increase in the H 2 O ice signature on the south polar residual cap throughout summer, and is distributed predominantly on the western side of the cap. This runs contrary to the results of Montmessin et al. (Montmessin et al., 2007) who modeled a pole-symmetric cap and found that more water ice deposited in the pole, and less deposited on the periphery.The source of the H 2 O ice is uncertain at this stage, but we have proposed three non-exclusive possibilities:Observations of the H 2 O ice cycle on summertime Martian south polar cap
~ 24 ~
Observations of the H 2 O ice cycle on summertime Martian south polar cap~ 34 ~
MRO
Planning
Cycle
DOY (2007-
2013)
(MY) and Ls
Range
S channel
observations
L channel
observations
18
(07)172-181
261.5-267.1
234
232
19
188-198
271.5-277.8
346
346
20
199-212
278.4-286.5
199
200
21
213-219
287.1-290.8
123
125
22
227-240
295.6-303.4
119
118
23
241-254
304.0-311.6
146
146
24
255-268
312.2-319.7
210
210
25
269-282
320.2-327.5
180
180
26
283-296
328.1-335.2
172
173
27
297-309
335.7-342.1
152
150
Mars Year 28
Total
1881
1880
28
350-352
(29) 3.1-4.1
26
26
29
353-001
4.6-10.9
183
183
30
(08)002-012
11.4-16.2
60
60
31
016-026
18.1-22.8
35
35
58
(09)113-125
252.4-260.0
43
43
59
127-138
260.9-268.4
42
42
60
140-153
269.3-277.5
59
59
61
154-167
277.9-286.3
27
26
62
168-179
286.7-293.5
28
28
63
184-192
296.4-301.6
65
66
64
196-209
303.7-311.6
117
116
65
210-223
312.0-319.7
39
39
66
224-237
319.8-327.6
174
174
Mars Year 29
Table A .
A1 -CRISM observations of Mars south pole in the nearsummertime from MY 28, L s =260 to MY 31 L s =342. L s = Deg of solar longitude. Southern summer starts at L s = 270 and ends at L s = 360.
Table A .1
Ashows the CRISM multispectral summer images that were taken of the Martian south pole from the start of the MRO mission to 27 June 2013. et al.Locations and observation dates of the spectra shown inFigure 3:Brown ~ 35 ~
Ls
MSP ID
MY
MRO Cycle
Earth Day
261.45
6508_01
28
18
2007_172 (21 Jun 07)
275.64
69F5_05
28
19
2007_194 (13 Jul 07)
285.85
6D6E_03
28
20
2007_210 (29 Jul 07)
296.49
7256_03
28
22
2007_228 (16 Aug 07)
311.67
79AA_01
28
23
2007_253 (10 Sep 07)
318.79
7D81_01
28
24
2007_266 (23 Sep 07)
324.60
8040_01
28
25
2007_276 (3 Oct 07)
333.67
850B_01
28
26
2007_293 (20 Oct 07)
337.0
86FC_01
28
27
2007_299 (26 Oct 07)
Table A .
A2 Locations and observation dates of the spectra shown in
AcknowledgementsWe would like to thank the entire CRISM Team, particularly the Science Operations team at JHU APL. We also thank Ted Roush for supplying the palagonite optical constants and Franck Marchis and Peter Jenniskens and referees Yves Langevin and Francois Forget for helpful comments on the
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| sample_936 | 0.984 | arxiv | |
Hasselmann's Program and Beyond: New Theoretical Tools for Understanding the Climate Crisis
Valerio Lucarini
Mickaël D Chekroun
Department of Mathematics and Statistics
Centre for the Mathematics of Planet Earth
University of Reading
RG6 6AXReadingUK
Department of Earth and Planetary Sciences
University of Reading
RG6 6AXReadingUK
Department of Atmospheric and Oceanic Sciences
Weizmann Institute of Science
76100RehovotIsrael
University of California
90095-1565Los AngelesCAUSA
Hasselmann's Program and Beyond: New Theoretical Tools for Understanding the Climate Crisis
(Dated: March 22, 2023)
Klaus Hasselmann's revolutionary intuition was to take advantage of the stochasticity associated with fast weather processes to probe the slow dynamics of the climate system. This has led to fundamentally new ways to study the response of climate models to perturbations, and to perform detection and attribution for climate change signals. Hasselmann's program has been extremely influential in climate science and beyond. We first summarise the main aspects of such a program using modern concepts and tools of statistical physics and applied mathematics. We then provide an overview of some promising scientific perspectives that might better clarify the science behind the climate crisis and that stem from Hasselmann's ideas. We show how to perform rigorous model reduction by constructing parametrizations in systems that do not necessarily feature a timescale separation between unresolved and resolved processes. We propose a general framework for explaining the relationship between climate variability and climate change, and for performing climate change projections. This leads us seamlessly to explain some key general aspects of climatic tipping points. Finally, we show that response theory provides a solid framework supporting optimal fingerprinting methods for detection and attribution. FIG. 1: A Mitchell's diagram [3] depicting a qualitative representation of the climate variability across a vast range of scales, with indication of the relative role of each climatic subcomponent, and indication, on top, of the acting forcings. From [5].
I. INTRODUCTION
The climate is a complex and complicated system comprising of five subsystems -the atmosphere, the hydrosphere, the cryosphere, the biosphere, and the land surface -which differ for physical-chemical features, dominants dynamical processes, and characteristic time scales. Such subsystems are coupled through a complex array of processes of exchange of mass, momentum, and energy [1, 2]. The climate system is multiscale as it features variability over a vast range of scales, as a result of the interplay of a very diverse array of forcings, instabilities, and feedbacks [3,4], with different subsystems playing the dominant role in different considered temporal (and spatial) ranges [5]; see Fig. 1. Major knowledge gaps on the climate system comes from the lack of homogeneous, highresolution, and coherent observations, because of a) the sheer size and practical accessibility of the climate subdomains, b) changes in the technology of data collection in the industrial era, and c) the need to resort to proxy (hence, indirect) data for the pre-industrial epoch. Thus, it is extremely challenging to construct satisfactory theories of climate dynamics and is virtually impossible to develop numerical models able to describe accurately climatic processes over all scales. Typically, different classes of models and different phenomenological theories have been and are still being developed by focusing on specific scales of motion and specific processes [6].
As a result of the presence of unsteady external forcings and of a very nontrivial internal multiscale dynamics, and of the fact that we experience only one realization of the state of the climate, it is hard to clearly separate climate variability from any climate change signal [7]. As documented in successive assessment reports of the Intergovernmental Panel for Climate Change the scientific community has painstakingly come to an agreement regarding 1) the presence of a statistically significant climate change signal with respect to the conditions prevailing in the XIX century; and 2) the possibility of attributing such a signal to anthropogenic causes. The detection and attribution of the climate change signal to specific forcings (anthropogenic or otherwise) requires being able to compare the state of the climate system with the outputs of carefully devised model simulation, taking into account the unavoidable uncertainty due to natural variability and model error [8].
In the course of the years, the research focus has progressively shifted from making statements on globally averaged climatic quantities, to assessing climate change at regional level, to studying the changes in the higher statistical moments and in extreme events, and to investigating how the climate change can manifest itself in the form of critical transitions. The current focus on the study of extremes [9] and critical phenomena (often referred to as tipping points [10,11]) has led the scientific community to use expressions like climate crisis or climate emergency instead of climate change [12]
I.1. A Brief Summary of Hasselmann's Program
In the latter part of the XX century, Hasselmann proposed a coherent scientific angle on the climate system, with the goal of understanding climate variability, of detecting and interpreting the climate change signal, and of characterizing the behaviour of climate models. A very informative summary of the so-called Hasselmann program, of some of its key developments in climate science, and of some of its implications for mathematics and physics at large is given in [13]. We discuss below three main axes of Hasselmann's program.
I.1.1. Stochastic Climate Models
The starting point of this journey comes with the seminal work [14], where Hasselmann proposed to seek for improvement of the modeling of slow climate variables by parameterizing the influence of fast weather variables by means of an appropriate stochastic forcing. At the core of this Hasselmann's stochastic program, lies thus the derivation of an effective model with improved capability to capture the dynamics and the statistical properties of the slow variables. Following [15], we assume that our climate model writes as the following large-dimensional system of ordinary differential equationṡ x = f (x, y), x slow climate variables, y = 1 δ g(x, y), y fast weather variables,
where x (resp. y) lies in R d (resp. R D ), and f (resp. g) is a smooth mapping from R d+D into R d (resp. R D ). The parameter δ is aimed at describing the existence of a tentative time scale separation between the dynamics of the two sets of variables, hence typically one assumes 0 < δ 1. In mathematical language, the Hasselmann's program consists of deriving in the δ → 0 limit, an effective reduced equation of Eq. (1) to approximate the statistical behavior of the climate variables. When y follows some fast chaotic dynamics, the latter is known to take the form of the following system of Itô stochastic differential equations (SDEs),
dx = F(x) dt + Σ(x) dW t .(2)
The derivation of such a limiting SDE in the presence of infinite timescale separation has a long history [16][17][18][19][20] and may be obtained through diverse routes pertaining to homogenization [19], averaging [21], or singular perturbation techniques [22,23]. The MTV approach [18,24] building up on such techniques provides a modern treatment of the topic in the context of climate dynamics, including rigorous results when nonlinear self-interactions between e.g. the fast waves can be modeled by means of Ornstein-Uhlenbeck processes.
The terms F and Σ in Eq.
(2) have then intuitive interpretations. Typically, the deterministic component F (also called drift term) provides the average contribution of f (x, y) to the dynamics of the slow variables, after averaging out the fast variables [17]. The second term, is aimed at parameterizing the effects of the fluctuations left over due to averaging, and takes the form of a state-dependent noise, in which the d × pmatrix Σ with (possible) nonlinear entries in x, is driven a vector of increments dW t (white noise) of a p-dimensional Wiener process W t . Physically, getting to the limit (2) allows for interpreting the fast weather dynamics as inducing a diffusion process. As such, the understanding of the complex nonlinear interactions of e.g. unstable modes with (possibly deep) stable ones [25], at the core of the chaotic nature of many geophysical flows [26][27][28] is replaced by the understanding of the interactions between noise and nonlinear effects [29][30][31].
As appealing are such attributes, the infinite timescale separation assumption underlying Eq. (2) is often challenged in climate applications and we discuss below how to amend Hasselmann's program in such situations, either by seeking for natural extensions to Eq. (2) (Sec. II.1), or stochastic alternatives (Sec. II.3). In the climate system, there is actually a multiplicity of spatio-temporal scales interacting across a wealth of processes (Fig. 1) and the Hasselmann ansatz, whilst indeed inspiring, calls for its revision.
In any event, because the impact of unresolved scales of motion on the scales of interest cannot be approximately reproduced by using bulk formulas (contributing to the drift term) only. This is the fundamental motivation behind the development of stochastic parametrizations for weather and climate models, some of which used in operational situations [32,33].
An important implication of Hasselmann's approach though is the provision of a probabilistic interpretation of climate dynamics, going beyond the study of individual trajectories. Indeed, the SDE (2) can then be translated into a Fokker-Planck equation (FPE) providing the probability distribution of the climate's states, ρ(x, t), according to
∂ t ρ = L 0 ρ = −∇ · (F(x)ρ) + 1 2 ∇ · ∇ ΣΣ T (x)ρ . (3)
In practice, ρ(x, t) is constructed using an ensemble of trajectories; see [34] for a recent summary of the use of ensembles in climate modeling. ΣΣ T is the non-negative definite noise covariance matrix. The unperturbed climate is then given by the stationary solution ρ 0 (x) to the FPE defined by L 0 ρ 0 = −∇ · Fρ 0 + 1 2 ∇ · ∇ ΣΣ T ρ 0 = 0 When the noise term in Eq. (2) is sufficiently nondegenerate, i.e. when, roughly speaking, the noise propagates out in the whole phase space through interactions with the nonlinear terms, the probability density ρ 0 is smooth; see e.g. [35,Appendix A.2]. In contrast, when Σ = 0, Eq. (3) becomes the Liouville equation and, in the case of dissipative chaotic systems, the probability distribution ρ 0 is typically singular with respect to the Lebesgue volume in R d [36].
Assuming that dxρ 0 (x) = 1, the reference climatological mean for a general observable Ψ is Ψ 0 = dxρ 0 (x)Ψ(x). The function Ψ could be any quantity of climatic interest, corresponding to local properties described at a specific grid point, or spatially averaged ones. It makes sense to associated possible Ψ's with essential climate variables (ECVs), which are key physical, chemical, or biological variables that critically contribute to the characterization of Earth's climate and are targeted for observations [37], or the quantities used for defining performance metrics for Earth System Models [38]. This viewpoint allows for casting the problem of climate change as the response of the system's probability distribution or in the statistics of the Ψ's to (possibly time-dependent) perturbations to the drift term or the noise law in Eq. (2) [6,39].
I.1.2. Climate Response to Forcings
A second landmark of the Hasselmann research program deals with the study of the response of climate models to perturbations. Aiming at studying how a climate model relaxes to steady state conditions or responds to perturbations, like a sudden CO 2 increase, Hasselmann and collaborators heuristically proposed a methodology inspired by the dynamics of linear systems [40,41]. They showed that one can express the variation δΨ(t) describing the departure of the model from steady state conditions (or convergence to it) by performing the convolution of a suitably defined causal Green's function G Ψ (t) with the time modulation of the acting perturbation f (s):
δΨ(t) = dsG Ψ (t − s)f (s),(4)
where Ψ describes a climate variable of interest. This amounts to treating the problem of climate change using response theory. Leith pioneered this angle [42] by proposing the use of the fluctuation-dissipation theorem (FDT) [43] for expressing the Green's functions in terms of readily accessible correlations of climatic observables in the unperturbed state. Additionally, Hasselmann and collaborators expressed the Green's function G Ψ as a sum of exponential terms:
G Ψ (t) = k α k Ψ exp(λ Ψ k t),(5)
where each of the λ k encode an acting feedback and can be deduced from the properties of the linear system describing the dynamics. The Green's function-based method was shown to have good skill in performing climate change projections for individual model runs, after filtering the natural variability [41] and for studying the carbon cycle in a climate model [40].
I.1.3. Detection and Attribution of Climate Change
Using stochastic climate models one can make statements on climate change in terms of probability distributions, averages, and higher statistical moments, whereas we live in a single realization of the process. Separating climate variability and climate change in the course of such a single realization is clearly a hard task. Additionally, since we cannot run the climate experiment again, it is even harder to attribute climate change to any specific forcing. In the '90s Hasselmann and collaborators proposed the basic conceptual framework for performing detection and attribution studies of climate change. [44][45][46]. This has played a major role in clarifying that we are presently experiencing a statistically relevant and physically attributable shift from previous climatic conditions [47]. Following [48], the problem can be cast as follows:
Y k = M p=1X p k β p + R kX p k = X p k + Q p k(6)
with k = 1, . . . , N hereby a vector describing the observed climate change with components Y k modelled as a linear combination of M regressors or fingerprints, i.e. externally forced signalsX p k associated with M different forcing, plus a vector describing the natural variability of the system [44-46, 49, 50]. The p th fingerprintX p k is obtained from several climate models runs, all targeted to the p th considered forcing, e.g. by performing ensemble averaging. Hence, what we can practically have access to is its approximation X p k , whereby the difference Q p k with respect to the true value is associated with our incomplete sampling of the model response and with model error. In many applications, information coming from different climate models is bundled together [51].
The goal is to perform an optimal inference of the coefficients β p given the uncertainties described by R k and Q p k , hence the expression optimal fingerprinting. Usually the vectors column errors R k and Q p k , are modelled as independent, normally distributed stochastic vectors with zero mean and covariance matrices C and Ω p , respectively. The matrix C is constructed taking into account the correlations of the climatic variables in the unperturbed climate. A simpler version of the theory above assumes Ω p = 0 for all p [49]. In this case, via linear algebra one derives a relatively simple expression for the best estimates for the β's along with their uncertainties. As a next step, if one assumes that the natural variability simulated by the climate models matches that of the observations and one estimatesX p k as the average of L runs from a single climate model under the p th forcing, then, under the approximation above, one gets Ω p = C/L [50].
One speaks of detection of climate change for the p th fingerprint is the confidence interval of β p does not intersect zero and includes positive values, and attribution of climate change if such confidence interval includes the value one. The procedure is truly successful if the confidence intervals for the β p 's are not too spread out. Optimal fingerprinting relies critically on the implicit linear dependence of the response to forcing. Additionally, the method, despite its great success, has recently been criticised as it has been suggested that uncertainties in the inference are sometimes underestimated [52], or, more radically, on the basis that the statistical foundation of the procedure are not very solid [53]; see also discussion in [54]. In Sec. III below, we describe how the Hasselmann's optimal fingerprinting method benefits of new insights when reframed within the response theory of dynamical systems.
I.2. This Review
Our goal here is to give a critical appraisal of the Hasselmann programme based on some ideas and concepts that have emerged in statistical mechanics and functional analysis, for the most part, in the last two decades. We also propose a comprehensive framework for understanding the multiscale nature of climate variability and climate response to forcing and for fundamentally advancing our understanding of the ongoing climate crisis. This paper is structured as follows.
Section II is devoted to exploring possible avenues to devise rigorous theory-informed and effective data-driven model reduction strategies and to highlight connections and integration between between the top-down and bottom-up approaches, in order to relax the assumption of infinite time-scale separation discussed in Sect. I.1.1. There, we show how to relax the assumptions of (strong) time-scale separation between the variables of interest and those we want to parametrize. Reduced order modelling is inextricably associated with performing partial observations, i.e. gaining only a partial, imperfect knowledge of the properties of a system. As clarified by the Mori-Zwanzig (MZ) formalism [55,56], the effective dynamics defining the evolution on the projected space of the variables of interest Markovian deterministic, stochastic, and non-Markovian components even if the dynamics of the whole system is purely deterministic; see e.g. [57,58]. Based on recent results from the literature, accounting for possibly the usage of neural parameterizations, we clarify physical situations in which the role of memory effects is secondary compared to that played by the conditional expectation and stochastic effects due to the unobserved variables in the reduced model. For the sake of completeness, we also review the different approaches for approximating the memory effects, and clarify the challenges posed by situations in which the time-scale separation between the resolved and unresolved variables is weak. In Sect. III we show how response theory for nonequilibrium systems [59][60][61][62][63][64][65] allows one to find explicit formulas and to devise clear experimental protocols aimed at computing such time-varying statistics, hence allowing for performing climate change projections using climate models of different levels of complexity [66][67][68][69]. Hence, we shed light of some of the key aspects discussed in Sect. I.1.2. We show that the use of a formalism based on Green's functions does not requires assuming linearity of the model, but just to linearize the properties of the model around it steady state, but requires considering ensemble averages. Taking advantage of the Koopman operator formalism [70][71][72], we show that it is indeed possible to write any Green's function as a weighted sum of exponentials, and we carefully explain the meaning of the weights and of the decay rates. This angle also facilitates understanding the basic properties of tipping points, and associating their presence to the divergence of the response operators [35,65,73]. In Sect. IV we show how the linear response formalism developed in Sect. III provides the mathematical and physical backbone behind the optimal fingerprinting method for detection and attribution of the climate change signal presented in Sect. I.1.3. Additionally, our angle allows one to better appreciate the approximations taken in the practice of detection and attribution studies (especially regarding the definition of the error terms), clarify some fundamental issues associated with the use of mixtures of different climate models in the definition of the fingerprints, and elucidate why the fitting strategy might fail in the proximity of tipping points. This allows to convincingly prove the strong link between the three main axes of Hasselmann's research programme. In Sect. V we present our conclusions and perspectives for future work.
II. THEORY-GUIDED AND DATA-DRIVEN MODEL REDUCTION
II.1. Mori-Zwanzig decomposition from perturbation theory of the Koopman semigroup
We consider a dynamical systeṁ
X = F (X), X ∈ R N , N 1.(7)
Denoting by X x t the solution to Eq. (7) emanating from x in R N at t = 0, we assume that Eq. (7) possesses a stationary statistical equilibrium µ (invariant probability measure) that satisfies
lim T →∞ 1 T T 0 ϕ(X x t ) dt = ϕ(X) dµ(X),(8)
for almost every x (in the Lebesgue sense) that lies in the basin of attraction of µ, for any sufficiently smooth observable ϕ.
In general ϕ is a field quantity which represents perturbations of, e.g., density, pressure, electrostatic potential, etc. Note that when a global attractor exists, a statistical equilibrium µ satisfying (8) is supported by the global attractor; see e.g. [74]. Given an observable ϕ : R N → R, recall that the evolution of this observable along the flow associated with Eq. (7) is given by the Koopman semigroup, K t , defined as
[71] K t ϕ(x) = ϕ(X x t ) that satisfies the Liouville equation ∂ t K t ϕ = LK t ϕ with Lϕ = N j=1 F j (x)∂ j ϕ, denoting
the Lie derivative along the vector field F .
We are now given decomposition X = (a, b) in which a denotes p relevant variables (those resolved, typically), while b denotes the q = N − p neglected ones. We are interested in describing the evolution of any (sufficiently smooth) observable v of the variable a without having to resolve the b-equation in Eq. (7). In climate dynamics, this is motivated for instance by predicting/simulating a scalar field of interest (e.g. temperature, pression) over a coarse grid without having to resolve the subgrid processes (closure problem). In operator form, this operation consisting of parameterizing the coefficients depending of b in the transport equation
∂ t v = p j=1 F j (a x t , b x t )∂ j v,(9)
This partial differential equation (PDE) describes how the observable v depending on the a-variable only (coarse variable) is advected by the flow of Eq. (7) (accounting for the interactions with the subgrid variables b); it is obtained by observing that ∂ t v(a x t ) = ∇v · ∂ t a x t . To address this closure problem we introduce the conditional expectation operator
P Ψ (a) = Ψ(a, b) dµ a (b) = Ψ,(10)
in which µ a denotes the disintegration of the invariant probability measure µ [75, Theorem 5.3.1]; roughly speaking it gives the distribution of the b-variable on the attractor when the coarse-variable is frozen to a. The operator P corresponds thus to an averaging with respect to the neglected variable b as conditioned on a. Note that µ a = µ a for a = a for complex systems causing the variable b not to be identically and independently distributed (i.e. not i.i.d.). Now, by rewriting the transport equation (9)
as ∂ t (K t v) = K t Mv with M = p j=1 F j ∂ j , we have that ∂ t (K t v) = K t P Mv + K t (Mv − P Mv).(11)
Here, P M = p j=1 F j (a)∂ j denotes the averaged advection operator with respect to the neglected, "fast," variable b.
In Eq. (11), the operator,
M − P M = p j=1 F j (a, b) − F j (a) ∂ j ,
accounts for the fluctuations with respect to the conditional average and Kt(Mv − P Mv) informs thus on how these fluctuations are transported by the flow of Eq. (7). Hence, the operator δf = (Id − P )Mf = QMf encodes the fluctuations terms. It defines a fluctuation semigroup e tδ that is very useful to close Eq. (9). This can be accomplished by application of the perturbation theory of semigroups, in the Miyadera-Voigt variation-of-constants formulation [76,77], to the Koopman and fluctuation semigroups; see [78,Sec. 3.c] for a rigorous treatment.
The Miyadera-Voigt perturbation theorem gives then that
Ktf = e tδ f + t 0 K t−s P Me sδ f ds,(12)
for any observable f for which δf is well defined. Note that P e tδ f = 0 if P f = 0, i.e. the orthogonal complement of P , is invariant under e tδ . Note that the fluctuation semigroup e tδ gives the solution of the orthogonal dynamics equation
∂te tδ f = QMe tδ f.(13)
We refer to [79] for the study of existence of solutions to Eq. (13). Now let us take f = Mv −P Mv = QMv in (12) and observe that P f = 0. Then Eq. (11) becomes:
∂tKtv = KtP Mv + e tδ f + t 0 K t−s P Me sδ f ds = KtP Mv + t 0 K t−s Γ(s)v ds + η(t)v,(14)
with η(t)v = e tδ QMv denoting the orthogonal element of the MZ decomposition (since P QMv = 0 implying that η(t)v lies in ker(P )), while Γ(s) defines the operator Γ(s) = P Mη(s)
Box 1: Derivation of the GLE
By performing the change of variable s ← t − s in the integral term of Eq. (14) in Box 1, we arrive finally at the following equivalent formulation of Eq. (14)
∂ t v(a x t ) = P Mv(a x t ) + t 0 Γ(t − s)v(a x s ) ds + [η(t)v](x),(15)
which gives the desired closure of Eq. (9).
Eq. (15) is the Generalized Langevin Equation (GLE) [80] or the Mori-Zwanzig (MZ) decomposition. The effective dynamics defining the evolution of any observable of the reduced state space can be achieved by determining the Markovian, stochastic, and non-Markovian components appearing in Eq. (15) making the GLE, the fundamental equation to determine in the Mori-Zwanzig approach to closure [55][56][57][58]81]. As we clarify below, not all the terms are needed though in this triptych decomposition depending on the situations. In any event, MZ decompositions have attracted a lot of attention in the last two decades as a promising description for reduced modeling of coarse-grained variables [58,81,82], in many areas such as molecular dynamics [83][84][85], climate dynamics [86][87][88][89][90][91][92][93][94], or fluid problems [95][96][97][98] to name a few.
In Eq. (15), the kernel Γ(t − s) is typically a time-lagged damping kernel and η(t) is interpreted as an effective random forcing uncorrelated with the time-evolution of the resolved variable, a x t , but can be strongly correlated in time; see Sec. II.3 below. In the slow-fast system metaphor, the Markovian term P M provides the slow component of the dynamics, η(t) is void of slow oscillations, while Γ is supposed to account for the disparate interactions between the timescales.
As elegant it may be, the MZ decomposition is a technically challenging solution to the closure problem of disparate scale interactions and various assumptions about the memory kernel Γ are typically made to propose approximations to the GLE.
The memory kernel Γ and the "noise" operator η(t) involve the implicit knowledge of the fluctuation semigroup e sδ , accounting for the effects of the neglected variables on the fluctuations with respect to the average slow motion. This operator is difficult to resolve as it boils down of solving the orthogonal dynamics equation Eq. (13) [99].
The noise and memory terms can be extremely complicated to calculate, especially in cases with weak or no obvious timescale separation between the resolved and unresolved variables. The approximation of these terms constitutes thus the main theme of most research on the MZ decomposition.
Many techniques have been proposed to address this problem in practice and can be grouped in two categories: (i) datadriven methods, and (ii) methods based on analytical insights tied to the very derivation of the MZ decomposition. Datadriven methods aim at recovering the MZ memory integral and fluctuation terms based on data, by exploiting sample trajectories of the full system. Data-driven methods can yield accurate results, but they often require a large number of sample trajectories to faithfully capture memory effects [100][101][102][103]. Typical examples include the NARMAX (nonlinear auto-regression moving average with exogenous input) technique developed by [104][105][106], the rational function approximation proposed in [101], the conditional expectation techniques of [103], and methods based on Markovian approximations by means of surrogate hidden variables [87,90,101].
Methods based on analytical considerations aim at approximating the MZ memory integral and fluctuation terms based on the original equations, without using any simulation data. The first effective method developed within this class can be traced back to the continued fraction expansion of Mori [107], which can be conveniently formulated in terms of recurrence relations [108,109]; see also [110]. Other analytical methods to compute the memory and fluctuations terms in the MZ decomposition include optimal prediction methods [111][112][113], mode coupling techniques [114,115], methods based on approximations of the orthogonal equations [116], matrix function methods [84], series expansion methods [95,96,[117][118][119], perturbation methods [120], and methods based on Ruelle's response theory [88,121]. These analytically grounded methods can lead to the effective calculations of the non-Markovian effects in various applications such as e.g. in coarse-grained particle simulations [82,122] or some fluid problems [95,96], including intermediate complexity climate models [123]. However, these calculations are often quite involved and they do not generalize well to systems with no scale separation [58]; see, instead, an example of scale adaptivity in [124].
In fact to better appreciate the difficulty posed by the lack of timescale separation it is useful to recall that for instance longrange memory approximation consisting of keeping the zeroth order term in a Taylor expansion of the memory integrand in Eq. (15) allows for simplifying significantly the memory term calculation, but at the price of restrictive conditions. Indeed, such a long-range approximation shows relevance if the unresolved modes exhibit sufficiently slow decay of correlations (tmodel [112,125]), essentially by assuming information about initial value to be sufficient to make predictions. Assuming the unresolved modes to have fast decay of correlations, one is left with short-range memory approximation schemes. As was shown in [112], the two cases, of extreme or very weak nonlocality in time, are the two sides of the same coin. Most of the challenging cases for closure lies thus in the intermediate cases [113], for which there is no neat separation of timescales such as populating climate science [6].
Keeping higher-order terms in the Taylor expansion of the memory integrand is a natural way to handle cases of weak timescale separation. It is illuminating in many ways, including to design data-driven methods, as explained below. This higher-order approximation approach of the memory integrand has been retained by Stinis in [99] and further developed and analyzed by Zhu et al. in [118]. The approach consists of breaking down the memory approximation problem into a hierarchy of auxiliary Markovian equations.
Denoting by m 0 (t) the integral term in Eq. (15), such a Markovian approximation is accomplished by observing that m 0 (t) = t 0 K s P Me (t−s)QM QM satisfies the following infinite-dimensional system of PDEs [99,118]
dm n−1 dt = K t P M(QM) n v + m n (t), n = 1, . . . . (16)
Integrating Eq. (16) backward, i.e., from the "last" equation to the first one, to obtain a Dyson series representation of m 0 (t) involving repeated integrals [118]. In practice, one performs a truncation of Eq. (16), which consists of keeping the first n equations, while closing the last equation by using an ansatz in place of m n (t), such as m n (t) = 0 [99] or m n (t) given by Chorin's t-model; see [118] for other choices. Depending on the the order of truncation retained and the corresponding choice of the ansatz for m n , error estimates with respect to the genuine memory integral in Eq. (15) are available [118].
The implementation of such Markovian schemes is however not trivial to conduct as it requires computing (QM) n to a high-order in n, a delicate operation to accomplish especially when the original system is large, recalling that QM is the generator of the orthogonal equation (13). Nevertheless, the layered structure of Eq. (16) and related error estimates provide a strong basis for the design of datadriven methods based on Markovianization ideas to approximate the memory integral term. We mention that such ideas are commonly used for the mathematical analysis of physical models involving integro-differential equations; see e.g. [126,127] and references therein.
Although not aware of such theoretical foundations not even with the connection with the MZ-decomposition pointed out only later on in [90], the data-driven approach proposed initially by Kravtsov et al. in [128] is intimately related to such Markovianization ideas. The class of data-driven models of [128] involves also mulitlayered SDEs of a structure very similar to that of Eq. (16) that has been generalized in [90] to handle the approximation of more complex memory kernels, from a data-driven perspective. The usage of such mulitlayered SDEs to provide approximation of the GLE is further discussed in Sec. II.2 below.
Efforts to approximate the memory and noise terms should not, however, make us lose sight of another key problem, namely the problem of approximating the conditional expectation, namely the Markovian terms in Eq. (15). This is where recent hybrid approaches exploiting the original equations and simulated data have shown relevance.
In that respect, the data-informed and theory-guided variational approach introduced in [129] allows indeed for computing approximations of the conditional expectation term, P M, by relying on the concept of the optimal parameterizing manifold (OPM) [129,Theorem 5]. The OPM is the manifold that averages out optimally the neglected variables as conditioned on the resolved ones [129,Theorem 4]. The approach to determine OPMs consists at first deriving analytic parametric formulas that match rigorous leading approximations of unstable/center manifolds or slow manifolds near e.g. the onset of instability, and then to perform a data-driven optimization of the manifold formulas' parameters to handle regimes further away from that instability onset [129,Sec. 4]. There, the optimization stage allows for alleviating the small denominator problems rooted in small spectral gaps, and derive thereby meaningful parameterizations in regimes where constraining spectral gap or timescale separation conditions are responsible for the well-known failure of standard invariant/inertial or slow manifolds.
For multiscale dynamics, failure in resolving accurately the conditional expectation results typically into a residual that contains too many spurious frequencies to be efficiently resolved by data-driven methods based e.g. on the aforementioned multilayered SDEs, the latter exploiting either polynomial libraries of functions or other specified interaction laws [90] between the resolved and unresolved variables.
Lately, much efforts relying on machine learning (ML) techniques have been devoted for the learning of memory terms in MZ-decompositions [98,130,131]. These go beyond prior efforts involving polynomial libraries of specific interaction laws between the slow and fast variables [88,90,128]. However, these recent ML works advocate too often an excessive usage of complex neural architectures that hide the simple structures at work for an efficient design of the noise terms, obstructing physical interpretations as the examples discussed below show.
II.2. Variational approach to closure
In the context of subgrid parameterizations, nonlocality in time in the GLE (15) means that the subgrid variables exert reactive as well as resistive forces on the resolved variables, and as noted in [132] this may play an important role in reproducing finite-amplitude instabilities and other properties of these variables. Actually, such a situation is expected to occur in presence of a lack of clean separation between explicit and subgrid variables. In this case, the latter variables exert fluctuating driving forces on the explicit variables which are conceptually distinct from eddy viscosity (or even negative eddy viscosity) [133].
We assume thus that F in Eq. (7) proceeds from a forced fluid model, i.e. that F (X) = LX + B(X, X) + f with B denoting a bilinear operator, L a linear operator, and f a force. We are interested in finding an accurate closure in the slow/coarse-scale a-variable. To achieve this goal, the parameterization of the a-b and b-b interaction-terms in the original a-equation, i.e. the terms accounting for the disparatescale and fast-scale interactions, is the key issue. Denoting by τ int the grouping of these interaction terms, a convenient way to address this problem is by seeking for τ opt that solves the minimization problem
min τ T 0 τ (a(t)) − τ int (a(t), b(t)) 2 dt, T 1. (17)
The optimal parameterization, τ opt , relates naturally to the conditional expectation of F given by (10) as τ opt (a) = F minus the linear and a-a interaction terms that project onto the coarse-scale variables. The aforementioned OPM, Φ opt , providing the best approximation in a least-square sense of b as a mapping of a, satisfies then that τ int (a, Φ opt (a)) ≈ τ opt (a), with a small residual error when the b-b interaction terms are negligible after averaging in the original a-equation (such as [18, Assump. A4]); see [129,Theorem 5]. At this stage, knowing τ opt or Φ opt allows us thus to approximate the average motion of a(t) when averaging is performed over the "fast" variable b(t).
If one wants to recover beyond averaging, the effects of the (fast) fluctuations onto the dynamics of a(t), then the MZ formalism recalled in Sec. II.1 invites us to revise the minimization problem (17) into solving the following one
min τ ,Γ T 0 τ (a(t)) + t 0 Γ(t − s)τ (a(s)) ds − τ int (a(t), b(t)) 2 dt, T 1.(18)
Solving this second minimization problem consists thus of decomposing the nonlinear interaction term to account for a memory function and a fluctuating force, namely τ int (a(t), b(t)) ≈τ (a(t))
+ t 0 Γ(t − s)τ (a(s)) ds + f (t).(19)
The minimization of (18) can be addressed by means of recurrent neural networks such as long short-term memory NNs [98,130,131], but their constitutive elements suffer from interpretability and do not easily allow for anticipating the need of memory and/or noise terms. Another approach consists of pursuing the minimization of (18) via Markovianization which consists of breaking down the memory terms and noise terms by means of SDEs with a multilayer structure (similar to Eq. (16)) whose coefficients are learned successively via recursive regressions using surrogate, stochastic, variables that account for the residual errors produced by the successive regressions until a white noise limit is reached [87,90]. This data-driven approach [128] has led to striking results in many fields of applications such as for the modeling of El-Niño-Southern Oscillation (ENSO) [134][135][136], extratropical atmospheric dynamics [137], paleoclimate [92], or the Madden-Julian Oscillation [138] to name a few.
These regression-based multilayered SDEs to approximate the MZ decomposition Eq. (15) benefit furthermore from useful theoretical insights. Indeed, intimate connections with the multilayered SDEs derived in [88,121] based on Ruelle's response theory [139], were shown to hold for a sub-class of multilayered SDEs considered in [87,90]; see [139]. These connections allow in particular for clarifying circumstances of success for multilayered SDEs with linear coupling terms between the layers corresponding to approximating the memory integrand Γ in Eq. (15) by repeated convolutions of exponentially decaying kernels [90]. The multilayered SDEs of this form were shown to be particularly relevant for weakly coupled slow-fast systems and the corresponding memory and noise terms were shown to relate naturally to the Koopman eigen-elements of the "unperturbed weather" Koopman semigroup K w t whose generator is G j (b)∂ j when g(a, b) = G(b) + C(a, b) in Eq. (1) with small; see [139, Theorem 2.1]. The approximation of the MZ decomposition Eq. (15) via Markovianization sheds thus new lights onto Koopman modes [71] and related dynamic mode decomposition (DMD), widely praised in fluid dynamics over the last decade [72,140,141], and as such with the Principal Oscillation Pattern modal proposed earlier in atmospheric sciences by Hasselmann [142,143].
However as mentioned earlier, it is not always required, depending on the problem, to determine the memory and/or noise terms, and we should thus always look first for the virtue of solving the minimization problem (17) in the first place instead of solving the more challenging minimization problem (19) (see Sec. II.4 below), which may involve memory or noise terms of negligible importance for closure.
An emblematic example is found the context of the Primitive Equations of the atmosphere, it is known that at low Rossby number, the conditional expectation coinciding with the Balance Equation is amply sufficient for an accurate closure [144]. However, once a critical Rossby number is crossed, the Balance Equation needs to be seriously amended to capture the complex interactions between the Rossby waves and inertia gravity waves; the latter becoming non-negligible at large Rossby number. The next section reviews such a physical example. rich of teachings in terms of MZ-decomposition.
II.3. The atmospheric Lorenz 1980 model: Markovian and noise terms but no memory
Atmospheric and oceanic flows constrained by Earth's rotation satisfy an approximately geostrophic momentum balance on larger scales, associated with slow evolution on time scales of days, but they also exhibit fast inertia-gravity wave oscillations. The problems of identifying the slow component (e.g., for weather forecast initialization [147][148][149][150]) and of characterizing slow-fast interactions are central to geophysical fluid dynamics. The former was first coined as a slow manifold problem by Leith [151]. The Lorenz 63 model [152] famous for its chaotic strange attractor is a paradigm for the geostrophic component, while the Lorenz 80 (L80) model [145] is its paradigmatic successor both for the generalization of slow balance and for slow-fast coupling.
The L80 model, obtained as a nine-dimensional truncation of the PE onto three Fourier modes with low wavenumbers [145], can be written as [153]:
a i dx i dt = a i b i x j x k − c(a i − a k )x j y k − c 2 y j y k + c(a i − a j )y j x k − N 0 a 2 i x i + −2 a i (y i − z i ), a i dy i dt = − a k b k x j y k − a j b j y j x k + c(a k − a j )y j y k − a i x i − N 0 a 2 i y i , dx i dt = − b k x j (z k − H k ) − b j (z j − H j )x k + cy j (z k − H k ) − c(z j − H j )y k + g 0 a i x i − K 0 a i z i + F i .
The variables (x, y, z) are amplitudes for the divergent velocity potential, streamfunction, and dynamic height, respectively. Transitions to chaos occurs as the Rossby number is increased; see [153,154].
At small , the solutions to the L80 model remain entirely slow for all time (i.e. dominated by Rossby waves) whereas spontaneous emergences of fast oscillations get superimpose to such slow solutions as the Rossby number is further increased. In such regimes, the balance equation (BE) manifold on which lie balanced solutions [154,155] is no longer able to encode the dynamics (see schematic), as the L80 dynamics associated inertia gravity waves (IGWs) get transverse to the BE manifold [129,Sec. 3.4]. These regimes with energetic bursts of IGWs lie beyond the parameter range Lorenz initially explored in [145] (see [156]) as well as beyond other regimes with exponential smallness of IGW amplitudes as encountered in the subsequent Lorenz 86 model [157][158][159] and the full PE [160] at smaller Rossby numbers; see [161].
Box 2: The L80 model and bursts of inertia-gravity waves
Contrarily to other slow-fast systems, this physically-based model exhibits regimes with energetic bursts of fast oscillations superimposed on slow ones that complicate greatly their parameterization [153]; see Box 2. Regimes beyond exponential smallness of the fast oscillations are not only intimate to the L80 model. They have been observed in other PE models as conspicuously generated by fronts and jets [162,163], and in cloud-resolving models in which large-scale convectively coupled gravity waves spontaneously develop [164]. Regions of organized convective activity in the tropics generates also gravity waves leading to a spectrum that contains notable contributions from horizontal wavelengths of 10 km through to scales beyond 1000 km [165] and such IGWs have been also identified from satellite observation of continental shallow convective cumulus forming organized mesoscale patterns over forests and vegetated areas [166].
The L80 model provides a remarkable metaphor of such regimes with a lack of timescale separation at large Rossby numbers, in which the solutions have slow and fast components (mixture of high and low frequencies (HLF)) exhibited by all the components of the model causing a breakdown of slaving relationships where the fast variables at time t are a function of the slow variables at the same time instant, calling thus for a revision of slow manifold methods [151] and the like.
Only recently, the generic elements for solving such hard closure problems with lack of timescale separation, have been identified [146]. Key to its solution is the Balance Equation (BE) manifold [154,155] as rooted in the works of Monin [167], Charney and Bolin [147,168] and Lorenz [169]. The BE manifold has been shown to provide, even for large Rossby number, the slow trend motion of HLF solutions to the L80 model as it optimally averages out the fast oscillations; nearing this way the OPM, Φ opt , to a high precision [153].
For such regimes, the L80 dynamics evolves onto this manifold and experiences excursions off this manifold, corresponding to bursts of fast oscillations caused by IGWs; see Box 2 and Fig. 2A. The residual off the BE manifold is mainly orthogonal to it, causing the memory terms to be negligible [146] and making the stochastic modeling of the η(t)-term central in the MZ decomposition Eq. (15). An inspection of this residual in the time-domain shows that it is strongly correlated in time, narrowband in frequency and modulated in amplitude (Fig. 2B). Recent progresses in characterizing the spectral signature in terms of Ruelle-Pollicott resonances and Koopman eigenvalues (and the like [91,170]) of such time series [35,171], allow for inferring that such residuals can be efficiently modeled by means of a network of Stuart-Landau oscillators (SLOs) of the forṁ z j = (µ + iω)z j − (α + iβ)z j |z j | 2 + 'coupling terms' + 'white noise'; (20) see Fig. 2C and [146] for more details. The BE manifold operates here a remarkable feast: It provides a nonlinear separation of variables allowing for decomposing the mixed HLF dynamics of the L80 model into a slow component captured by the BE, and a fast one modeled by a network of SLOs. The resulting closure takes then the OPM-SLO form in which Π denotes the projector onto the coarse variables, and ξ t , modeled by means of the auxiliary networks of SLOs (20) allow-through its interactions with the parameterization of the slow motion Φ opt (a) (and the a-variable)-to recover, with a remarkable ability the multiscale dynamics of the L80 model along with its complex bursts of fast oscillations caused by IGWs; see [146, Fig. 7].
da dt = Π(La + B(a + Φ opt (a) + ξ t , a + Φ opt (a) + ξ t )),(21)
In terms of Hasselmann's program, the L80 model is thus rich of teachings. It shows that an efficient modeling of regimes with a lack of timescale separation characterized by a mixture of intertwined slow and fast motions, requires (i) a good approximation of the OPM capturing the slow motion, (ii) to go beyond stochastic homogenization and the like [18] to model the noise; the use of network of SLOs showing a great deal of promises in that respect.
Finally it is worth noting that thinking of the bilinear terms B in Eq. (21) as proceeding from advective terms in the L80 model, one may interpret the nonlinear terms involving ξ t in the stochastic OPM-SLO closure (21) as stochastic advective terms. Other recent approaches have shown the relevance of such terms to derive stochastic formulations of fluid flows as well as for emulating suitably the coarse-grained dynamics [172][173][174].
From a practical viewpoint, the interest of disposing of an accurate stochastic closure such as Eq. (21) lies in its ability of simulating key feature aspects of the multiscale dynamics, offline, in an uncoupled way (here the IGWs) by the network of SLOs (20).
The OPM-SLO approach is thus promising to be further applied to the closure of other more complex slow-fast systems, in strongly coupled regimes. In particular, regimes exhibiting a mixture of fast oscillations superimposed on slower timescales such as displayed by the L80 model provide a challenging ground for closure in more sophisticated fluid problems. Such regimes are known to arise in multilayer shallow water models; see e.g. [175,Fig. 5]. In certain regions of the oceans, it has been shown that IGWs can account for roughly half of the near-surface kinetic energy at scales between 10 and 40 km [176], making IGWs energetic on surprisingly large scales. Thus, geophysical kinetic energy spectra can exhibit a band of wavenumbers within which waves and turbulence are equally energetic [177]. We believe in the ability of the OPM-SLO approach to show closure skills for such problems. There, the approximation of the OPM/conditional expectation should benefit from recent progresses accomplished in neural turbulent closures, as explained below, and the fast component of the motion should also benefit from the wealth of dynamics that networks of SLOs can embody (see Sec. II.5 below).
II.4. Neural turbulent closures: No memory, no noise, but spatially non-local Markovian terms
Much efforts have been devoted lately into the learning of successful neural parameterizations for the closure of fluid models in turbulent regimes such as the forced Navier-Stokes equations or quasi-geostrophic flow models on a β-plane; see e.g. [178][179][180][181][182].
These neural closure results are typically obtained with convolutional neural networks (CNNs) [183] that are by definition non-local in space and aim at parameterizing the sub-grid scale stress (SGS) tensor in terms of coarse-grained variables. Among the achievements accomplished by these neural closures, have been reported their ability to provide accurate closures for cutoffs within the inertial range and for high Reynolds numbers, outperforming more standard schemes such as based on the Smagorinsky parameterizations and the like.
This problem is known to be difficult as small errors at the level of the SGS typically amplify the errors at the large scales due to the inverse cascade [184,185]. To dispose of SGS parameterizations at low cutoff levels for such turbulent flows with a controlled error is thus one of the challenges to resolve. The accuracy and stability of the closure results in [178][179][180][181][182]. are thus strongly supportive for the existence of a nonlinear function τ CN N such that the SGS, τ , satisfies, after spin up, a relation of the form
τ = τ CN N (u, v) + ,(22)
where the residual is a spatio-temporal function whose fluctuations are controlled and small in a mean square sense, while u and v denote the coarse-grained velocity variables. Actually, (22) is a consequence of the very construction of Φ CN N obtained by minimization of loss functions of the form (17) up to some regularization term. In Eq. (22), τ CN N denotes the function found by means of shallow CNNs trained by minimizing a loss function reminiscent to that involved in (18). The relation (22) based on the quality of the closure results reported in [178][179][180][181][182] suggests thus that τ CN N , in the respective cases, is close to the conditional expectation τ [129], namely the best nonlinear functional averaging out the unresolved variables as conditioned on the coarse variables. Thus, finding a good approximation of τ is sufficient for the closure of forced two-dimensional turbulence problems at high Re.
As such, these neural closure results rule out for turbulent problems, even at low cutoffs, the use of memory terms in the Mori-Zwanzig interpretation (Sec. II.1); memory terms that have been thus unecessarily praised in other closure studies relying on the MZ formalism; see e.g. [96,186,187]. Similarily, memory terms have been advocated for the closure of Kuramoto-Sivashinsky turbulence in the reduced state space spanned by the unstable modes [105,187], whereas a good learning of the conditional expectation has been shown to be also amply sufficient for closure in such reduced state spaces, for even more turbulent regimes [129,Sec. 6].
The neural turbulent closure results of [178][179][180][181][182] restore thus some credentials to ideas proposed in the late 80s by [188,189] envisioning two-dimensional turbulence as essentially finite-dimensional with turbulent solutions lying in some thin neighborhood, in a mean square sense, of a finite-dimensional manifold [129,Eq. (1.5)]; ideas that were watered down as shown to be valid, only for cutoff wave numbers within or close to the dissipation range [190] when relying on traditional analytic parameterizations such as initially proposed in [188]. The usage of neural networks shed thus new lights on this old problem as pushing the validity of relationships such as (22) for cutoff within the inertial range.
II.5. The good choice of resolved variables: A baroclinic ocean model example
We should not loose sight that the MZ framework is conditioned to the choice of resolved and neglected variables inherent to that of the reduced state space in which a closure is sought. This is actually a key step in data-driven modeling where one typically compress the original field into a few variables to model. Principal components (PCs) as extracted from an empirical orthogonal function (EOF) decomposition [191,192] are usually used for that purpose as in [93,[134][135][136], but many other decompositions may be used such as nonlinear [193,194] or probabilistic versions [195] of EOFs, spectral versions of EOFs [196] and the like [91,197] or techniques reflecting the the (local) geometry and density of the data [198], to name a few.
Whatever the decomposition method retained one may face the problem of mixture of timescales as encountered in Sec. II.3 for the L80 model, depending on the timescale of interest one wishes to resolve via a reduced model. This is for instance encountered in wind-driven baroclinic quasigeostrophic (QG) models of the ocean on decadal timescales. The ocean circulation of eddy-resolving simulation with ∼ 10 6 spatial degrees of freedom at reference model parameters [199] is characterized by a robust large-scale decadal low-frequency variability (LFV) with a dominant 17-yr cycle, involving coherent meridional shifts of the eastward jet extension separating the gyres; see Fig. 3A. To this decadal variability is superimposed an interannual variability caused by the eddy dynamics; see [97]. Due to this highly turbulent and multiscale nature of the flow, the capture of the eddies' dynamics on a coarse-grid by a reduced model is highly challenging.
Within the reduced state space of (the first few dominant) PCs this challenge is manifested by the multiscale nature of the PCs' temporal evolution; a slow evolution (decadal) contaminated by "fast" interannual oscillations (due to the eddydynamics); see Fig. 3F. Such multiscale features constitute the main cause behind the failure of multilayered SDEs such as those of [87,128] in approximating, here, the memory and noise terms in the MZ-decomposition, in spite of their successes in other geophysical problems as recalled in Sec. II.2. The reason behind lies in the set of predictor functions used for the learning of the multilayered SDEs ingredients, either responsible for an explanatory deficit, or victim of a spectral bias if neural networks are employed [200]. This is where, multivariate signal decomposition methods such as [91,201] offer a precious alternative for remedying to such issues by extracting empirical modes of variability. Indeed, such methods, when effective in separating the slow and fast temporal components of the PCs (or analogues), provide a natural ground for the modeling of these temporal components by means of stochastic SLOs such as in Eq. (20), this time ranked by frequency to be resolved, and introduced as Multiscale Stuart-Landau Models (MLSMs) in [91]. The fact that such MSLMs provide remarkable closure skills for such challenging QG turbulent problems (see [97] and Fig. 3), invites for more studies exploiting MSLMs and signal decomposition methods to tackle the closure of more realistic PE models, as well as for more understanding. The MSLMs being stochastic oscillators, it raises the question whether the original quasiperiodic Landau's view of turbulence [202,203], with the amendment of the inclusion of stochasticity, may be in the end well suited to describe turbulence. First PC of the coarse QG's (resp. the MSLM) upper-ocean PV, and its decadal LFV content shown in red (resp. blue). The MSLM is able to remarkably reproduce the multiscale temporal variability of the QG coarse-grained dynamics.
III. DESCRIBING THE CLIMATE CRISIS VIA RESPONSE THEORY
We can address the problem of quantifying the climatic response to forcings by considering the impact of perturbations on the statistical properties of ensemble of trajectories evolving according to a given SDE. Hence, we consider the following d-dimensional Itô SDE
dx = F(x) + U u=1 ε u 1 g u 1 (t)G u (x) dt + Σ(x) + V v=1 ε v 2 g v 2 (t)Γ v (x) dW t ,(23)
where the unperturbed dynamics is given by Eq.
(2). We consider the case of general time-dependent perturbations acting on either the deterministic component (a parametric modulation of the system) or in the stochastic component (a perturbation to the noise law) associated e.g. with changes in the properties of the unresolved degrees of freedom. The perturbations to the drift term are embodied by the vector fields G u , each modulated by a (scalar) amplitude function g u 1 (t) and a small parameter ε u . The perturbations to the noise term are embodied by the d × p matrices Γ v , whose amplitude are controlled by the functions g v 2 (t) and the small parameters ε v . If one considers a background deterministic dynamics (Σ(x) = 0) and the time-dependent forcing in the drift terms are non-vanishing, finding the solution ρ ε (x, t) of the FPE corresponding to Eq. (23) amounts to studying the properties of the statistical equilibrium supported by the system's pullback attractor [204][205][206][207]. Following [65], let us assume that ρ ε (x, t) can be written as:
ρ ε (x, t) = ρ 0 (x)+ U u=1 ε u 1 ρ u 1,d (x, t)+ V v=1 ε v 2 ρ v 1,s (x, t)+h.o.t.
Such an asymptotic expansion is the starting point of virtually any linear response formulas for statistical mechanical systems; see [208,209] for a discussion of the radius of convergence of the expansion above. The expected value of Ψ at time t is
Ψ ρ t ε = dρ ε (x, t)Ψ(x) = Ψ 0 + δ (1) [Ψ](t) + h.o.t.
where the linear response is:
δ (1) [Ψ](t) = U u=1 ε u 1 g u 1 • G u d,Ψ (t) + V v=1 ε v 2 g v 2 • G v s,Ψ (t)(24)
where"•" indicates the convolution product between the forcing amplitudes g As discussed in [210], having analytic formulas for the linear response of a climate model to perturbation would entail having an exact theory for determining in particular the eddy-mean flow feedback. This is clearly not an easy task as it would require a fully coherent theory of climate dynamics, which is still far from having been achieved. Hence, we need to find ways to estimate the response operators. The Green's functions shown in the Box 3 (Eq. (25)) can be interpreted as lagged correlations between the observables Φ = L u/v 1,d/s (log ρ 0 ) and Ψ. This indicates a generalisation of the classical FDT [43,80,211]. The FDT has been applied in the past to the output of climate models to predict the climate response to changes in the solar irradiance [212], GHGs concentration [213,214] as well as to study the impact of localised heating anomalies [215]. Nonetheless, the use of gaussian or quasi-gaussian approximations for ρ 0 , which leads to using Green-Kubo formulas in the context of a non-equilibrium system, leads to potentially large errors in the estimate of the response [216]. In [217] one can find a rather detailed analysis of the reasons why classical FDT methods fail in reproducing the response operators, pointing, instead, to fundamental issues with data reduction techniques used to preprocess the data: features associated with weak modes of natural variability (which are possibly filtered out) can have an important role in determining the response.
The Green's functions G u/v d/s,Ψ are key tools for computing a system's linear response to perturbations. They can be written as
G u/v d/s,Ψ (t) = Θ(t) dρ 0 (x)e tL * 0 Ψ(x)L u/v 1,d/s (log(ρ 0 (x))), i.e. G u/v d/s,Ψ (t) = Θ(t) dxρ 0 (x)Ψ(x(t))Φ(x) = Θ(t)C Ψ,Φ (t),(25)
where Θ(t) is the Heaviside distribution which ensures causality [60,67,218]. The operators L * 0 , L u 1,d and L v 1,s are:
L * 0 Ψ = F · ∇Ψ + 1 2 ΣΣ T : ∇ 2 Ψ, (26a) L u 1,d ρ = −∇ · (Guρ) , 1 ≤ u ≤ U,(26b)
L v 1,s ρ = 1 2 ∇ 2 :
ΣvΓ T + ΓΣ T v ρ , 1 ≤ v ≤ V. (26c)
In (26a), L * 0 is the Kolmogorov operator, the dual of the Fokker-Planck operator L 0 associated with the unperturbed SDE given in Eq. (2), while ":" denotes the Hadamard product.
The sensitivity of the system as measured by the observable Ψ with respect to the forcing encoded by G u/v d/s,Ψ (t) measures the long-term impact of switching on the forcing and keeping it at a constant value, which corresponds to choosing a constant (unitary time modulation). Hence, such sensitivity can be written as S
u/v d/s,Ψ = ∞ 0 dtG u/v d/s,Ψ (t).
Box 3: Green's Functions and Sensitivity
A possible way forward is to estimate the Green's functions for the observable(s) of interest from a set of suitably defined simulations. As shown in [66,67,69] for the case of CO 2 forcing, it is convenient to perform an ensemble of N simulations where the CO 2 concentration is instantaneously doubled, and the runs continue until the new steady state is obtained. The Green's functions are estimated by taking the time derivative of the ensemble average of the response of the model to such a forcing, and can then be used for performing projections of climate response to arbitrary protocols of CO 2 increase. Figure 4 portrays the application of response theory to an Earth System Model, where accurate projections are obtained for the globally averaged surface temperature and for the Atlantic Meridional Overturning Circulation (AMOC) strength [219,220] for a 1% increase of the CO 2 concentration from pre-industrial conditions up to doubling. Note the very pronounced weakening of the AMOC and the slow recovery after the applied forcing stabilizes; see discussion in Sec. III.2 below.
Response theory can be used also for other problems of practical relevance in climate science, like estimating the point of no return for climate action [68] and explaining whether, along the lines of defining causal links, one can use a climate observable as a surrogate forcing acting on another observable of interest [218,221]. In [210] one can find a very useful discussion of additional potential uses of response theory in a climatic context. It can be used to solve an inverse problem like determining the forcing needed to achieve a given response and relates in that sense to (optimal) control ideas [222,Sec. 3]. A relevant application in this regard pertains the analysis of basic issues and uncertainties associated with geoengineering strategies related to the injection of aerosols in the stratosphere [223]. Additionally, one can use response theory to determine the forcing (of given norm) producing the largest response.
III.1. Response, Feedbacks, and Koopman Modes
Response theory allows one to frame classical concepts of climate science in a much broader context. Equilibrium Climate Sensitivity (ECS) is the long-term globally averaged surface air temperature increase due to a doubling of the CO 2 concentration [224]. From Box 3, one derives a formal definition of such a quantity as the time integral from 0 to ∞ of the Green's function describing the response of the globally averaged surface temperature to increases in the CO 2 concentration; see also [6] . Transient climate response (TCR) is the globally averaged surface air temperature increases recorded at the time at which CO 2 has doubled as a result of 1% annual increase rate, i.e. roughly after 70 years [225]. Intuitively, one has that ECS is larger than the TCR because of the thermal inertial of the climate system, namely the fact that following the forcing due to increased CO 2 concentration, the system needs some time to adjust to its final, steady state temperature. As shown in [66], it is possible to find an explicit formula relating ECS and TCR, which shows that the difference between the two quantities is associated with the properties of the Green's function at all temporal scales.
Response theory makes it possible to investigate the key features of the climatic feedbacks acting on different time scales. We provide a rewriting of the Green's functions in terms of individual components specifically associated with the eigenmodes of the unperturbed Kolmogorov operator L * 0 (Box 3). Let {λ j } M j=1 be M eigenvalues of finite algebraic multiplicity m j with largest real part. The λ j are either real or come in complex conjugate pairs. In the case of vanishing noise, these are the dominant Koopman eigenfunctions of the system. Namely, if λ j is an eigenvalue of L * 0 with eigenfunction ψ * j , so is e λj t of K t = e tL * 0 relative to the same eigenfunction. The eigenfunctions ψ * j are the analogue of the Koopman eigenfunctions in presence of noise and encode the stochastic system's natural variability, decay of correlations and (temporal) power spectra; see [35]. Koopman analysis and related methods have demonstrated great promises over the last decade in capturing modes of climate variability from high-dimensional model and observational data [226].
Following [35,73], it was shown in [65] that using the Koopman mode formalism it is possible to express the Green's functions G k,p introduced in Eq. (25) as a sum of exponential functions (possibly multiplied by polynomials):
G k d/s,Ψ (t) = Θ(t) Z j=1 mj −1 =0 α ,k,s/d j (Ψ) 1 ! e λj t t ,(27)
where the coefficient α ,k,s/d j (Ψ) are discussed in Box 4, whereas their expression can be found in [65]. In Eq. (27) we are neglecting the contribution to the response coming from the essential component of the spectrum of the Koopman/Kolmogorov operator [65]. This point is often implicitly assumed when performing extended DMD [227]. This derivation explains why the formula presented in Eq. (5) allowed to correctly interpret the climate feedbacks in [40,44]. We stress here that the λ j do not depend on either the observable or the forcing considered, but are instead a fundamental property of the reference system's dynamics.
III.2. Impact of Tipping Points
Since any Green's function for the observable Ψ can be interpreted as a correlation function between Ψ and a suitably defined observable Φ (Box 3), it should not come to a surprise that, considering Eq. (27), one has:
C Ψ1,Ψ2 (t) = Z j=1 mj −1 =0 β ,k j (Ψ 1 , Ψ 2 ) 1 ! e λj t t ,(28)
for any pair of observables Ψ 1 , Ψ 2 . Actually (28) [217,[228][229][230].
If we assume that say one parameter γ of our system is such that the spectral gap γ = Re(λ 1 ) vanishes as γ → γ c , we have that as γ nears it critical value γ c :
(i) Any Green function and any lagged correlation decays sub-exponentially unless the corresponding factors (α's and β's, respectively) vanish;
(ii) Due to the sensitivity formula given in Box 3, one immediately derives that as we near a tipping point, the sensitivity of the system become larger and larger; see also [231].
These two phenomena-critical slowing down and diverging sensitivity-are key manifestations of the proximity of tipping points [10]. In the case the dynamics of the system of interest can be approximated, in coarse grained sense, by a Ornstein-Uhlenbeck process, another manifestation of being near a tipping point is (iii) The increase in the variance of signal [232,233].
Indeed, in more general terms, item (iii) can be seen as increased sensitivity of the system to the presence of background noise, see [65,234]. The AMOC has long been seen as a climatic subsystem with potential tipping behaviour as a result of changing climatic conditions, and, specifically, of alternations in the hydrological cycle in the Atlantic basin [219,220,235]. Figure 5 shows results from [236] and [237] describing signs from observations that support a nearing of the AMOC to a highly plausible critical transition. These signs are typically characterized by an increase of the sensitivity and in the variance of an AMOC index tied to the sea surface temperature (SST), as well as by a decrease of the rate of decay of correlations of the same index; see also [236, Fig. 4]. Large sensitivity and slow recovery of the same large-scale climate driver has already been discussed in a modelling context in Fig. 4.
We can learn more about such critical behaviour by taking the Fourier transform of the Green function given in Eq. (25):
F G k d/s,Ψ (ω) = Z j=1 mj −1 l=0 α ,k,s/d j (Ψ) (iω − λ j ) l+1 .(29)
Equation (29) indicates that the coefficient α ,k,s/d j (Ψ) weight the contributions to the frequency-dependent response coming from the eigenmode(s) corresponding to the eigenvalue λ j (which has in general multiplicity m j ) for a given combination of observable and forcing. Note that there is a total of Z = Z 1 + 2Z 2 eigenvalues. [236] and [237]) Panel A: AMOC index SSTSG-GM [237] as a function of global mean temperature (GMT) and least-squares fit of the fixed point of a conceptual AMOC model from [236]. Panel B: The SST-based AMOC index SSTSG-GM, constructed by subtracting the global mean SSTs from the average SSTs of the subpolar gyre region (black), supplemented by the same least-squares fit (red) [236]. Panel C: Variance of fluctuations of the AMOC index around the fixed point (red) and corresponding sensitivity of the model, with control parameter T given by the global mean SSTs. These variances are estimated over a sliding temporal window and the results are plotted at the centre point of that window [236]. Panel D: Observational evidence of the nearing of the AMOC tipping point during the last century from [237]. Shown are time series of SST anomalies with respect to the global mean SST in the subpolar gyre (sg) and the Gulf Stream (gs) regions (HadISST data).
Box 4: Nonequilibrium Oscillator Strengths
Of these, Z 1 are real, and 2Z 2 are complex conjugate pairs. Hence, the α s are the non-equilibrium, classical equivalent of the wellknown oscillator strengths discussed in spectroscopy, which weight the contributions to the optical susceptibility from each of the allowed quantum transitions from the ground states to the accessible excited states [238,239]. Thus, Eq. (29) provides the basis for a spectroscopy of general nonequilibrium systems, and, specifically, of the climate system. Resonant terms are associated with tipping phenomena.
The poles of the susceptibility are located at ω = −iλ j . Equation (29) implies the existence of resonances in the response for real frequencies ω = Im(λ j ). Neglecting the possible existence of nonunitary algebraic multiplicities, the susceptibility at the resonance j is proportional to 1/Re(λ j ). Hence, as γ → γ c , the susceptibility for ω = Im(λ 1 ) diverges, thus implying a breakdown of the response operator. If at criticality Im(λ 1 ) = 0, the static response of the system diverges, indicating a saddle-node-like bifurcation phenomenon (turning point). If, instead, Im(λ 1 ) = 0, we face an oscillatory unstable phenomenon that is reminiscent to a Hopf bifurcation [171,240]. The viewpoint proposed here allows to link the fundamental features of the tipping phenomenology within a coherent framework.
IV. DETECTION AND ATTRIBUTION OF CLIMATE CHANGE
The statistical mechanical tools discussed above allow for performing climate change projections for ensembles of trajectories: statements are made in terms of (changes of) the expectation value of general observables. Clearly this is a mathematical construction that does not fully comply with the requirements of climate science, as we experience only one realisations of the dynamics of climate and we do not have to access to the hypothetical multiverse comprising of other statistically equivalent realisations. Nonetheless, linear response theory applied to climate provides a solid setting for detection and attribution studies.
Let Ψ k , k = 1, . . . , N be a collection of climate variables. Consider also the possibility that the forcing to the climate system comes from M different sources, be them anthropogenic or natural. We rewrite Eq. (24) by clamping together all the M acting forcings as δ (1) [Ψ k ](t) = M p=1 ε p (g p • G p,k ) (t). Hence we have that, at first order,
Y k (t) = Ψ k (t) − Ψ k 0 = M p=1X p k (t) + R k (t),(30)
where the termsX p k (t) = ε p (g p • G p,k ) (t) account for the forced variability, and R k (t) = Ψ k (t) − Ψ ρ t ε is a random vector whose correlations are governed by the probability distribution ρ t ε solving the FPE associated with Eq. (23). Equation (30) is cast into a form that is very close to the usual mathematical formulation of optimal fingerprinting for climate change given in Eq. (6). Response theory indicates that if we use the forced run of a model to perform detection and attribution of climate change as simulated by the same model, and if we are in the linear regime of response, all the β p 's should be unitary, apart from uncertainty. We stress that the linear response theory indicates that the optimal fingerprinting procedure could be applied seamlessly for different time horizons of the climate change signal and for suitably linearly filtered signals (e.g. considering time averages). This suggests that one should perform the optimal fingerprinting for different time horizons at the same time, and check the consistency of the obtained results (in terms of confidence intervals for the β's) across the time of the hindcast. Additionally, the fact that linear response theory applies for a large class of forcings and can even be adapted for studying extremes [241] explains why optimal fingerprinting finds such a broad range of applications.
The term R k (t) in Eq. (30) is not associated with the variability of the unperturbed climate-compare with Eq. (6)-but rather is tied to the system's variability encoded by the probability distribution ρ t ; see also discussions on time-dependent probability measures and pullback attractors in [39, 204-206, 242, 243]. Such remarks allow us to point out that the classical formulation of optimal fingerprinting lacks the proper framework to account for changes in variability due to climate change.
The expression for the Green function given in Eq. (27) provides useful information for better understanding the robustness of the optimal fingerprinting method. The model error manifests itself in the difference between the spectrum of eigenvalues (and eigenfunctions) of the Koopman operator of the "real" climate and that of the model used for constructing the fingerprints. Additionally, different climate models will in general feature different Koopman modes and associated eigenvalues. Hence, constructing fingerprints by bundling together information derived from different models seems not so promising in terms of reducing model error.
It is also clear that if only one between the actual climate system and the model used for optimal fingerprinting are close to a tipping point, one expects major uncertainties and biases because of the qualitative mismatch between the leading j = 1 term of all the involved Green functions, and, hence, between the model fingerprints and the actual climatic response to the considered forcings. This becomes even more critical if more models are used for estimating of the fingerprints, because heavily spurious information could be could added.
V. DISCUSSION
The Hasselmann program has had a great influence in the modern development of climate science, both regarding its everyday practice and its more foundational aspects. The fundamental idea boils down to treating noise not like a nuisance one needs to filter out to gather useful information, but rather as a key aspect of the climate system one needs to fully explore and appreciate in order to further its understanding and to link model output and observational data. This is key for making progress in detecting and attributing the climate change signals at different spatial and temporal scales.
The emphasis on the role of noise in creating -somewhat counterintuitively -meaningful signal at lower frequencies has led to fundamental discoveries like in the case of the mechanism of stochastic resonance, which stemmed as a direct application of Hasselmann paradigm in a climatic context [244][245][246][247] but has since had huge success in a plethora of other research areas [248]. Another important are of application of Hasselmann paradigm deals with one of the age-old problems of dynamical meteorology: the fast atmospheric processes due to baroclinic disturbances have been interpreted as acting as effective noise responsible for the low-frequency variability of the mid-latitudes due with the transitions betweeen competing regimes of circulations, mainly associated with zonal flow and blockings, respectively [249][250][251][252][253]. More recently, the stochastic formulation of climate dynamics, taking advantage of Fredilin-Wentzell theory of noise-induced escapes from attractors [254] and of large deviation theory [255], has been instrumental for developing a theory of metastability for geophysical flows [256,257] and for the climate system [258][259][260]. We also remark that more general classes of noise lawsspecifically α-stable Lévy processes -are sometimes invoked for studying climatic transitions where sudden jumps between competing states are observed [261][262][263]. For reasons of space and internal coherence, we have chosen not to cover these important research areas in this review. The Hasselmann program, by construction, leaves out the problem of finding the root causes of the noise that impacts the slow climatic variables In this sense, it can be seen as proposing a heuristic theory of climate. As well known, the noise comes from the fast fluid dynamical instabilities occurring at different scales, in the atmosphere and in the ocean, leading to chaotic behaviour [4,7]. The details of the fast processes, in fact, do matter, exactly because there is no time separation one can use to separate the variables of interest from those one wants to parametrize, so that the kind of parsimony one would derive from the use of homogeneization theory cannot be recovered [80]. On the other hand, there is no dichotomy between deterministic behaviour and stochastic representation, because chaos generates stochastic processes. In order to advance in the direction of constructing a theory of climate able to account for variability and response to forcings, and able to provide useful and usable information to address the climate crisis, there is need to inform the stochastic angle on climate with the key details obtained by a multiscale analysis of the dynamical processes. This review is a preliminary attempt to go in this direction.
FIG. 2 :
2An example of no need of memory but noise term in the MZ-decomposition Eq.(15). Example from the atmospheric Lorenz 80 (L80) model[145] following[129, Sec. 3.4] and[146]. Panel A: The OPM is the BE manifold shown by blue dots. It provides the slow motion of the L80 dynamics. The L80 dynamics (black curve) evolves onto this manifold and experiences excursions off this manifold, corresponding to bursts of fast oscillations caused by IGWs (see Box 2). The residual off the BE manifold is mainly orthogonal to it causing memory terms to be negligible, and making their stochastic modeling central as the η(t)-term in the MZ decomposition Eq.(15). Panel B: This residual in the time-domain is strongly correlated in time and can be grouped in pairs that are narrowband in frequency and modulated in amplitude with possible combination of 'tones' (bottom panel). Panel C: Networks of stochastic oscillators such as given in[146, Eq. 12] are well suited to model such properties.
FIG. 3 :
3Upper-ocean potential vorticity (PV) anomalies, its time-evolution, and standard deviation: QG vs MSLM (from [97]). Panel (A): Instantaneous upper-ocean PV anomaly field from a high-resolution simulation (HRS) of a baroclinic QG turbulent model. Panel (B): Standard deviation of this HRS over a 64 × 26 coarse-grid. Panel (C): Standard deviation as simulated by the MSLM reduced model over the same coarse grid. Panels (D) and (E): Instantaneous upper-ocean PV anomalies from the coarse-grained QG model and its MSLM reduced model, respectively. Panel (F) and (G):
FIG. 4 :
4Prediction of a) Globally averaged surface temperature and b) Atlantic Meridional Overturning Circulation (AMOC) strength as a result of an annual 1% increase of the CO 2 concentration from pre-industrial conditions up to doubling. In each panel the blue curve indicates the prediction by application of response theory while the thick red curve shows the ensemble mean of the model runs (yellow curves).) From[69].
FIG. 5: (Adapted from [236] and [237]) Panel A: AMOC index SSTSG-GM [237] as a function of global mean temperature (GMT) and least-squares fit of the fixed point of a conceptual AMOC model from [236]. Panel B: The SST-based AMOC index SSTSG-GM, constructed by subtracting the global mean SSTs from the average SSTs of the subpolar gyre region (black), supplemented by the same least-squares fit (red) [236]. Panel C: Variance of fluctuations of the AMOC index around the fixed point (red) and corresponding sensitivity of the model, with control parameter T given by the global mean SSTs. These variances are estimated over a sliding temporal window and the results are plotted at the centre point of that window [236]. Panel D: Observational evidence of the nearing of the AMOC tipping point during the last century from [237]. Shown are time series of SST anomalies with respect to the global mean SST in the subpolar gyre (sg) and the Gulf Stream (gs) regions (HadISST data).
can be derived as a consequence of the decomposition formula of correlation functions for stochastic systems, in terms of the spectral elements of the Kolmogorov operator [35, Corollary 1]. From Eqns. (27)-(28) it is clear that the rate of decay of any Green's function as well as of any lagged correlation is dominated over large time horizons by the real part of the subdominant pair of the Kolmogorov spectrum. The eigenfunctions correspond to the slowly decaying eigenvalues are the rigorous counterpart of the so-called neutral climate modes that have been widely discussed in the literature
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| sample_947 | 0.9872 | arxiv | |
CODYRUN, OUTIL DE SIMULATION ET D'AIDE A LA CONCEPTION THERMO-AERAULIQUE DE BATIMENTS
Harry Boyer
Département Génie Civil
LGI -Equipe GCTH -Université de La Réunion -IUT de Saint Pierre
40 Avenue de Soweto97410
Alain Bastide
Département Génie Civil
LGI -Equipe GCTH -Université de La Réunion -IUT de Saint Pierre
40 Avenue de Soweto97410
Philippe Lauret
Département Génie Civil
LGI -Equipe GCTH -Université de La Réunion -IUT de Saint Pierre
40 Avenue de Soweto97410
CODYRUN, OUTIL DE SIMULATION ET D'AIDE A LA CONCEPTION THERMO-AERAULIQUE DE BATIMENTS
CODYRUNsimulationmodelling
Saint Pierre -Ile de la Réunion RESUME. Cet article présente le code de simulation CODYRUN développé à l'Université de La Réunion. Il s'agit d'un logiciel de simulation thermique multizone, intégrant un module aéraulique et un modèle hydrique. Une de ses particularités est celle d'être simultanément un outil de recherche autour duquel beaucoup de nos travaux se sont articulés (plateforme d'intégration de modèles, validation, ...), un outil d'aide à la conception utilisé par le laboratoire et des professionnels et enfin un outil pédagogique utilisé en enseignement à plusieurs niveaux. Après une présentation du caractère multimodèles de l'application dans une première section, les trois modules liés à la physique des phénomènes intégrés sont explicités. Des éléments de la validation sont évoqués dans la section suivante et, enfin, quelques éléments de l'interface du code sont donnés.MOTS-CLÉS : CODYRUN, simulation, modélisation.ABSTRACT. This article presents the CODYRUN software developped by University of La Réunion. It is a multizone thermal software, with detailled airflow and humidity transfer calculations. One of its specific aspects is that it constitutes a research tool, a design tool used by the lab and professionnals and also a teaching tool. After a presentation of the multiple model aspect, some details of the tree modules associated to physical phenomenons are given. Elements of validation are exposed in next paraghaph, and then a few details of the front end.
INTRODUCTION
Cet article présente le code de simulation CODYRUN développé à l'Université de La Réunion et initié, il y a plus de 10 ans, dans le cadre d'une collaboration Université de La Réunion / INSA de Lyon. Il s'agit d'un logiciel de simulation thermique multizones, intégrant un module aéraulique et un modèle hydrique. Au cours du temps, ce logiciel a fortement évolué suivant les nombreuses sollicitations internes et externes au laboratoire. Une de ses particularités est celle d'être simultanément un outil de recherche autour duquel beaucoup des travaux de l'équipe se sont se sont articulés (plateforme d'intégration de modèles, validation, édiction de règles expertes, ...), un outil d'aide à la conception utilisé tant par le laboratoire (dans le cadre de contrats) que par des professionnels (BET, architectes) et enfin un outil pédagogique utilisé en enseignement à plusieurs niveaux d'étude. Après une présentation du caractère multimodèles de l'application, les trois modules liés à la physique des phénomènes intégrés sont détaillés. Des éléments de la validation sont évoqués dans la section suivante suivant et enfin, quelques éléments de l'interface du code sont donnés.
L'ASPECT MULTI-MODELES DE L'APPLICATION
Cette caractéristique de l'application (Boyer & al., 1998) a fortement contraint l'architecture de l'application en terme de décomposition par blocs, de choix de schémas de résolution et est donc présentée en préalable.
Dès les premières années de diffusion significative des outils de simulation et de conception, l'un des problèmes posés a été celui de leur adéquation a besoins des acteurs du processus de conception. En considérant la façon dont ils sont produits, les modèles thermiques sont le plus souvent obtenus par assemblage de modèles élémentaires, décrivant chacun le comportement thermique des éléments constituant le bâtiment. Une fois les modèles élémentaires choisis (en terme de précision, de temps calcul, de sorties disponibles, de la faisabilité du couplage avec d'autres modèles, ...), cette approche conduit à un modèle du bâtiment figé ou monolithique. Il répond précisément au besoin d'un acteur (dimensionnement de systèmes de climatisation par exemple). Ainsi, au vu des besoins très différents des acteurs du domaine (allant du concepteur au physicien du bâtiment), un outil dont les modèles élémentaires sont figés ne saurait répondre à lui seul à l'ensemble des besoins des acteurs du processus de conception. Par exemple, deux objectifs différents sont d'une part d'évaluer une consommation énergétique annuelle et d'autre part d'étudier la réponse (horaire ou sub-horaire) d'un composant du bâtiment sur une séquence climatique donnée. Intuitivement, l'emploi d'un modèle thermique détaillé dans le premier cas conduira à des temps de calculs importants. De même, l'utilisation d'un modèle trop simplifié ne pourra mener qu'à des estimations peu précises, mais rapides, dans le cas de la réponse. Un lien fort existe donc entre notion de qualité de modèle, objectif de la simulation et temps de calcul.
Notre démarche, et de ce fait notre contribution, a été différente. Elle vise à l'intégration d'une bibliothèque de modèles élémentaires interchangeables. Dans la plupart des logiciels de simulation existants, le choix des modèles élémentaires est effectué lors de phase d'analyse et l'usage de ces modèles est globale à l'ensemble du bâtiment (par exemple, le même modèle conductif est enclenché pour toutes les parois opaques). En conséquence, si ces modèles sont un tant soit peu détaillés, les temps de calcul ne sont plus compatibles avec un outil de conception. Pour contourner le compromis entre précision et temps de calcul, il nous est apparu intéressant de permettre, pour certains des phénomènes (ou systèmes), une application sélective des modèles. Il s'agit d'offrir la possibilité de choisir des modèles différents pour des entités de même niveau hiérarchique (les zones ou les parois par exemple). Le but poursuivi est alors d'asservir une entité à un niveau de complexité souhaité. Il est clair que cette démarche sélective doit s'assurer d'un préalable concernant l'intensité des couplages des systèmes de même niveau (et des zones en particulier), préalable qui est du ressort de l'utilisateur expert.
En terme d'objectif des simulations, la logique précédente conduit à autoriser différents types de simulations multizones, répondant au problème thermique sans aéraulique (bâtiment fermé ou équipé de VMC), thermique avec aéraulique à débit détaillé (modèle en pression), aéraulique ou encore thermique, aéraulique et hydrique. C'est alors une architecture par blocs correspondant à chacun des phénomènes (thermique, aéraulique, hydrique) qui se prête le plus facilement à cette démarche. Les couplages entre ces phénomènes sont gérés de manière itérative, en laissant de surcroît à l'utilisateur expert le choix des options de couplage (par exemple entre les modules thermique et aéraulique) et des critères associés.
PRESENTATION DES MODULES LIES A LA MODELISATION PHYSIQUE DES PHENOMENES :
PRESENTATION DU MODULE THERMIQUE
Cette partie est détaillée au niveau de la référence (Boyer,96). Avec les hypothèses classiques d'isothermie du volume d'air des zones, de transferts conductifs unidirectionnels, d'échanges superficiels linéarisés, de l'analyse nodale intégrant les différents modes de transfert (conduction, convection et rayonnement) permettant d'atteindre pour chaque zone thermique constitutive du bâtiment l'ensemble des réponses de l'ambiance (et éléments associés).
Le modèle physique d'une zone est alors obtenu en assemblant les modèles thermiques de chacun des éléments parois, vitrages, volume d'air, qui constituent la zone. Pour fixer les idées, les équations rencontrées du type :
) 4 ( 1 ) 3 ( 1 ) ( ) 2 ( ) 1 ( ) ( 0 ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( T T A h T T Q c T T S h dt T d C T T K T T h T T h dt T d C T T K T T h T T h dt T d C j
Les équations de type (1) et (2) traduisent les bilans thermiques respectifs des noeuds de surface intérieurs et extérieurs. N w désignant le nombre de parois de l'enveloppe, l'équation (3) est celle du bilan thermoconvectif de l'air, compte tenu d'un débit Q entre l'intérieur et l'extérieur. (4) est l'équation d'équilibre radiatif du noeud de température radiante moyenne.
Le caractère générique de l'application (pas dédiée à un nombre de zones ou à un type de zone particulier) nécessite de porter une attention particulière à la génération du maillage du bâtiment. Dans la même logique que précédemment (application sélective des modèles), vis à vis du multizonage, c'est un procédé de couplage itératif entre les zones qui est implanté. De nouveaux modèles ont été implémenté au cours du temps (et ce depuis la version initiale de l'outil). Ils sont liés, entre autre, à la méthode des radiosités, à la gestion du couplage radiatif (Courte Longueur d'Onde) des zones (à travers les vitrages) ou encore à l'intégration de la réduction du diffus par les masques proches . Pour une étude spécifique liée à l'intégration d'algorithmes de réduction modale (Berthomieu & al., 2003), la mise sous forme canonique d'état (au sens de l'automatique) du système thermique obtenu par zone a été utilisée.
En terme d'utilisation effective, les principales sorties de ce module de thermique sont celles liées aux températures des éléments discrétisés, aux flux surfaciques, aux indices de confort des différentes zones, à la consommation des appareils de climatisation, ...
PRESENTATION DU MODULE AERAULIQUE
Un modèle en pression pour le calcul effectif des débits prend en compte les effets moteurs vent et le tirage thermique. A ce jour, les composants aérauliques intégrés sont les bouches de ventilation, les petites ouvertures (régies par l'équation de crack flow,
n P K m ) (
) et les grandes ouvertures verticales intérieures. Le modèle (Roldan, 1984) des grandes ouvertures extérieures nous ayant récemment montré ses limites (par comparaison avec la CFD), il sera réputé non intégré, bien qu'il fasse l'objet de développements actuels.
Le bilan massique de chaque zone (en présence de ventilation mécanique) conduit à l'établissement d'un système non linéaire admettant comme inconnues les pressions de référence des zones.
1 N i 0 i N i 2 i 0, i N i 1 i 0, i 0 ) N ( m N) (i, m ... 0 ) 2 ( m (i,2) m 0 ) 1 ( m (i,1) m vmc vmc vmc j) (i, m
est le débit (kg/s) de la zone i vers j, ) k ( m vmc celui extrait de la zone k et N le nombre total de zones. Après l'établissement automatique de ce système non linaire, sa résolution est effectuée à l'aide d'une variante de la méthode de Newton Raphson (sous relaxée), mettant en oeuvre l'algorithme de Picard (pour initialiser les valeurs de pression entre 2 itérations) pour promouvoir la convergence.
PRESENTATION DU MODULE HYDRIQUE
En raison du découplage opéré, les températures sèches de chacune des zones ainsi que les débits inter zones ont été préalablement calculés. A ce moment précis du calcul, pour un bâtiment donné, une
équation matricielle du type C r A r B h h h
régit l'évolution des humidités spécifiques de chaque zone.
Une amélioration du modèle hydrique (Lucas, & al., 2003) a été apportée au travers de l'intégration d'un tampon hygroscopique, selon le modèle de Duforestel. Si n est le nombre de zones, un système linéaire de dimension 2n est établi et résolu à l'aide d'un schéma aux différences finies.
ELEMENTS DE VALIDATION DU CODE
La validation du code a été menée en plusieurs étapes dont seules quelques unes sont rappelées cidessous. Certaines comparaisons inter logiciels ponctuelles ne sont que mentionnées (CODYBA et TRNSYS pour la partie thermique, BREEZE, COMIS, CONTAM93 pour l'aéraulique sur un cas de l'AIVC TN51), de même que des confrontations analytiques (en aéraulique).
PROCEDURE IEA -BESTEST MONOZONE
CODYRUN a passé la procédure IEA BESTEST Task 12 (cas monozones, séries 600 et 900). La procédure prévoit plus d'une centaine de simulations (Soubdhan & al., 1999) et sur les cas traités, CODYRUN affichait des résultats compatibles avec la majorité des programmes de référence, excepté pour quelques uns ayant permis de corriger des erreurs. Un exemple de résultat issu de cette confrontation est le suivant :
CONFRONTATIONS EXPERIMENTALES
Dans le cadre de campagnes de mesures sur des supports de laboratoire (cellule LGI, STA-TRON, ISOTEST, ETNA EDF-DER) et de logements réels (Trinité, Découverte, ...), un ensemble d'éléments du modèles ont pu être confrontés à des mesures (et pour certains améliorés), principalement vis à vis d'aspects thermiques et hydriques. De manière non exhaustive, certains de ces aspects sont présentés dans les articles , et .
PRESENTATION DE L'INTERFACE DE L'APPLICATION
Pour des rasions de portabilité, l'application est décomposée en 2 parties : le noyau de calcul est développé en C (pour des raisons de portabilité) alors que l'interface est sous C/Windows. Ce découpage a permis le portage du noyau sous l'environnement TRNSYS , sous la forme d'un type autonome.
L'interface du code est assez simple, CODYRUN manipulant des fichiers Bâtiment (extension BTM), des fichiers météorologiques (.MTO, du même format que CODYBA) pour générer des fichiers résultats (dont le contenu est modulable) en mode texte. En particulier pour la partie de description du bâtiment, cette interface constitue la partie la plus dépouillée de l'application. Il s'agit de fenêtres Windows en mode texte, au sein desquelles toute l'information descriptive (et de choix de modèles) doit être effectuée. Bien que robuste parce qu'éprouvée par de nombreux utilisateurs (étudiants, professionnels et membres de l'équipe), c'est le temps de description qui peut devenir problématique. Pour fixer les idées, le ratio du nombre de zones du bâtiment par rapport aux heures à consacrer à la description (bien que variable selon l'utilisateur) avoisine l'unité.
La structure de fenêtres est l'image de la structure de données de CODYRUN, bien représentée par l'arborescence suivante :
Figure 2 : Arborescence de données
Les inter ambiances se définissent comme le lieu d'appartenance des composants séparant 2 zones. Les composants appartiennent à la liste se suivante et se distinguent par leur élément d'appartenance (zone ou inter ambiance) :
Tableau 1 : Types de composants
Pour chacun de ces composants des informations spécifiques sont à renseigner pour construire le bâtiment. Un exemple de fenêtre est celle d'un composant de type paroi :
CONCLUSION
Conduits de façon très autonome et soutenue depuis plus de 10 ans, les développements menés autour de cette application ont conduit notre équipe à disposer d'un environnement de simulation propriétaire et à bâtir en périphérie des thématiques structurantes telles que la validation ou l'application à grande échelle du code dans le cadre de prescriptions architecturales . Cet environnement évolutif nous a permis de conduire des développements dans des domaines méthodologiques (réduction modale, analyse de sensibilité, couplage avec des algorithmes génétiques, réseaux de neurones, méta modèles, ...) ou liés à des aspects technologiques (masques, intégration de split-system, prise en compte des produits minces réfléchissants, ...).
Figure 1 :
1Exemple de résultat 4.2. PROCEDURE IEA -BESTEST MULTIZONE Les cas multizones IEA: SHC Task 34 / ECBCS Annex 43 (Multi-Zone Conduction Cases) (MZ200 -> MZ310) ont été réalisés sans difficulté. Nous avons initié les cas suivants, i.e. les cas MZ320 -> MZ360. Pour le dernier, MZ360 (internal window) il a été nécessaire de prendre en compte les vitrages interzones (et un algorithme de répartition des flux entre zones).
Figure 3 :
3Fenêtre principale du composant paroi
La description d'un bâtiment se fait au travers d'éléments classiques. Ils se décomposent de la manière suivante : le bâtiment, les zones, les séparations entre zones (nommées inter ambiances) et enfin les composants. L'architecture sera détaillée plus en avant. Compte tenu du caractère sélectif des modèles, il est nécessaire de distribuer les informations liées aux modèles dans les structures de description des entités et donc au niveau des fenêtres de l'application (cf par exemple celle du composant paroi, qui fait apparaître des informations liées au modèle conductif)
notre domaine se complexifie de part l'intégration d'autres aspects que ceux initialement liés à la thermique et à l'aéraulique (qualité des ambiances. . Hqe, Accompagné par la croissance de la puissance des machines et faisant l'objet d'un forte demande environnementale. Simultanément, il est indispensable de rechercher une meilleure efficacité dans le. transfert de connaissances et le caractère opérationnel (i.e. en production) des outilsAccompagné par la croissance de la puissance des machines et faisant l'objet d'un forte demande environnementale (HQE, ...), notre domaine se complexifie de part l'intégration d'autres aspects que ceux initialement liés à la thermique et à l'aéraulique (qualité des ambiances, incluant éclairagisme, polluants, acoustique, ...). Simultanément, il est indispensable de rechercher une meilleure efficacité dans le transfert de connaissances et le caractère opérationnel (i.e. en production) des outils.
Dans sa version actuelle, notre contribution à la communauté est téléchargeable sur www.univreunion.fr\iut_dpt_gc, rubrique Téléchargement. Dans sa version actuelle, notre contribution à la communauté est téléchargeable sur www.univ- reunion.fr\iut_dpt_gc, rubrique Téléchargement.
. Bibliographie, BIBLIOGRAPHIE
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A multi-model approach to building thermal simulation for design and research purposes. H Boyer, F Garde, J C Gatina, J Brau, Energy and Buildings. 28H. Boyer, F. Garde, J.C. Gatina, J. Brau (1998) « A multi-model approach to building thermal simulation for design and research purposes», Energy and Buildings, 28, 1, pp. 71-79
Building ventilation : a pressure airflow model computer generation and elements of validation. H Boyer, A P Lauret, L Adelard, T A Mara, Energy and Buildings. 29Boyer H., Lauret A.P., Adelard L., Mara T.A. (1999) « Building ventilation : a pressure airflow model computer generation and elements of validation », Energy and Buildings, 29, pp. 283-292.
« A validation methodology aid for improving a thermal building model : how to account for diffuse radiation in a tropical climate. A J P Lauret, T A Mara, H Boyer, L Adelard, F Garde, Energy and Buildings. 33Lauret A.J.P., Mara T. A., Boyer H., Adelard L., Garde F. (2001) « A validation methodology aid for improving a thermal building model : how to account for diffuse radiation in a tropical climate », Energy and Buildings, 33, pp. 711-718.
« Intégration de la réduction équilibrée à un code de simulation hygro-thermo-aéraulique de bâtiments ». T Berthomieu, H Boyer, Annales du Bâtiment et des Travaux Publics. 6Berthomieu T., Boyer H. (2003), « Intégration de la réduction équilibrée à un code de simulation hygro-thermo-aéraulique de bâtiments », Annales du Bâtiment et des Travaux Publics, n°6, Sept. 2003
F Lucas, L Adelard, F Garde, H Boyer, Study of moisture in buildings for hot humid climates », Energy and Buildings. 34Lucas F., Adelard L., Garde F., Boyer H. (2001) « Study of moisture in buildings for hot humid climates », Energy and Buildings, 34, 4, pp. 345-355
Use of BESTEST procedure to improve a building thermal simulation program », Renewable Energy,part III. T Soubdhan, T A Mara, H Boyer, A Younes, T. Soubdhan, T. A. Mara, H. Boyer, A. Younes (2000) « Use of BESTEST procedure to improve a building thermal simulation program », Renewable Energy,part III, p. 1800-1803
Empirical validation of a solar test cell. T Mara, F Garde, H Boyer, M Mamode, Energy and Buildings. 336Mara T., Garde F., Boyer H., Mamode M. (2001) « Empirical validation of a solar test cell », Energy and Buildings, 33 (6):589-599.
Bringing simulation to implementation : Presentation of a global approach in the design of passive solar buildings under humid tropical climates. F Garde, H Boyer, R Célaire, Solar Energy. 712Garde F., Boyer H., Célaire R. (2001) « Bringing simulation to implementation : Presentation of a global approach in the design of passive solar buildings under humid tropical climates », Solar Energy, 71 (2):109-120.
« D'un code de simulation thermique du bâtiment à l'observation d'état : présentation de deux applications. H Boyer, P Lauret, A Younes, A Bastide, T Mara, Lyonième colloque interuniversitaire franco-québecquoisBoyer H., Lauret P., Younes A., Bastide A., Mara T. (2001) « D'un code de simulation thermique du bâtiment à l'observation d'état : présentation de deux applications », V ième colloque inter- universitaire franco-québecquois, Lyon, mai 2001.
. A Bastide, H Boyer, P Lauret, F Lucas, F Garde, LyonIntégration à TRNSYS du noyau de CODYRUN, code de simulation thermo-aéraulique de bâtiments : le Type 59 », 4 ième séminaire TRNSYS-EES francophoneBastide A., Boyer H., Lauret P., Lucas F., Garde F. (2001) « Intégration à TRNSYS du noyau de CODYRUN, code de simulation thermo-aéraulique de bâtiments : le Type 59 », 4 ième séminaire TRNSYS-EES francophone, Lyon.
Roldan, A. «Etude thermique et aéraulique des enveloppes de bâtiment. Influence des couplages intérieurs et du multizonage. Institut National des Sciences Appliquées de LyonRoldan (1985), A. «Etude thermique et aéraulique des enveloppes de bâtiment. Influence des couplages intérieurs et du multizonage » Thèse : Sci. : Institut National des Sciences Appliquées de Lyon
| sample_976 | 0.861 | arxiv | |
Stochastic Climate Theory and Modelling
1 Sep 2014 September 2, 2014
Christian L E Franzke christian.franzke@uni-hamburg.de
Meteorological Institute and Centre for Earth System Research and Sustainability (CEN)
University of Hamburg
HamburgGermany
Corresponding Author; Meteorological Institute and Centre for Earth System Research and Sustainability
University of Ham-burg
Grindelberg 7D-20144HamburgGermany
Terence J O'kane
Centre for Australian Weather and Climate Research
CSIRO Marine and Atmospheric Research
HobartAustralia
Judith Berner
National Center for Atmospheric Research
BoulderUSA
Paul D Williams
Department of Meteorology
University of Reading
ReadingUK
Valerio Lucarini
Meteorological Institute and Centre for Earth System Research and Sustainability (CEN)
University of Hamburg
HamburgGermany
Department of Mathematics and Statistics
University of Reading
ReadingUK
Stochastic Climate Theory and Modelling
1 Sep 2014 September 2, 2014arXiv:1409.0423v1 [physics.ao-ph] 1
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modelling. In this review we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspectives. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.The last few decades have seen a considerable increase in computing power which allows the simulation of numerical weather and climate prediction models with ever higher resolution and the inclusion of ever more physical processes and climate components (e.g. cryosphere, chemistry). Despite this increase in computer power many important physical processes (e.g. tropical convection, gravity wave drag, clouds) are still not or only partially resolved in these numerical models. Despite the projected exponential increase in computer power these processes will not be explicitly resolved in numerical weather and climate models in the foreseeable future 120,171 . For instance, Dawson et al. 24 have demonstrated using the ECMWF integrated forecast system that extremely high resolutions (T1279, which corresponds to a grid spacing of about 16km) are required to accurately simulate the observed Northern hemispheric circulation regime structure. This resolution, typical for limited area weather and climate models used for short term prediction, remains unfeasible for the current generation of high resolution global climate models due to computational and data storage requirements. Hence, these missing processes need to be parameterized, i.e. they need to be represented in terms of resolved processes and scales 153 . This representation is important because small-scale (unresolved) features can impact the larger (resolved) scales 84,162 and lead to error growth, uncertainty and biases.At present, these parameterizations are typically deterministic, relating the resolved state of the model to a unique tendency representing the integrated effect of the unresolved processes. These "bulk parameterizations" are based on the notion that the properties of the unresolved subgrid-scales are determined by the large-scales. However, studies have shown that resolved states are associated with many possible unresolved states 22,144,167 . This calls for stochastic methods for numerical weather and climate prediction which potentially allow a proper representation of the uncertainties, a reduction of systematic biases and improved representation of long-term climate variability. Furthermore, while current deterministic parameterization schemes are inconsistent with the observed power-law scaling of the energy spectrum 5,142 new statistical dynamical approaches that are underpinned by exact stochastic model representations have emerged that overcome this limitation. The observed power spectrum structure is caused by cascade processes. Recent theoretical studies suggest that these cascade processes can be best represented by a stochastic non-Markovian Ansatz. Non-Markovian terms are necessary to model memory effects due to model reduction 19 . It means that in order to make skillful predictions the model has to take into account also past states and not only the current state (as for a Markov process).We first review observational evidence of stochasticity in laboratory geophysical fluid experiments (section 2), then discuss stochastic climate theory in fast-slow systems (system 3). In section 4 we present statistical physics approaches and in section 5 we review the current state of stochastic-dynamic weather and climate modelling. We close with an outlook and challenges for the future of weather and climate modelling (section 6).Research on the climate system is somewhat hindered by the obvious difficulties of performing reproducible experiments on the atmosphere and ocean in different parameter regimes. For example, an optical physicist studying the nonlinear response of isolated atoms to intense electromagnetic waves can easily change the incident wavelength 110 . In contrast, climate scientists cannot (and arguably should not!) change the rotation rate of the planet or the intensity of the incoming solar radiation. To some extent, numerical simulations come to the rescue, by allowing us to perform virtual experiments. However, the grid spacing in climate models is orders of magnitude larger than the smallest energized scales in the atmosphere and ocean, introducing biases.Fortunately, there is another option available to us. It is possible to exploit dynamical similarity 30 to study analogues of planetary fluid flow in bespoke laboratory experiments. The traditional set-up is the classic rotating annulus, which has been used for decades to study baroclinic instability and other large-scale phenomena 61 . Recent observations of small-scale inertia-gravity waves embedded within a large-scale baroclinic wave85,172,173have allowed the scale interactions between these two modes to be studied in a laboratory fluid for the first
Introduction
time. The experimental apparatus consists of a two-layer isothermal annulus forced by a differentially rotating lid, which drives a shear across the internal interface and represents the mid-latitude tropospheric wind shear.
The large-scale baroclinic wave in these laboratory experiments exhibits regime behavior, equilibrating at finite amplitude with a zonal wavenumber of typically 1, 2, or 3. These simple wave modes are regarded as prototypes of the more complicated regime behavior in the atmosphere, such as mid-latitude blocking 160,164 . A notable finding from repeated experiments using this apparatus is that small-scale inertia-gravity waves can induce large-scale regime transitions, despite the separation of wavelengths by an order of magnitude 168 . An example of this process is illustrated in Figure 1. A wavenumber 2 mode without co-existing inertia-gravity waves (upper row) remains a wavenumber 2 mode indefinitely, drifting around the annulus with the zonal-mean flow. In contrast, with the same parameter values, a wavenumber 2 mode with co-existing inertia-gravity waves (lower row) is found to have a finite probability of transitioning to a wavenumber 1 mode. The amplitude of the inertia-gravity waves is controlled here without directly affecting the large-scale mode, by slightly varying the interfacial surface tension between the two immiscible fluid layers.
The laboratory transitions discussed above are reminiscent of noise-induced transitions between different equilibrium states in a meta-stable dynamical system 158 . To test this interpretation, a quasi-geostrophic numerical model that captures the meta-stability of the large-scale flow in the rotating annulus 174 was run with and without weak stochastic forcing added to the potential vorticity evolution equation for each fluid layer. The stochastic forcing was an approximate representation of the inertia-gravity waves, which are inherently ageostrophic and are therefore forbidden from the quasi-geostrophic model. Consistent with the laboratory experiments, only when the noise term was activated did the numerical simulations exhibit large-scale wave transitions in the equilibrated flow 169 . In further numerical experiments, the noise was found to be able to influence wavenumber selection during the developing baroclinic instability.
In summary, the above laboratory experiments constitute the first evidence in a real fluid that small-scale waves may trigger large-scale regime transitions. In a numerical model in which the small-scale waves were absent, the transitions were captured through the addition of stochastic noise. Note that the small-scale waves satisfy the dispersion relation for inertia-gravity waves and are therefore coherent in space and time, and yet apparently they are 'sensed' by the large-scale flow as if they were random fluctuations. These results have led to a possible interpretation of sudden stratospheric warmings as noise-induced transitions 9 . Furthermore, these laboratory results help to motivate the development of stochastic parameterizations in climate models and a more general development of stochastic climate theory.
Stochastic Climate Theory
Climate is a multi-scale system in which different physical processes act on different temporal and spatial scales 69 . For instance, on the micro-scale are turbulent eddies with time scales of seconds to minutes, on the meso-scale is convection with time scales of hours to days, on the synoptic scale are mid-latitude weather systems and blocking with time scales from days to weeks, on the large-scale are Rossby waves and teleconnection patterns with time scales of weeks to seasons. And there is the coupled atmosphere-ocean system with time scales of seasons to decades. The crucial point here is that all these processes acting on widely different temporal and spatial scales, interact with each other due to the inherent nonlinearity of the climate system. We have shown an illustrative laboratory example for this in the previous section.
For many practical applications we are only interested in the processes on a particular scale and not in the detailed evolution of the processes at smaller scales. Often the scales of interest are linked to inherently predictable processes, while the smaller scales processes are unpredictable. For instance, in the above laboratory experiment we are interested in the regime behavior and not in the detailed evolution of the inertia-gravity waves. In numerical simulations the fastest scales, which are typically also the smallest scales, use up the bulk of computing time, slowing down the computation of the processes of actual interest. In numerical weather and climate prediction many of the small scale processes are currently not explicitly resolved and won't be in the foreseeable future. This neglect of these processes can lead to biases in the simulations. Because of that the unresolved processes need to be parameterized as demonstrated in the previous section.
Stochastic climate theory is based on the concept of scale separation in space or time. Hasselmann 56 was the first to propose to split the state vector z into slow climate components x and fast weather fluctuations y and then to derive an effective equation for the slow climate variables only. In this equation the effect of the now unresolved variables is partially represented as a noise term. The physical intuition behind this idea is, for example, that the aggregated effect of 'fast' weather fluctuations drives fluctuations in the 'slower' ocean circulation. To first order such a model can explain the 'red' spectrum of oceanic variables 36,64 . It has to be noted that there is no scale separation in the climate system. This lack of time-scale separation introduces non-Markovian (memory) effects and complicates the derivation of systematic parameterizations.
Rigorous mathematical derivations for this approach have been provided by Gottwald Givon et al. 50 and the text book by Pavliotis and Stuart 125 . This approach has been applied to climate models by Majda and coworkers 29,37,38,[89][90][91][92][93][94]96 . Climate models have the following general functional form
d z = F +L z +B( z, z) dt(1)
whereF denotes an external forcing,L a linear operator andB a quadratic nonlinear operator. Eq. (1) constitutes the form of the dynamical cores of weather and climate prediction models. Now splitting the state vector z into slow x and fast y components (which amounts to assuming a time scale separation) and assuming that the nonlinear self-interaction of the fast modesB( y, y) can be represented by a stochastic process 37,38,89,90 leads to a stochastic differential equation. The stochastic mode reduction approach 37,38,89,90 then predicts the functional form of reduced climate models for the slow variable x alone:
d x = (F + L x + B( x, x) + M ( x, x, x)) dt + σ A d W A + σ A ( x)d W M(2)
Structurally new terms are a deterministic cubic term which acts predominantly as nonlinear damping and both additive and multiplicative (state-dependent) noise terms. The fundamentals of stochastic processes and calculus are explained in Box 1. The multiplicative noise and the cubic term stem from the nonlinear interaction between the resolved and unresolved modes 37 . The above systematic procedure allows also a physical interpretation of the new deterministic and stochastic terms 37 . The additive noise stems both from the nonlinear interaction amongst the unresolved modes and the linear interaction between resolved and unresolved modes 37 .
BOX 1 STOCHASTIC PROCESSES
In contrast to deterministic processes stochastic processes have a random component. See the books by Lemons 86 and Gardiner 49 for intuitive introductions to stochastic processes. Typically stochastic processes are driven by white noise. White noise is a serially uncorrelated time series with zero mean and finite variance 49 . A stochastic differential equation (SDE) is a combination of a deterministic differential equation and a stochastic process. In contrast to regular calculus, stochastic calculus is not unique; i.e. different discretizations of its integral representation lead to different results even for the same noise realization. The two most important calculi are Ito and Stratonovich. See details in Gardiner 49 . The physical difference is that Ito calculus has uncorrelated noise forcing while Stratonovich allows for finite correlations between noise increments. Hence, physical systems have to be typically approximated by Stratonovich SDEs. On the other hand, it is mathematically straightforward to switch between the two calculi. So one only needs to make a decision at the beginning which calculus is more appropriate for modeling the system under consideration and can then switch to the mathematically more convenient form. SDEs describe systems in a path wise fashion. The Fokker-Planck equation (FPE) describes how the probability distribution evolves over time 49 . Thus, SDEs and the FPE offer two different ways at looking at the same system. The parameters of SDEs and their corresponding FPE are linked; thus, one can use the FPE to estimate the parameters of the corresponding SDE 3,146 .
Multiplicative (or state-dependent) noise is important for deviations from Gaussianity and thus extremes. The intuition behind multiplicative noise is as follows: On a windless day the fluctuations are very small, whereas on a windy day not only is the mean wind strong but also the fluctuations around this mean are large; thus, the magnitude of the fluctuations dependent on the state of the system.
The first practical attempts at stochastic climate modelling were made using Linear Inverse Models (LIM) 127,128,166,176 and dynamically based linear models with additive white noise forcing 26,27,34,35,179 . These approaches linearise the dynamics and then add white noise and damping 166 in order to make the models numerically stable (i.e. the resulting linear operator should only have negative eigenvalues to ensure stability and reliasability of the solutions). While these models have encouraging predictive skill, especially for ENSO, they can only produce Gaussian statistics and, thus, are less useful for predictions of high impact weather.
Recently there are encouraging attempts in fitting nonlinear stochastic models to data. These include multilevel regression 70,74 , fitting the parameters via the Fokker-Planck equation 3,146 , stochastic averaging 23,103 , optimal prediction 18,154 or Markov Chains 21 . Most of the previous approaches fitted the parameters of the stochastic models without taking account of physical constraints, e.g. global stability. Many studies linearized the dynamics and then added additional damping to obtain numerically stable models 1,2,166,179 . Majda et al. 96 developed the nonlinear normal form of stochastic climate models and also physical constraints for parameter estimation. Recent studies use these physical constraints to successfully derive physically consistent stochastic climate models 57,97,126 .
Most of the above approaches are based on an implicit assumption of time scale separation. However, the climate system has a spectrum with no clear gaps which would provide the basis of scale separation and the derivation of reduced order models. Such a lack of time scale separation introduces memory effects into the truncated description. Memory effects mean that the equations become non-Markovian and that also past states need to be used in order to predict the next state. This can be explained by considering the interaction between a large-scale Rossby wave with a smaller scale synoptic wave. At some location the Rossby wave will favor the development of the synoptic wave. Initially this synoptic wave grows over some days without affecting the Rossby wave. Once the synoptic wave has reached a sufficient large amplitude it will start affecting the Rossby wave. Now in a reduced order model only resolving the Rossby wave but not the synoptic wave this interaction cannot be explicitly represented. However, because the Rossby wave initially triggered the synoptic wave which then in turn affects it some days later, this can be modeled with memory terms which takes into account that the Rossby wave has triggered at time t 0 an anomaly which will affect it at some later time t n .
Recently, Wouters and Lucarini 177 have proposed to treat comprehensively the problem of model reduction in multi-scale systems by adapting the Ruelle response theory 136,137 for studying the effect of the coupling between the fast and slow degrees of freedom of the system. This theory has previously been used in a geophysical context to study the linear and nonlinear response to perturbations 87,88 , which also allows climate change predictions. This approach is based on the chaotic hypothesis 48 and allows the general derivation of the reduced dynamics of the slow variables able to mimic the effect of the fast variables in terms of matching the changes in the expectation values of the observables of the slow variables. The ensuing parametrization includes a deterministic correction, which is a mean field result and corresponds to linear response, a general correlated noise and a non-Markovian (memory) term. These results generalize Eq. (2). In the limit of infinite time-scale separation, the classical results of the averaging method is recovered. Quite reassuringly, the same parametrizations can be found using a classical Mori-Zwanzig approach 19 , which is based on projecting the full dynamics on the slow variables and general mathematical results provide evidence that deterministic, stochastic and non-Markovian components should constitute the backbone of parameterizations 17,178 . Recent studies show improvements over approaches based on time-scale separation 17,177,178 .
Recent studies have shown that stochastic approaches are also important for the prediction of extreme events and tipping points 40,41,155,156 . Sura 156 discusses a stochastic theory of extreme events. He especially focuses on deviations from a Gaussian distribution; i.e. skewness and kurtosis, as first measures of extremes. He shows that multiplicative noise plays a significant role in causing non-Gaussian distributions. Franzke 40 shows that both deterministic nonlinearity and multiplicative noise are important in predicting of extreme events.
Statistical Physics Approaches to Stochastic Climate Theory
Significant progress has been achieved in the development of tractable and accurate statistical dynamical closures for general inhomogeneous turbulent flows that are underpinned by exact stochastic models (see Box 2). For an accessible review see the text book by Heinz 58 . The statistical dynamical closure theory, pioneered by Kraichnan 71 , has been recognized as a natural framework for a systematic approach to modelling turbulent geophysical flows. Closure theories like the Direct Interaction Approximation (DIA), 71 for homogeneous turbulence and the Quasi-Diagonal Direct Interaction Approximation (QDIA), 42 for the interaction of mean flows with inhomogeneous turbulence have exact generalized Langevin model representations 60 . This means that such closures are realizable; i.e. they have non-negative energy.
The first major application of turbulence closures has been the examination of the predictability of geophysical flows. Early approaches applied homogeneous turbulence models to predicting error growth 77,79,83 whereas more recent advances by Frederiksen and O'Kane 46 , O'Kane and Frederiksen 113 , building on the pioneering studies of Epstein 32 and Pitcher 130 , have enabled predictability studies of inhomogeneous strongly non-Gaussian flows typical of the mid-latitude atmosphere. Turbulence closures have also been used for Subgrid-Scale Parameterisation (SSP) of the unresolved scales, for example eddies in atmospheric and ocean general circulation models. Since it is generally only possible to represent the statistical effects of unresolved eddies while their phase relationships with the resolved scales are lost 100 , statistical dynamical turbulence closures are sufficient to allow SSPs to be formulated in a completely transparent way 42,43,73,77,80,112,134 . Insights gained through the development of inhomogeneous turbulence closure theory have motivated the recent development of general stochastic forms for subgrid-scale parameterisations for geophysical flows 68 .
Statistical dynamical closure theory
BOX 2 CLOSURE PROBLEM
In order to describe the statistical behavior of a turbulent flow the underlying nonlinear dynamical equations must be averaged. For simplicity we consider a generic equation of motion with quadratic nonlinearity for homogeneous turbulence, in which the mean field is zero, and the fluctuating part of the vorticity in Fourier space,ζ k , satisfies the equation:
∂ ∂tζ k (t) = K kpqζ−p (t)ζ −q (t).(3)
where p and q are the other wave numbers describing triad interactions i.e. k = (k x , k y ) where δ(k + p + q) = 1 if k + p + q = 0 and 0 otherwise. Here K kpq are the interaction or mode coupling coefficients. The correlation between the eddies can now be represented by an equation for the covariance (cumulant in terms of wavenumbers k and l) which is found to depend on the third order cumulant in Fourier space:
∂ ∂t ζ k (t)ζ −l (t ′ ) = K kpq ζ −p (t)ζ −q (t)ζ −l (t ′ ) .(4)
Similarly the third order cumulant depends on the fourth order and so on such that we see that an infinite hierarchy of moment or cumulant equations is produced. Statistical turbulence theory is principally concerned with the methods by which this moment hierarchy is closed and the subsequent dynamics of the closure equations. The fact that for homogeneous turbulence the covariance matrix is diagonal greatly simplifies the problem. The majority of closure schemes are derived using perturbation expansions of the nonlinear terms in the primitive dynamical equations. The most successful theories use formal renormalization techniques 19,58 . The development of renormalized turbulence closures was pioneered by Kraichnan's Eulerian dia 71 for homogeneous turbulence. The dia, so named because it only takes into account directly interacting modes, can be readily regularised to include approximations to the indirect interactions 45,111 which are required to obtain the correct inertial range scaling laws. Other homogeneous closures such as Herring's self consistent field theory (scft 59 ) and McComb's local energy transfer theory (let), 99 were independently developed soon after. The dia, scft and let theories have since been shown to form a class of homogeneous closures that differ only in whether and how a fluctuation dissipation theorem (fdt i.e. the linear response of a system to an infinitesimal perturbation as it relaxes toward equilibrium) 15,25,44,71 is applied. As noted earlier, a consequence of the dia having an exact stochastic model representation is that it is physically realizable, ensuring positive energy spectra. This is in contrast with closures based on the quasi-normal hypothesis which require further modifications in order to ensure realizability; an example of such a closure is the eddy damped quasi-normal Markovian (EDQNM) closure 77,109,116 developed as a bets Markovian fit to the DIA. The EDQNM is dependent on a choice of an eddy-damping parameter which can be tuned to match the phenomenology of the inertial range. This Markovian assumption assumes that the rate at which the memory integral decays is significantly faster than the time scale on which the covariances evolve. The relative success of these turbulence closures has enabled the further study of the statistics of the predictability of homogeneous turbulent flows [77][78][79]102 .
Frederiksen 42 formulated a computationally tractable non-Markovian (memory effects) closure, the quasidiagonal direct interaction approximation (qdia), for the interaction of general mean and fluctuating flow components with inhomogeneous turbulence and topography. The qdia assumes that, prior to renormalisation, a perturbative expansion of the covariances are diagonal at zeroth order. In general, very good agreement has been found between the qdia closure results and the statistics of dns 45,46,111 .
The non-Markovian closures discussed above are systems of integro-differential equations with potentially long time-history integrals posing considerable computational challenges, however various ways to overcome these challenges exist 44,46,[111][112][113][114][115]135 and have been generalised to allow computationally tractable closure models for inhomogeneous turbulent flow over topography to be developed 42,46,111 . An alternative derivation of a stochastic model of the Navier-Stokes equations has been put forward by Memin 107 . It is based on a decomposition of the velocity fields into a differentiable drift and a stochastic component.
Statistical dynamical and stochastic subgrid modelling
Many subgrid-scale stress models assume the small scales to be close to isotropic and in equilibrium such that energy production and dissipation are in balance, similar to the eddy viscosity assumption of the Smagorinsky model 148 . Using the dia, Kraichnan 71 showed that for isotropic turbulence the inertial transfer of energy could be represented as a combination of both an eddy viscous (on average energy drain from retained to subgrid scales) and stochastic back-scatter (positive semi-definite energy input from subgrid to retained scales) terms. The nonlinear transfer terms represented by eddy viscosity and stochastic back-scatter are the subgrid processes associated with the respective eddy-damping and nonlinear noise terms that constitute the right hand side of the dia tendency equation for the two-point cumulant ∂ ∂t ζ k (t)ζ −k (t ′ ) . Leith 77 used the edqnm closure to calculate an eddy dissipation function that would preserve a stationary k −3 kinetic energy spectrum for twodimensional turbulence. Kraichnan 73 developed the theory of eddy viscosity in two and three dimensions and was the first to identify the existence of a strong cusp in the spectral eddy viscosity near the cutoff wavenumber representing local interactions between modes below and near the cusp. Rose 134 argued for the importance of eddy noise in subgrid modelling.
O'Kane and Frederiksen 112 calculated qdia based ssps considering observed atmospheric flows over global topography and quantifying the relative importance of the subgrid-scale eddy-topographic, eddy-mean field, quadratic mean and mean field-topographic terms. They also compared the qdia based ssps to heuristic approaches based on maximum entropy, used to improve systematic deficiencies in ocean climate models 62 . While closure models may be the natural starting place for developing subgrid-scale parameterisations, their complexity makes them difficult to formulate and apply to multi-field models like gcms, even though sucessfull studies exist 68,180 .
Stochastic Parametrisation Schemes in Comprehensive Models
Climate and weather predictions are only feasible because the governing equations of motion and thermodynamics are known. To solve these equations we need to resort to numerical simulations that discretize the continuous equations onto a finite grid and parameterize all processes that cannot be explicitly resolved. Such models can be characterized in terms of their dynamical core, which describe the resolved scales of motion, and the physical parameterizations, which provide estimates of the grid-scale effect of processes which cannot be resolved by the dynamical core. This general approach has been hugely successful in that nowadays predictions of weather and climate are made routinely. On the other hand, exactly through these predictions it has become apparent that uncertainty estimates produced by current state-of the art models still have shortcomings.
One shortcoming is that many physical parameterizations are based on bulk formula which are based on the assumption that the subgrid-scale state is in equilibrium with the resolved state 118 . Model errors might arise from a misrepresentation of unresolved subgrid-scale processes which can affect not only the variability, but also the mean error of a model 129,141 . An example in a comprehensive climate model is e.g., the bias in the 500hPa geopotential height pattern, which is reduced when the representation of the subgrid-state is refined 7 (Fig. 2).
In recent years, methods for the estimation of flow-dependent uncertainty in predictions have become an important topic. Ideally, uncertainties should be estimated within the physical parameterizations and uncertainty representations should be developed alongside the model. Many of these methods are "ad hoc" and added a posteriori to an already tuned model. Only first steps to develop uncertainty estimates from within the parameterizations have been attempted 20,131 . The representation of model-error in weather and climate models falls in one of two major categories: Multi-model approaches and stochastic parameterizations. In the multi-model approach each ensemble member consists of an altogether different model. The models can differ in the dynamical core and the physical parameterizations 55,63,75 or use the same dynamical core but utilize either different static parameters in their physical parameterizations 151 or altogether different physics packages 6,31,106,152 . Both approaches have been successful in improving predictions of weather and climate over a range of scales, as well as their uncertainty. Multi-model ensembles provide more reliable seasonal forecasts 122 and are commonly used for the uncertainty assessment of climate change predictions e.g., as in the Assessment Report 5 of the Intergovernmental Panel on Climate Change (IPCC) 157 . Stochastic parameterizations are routinely used to improve the reliability of weather forecasts in the short-6 and medium-range 5,10,123 as well as for seasonal predictions 4,28,165 .
In the stochastic approach, the effect of uncertainties due to the finite truncation of the model are treated as independent realizations of stochastic processes that describe these truncation uncertainties. This treatment goes back to the idea of stochastic-dynamic prediction 33,118,130 . While the verdict is still open if subgrid-scale fluctuations must be included explicitly via a stochastic term, or if it is sufficient to include their mean influence by improved deterministic physics parameterizations, one advantage of stochastically perturbed models is that all ensemble members have the same climatology and model bias; while for multi-parameter, multi-parameterization and multi-model ensembles each ensemble member is de facto a different model with its own dynamical attractor. For operational centers the maintenance of different parameterizations requires additional resources and due to the different biases makes post-processing very difficult.
Stochastic Parameterizations in Numerical Weather Prediction
Due to the chaotic nature of the dynamical equations governing the evolution of weather, forecasts are sensitive to the initial condition limiting the intrinsic predictability of the weather system 82,84 . Probabilistic forecasts are performed by running ensemble systems, where each member is initialized from a different initial state and much effort has gone into the optimal initialization of such ensemble systems 63,108,161 . Nevertheless state-ofthe-art numerical weather predictions systems continue to produce unreliable and over-confident forecasts 14 . Consequently, the other source of forecast uncertainty -model-error -has received increasing attention 117,118 .
Since for chaotic systems model-error and initial condition error will both result in trajectories that will diverge from the truth, it is very difficult to disentangle them 149 .
The first stochastic parameterization used in an operational numerical weather prediction model was the stochastically perturbed physics tendency scheme (SPPT), sometimes also referred to as stochastic diabatic tendency or Buizza-Miller-Palmer (BMP) scheme 13 . SPPT is based on the notion that -especially as the horizontal resolution increases -the equilibrium assumption no longer holds and the subgrid-scale state should be sampled rather than represented by the equilibrium mean. Consequently, SPPT multiplies the accumulated physical tendencies of temperature, wind and moisture at each grid-point and time step with a random pattern that has spatial and temporal correlations. In other words, SPPT assumes that parameterization uncertainty can be expressed as a multiplicative noise term. Ensemble systems perturbed with the SPPT scheme show increased probabilistic skill mostly due to increased spread in short and medium-range ensemble forecasts 8,13,132,159 .
A second successful stochastic parameterization scheme, is the so-called stochastic kinetic energy-backscatter scheme (SKEBS) whose origin lies in Large-Eddy Simulation modeling 98 and has recently been extended to weather and climate scales 142,143 . The key idea is that energy associated with subgrid processes is injected back onto the grid using a stochastic pattern generator. This method has been successfully used in a number of operational and research forecasts across a range of scales 5,6,8,10,11,16,138 . Similar to the SPPT scheme, ensemble systems with SKEBS increase probabilistic skill by increasing spread and decreasing the root-meansquare (RMS) error of the ensemble mean forecast. First results of these schemes at a convection-permitting resolution of around 4km report also a positive impact on forecast skill, in particular more reliable precipitation forecasts 12,133 .
Stochastic Parameterizations in Climate Models
The use of stochastic parameterization in climate models is still in its infancy. Climate prediction uncertainty assessments, e.g., IPCC 150 , are almost exclusively based on multi-models, mostly from different research centers. Part of the problem is that on climate timescales, limited data for verification exists. A second reason is that on longer timescales, bias is a major source of uncertainty and traditional multi-models are very efficient at sampling biases, although such an experiment is poorly designed for an objective and reliable uncertainty assessment.
However, in recent years first studies have emerged which demonstrate the ability of stochastic parameterizations to reduce longstanding biases and improve climate variability (see Fig. 2 for an example). Jin and Neelin 81 developed a stochastic convective parameterization that includes a random contribution to the convective available potential energy(CAPE) in the deep convective scheme. They find that adding convective noise results in enhanced eastward propagating, low-wavenumber low-frequency variability. Berner et al. 7 investigate the impact of SKEBS on systematic model-error and report an improvement in the representation of convectively-coupled waves leading to a reduction in the tropical precipitation bias. Furthermore, Majda and colleagues developed systematic stochastic multi-cloud parameterizations for organized convection 47,67,94,95 . The multi-cloud approach is based on the assumption that organized convection involves three types of clouds and the evolution from one cloud type to another can be described by a transition matrix.
A longstanding systematic error of climate models is the underestimation of the occurrence of Northern Hemispheric blocking. Stochastic parameterizations have been demonstrated to be one way to increase their frequency 4,28,53,165 , although, e.g. increasing horizontal resolution, leads to similar improvements 7,24 . This suggests that while it might be necessary to include subgrid-scale variability in some form, the details of this representation might not matter. On the other side, Berner et al. 7 argue that this degeneracy of response to different subgrid-scale forcings warrants a cautionary note: namely that a decrease in systematic error might not necessarily occur for the right dynamical reasons. The opposite holds true, as well: Due to the necessary tuning of parameters in the parameterizations of comprehensive climate models, an improvement in the formulation of a physical process might not immediately lead to an improved model performance. A striking example of compensating model errors is described in Palmer and Weisheimer 119 , who report how an inadequate representation of horizontal baroclinic fluxes resulted in a model error that was equal and opposite to the systematic error caused by insufficiently represented vertical orographic gravity wave fluxes. Improvements to wave drag parameterization without increasing resolution unbalanced the compensating model errors, leading to an increase in systematic model bias.
Williams 175 studied the effect of including a stochastic term in the fluxes between the atmospheric and oceanic components in a coupled ocean-atmosphere model. He reports changes to the time-mean climate and increased variability of the El Nino Southern Oscillation, suggesting that the lack of representing of sub-grid variability in air-sea fluxes may contribute to some of the biases exhibited by contemporary climate models.
On seasonal timescales where sufficient observational data for a probabilistic verification exist, stochastic parameterizations have been reported to increase predictive skill. For example, ensemble forecasts of the sea surface temperatures over the Nino3.4 region showed increased anomaly correlation, decreased bias and decreased root mean square error in coupled ocean-atmosphere models 4,28,165 .
Conclusion
We postulate the use of stochastic-dynamical models for uncertainty assessment and model-error representation in comprehensive Earth-System models. This need arises since even state-of-the-art weather and climate models cannot resolve all necessary processes and scales. Here we reviewed mathematical methods for stochastic climate modeling as well as stochastic subgrid-scale parameterizations and postulate their use for a more systematic strategy of parameterizing unresolved and unrepresented processes.
In the last decade, a number of studies emerged that demonstrate the potential of this approach, albeit applied in an ad hoc manner and tuned to specific applications. Stochastic parameterizations have been shown to provide more skillful weather forecasts than traditional ensemble prediction methods, at least on timescales where verification data exists. In addition, they have been shown to reduce longstanding climate biases, which play an important role especially for climate and climate change predictions.
Here we argue, that rather than pushing out the limit of skillful ensemble predictions by a few days, more attention should be given on the assessment of uncertainty (as already proposed, e.g., Smith 149 ). Ideally, it should be carried out alongside the physical parameterization and dynamical core development and not added a posteriori. The uncertainty should be directly estimated from within the parameterization schemes and not tuned to yield a particular model performance, as is current practice. For example, Sapsis and Majda 139 , 140 propose a statistical framework which systematically quantifies uncertainties in a stochastic fashion.
The fact that according to the last two assessment reports (AR) of the IPCC (AR4 147 and AR5 150 ) the uncertainty in climate predictions and projections has not decreased may be a sign that we might be reaching the limit of climate predictability, which is the result of the intrinsically nonlinear character of the climate system (as first suggested by Lorenz 82 ).
Recently Palmer 121 argued that due to limited computational and energy power resources, predictable scales should be solved accurately, while the unpredictable scales could be represented inaccurately. This strategy is at the core of the systematic mode reduction reviewed here, but has only recently been considered for comprehensive Earth-System Models. Stochastic models focus on the accurate simulation of the large, predictable, scales, while only the statistical properties of the small, unpredictable, scales are captured. This has been demonstrated, e.g, by Franzke and Majda 38 , Kravtsov et al. 74 , who successfully applied mode reduction strategies to global atmospheric circulation models. They showed that these reduced models consisting of only 10-15 degrees of freedom reproduced many of the important statistics of the numerical circulation models which contained a few hundreds degrees of freedom. Vanden-Eijnden 163 proposed numerical approaches for multi-scale systems where only the largest scales are explicitly computed and the smaller scales are approximated on the fly.
The recent result of Wouters and Lucarini 177,178 provide a promising path towards a general theory of parametrizations for weather and climate models, and give theoretical support that parameterization schemes should include deterministic, stochastic and non-Markovian (memory) components. Moreover, Wouters and Lucarini's results suggest that there is common ground in developing parameterizations for weather and climate prediction models. Optimal representations of the reduced dynamics based on Ruelle's response theory and the Mori-Zwanzig formalism coincide, thus, providing equal optimal representations of the long-term statistical properties and the finite-time evolution of the slow variables.
One exciting future research area is the use of stochastic methods for use in data assimilation, which is already an active field of research 51,54,65,104,114,115,133 . Stochastic methods have been shown to increase the ensemble spread in data assimilation, leading to a better match between observations and model forecasts 54,105,133 . A cutting-edge frontier is the use of order moments and memory effects in Kalman filter data assimilation schemes 115 . Another emerging field is the use of stochastic parameterizations in large climate ensembles, which would allow the comparison of uncertainty estimates based in multi-models to that of stochastically perturbed ones.
Our hope is that basing stochastic-dynamic prediction on sound mathematical and statistical physics concepts will lead to substantial improvements, not only in our ability to accurately simulate weather and climate, but even more importantly to give proper estimates on the uncertainty of these predictions. Acknowledgments: CLEF is supported by the German Research Foundation (DFG) through the cluster of Excellence CliSAP, TJO is an Australian Research Council Future Fellow, PDW acknowledges a University Research Fellowship from the Royal Society (UF080256) and VL funding from the European Research Council (NAMASTE).
Figure 1 :
1Regime transitions in a rotating two-layer annulus laboratory experiment, viewed from above. Different colours correspond to different internal interface heights, through the use of a sophisticated visualisation technique170 . In the upper row, small-scale inertia-gravity waves are absent, and large-scale regime transitions do not occur. In the lower row, small-scale inertia-gravity waves are present locally in the troughs of the large-scale wave, and a large-scale regime transition does occur. From the laboratory experiments of Williams et al.168,169,172,173 .
Figure 2 :
2Mean systematic error of 500 hPa geopotential height fields (shading) for extended boreal winters (December-March) of the period 1962-2005. Errors are defined with regard to the observed mean field (contours), consisting of a combination of ERA-40 (1962-2001) and operational ECMWF analyses (2002-2005). (a) Systematic error in a numerical simulation with the ECMWF model IFS, version CY32R1, run at a horizontal resolution of T L 95 (about 210km) and 91 vertical levels. (b) Systematic error in a simulation with a stochastic kinetic-energy backscatter scheme (SKEBS). Significant differences at the 95% confidence level based on a Student's t-test are hatched. After Berner et al. 7 .
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Different colours correspond to different internal interface heights, through the use of a sophisticated visualisation technique 170 . In the upper row, small-scale inertia-gravity waves are absent, and large-scale regime transitions do not occur. In the lower row, small-scale inertia-gravity waves are present locally in the troughs of the large-scale wave, and a large-scale regime transition does occur. From the laboratory experiments of Williams et al. 168,169,172,173. M J Zidikheri, After Berner et al. 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23J S Frederiksen, After Berner et al. 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23; . . . . . . . . . . . , After Berner et al. 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23J. Atmos. Sci. 662844Significant differences at the 95% confidence level based on a Student's t-test are hatchedZidikheri M. J. and J. S. Frederiksen, 2009: Stochastic subgrid parameterizations for simulations of atmospheric baroclinic flows. J. Atmos. Sci., 66, 2844. List of Figures 1 Regime transitions in a rotating two-layer annulus laboratory experiment, viewed from above. Different colours correspond to different internal interface heights, through the use of a sophisti- cated visualisation technique 170 . In the upper row, small-scale inertia-gravity waves are absent, and large-scale regime transitions do not occur. In the lower row, small-scale inertia-gravity waves are present locally in the troughs of the large-scale wave, and a large-scale regime transition does occur. From the laboratory experiments of Williams et al. 168,169,172,173 . . . . . . . . . . . . . . . 22 2 Mean systematic error of 500 hPa geopotential height fields (shading) for extended boreal winters (December-March) of the period 1962-2005. Errors are defined with regard to the observed mean field (contours), consisting of a combination of ERA-40 (1962-2001) and operational ECMWF analyses (2002-2005). (a) Systematic error in a numerical simulation with the ECMWF model IFS, version CY32R1, run at a horizontal resolution of T L 95 (about 210km) and 91 vertical levels. (b) Systematic error in a simulation with a stochastic kinetic-energy backscatter scheme (SKEBS). Significant differences at the 95% confidence level based on a Student's t-test are hatched. After Berner et al. 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
| sample_997 | 0.9791 | arxiv | |
Analyzing The Effect of Combining Carbon Price and Border Adjustments in The US Power Grid
19 Feb 2023
Huynh Trung
Department of Electrical & Computer Engineering
North Carolina A&T State University
27411GreensboroNC
Thanh Tran
Department of Electrical & Computer Engineering
North Carolina A&T State University
27411GreensboroNC
Hieu Trung Nguyen
Department of Electrical & Computer Engineering
North Carolina A&T State University
27411GreensboroNC
Analyzing The Effect of Combining Carbon Price and Border Adjustments in The US Power Grid
19 Feb 2023Carbon emissions reductioncarbon priceemissions leakageborder adjustmentsCOBRA
Border adjustment is a crucial key to mitigating emission leakage. This study conducts a combination of carbon price and border adjustments in the US power grid to analyze the impact on decarbonization and leakage mitigation of those policies. The combination is simulated based on the direct current optimal power flow (DCOPF) model and allocation constraints from the PJM study. In the study, the public health assessment tool (COBRA) is used to estimate the health benefits associated with emission reduction at the county level. The study finds that the border adjustments enhance the effect of the carbon price on the unregulated regions which results in mitigating the leakage. Gaining tax revenues from carbon emissions and mitigating the difference between the carbon price and non-carbon price regions. The study also shows that renewable energy in the carbon price regions affects the outcome of combining carbon price and border adjustments.
Set and indices CA
Set of generators and buses inside CA CA * Set of generator and buses outside CA G, g Set and index of generators, g ∈ G Re * Set of generators are not renewable energy Re
Set of renewable energy generators I, i
Set and index of nodes, i ∈ I L, = ij Set and index of lines, connecting bus i to bus j, ∈ L Parameters a g , b g , c g Coefficients of a polynomial cost function λ CO2
Tax for each ton of carbon emissions D i
Real power demand at node i r g Carbon emissions rate of generator g x Reactance of line
Variables δ i
Phase angle of node i F Transmission power of line P g Total power of generator g P C g Power with the carbon price of generator g P N C g Power without the carbon price of generator g Table 1: Glossary 1. Introduction
Background and literature review
For decades, climate change, or the greenhouse effect has been the biggest concern around the world. In addition to electric generation, transportation, industrial manufacturing, residential and commercial building energy use account for the majority of emissions [1]. Electricity generation accounts for 27 percent of total greenhouse gas emissions in the US in 2018, followed by coal and natural gas at 65 and 33 percent, respectively [2]. Many countries together try to reach a common purpose is to keep the temperature not exceeding 2 0 C comparing pre-industrial levels [3][4][5]. Nevertheless, the annual carbon emissions reach 36,790 megatons (Mt) in 2017, which means the budget for limiting global warming to less than 2 0 C is approximately 1,109,000 Mt for the next 26 years [4]. Thus, there is a challenge for all sectors including power energy. Various methods, policies, and technologies have been discussed to deal with that challenge in the energy sector. [6] investigates how storage electricity could decrease carbon emissions. The authors perform the studies in the Electricity Reliability Council of Texas (ERCOT) and claim that grid-scale electricity storage would help to decrease carbon emissions from 2025 to 2045. In [4], the authors develop a framework to integrate short-term and long-term demand responses, then apply it to the EU-GEN model to find the optimal level of energy efficiency investment, quantify its contribution to decarbonizing the European power sector, and discuss how short-term demand responses interact with supply. The study found that compared to a scenario where a short-term demand response and energy efficiency investments were not implemented, 70 GW of gas power would be decommissioned immediately and 180 GW less gas capacity is needed in 2050.
In terms of policies, carbon pricing is considered a cost-effective way to curb carbon emissions. In the carbon pricing program, emitters are charged for the tons of carbon dioxide (CO 2 ) they emit. There are two main forms of carbon pricing: 1) cap-and-trade and 2) carbon tax programs. Under cap-and-trade regulation, the producers receive emissions credits or emission allowances (the limited credits (allowances) are called "the cap") from government agencies. If the producers' emissions exceed the emission allowances, they can purchase the allowances from another through the carbon trading market and vice versa [7]. There are several carbon trading markets including European Union Emissions Trading Scheme (EU ETS), Certified Emission Reductions (CERs), Emission Reduction Units (ERUs) and European Emission Allowances (EUAs) [8]. Because the allowances can be traded among polluters, the price for each unit of carbon emissions is varying and is dependent on the trading market. However, a financial penalty is imposed on agents who fail to offset their emissions at the end of the year [8]. In the US, The cap-and-trade program applied to Sulfur dioxide (SO 2 ) was established under the US Clean Air Act Amendments of 1990. In 1994, California's South Coast Air Quality Management District launched a Regional Clean Air Incentives Market (RECLAIM) program in the Los Angeles area to reduce (SO 2 ) and nitrogen-oxide (NO x ) [9]. The Regional Greenhouse Gas Initiative (RGGI) launched in 2009 is a cap-and-trade program for carbon emissions (CO 2 ) [10]. Under the carbon tax program, producers are charged a fixed tax per unit of carbon emissions they emit [2]. In the past two decades, many studies have been done to investigate the effectiveness of carbon pricing on decarbonization [1,2,[10][11][12].
In the power sector, by applying the tax for carbon emissions, carbon pricing raises wholesale electricity prices leading to higher retail electricity.
In the short run, consumers can respond to higher retail prices by reducing electricity consumption through energy conservation efforts such as using appliances less frequently [2]. In the long run, the prospect of continuing and rising carbon prices encourages firms to lower their emission reduction costs by innovating new technologies with low or zero-emitting [2,13]. For other policies, such as technology mandates, choose a single method for a wide range of firms. It may become unnecessarily costly for some firms to reduce emissions with such a one-size-fits-all approach if they can find cheaper alternatives [1,5]. Carbon pricing not only are innovations encouraged to reduce emissions but also social welfare can be improved in multiple ways through tax revenues [13]. Corporate tax cuts, personal income tax cuts, and low-income tax cuts could be achieved without an increase in government spending through tax revenues of carbon emissions [5].
Although carbon pricing policies are more efficient and cost-effective ways to reduce carbon emissions, these regulations are not implemented at a nationwide level. Denmark, Norway, Sweden, Switzerland, the UK, Finland, and the Netherlands are counties that have implemented these programs in European [14], and in the US, California, Oregon, Washington, Hawaii, Pennsylvania, and Massachusetts are the states that have introduced them [15]. To keep minimize the production cost, producing electricity by the low rate carbon emission generators or using renewable sources (renewable penetration) is the solution. Because the carbon price does not apply at a national level, another solution is decreasing the power generated in the carbon price sub-regions and increasing the power generated in the non-carbon price sub-regions. This solution could reduce the emissions in the carbon price sub-regions and minimize the total production cost of the whole system, but leads to another environmental issue. Due to the increase of power generated in the non-carbon price sub-regions, the emissions of that subregions grow up and the pollution moves from the regulated sub-regions to the unregulated sub-regions [16,17]. This issue is called emissions leakage. Therefore, carbon pricing alone does not seem enough to reduce emissions comprehensively, and there is a need for more policies or technologies to address emissions leakage. Many studies and discussions have been done and border adjustment is considered a key role of climate policies to mitigate the leakage [18][19][20][21][22][23].
Border adjustment is the environmental trade policy that includes import charges and sometimes export rebates on carbon emissions-related products from unregulated regions [24]. In European, the border adjustment is designed and implemented in a Carbon Border Adjustment Mechanism (CBAM) [22,23]. CBAM is centered on the border charge on imports. Even so, it can be combined with a rebate or abatement on exports. Rebates can be direct subsidies such as refunds of a carbon tax or indirect subsidies such as free allocations of allowances based on exports [23]. As a result, the CBAM extends the carbon price to products imported from non-EU countries with high-rate carbon emissions in the production process in order to broaden EU carbon pricing's geographic reach [20]. In the US, border adjustment has been introduced in two programs. One of these is the Waxman-Markey bill, which is a more detailed bill. By January 1, 2018, if no international agreement is reached on climate change, the president of the United States must create an "international reserve allowance program". Imports in a covered sector will be prohibited after 2020 unless the importer has obtained an "appropriate" amount of emission allowances from the international reserve allowance program. Similarly, the US Senate's cap-and-trade bill provides for border adjustments, but with fewer details [19]. There are many works have been done in the energy sector to investigate the effectiveness of border adjustment. [22] provides a preliminary assessment of the possible implications of the CBAM on the EU trading partners. A new mechanism for border adjustment has been designed by the authors in the [20] called an "individual adjustment mechanism" (IAM). The analysis of the border adjustment mechanism between the US and EU was done in [18]. While most border adjustment measures (CBAM and cap-and-trade) focus on imports from the non-carbon price sub-regions to carbon price sub-regions, a border adjustment on both exports and imports would have a great effect to mitigate the leakage [21]. Thus, the combination in this study is not only for imports but also for both imports and exports.
Along with CO 2 , sulfur dioxide (SO 2 ), methane (CH 4 ), nitrogen oxides (NO x ), and particulate matter (PM 2.5 ), which harm the human health, are also emitted into the atmosphere [25]. Various health effects, including respiratory and cardiovascular diseases, diabetes, and neonatal disorders can result from air pollution exposure, leading to death and disability. Around the world, air pollution causes an estimated 6.7 million deaths among adults and children including 40% of deaths from Chronic obstructive pulmonary disease (COPD), 30% of deaths from lower respiratory infections, 26% of deaths from strokes, and 20% of neonatal deaths in 2019. When decrementing the power of fossil fuel generators, not only CO 2 is reduced, but also it will result in a reduction in PM 2.5 , SO 2 , and NO x and improving the air quality [26]. Recently, a concept of co-benefits occurs to emphasize the benefit for both climate and human health. The health impacts of air pollutants depend on the source, location and concentration of the pollutants, as well as the weather patterns that disperse those pollutants. Thereby, some regions will benefit more than others [27]. Several works have been done to investigate the co-benefits of power sector decarbonization [25,28,29]. However, these studies just analyze the co-benefits of different decarbonization pathways. This study will show the distribution of health benefits at the county level.
Approach and contribution
The purpose of the study is to investigate the effect of combining carbon price and border adjustment in the US grid systems as well as the health benefits on humans in various decarbonization scenarios. Because the US has several grids with different scales, this study starts with Western Interconnection. The Western Interconnection, which is operated by the Western Electricity Coordinating Council (WECC), covers almost 14 western states in the US, two provinces of Canada, and a portion of Mexico. Approximately 20 percent of the North American generation comes from the Western Interconnection. Hydroelectricity and variable energy sources (wind and solar) account for a significant share of generation [30]. A 10,000-bus synthetic grid of Western Interconnection (10k-bus grid) is shown in Figure 1.
After simulating the 10k-bus grid on Python in a Direct Current Optimal Power Flow (DCOPF) model, carbon price was added to form a model for a non-border adjustment measure (without applying border adjustment). Then based on the PJM study [32], the study has modified the non-border adjustment model by adding the custom constraints corresponding to two border adjustment measures and received two new models. The first one is the non-border adjustment model combined with a custom constraint for the power importing from outside to CA and called a one-way border adjustment. Its' formulation is presented in section 3.3. The second one is the non-border adjustment model combined with a custom constraint for both importing to and exporting from CA and called a two-way border adjustment. The formulation of that is shown in section 3.4. The outputs of emissions from all models are used to implement into the COBRA tool to estimate the economic value of health benefits. Using health benefits, we analyze the effectiveness of decarbonization between the three models on the human health of WECC's area at the county level. [31] . The rest of the paper is organized following: section 2 provides some information about the COBRA tool and how to estimate health benefits from it. The formulations of study models are present in section 3. Section 4 shows the numerical results and the summary of the study is in the last section.
Health Benefits Model
The CO-Benefits Risk Assessment Health Impacts Screening and Mapping Tool (COBRA) is a free tool offered by the US Environmental Protection Agency (EPA). COBRA provides preliminary estimates of the impact of changes in air pollution emission levels on ambient particulate matter (PM) concentrations, translates these impacts into health effects, and then monetizes them. Neither air quality modeling nor health effects assessment nor economic valuation is required to use the model. In COBRA, emission inventories, a simplified air quality model, health impact equations, and economic valuations are included. These assumptions are based on recommendations from the EPA. Aside from emissions inventories, population, incidence, health impact functions, and valuation functions, COBRA also allows advanced users to import their own datasets. It is possible to analyze emissions at the state or county level and across the 14 major categories (known as "tiers") in the National Emissions Inventory. In other words, The COBRA can use to:
• Estimate the effect that clean energy policies and programs, such as energy efficiency and renewable energy, have on air pollution which affects people's health at a local, state, or national level.
• Compare the cost of clean energy policies and programs with the economic value of the health benefits associated with them.
• Air quality, human health, and health-related economic benefits can be visualized by mapping and visualizing reduced emissions of particulate matter (PM 2.5 ), sulfur dioxide (SO 2 ), nitrogen oxides (NO x ), ammonia (NH 3 ), and volatile organic compounds (VOCs) associated with clean energy policies and programs [33].
For the COBRA version 4.1, there are 3 default baseline emissions including 2016, 2023, and 2028. Federal and state regulations as of May 2018 are taken into account in these baseline emissions estimates. To customize the emissions scenarios, users could use the EPA's Avoided Emissions and Generation Tool (AVERT) to create and import the emissions changes to CO-BRA. The AVERT program evaluates energy efficiency and renewable energy programs designed for state air quality controllers and users with minimal knowledge of electrical systems. On the basis of historical patterns of actual electricity generation in a given year, it represents the dynamics of electricity dispatch. According to EPA's Air Markets Program Data (AMPD) and National Emission Inventory, the AVERT Statistical Module analyzes hourly "prepackaged" data to determine how past generation, heat input, PM2.5, SO2, NOx, CO2, VOCs, and NH3 emissions changed given regional demand levels. Users can also modify AVERT's Excel-based Future-Year Scenario Template to analyze data modified in the Statistical Module. AVERT's Regional Data Module produces data files that are input into the Excel-based Main Module. With AVERT's Main Module, users can choose one of 14 regional data files and enter energy changes (MWh, MW, or the number of electric vehicles by type) from a menu. According to the regional data files as well as the impacts entered into the tool, the AVERT Main Module calculates emissions impacts. Then the output files from AVERT can implement directly to set up the emission change in the COBRA tool.
After setting up the baseline emissions and emission changes, users have to choose the discount rate before running the estimate. There are two discount rates including 3% and 7%. Depending on the purpose of a design, if the discount rate is high (7%), investments with immediate benefits are favored and future benefits are reduced more than if the rate is low (3%), in which case future benefits are more valuable to society. During running, Changes in PM 2.5 concentrations between the baseline and control scenarios (emissions changes) are generated through a source-receptor matrix. Using a variety of health impact functions, COBRA translates changes in ambient PM2.5 into changes in human health effects. A dollar value is assigned to each of these health effects at the end of the process (economic value of these impacts). These values vary and depend on the health endpoints that have associated with PM 2.5 . The health endpoints include:
• Mortality among adults and infants;
• Cardiomyopathy that is non-fatal;
• Hospitalizations caused by respiratory and cardiovascular diseases;
• Bronchitis with acute symptoms;
• Symptoms of upper and lower respiratory tract infections;
• Emergency room visits associated with asthma;
• Exacerbations of asthma;
• Restricted activity days of minor severity; and
• Illness-related lost work days [34]; Figure 2 shows the process of calculating health benefits in COBRA. The results can view in tabular or map form as well as exported to the data at the county or state level so that policy analysts can get a first-order estimate of the benefits of different mitigation scenarios.
In this paper, we use the database emissions of 2016 and the discount rate is 3% to estimate the health benefits of three models. The emission scenarios have been created by using the results from Python and then modifying them in the AVERT tool.
Study models
In this section, the paper presents the formulation of the non-border, oneway border and two-way border adjustment based on the DCOPF model. DCOPF is well-known as a linear model used to minimize the total production cost of a power network. DCOPF could use in the system with and without transmission loss, this study focuses on the system without the loss, hence, the DCOPF without losses is chosen.
DCOPF without losses
min F ,Pg,δ i g∈G (a g P 2 g + b g P g + c g ) (1a) Subject to F = 1 x (δ i − δ j ), ∀ = ij ∈ L (1b) −F ≤ F ≤ F , ∀ ∈ L (1c) g P g,i + k:k→i F ki − j:i→j F ij = D i , ∀i ∈ I (1d) P g ≤ P g ≤ P g , ∀g ∈ G (1e)
Where F is the limited power of each transmission line. g P g,i is the summation of all generators which connect at bus i. k:k→i F ki is the summation of transmission flow to node i, j:i→j F ij is the summation of transmission flow from node i. P g and P g are the limited power dispatch of each generator. Equation (1a) is the objective function of the model, which minimizes the total production cost of the system. Constraint (1b) determines the transmission flow on line . Constraint (1c) explicit the limited transmission flow of each line. This constraint has a negative sign of the limited transmission flow because the transmission flow is negative when it leaves the node and positive when it enters. Constraint (1d) is a power balance equation at node i. Constraint (1e) requires the limited power dispatch of generators.
Non-border adjustment model
A non-border adjustment model is formulated using a modified DCOPF without losses model that applies the carbon price to all generator power in California (CA). It can be written as:
min F ,Pg,δ i g∈G (a g P 2 g + b g P g + c g ) + g∈CA λ CO2 r g P g(2)
Subject to
(1b) − (1e)
Where g∈CA λ CO2 r g P g is the total carbon emissions tax inside CA. It is proportional to the carbon emissions rate (r g ) of each generator. The constraints for the non-border adjustment are similar to the DCOPF model.
One-way border adjustment model
For the one-way and two-way border adjustment measures, the study divides the power of each generator into two parts. The first is the power have carbon price P C g , and the second is the power that does not have carbon price P N C g . The one-way border adjustment is written as:
min F ,Pg,P C g ,P N C g ,δ i g∈G (a g P 2 g + b g P g + c g ) + g∈CA λ CO2 r g P g + g∈CA * λ CO2 r g P C g (3a) Subject to (1b) − (1e)
The additional constraint
P g = P C g + P N C g , ∀g ∈ G (3b) P C g = 0, ∀g ∈ Re (3c) g∈CA * P g ≤ g∈Re * ,CA * P C g + i∈CA * P d i (3d)
Where g∈CA * λ CO2 r g P C g is the carbon emissions tax of the amount of power generated in the outside of CA and consumed in CA. g∈CA * P g is the summation of power generating outside of CA. g∈G * ,CA * P C g is the summation of power from outside fossil-fuel-consuming generators and transmitted to CA. i∈CA * P d i is the summation of real power demand outside of CA. The tax of carbon emissions on the amount of power transmitted from outside to CA ( g∈CA * λ CO2 r g P C g ) is added to the objective function (2) and obtaining equation (3a). All constraints of the non-border adjustment model are also subject to the one-way border adjustment model and three additional constraints are added. Constraint (3b) requires that the amount of power with and without carbon price of each generator must be less than the physical dispatch of this generator. Constraint (3d) restricted the amount of power P C g from the generators outside of CA which consume fossil fuels to generate power and transmit it to CA. The study assumes that power from renewable sources is a priority use in the generated area, as represented in the constraint (3c).
Two-way border adjustment model
The two-way border adjustment measure allows a part of the power generated inside the CA to transmit to the outside of the CA with the rebate of tax. Hence, there is the carbon price, and without the carbon price on the power for both areas. The two-way border adjustment now is written as:
min F ,Pg,P C g ,P N C g ,δ i g∈G a g P 2 g + b g P g + c g + λ CO2 r g P C g (4a)
Subject to
(1b) − (1e)
The additional constraint
P g = P C g + P N C g , ∀g ∈ G (4b) P C g = 0, ∀g ∈ Re (4c) g∈CA P N C g ≤ g∈Re * ,CA * P C g + g∈CA P g − i∈CA P d i (4d)
Where λ CO2 r g P C g is the tax revenues of carbon emissions on both sides. g∈CA P N C g is the summation of power inside CA with rebated tax when transmitted to the outside of CA. g∈CA P g is the summation of power generating inside CA and i∈CA P d i is the summation of real power demand inside CA.
The objective function of the two-way border adjustment (equation (4a)) is the sum of the total production cost and the total carbon emissions tax of the amount of power consumed in the CA (λ CO2 rP C g ). According to constraint (4d), fossil fuel generators could only transmit a certain amount of power from both sides. The constraints (4b) and (4c) are similar to the constraints (3b) and (3c).
Numerical results
The WECC's power system, which has 10,000 buses, 12,706 transmission lines, and 2,485 generators, is simulated on Python version 3.9. The CVXPY is used to create the optimization problems and solve them by CPLEX for all three models on the PC with Windows 10 configured by Intel(R) Core(TM) i9-10900 CPU @ 2.80 GHz and 32.0 GB of RAM [36]. The results of the three models are presented in hourly operation. Figure 3 illustrates the total emissions of WECC's system corresponding to the carbon price, in which the total emissions decrease from the non-border adjustment measure to the one-way border adjustment and is the lowest at the two-way border adjustment measure. To be more specific, Figure 4 shows how the emissions on both side change. Emissions within CA reduce when the carbon price increases, while emissions increase outside CA for all three measures. For the CA, the emissions of the non-border adjustment measure are the lowest, rising in the one-way border adjustment measure, and highest in the two-way border adjustment measure. It decreases quickly when the carbon price is up to $50 per ton and then reduces steadily. The reason for that is in normal operation the power system generates electricity with many generators at a high-level rate of carbon emissions. After the carbon price applies, the generators with the high-level rate of CO 2 are turned off to minimize the total production cost of the system. Meanwhile, outside of CA, the emissions increase rapidly along with the carbon price from $1 to $50, in which emissions of non-border adjustment measure is highest, lower in the one-way border adjustment measure, and lowest in the two-way border adjustment measure.
Another notice is that while emissions of all measures decline at a rate nearly the same inside CA, emissions of the two-way border adjustment measure increase much lower than the two others. And with the raise of the carbon price the gap between the two-way measure and others is bigger. The reason for that is the two-way border adjustment measure allows power from CA transmitted to outside with a rebate in tax. For non-border and one-way border adjustment when the carbon price goes up and all generators with a low rate of carbon emissions have been operated at the highest power, the need for an increment in power leads to raises the power of a higher rate. For the two-way border adjustment, a part of the power generated from lowerrate emissions generators (when compared with the generators outside) could export to the outside, as a result, emissions inside CA of the two-way border adjustment is higher but the emissions outside, as well as the total emissions, is much lower. These results prove that the border adjustments help to mitigate the emissions leakage and the border adjustment for both imports and exports would have a greater effect. Similar results were obtained in the PJM study [37].
With a reduction of emissions in CA, the health benefits of CA will increase, and when the carbon price rises, it will reach the upper bound. The opposite trend is true for the health benefits outside of CA. Similar to emissions, the health benefits inside CA increases rapidly when the carbon price reaches $50 and then gradually thereafter. Meanwhile, the health benefits outside of CA decrease due to the emissions leakage. Figure 5 shows the change of health benefits in both CA and outside CA. While the health benefits inside CA for non-border and one-way border adjustment measures get around $400,000 instantly after applying the carbon price ($1), the health benefits of the two-way border adjustment measure starts from several thousand dollars. It is because for the non-border and one-way border adjustment measures all the power from the generators in CA has the carbon tax, thus emissions of CA have already been reduced at the carbon price is $1. The two-way border adjustment measure does not impose a carbon tax on power generated inside CA and exported outside of CA. Power from generators with a higher cost inside CA (with the tax of carbon emissions) exchange with power from lower cost (after applying the carbon price) outside. Hence, emissions are not significantly reduced, and the health benefits is low. However, the increasing rate of health benefits in the two-way border adjustment measure is higher than the non-border and one-way border adjustment measures for the carbon price from $1 to $50. Therefore, all measures have close values of health benefits inside CA after the carbon price reach $100 per ton. For the outside, the health benefits of the non-border and one-way border adjustment measures are decreased at the same rate, but that of the two-way border adjustment measures is decreased at a lower rate. As a result, there is an increase in the gap between two-way border adjustment and two others which means the total health benefits of the two-way border adjustment is higher when the carbon price rises. Nevertheless, Figure 4 and Figure 5 also show that emissions and health benefits inside CA reach a bound for all measures. It means that we could not reduce more emissions (improving health benefits) when raising the carbon price and it just leads to increasing the total production cost as well as the electricity wholesale price.
To investigate the health benefits in more detail, the result of that at the county level is shown in Figure 6. The figure not only shows the health benefits in normal operation (with a capacity scale factor of renewable energy inside CA is 1) but also for two other scenarios with capacity scale factors are 0.8 and 1.3, respectively. When the border adjustments are applied (one-way and two-way border adjustment), health benefits inside CA slightly changes. For the outside, in some counties, the color is changed from red or orange (negative values) to yellow or green (neutral or positive values). The health benefits of the non-border and one-way border adjustment just change a little, while that of the two-way border adjustment can be seen clearly. Because the health benefits depend on the source, location and concentration of pollutants, there are differences between the health benefits of counties in WECC's area. Some counties inside CA have very high health benefits and the remaining have much smaller ones (for all capacity scale factors). In the meantime, most of the counties outside CA have negative health benefits (for the non-border and one-way border adjustment), in which several counties have much more harmful than the remains. In addition, while some counties near the CA have positive health benefits, several counties in the same state have negative values such as state Nevada and Arizona. The inequity not only occurs in the counties near the CA but also in some counties of Colorado and Washington. Figure 6 also shows that the number of renewable energy impacts the total health benefits which are presented in Figure 7. When the capacity scale factor (K) is 0.8, although it has an increase in the health benefits from the non-border to two-way border adjustment, the number of counties has negative values more than K = 1 and K = 1.3 (for each measure). Thus, the total health benefits increase from K is 0.8 to 1.3 (the comparison is just in the range of the study). When the amount of renewable energy inside CA increases, it not only helps to enhance the leakage mitigation effect of border adjustment measures but also alleviates the inequity in health benefits outside CA, especially, in the two-way border adjustment. For K = 1 and K = 1.3, the gap between counties in health benefits is not much and many Carbon pricing policies not only reduce emissions but also gain tax revenues from carbon emissions. The total tax of carbon emissions is shown in Figure 8. With the increase in the carbon price the tax revenues from carbon emissions increment in all measures, and because the carbon tax of the non-border adjustment (show in Figure 8a) is just from the inside CA, it is less than the others. The border adjustment measures enhance the tax for carbon emissions to all power generated inside CA or transmitted from the outside CA, so it enhances the effect of the carbon price on the outside. Furthermore, the tax revenues for carbon emissions of the two-way border adjustment is higher than the one-way border adjustment, which means that the amount of power imported from the outside to CA is higher. Combined with the emissions in Figure 4, although the amount of power transmitted to CA is higher when compared to the one-way border adjustment, emissions in the two-way border adjustment is lower. This means that the one-way border adjustment just cut down the operation of generators with high-rate carbon emitting inside CA when the outside of CA with high-rate carbon emitting generators still working. In the two-way border adjustment, the generators in both sub-region are working with the low-rate carbon emitting due to the minimizing of the production cost and carbon tax. By enhancing the effect of the carbon price on the outside the border adjustment not only gain the carbon tax but also cut down the power of high-rate carbon emission on both side. Therefore, the carbon emissions of the whole system reduce, the leakage is mitigated, and tax revenues gain. The government, then, could use these taxes for government activities, government programs, or other policies to improve air quality as well as social welfare. When applying the carbon price the locational marginal pricing of the system also increases leading to higher production and operating costs. The LMP and total production cost of the system are shown in Figure 9 and Figure 10 (remark: the LMP of both sub-regions is the same value when the system operates without the carbon price). Figure 9a shows that without border adjustment, the LMP inside CA is much higher than that of outside. This is because the LMP not only depends on the production cost but also on the delivery conditions. Losses and/or congestion of the network may cause an increase in LMP [38]. When the carbon price applies, the power inside CA declines causing a bulk amount of power transmitted from outside through several buses. Thereby, the congestion may occur more likely and the LMP goes up. For the one-way border adjustment, the difference in LMP between the two sides is mitigated, however, the LMP outside rises. The production cost increases lead to higher electricity prices and low-income households would spend a larger share of their income on energy prices [39]. Figure 9b shows that the two-way border adjustment will result in lower LMP and mitigate the gap between CA and outside.
Conclusion
This paper presents the study to investigate the effect of combining the carbon price and border adjustment measures on carbon emissions reduction and leakage mitigation in the US power grid. The three models are simulated based on the DCOPF in Python by CVXPY embed and solved by the CPLEX solver. The numerical results of the US Western Interconnection are conducted to analyze the effect of the combination. There are some key findings in the study: First, the border adjustment measures help to enhance the impact of the carbon price on the non-carbon price sub-regions. As a result, carbon emissions in unregulated regions reduces, the emission leakage mitigates and health benefits improves. Besides, together with the carbon pricing policy and border adjustment measures, renewable sources play a crucial role in decarbonization and mitigating emissions leakage. If we have more renewable energy the effect of decarbonization will be enhanced with the leakage very small, and vice versa, if the renewable sources are not enough the decarbonization inside the regulated sub-regions still be fulfilled but the emissions leakage to the unregulated sub-regions will be more serious. Second, using border adjustment results in higher tax revenues and successfully cut down the power of high-rate carbon emission generators. Finally, the border adjustment also helps to mitigate the gap of LMP between the carbon price regions and non-carbon price regions, which avoids the increase in energy prices and make the electricity price more affordable.
For all findings, the border adjustment for both imports and exports from the regulated (two-way border adjustment) regions has more effect than for only imports (one-way border adjustment). However, for both measures, there is still a limit in health benefits as well as emission reduction. Combining appropriate various of climate policies will help to reduce carbon emissions in a comprehensive way. This paper just presents the results for the Western Interconnection, the future work of this study is to analyze the effect of this combination on other US power grids.
Fig. 1 :
110,000-bus Synthetic Grid Of The Western United States
Fig. 2 :
2Health Benefits calculation in COBRA[35].
Fig. 3 :
3Total emissions
Fig. 4 :
4Emissions of CA and outside CA Fig. 5: Health Benefits of CA and outside CA
Fig. 6 :
6Spatial-temporal communities' health benefits as an implicit function of pollutants induced by power system operations.
Fig. 7 :
7Total Health Benefits counties have near values. At K = 1.3, the number of counties has a negative value of health benefits is much less than the number of counties has positive values. This means the number of renewable sources inside the carbon price regions not only impacts the effect of reducing emissions inside but also the effect of emission leakage on the outside.
One-way border adjustment (c) Two-way border adjustment
Fig. 8 :
8Taxes for carbon emission
a) Non-border and one-way border adjustment (b) Two-way border adjustmentFig. 9: Average LMP
Fig. 10 :
10Total production cost
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| sample_1022 | 0.9997 | arxiv | |
Thermal load models for the static design of steel-concrete composite girders
Ruizheng Wang
School of highway
Chang'an University
710054Xi'anChina
Kai Peng
School of highway
Chang'an University
710054Xi'anChina
Chen Peng
School of Civil Engineering
Tongji University
200092ShanghaiChina
Changhao Wang
Department of Chemistry
College of Chemistry and Chemical Engineering
Discipline of Intelligent Instrument and Equipment
Xiamen University
361005XiamenChina
School of Materials Science & Engineering
Zhejiang University
310027HangzhouChina
C Wang
)
Thermal load models for the static design of steel-concrete composite girders
1steel-concrete composite girdertemperature fieldtemperature gradientthermal effectstatistical analysis
Although the recommended temperature gradient models of composite girders are considered in current specifications for classifying temperature effects in various countries, they are not appropriate enough for static design. Moreover, existing national standards cannot explain the mechanism of the thermal effect on the bridge. To further investigate thermal load models of composite girders, this work proposed a decomposing method for vertical nonlinear temperature gradients based on thermal effects and a calculating method for the thermal stress of composite girders. Equivalent temperature (equivalent uniform temperature, equivalent linear temperature, and equivalent nonlinear temperature), temperature difference, and cyclic equivalent uniform temperature are analyzed to reflect the characteristics of thermal effect in composite girders. The stand values of temperature differences and equivalent temperature with a 50-year return period were investigated via probabilistic statistical analysis.Additionally, two vertical thermal load models (VTLM Ⅰ and VTLM Ⅱ) were set up to facilitate the design and applied to stress analysis. The result demonstrates that the proposed thermal load model is more suitable than the Chinese Specification for calculating the thermal effects of composite girders.IntroductionBridges are subjected to periodic thermal loads that can lead to thermal self-stress, secondary thermal stress, and thermal deformation, similar to static and dynamic loads, the above three phenomena can damage the bridge structures [1-3]. A large temperature difference between the concrete deck and steel girder along the steel girder depth can cause interface shear force, relative slippage, and large thermal stress[4,5]. Thermal stress is one of the 2 main factors causing the crack of concrete bridge decks[6,7], and the thermal loads of composite girders can sometimes cause thermal stress equivalent to live load[8]. Therefore, a comprehensive understanding of temperature effect mechanism and structural behavior in composite girders is greatly important to new types/designs and construction of composite girders and the evaluation of the bridge's lifetime.Most studies focused on the extreme temperature distribution and thermal stress of bridges in different regions in the past 20 years[9][10][11][12]. The numerical analysis models of the temperature field distribution of the bridge were established and analyzed by Mirambell and Aguado[13], which indicated that spatial temperature can be simplified to a 1D temperature distribution. Roberts-Wollman et al. [14] studied the thermal stress of the concrete box girder by conducting a field experiment and the result demonstrated that the thermal stress depends largely on the form of temperature distribution. Zuk et al. [15] carried out a field test on a steel-concrete composite girder to investigate temperature gradient and found that the extreme temperature difference is 22°C. Wang et al. [16] built a temperature gradient model for steel box girders based on long-term monitoring data. To further simplify the calculation of thermal stress, many researchers proposed various simplified temperature difference gradient patterns for the design of bridge structures, such as multiple parabolic forms [17] and multisegment line forms[18][19][20]. Thermal loads are classified into uniform temperature and temperature difference gradients[21][22][23][24]. However, the temperature difference gradient models of steel-concrete composite girder bridges in JTG/T D65-06-2015 are mainly modified based on the temperature difference gradient of AASHTO, which considered the characteristics of China's climate.Additionally, the temperature gradient models of AASHTO were obtained from the statistical analysis of thermal loads in concrete bridges. Therefore, the applicability of the temperature difference gradient modes for composite girder bridges in China must be further discussed.Existing national standards divide the thermal effect into uniform temperature and temperature gradient according to environmental factors[25][26][27][28][29]. Although this classification is easy to understand, it can not explain the mechanism of the thermal effect on the bridge. Uniform temperature causes axial expansion deformation in the statically determinate bridge structure and axial secondary stress in the statically indeterminate bridge structure[30].In the statically determinate structure, the temperature gradient can cause a small part of axial expansion deformation, bending deformation, and self-balanced thermal self-stress[31,32]. In the statically indeterminate structure, the temperature gradient can generate axial secondary stress, thermal self-stress, and bending secondary stress[33,34]. The prior temperature gradient modes are mixed with the secondary thermal effect and self-generated thermal effect. Therefore, these temperature gradient frameworks ignore the mechanical principle of the temperature effect.
3
To solve the above issues, this work aimed to investigate thermal load models for designing steel-concrete composite girders and proposed an innovative calculation method for decomposing vertical nonlinear thermal loads based on the thermal effect equivalence principle. A systematic approach was established for two vertical thermal loads, and long-term data of temperature field distribution in composite girder were collected and analyzed.
Temperature difference and equivalent temperature with a 50-year recurrence period were determined using the probability limit-state method. Finally, two vertical thermal load models (VTLMs) were established, and a calculation method for thermal stress was proposed. Thermal stress was compared between the designed thermal load model and the recommendations in Chinese Specification (CS), and the relationship between the thermal effect and loads was also examined.
1 Innovative method to establish a design thermal load model 1
.1 Decomposition of vertical nonlinear temperature gradient
Suppose the vertical nonlinear temperature gradient curve of the steel-concrete composite girder cross-section is () Ty and the origin of the vertical coordinate (y-axis) is taken at the centroid of the converted section of steelconcrete composite girder with a positive value toward an upward direction, the free deformation of the section with thermal variation is expressed as ( ) ( ) y T y (taking per unit length of the girder for analysis) as shown in Fig. 1.
The stress caused by the free deformation of the section can be expressed as follows: (1) where () Ey is Young's modulus of the materials at y position and () y is the thermal expansion coefficient of the materials at y position.
Considering self-stress and secondary stress caused by thermal loads, the overall thermal stress of the composite girder can be determined as follows: (2) where sum () y is the total strain of the selected section containing the sectional fiber constraints and structural boundary constraints.
The overall stress at any position also can be presented as follows based on the plane section assumption:
where 0 is the axial strain at the centroid of the cross-section considering the sectional fiber constraints and structural boundary constraints. and y denote the curvature of the whole section and the depth of object fiber to T the centroid of the converted section, respectively.
Additionally, the overall stress caused by thermal loads at height y is as follows: (4) Simultaneously solving equations (3) and (4) reveals the relationship between the total stress sum () y and the vertical temperature gradient curve () Ty as follows: (5) According to the relationship between the stress and the internal force, equations (6) and (7) can be obtained.
(6)(7)
where b(y) is the width at height y, is the distance from the origin to the top surface of the concrete deck, and is the distance from the origin to the bottom of the steel girder floor.
Here, the bending moment and axial force caused by the free deformation of the section under arbitrary temperature distribution are defined as the nominal bending moment and the nominal axial force, respectively, which can be expressed as follows:
(8)(9)
The thermal expansion coefficient of the transformed section is as follows: (10) As shown in Fig. 1, the relationship between nominal axial force and the equivalent uniform temperature of the cross-section with arbitrary nonlinear temperature gradient can be expressed as follows: (11) where T T is the equivalent uniform temperature of the composite girder. 0 A is the area of the conversion section denoted as 0 c Es The curvature of the conversion section caused by the nominal bending moment with a nonlinear temperature gradient is equal to that of the composite girder caused by the equivalent linear temperature gradient. can be obtained as follows: (12) where L T is the equivalent linear temperature, 0 I is the inertial moment of the transformed section , and H is the height of the steel-concrete composite girder.
s =/ A A A + ,T sum ( ) ( ) ( ) y y y =+ sum 0 ( ) ( )[ ( ) ( )] y E y y y T y = + − 2 1 sum ( ) ( ) h h N y b y dy = 2 1 sum ( ) ( ) h h M y yb y dy = 1 h 2 h 2 1 TT = = ( ) ( ) ( ) ( ) h Ah N dA E y y T y b y dy 2 1 TT = = ( ) ( ) ( ) ( ) h Ah M y dA E y y T y b y ydy sc 0 () = 2 + T s 0 T 0 = N E T A 0 L T s0 == TM H E I 5
After substituting equation (8) into equation (11), T T can be obtained: (13) After substituting equation (9) into equation (12), L T can be obtained:
The equivalent linear temperature gradient curve is a linear function of special slope k (Fig. 1), which is named as induced thermal linear slope and can be calculated by the equation (15): (15) Additionally, the equivalent linear temperature gradient is denoted as () Gy, which can be calculated byhe following equation: (16) where y0 is the distance between the section neutral axis and the top surface of the bridge deck.
Furthermore, the primary thermal strain of the composite girder can be calculated as follows: (18) where NL () Ty is the equivalent nonlinear temperature. Given that the bridge is in the linear elastic phase under thermal loads, equation (19) can be obtained according to the superposition principle: (19) The equivalent nonlinear temperature gradient curve can be written as follows: (20) The authentic temperature gradient of the composite girder can be expressed as follows:
(21) 2 1 T s0 ( ) ( ) ( ) = h h E y T y b y dy T EA 2 1 L s0 ( ) ( ) ( ) = h h H E y T y yb y dy T EI 2 1 s0 ( ) ( ) ( ) = h h E y T y yb y dy k EI 0 ( ) ( ) G y k y y =− T = ( ) u y T = ( ) w y ky = ( ) (y) v y T NL = ( ) ( ) l y T y = v u w l ++ NL T ( )= ( ) T y T y T ky −− T NL ( )= ( ) ( ) T y T G y T y ++ 6 O Free-form deformation O Equivalent linear temperature gradient ky Actual nonlinear temperature gradient T(y) T T T ( ) y ky N L ( ) ( ) y T y u L T h1 h2 b(y) O y ( ) ( ) yT y (b) (c)
Concrete deck
Steel girder
Analysis process
After the temperature distribution of the composite girder is obtained throughout the monitoring period, T T , NL () Ty , and L T can be calculated based on the theory in Section 1.1. The temperature difference gradient can also be determined by fitting the monitored vertical temperature difference curve. The probability density function (PDF) of T T , L T , and the temperature difference can be statistically analyzed. Accordingly, the stand value of T T , NL () Ty , L T , and the temperature difference can be proposed based on probabilistic limit-state design. Next, the temperature difference gradient of cross-section is used as VTLM Ⅰ, and a combination of T T , L T , and NL () Ty is adopted as VTLM Ⅱ. For further exploration of the relationship between thermal loads and thermal effects, thermal stress is analyzed based on VTLM Ⅰ, VTLM Ⅱ, and collected temperature data. The analysis flow of this article is shown in Fig. 2 The layouts of the measuring points at the cross-section are shown in Fig. 3 larger than that of the east web, and the overall temperature of the west web is higher than that of the east web. The maximum positive temperature difference appears at 13:00, and the maximum negative temperature difference appears at 5:00. The statistical results also illustrate this phenomenon. periodic change, and the change in L T is more stable than that in T T . L T has positive and negative values, indicating that the equivalent linear temperature gradient curve may be a negative or a positive function.
Temperature characteristics of composite girder
The calculation results of NL T are shown in Fig. 6 (b). The maximum and minimum NL T of E1 measured point are 7.9°C and −10.8°C, respectively, and those of E2 measured point are 1.9°C and −2.3°C, respectively. The absolute value of NL T on the top concrete slab is higher than that at the bottom steel girder, so the temperature difference in NL T is evident.
Profiles of vertical temperature difference gradient
Thermal loads of the composite girders can be divided into uniform temperature and temperature difference gradient. The uniform temperature will lead to the axial expansion deformation of the bridge, which is an essential factor in selecting appropriate expansion joints, bearings, and piers. Additionally, the uniform temperature of the composite girder can be obtained by equation (12). The detailed analysis process is shown in Section 3.3.1.
In this investigation, two VTLMs (vertical thermal load models) are proposed (Fig. 8, 15) ( Figs. 8 (a-b)).
According to the measured data, the profiles 1 (PVTG) and 2 (NVTG) for the thermal load model Ⅰ can be obtained by the following equations:
Profile 1 (positive vertical temperature gradient):
c P2 P1 P1 P2 P3 P2 P2 P3 c c profile1 c P3 2( ) ,(0 ) 2 (2 ) ,( 0.5m) () 0.5 / 2 1 2 (1 ),(0.5m 1.0m) 2 0,(1.0m ) c c h TT y T y h T T T T T h h yy Ty hh T yy yh − + − − − + = −− − (22)
where y is the distance from the top surface of the bridge deck to the calculated point, m. Tp1-Tp3 are the base numbers of positive temperature differences, and hc is the height of the concrete deck.
Profile 2 (Negative vertical temperature gradient): N2 N1 c N1 profile2 N2 c 2( ) , (0 ) 2 ( ) 0, (0.5m ) (0.5-), ( 0.5m) 0.5 / 2 2 c c T T h y T y h T y y h Th yy h − + = − (23)
where TN1 and TN2 are the base numbers of negative temperature difference. Thermal load model Ⅰ can be regarded as the temperature difference distribution that represents the relative value of the temperature load. The VTLM Ⅰ can be obtained through the statistical and reliability analyses of the temperature difference. The temperature gradient profiles composed of equivalent uniform temperature, equivalent nonlinear temperature gradient, and equivalent linear temperature gradient are named as VTLM Ⅱ. VTLM Ⅱ is obtained from the probabilistic analysis of the equivalent temperature (equivalent uniform temperature, equivalent linear temperature, and equivalent nonlinear temperature) of the composite girder, which is different from the analysis method for thermal load model Ⅰ. However, the thermal effects of the two thermal load models are guaranteed to be consistent. Thermal load model Ⅰ is reasonable because the temperature effect caused by thermal load model Ⅱ is consistent with that caused by thermal load model Ⅰ at any point.
The calculated daily extreme values of TP1-TP3 and TN1-TN2 are shown in Fig. 9. The daily extreme value of each temperature difference exhibits a different annual distribution. These seasonal distribution deviations are mainly due to the influence of ambient temperature and solar radiation.
Thermal load model
Cycling variation of equivalent uniform temperature
In the design of a long-span steel-concrete composite girder, the maximum and minimum equivalent uniform temperatures can be used to predict the degree of expansion and contraction in composite girders. a cyclic equivalent uniform temperature in the thermal load model is proposed to quantify the cumulative displacement of the longspan composite girders. 13 For the measured data of August 5, 2021 ( Fig. 10 (a)), four key equivalent uniform temperatures are identified, namely, first temperature t1, lowest temperature t2, highest temperature t3, and last temperature t4. The daily cycling variation of the day is composed of one heating process and two cooling processes ( Fig. 10 (a)) with values of 11.7°C, −6.1°C, and −6.4°C, respectively. The daily cycling variation of August 5, 2021, is 24.2°C. Fig. 10 (b) shows the frequency chart of the cyclic equivalent uniform temperature during a 300 day monitoring period, and the total daily cycling variation value is 6885°C. The cyclic equivalent uniform temperature TCUT of one-year can be obtained as follows:
CUT 365 = 6885=8376 300 T ℃(24)
The cyclic equivalent uniform temperature TCUT can be considered with live loads to predict total axial displacement of bearings. Using the results as the basis, their conditions during the service period can be evaluated.
Vertical thermal load model Ⅰ
After comparing the goodness of fit of multiple distribution models, the normal distribution function is finally used to describe the probability distribution of temperature difference [35,36]. The PDF of the temperature difference distribution can be expressed as follows [37]:
( ) 2 2 1 ( , ) 2 exp 2 , h TD TD = − − (25)
where TD is the temperature difference of the composite girder.
where P is exceeding probability. The exceeding probability of a designed reference period within 100 years is 2%.
The frequency distribution histogram and simulated PDFs of TP1 and TN1 are chosen as a representative and 14 plotted in Figs. 11(a-b). TP1 and TN1 fit the normal distribution. According to the probability analysis, the probability density curves can be fitted for TP1-TP3 and TN1-TN2. The parameters of fitted normal distribution and the extreme values of TP1-TP3 and TN1-TN2 are plotted as shown in Figs. 12 (a-b) and
Vertical thermal load model Ⅱ
Equivalent uniform temperature and equivalent linear temperature
Equivalent uniform temperature provides essential information for steel-concrete composite designs following the specifications. Fig. 5 indicates that the temperature distribution on the composite girder section is non-uniform.
Therefore, rather than individual temperature data, the equivalent uniform temperature of the whole section should be used to predict the thermal effect. Equivalent linear temperature gradient is the main factor that causes the secondary effect of statically indeterminate structure. The most unfavorable values (the stand values) of T T and L T in the design reference period are determined by probability statistics based on the requirements of the probabilistic limit-state design.
Gaussian mixture model (GMM) is trained by an expectation maximization algorithm. In theory, it can fit any type of distribution and is usually used to solve the problem, that is, the data under the same set contain multiple different distributions [38,39]. The PDF of GMM can be expressed as follows:
2 2 1 () 1 ( ) exp[ ] 2 2 M i i i i T fT = −− = (27)
where T is the equivalent temperature of the calculated point; Table 4 to facilitate its use in the design of composite girder bridges. The PTLM and NTLM of VTLM Ⅱ consist of TT, TL, and TNL (Figs. 8 (a-b)). VTLM Ⅱ is more conducive to explaining the influence of thermal load on the bridge structure from the perspective of mechanism. Fig. 16 shows the relationship between the thermal effect and thermal loads based on VTLM Ⅰ and VTLM Ⅱ toward the steel bridge and concrete bridge in service. VTLM Ⅱ is more convenient to calculating the thermal effect from the secondary effect and the spontaneous effect than VTLM I. Generally, conventional bridges obey the axial free expansion and deformation of girders under the thermal effect; hence, con =0 N . After substituting equations (30) and (31) into equation (5), the overall thermal stress at any position can be obtained by equation (32):
0 0 con sum ( ) ( ) ( ) ( ) ( ) ( ) ( ) E y N E y y M M y E y y T y EA EI + = + − .(32)
When con =0 M is set in equation (32), the thermal self-restraint stress can be denoted as follows:
00 s ( ) ( ) ( ) ( ) ( ) ( ) E y N E y yM y E y y T y EA EI = + − .(33)
Thermal self-restraint stress caused by the equivalent nonlinear temperature gradient can be calculated by equations (20) and (33).
After substituting ( )= ( ) T y G y , T ( )= T y T , and NL ( )= ( ) T y T y into equation (32), the thermal stress caused by structural boundary constraints can be calculated by equation (34):
con con () = E y M y EI .(34)
Suppose an (n + 1)-span continuous composite girder, the bending moment caused by the redundant constraints are ( 1, 2,..., )
i P i n =
, and the bending moment caused by the redundant constraints of (n + 1)-span continuous girder is as follows:
con 1 n ii i M P M = = .(35)
The relative rotation angle P at any support P in the direction of redundant force can be expressed as equation (36) based on the principle of virtual work:
0 PP L M dx = ,(36)
where P M is the reaction moment induced by unit rotation at support P.
Equations (31) and (34) are substituted into equation (35). =0 P can be obtained based on boundary coordination, so equation (35) can be calculated as follows:
0 =0 n i P P P i L L i M M M M Pdx dx EI EI = + , ( 1, 2,..., ) in = .(37)
The secondary bending moment can be obtained by solving equation (37).
Thermal stress analysis
The span arrangement of the example bridge is (2 × 30) As shown in Figs. 19 (a-b) Based on the above discussion, VTLM Ⅱ composed of TT, TL, and TNL is conducive to calculating the thermal stress of the composite girders from two aspects (secondary thermal stress and spontaneous thermal stress). First, the contribution of different temperature components to the secondary stress and spontaneous stress is easy to obtain.
Second, the relationship between the thermal effects and thermal loads is suitable for steel-concrete composite 22 girders (Fig. 16). The proposed thermal load model is expected to have guiding significance for improving the design safety of steel-concrete composite bridges.
Conclusions
To consider temperature effects and mechanical mechanism in designing the thermal load model of the composite girders, this work proposed a calculation method for decomposing vertical nonlinear temperature. Stand temperature difference and stand equivalent temperature (TT, TL, and TNL) were analyzed, and two thermal load models were obtained by calculating and analyzing the temperature field information of the composite girder. The following conclusions can be drawn as follow:
(1) The calculating method of decomposing vertical nonlinear temperature was set up based on the thermal effects equivalence method. Furthermore, the calculation method of thermal stress in composite girders was proposed. The vertical nonlinear temperature was divided into TT, TL, and TNL. These three parameters were solved by calculating 24 long-term temperature data. Stand values of TT, TL, TNL, and temperature difference with a 50-year return period were also obtained by probability analyses. (4) For the VTLM Ⅱ of the composite girders, TL is one of the main factors causing secondary thermal stress and can also cause secondary thermal stress for the statically indeterminate structure. However, the stress caused by TL and TT is quite small for the statically determinate structure. TT is the main factor causing the axial deformation of the composite girder. TNL mainly causes the thermal self-stress of the composite girders, but its contribution to the secondary thermal stress can be ignored. VTLM Ⅱ can clearly express the relationship between thermal loads and thermal effects.
(5) The cyclic equivalent uniform temperature TCUT is 8376°C. Large deviations exist among VTLM Ⅰ, VTLM Ⅱ, and the vertical temperature difference gradients in CS, which may lead to thermal stresses and deformations of composite girders being greater than the calculated values in CS.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
can be expressed as follows(Fig. 1):
Fig. 1
1Temperature distribution and thermal strain (a) section of a composite girder, (b) thermal-induced strain, and (c) temperature distribution.
Fig. 2
2Innovative method for thermal load model.
model and measuring point arrangement The experimental site is located at Lanzhou New Area, Gansu Province, China, and is the intersection of the Tibetan Plateau, Mongolian Plateau, and Loess Plateau with an average altitude of 2000 m. The annual average temperature is 6.9°C. The highest temperature is in July with a monthly average of 22.5°C, and the lowest temperature is in January with a monthly average of −5.6°C. Precipitation is mainly concentrated from May to October. The sectional model of the composite girder is 3.0 m in length and 1.45 m in depth (center line). The width of the concrete deck and bottom plate of the steel girder is 6.25 and 3.30 m. the height of the bridge deck is 0.25 m.
Fig. 4
4exhibits the daily extreme temperature of the bridge deck and steel girder throughout the test period. It is can be seen that the daily extreme temperature shows periodic cycle from the Fig. 4. The daily maximum temperature does not exceed 50°C, and the extreme value of the daily temperature is not less than −10°C. The daily maximum temperature of the floor sometimes exceeds the daily maximum temperature of the roof. However, the daily extreme temperature can be classified as nonstationary time series. The diurnal temperature amplitude is large because of the alternation of day and night and the change in weather conditions. Figs. 5 (a) and (b) denote the 24 h temperature cloud chart of the composite girder cross-section on July 15, 2021. These images show the temperature distribution along the roof, web, and floor of the cross-section and the change of the vertical temperature gradient with time. The influence of the solar radiation and ambient temperature on the composite girder is quite severe. The high-temperature distribution areas are mainly concentrated on the concrete deck and the bottom plate of the steel girder. The vertical temperature difference of the west web is
Fig. 6 (
6a) shows the calculation results of T T and L T . T T and L T possess the typical characteristic of 9
value of bridge deck minimum temperature value of bridge deck maximum temperature value of steel girder floor minimum temperature value of steel girder floor Fig. 4 Daily extreme temperature of the composite girder.
Fig. 5 A
524 h temperature cloud chart on July 15, 2021: (a) west side test point and (b) east side test point.
. 1
1Measured vertical thermal load model Figs. 7 (a-f) show the measured vertical temperature difference distribution, equivalent temperature gradients, and corresponding simplified profiles. The positive and negative temperature difference gradients can be fitted by a piecewise linear function (Figs. 7(a-b)), but the function forms of equivalent positive and negative nonlinear temperature gradients are complicated (Figs. 7(c-d)). The positive and negative temperature difference gradients can be simplified as a mathematical equation. The equivalent positive and negative linear temperature gradients jointly show linear variation(Figs. 7(c-d)). However, the linear functional relationship is still unclear(Fig. 7f). On October 2, 2021, the equivalent linear temperature gradient and induced thermal scope are opposite to the sign of the corresponding temperature gradients. This phenomenon is common for bridges installed with a short web height ratio between the composite girder and the large cantilever. However, theories of probability and statistics must be used to obtain the definite expression of the equivalent temperature gradient.
Fig. 7 .
7Vertical thermal load model recorded in experiments: (a) positive temperature difference gradient, (b) negative temperature difference gradient, (c) equivalent positive nonlinear temperature gradient, (d) equivalent negative nonlinear temperature gradient, (e) equivalent positive linear temperature gradient, and (f) equivalent negative linear temperature gradient.
Fig. 8 .
8Vertical thermal load model Ⅰ: (a) Profile 1 and (b) Profile 2.
Fig. 9 .
9Daily extreme values: (a) daily extreme values of TP1-TP3 and (b) daily extrmevalues of TN1-TN2.
Fig. 10 .
10(a) History of equivalent uniform temperature on August 5, 2021, and (b) frequency chart of the cyclic equivalent uniform temperature.
The extreme values of temperature difference TDe of composite girder can be obtained by
Fig. 11 .
11Frequency distribution histogram and simulated PDFs: (a) TP1 and (b) TN1.
Fig. 12 .
12Fitted PDFs: (a) TP1-TP3 and (b) TN1-TN2.
M are the weight and number of Gaussian component, respectively. 27) is transformed into equation (28) for operation, and the least square method is used to estimate the unknown parameters M,
TFig. 13 .
13is compared among multiple PDFs. The best fitting goodness is obtained when the , T T − , and L T − , respectively. Figs. 13 (a-d) show the probability density histograms of negative and positive equivalent uniform temperature, negative and positive equivalent uniform temperature, and the estimated curve. The estimated probability density curves can accurately reflect the statistical characteristics of the probability density of the calculated temperature samples. Table 3 lists the estimated parameters of the GMM for the equivalent temperature at each calculated point during the monitoring period. The standard equivalent linear temperature with a 50-year return period is 27.5°C and −12.3°C caused by the positive and negative temperature gradients, respectively, with the corresponding equivalent uniform temperature of 52.4°C and −13.5°C, respectively. Probability density histogram and estimated curve: (a) negative equivalent linear temperature, (b) positive equivalent linear temperature, (c) negative equivalent uniform temperature, and (d) positive equivalent uniform temperature.
. 2
2Vertical thermal load model Ⅱ The equivalent nonlinear temperature of the composite girder under the most unfavorable case can be calculated based on Section1.1. Figs. 14-15 present the VTLM Ⅱ of the composite girders. The profile 1 of vertical thermal load model Ⅰ and positive thermal load model shown in Fig. 14 (a) is equivalent to the thermal effects of the composite girder and the same as the profile 2 of vertical thermal load model Ⅰ and positive thermal load model (Fig. 14 (b)). The values of 17 equivalent linear temperature decomposed in the PTLM of VTLM Ⅱ and the NTLM of VTLM Ⅱ are 27.5°C and −12.3°C, respectively. The induced thermal linear slope k values are 18.9 and −12.3°C/m, respectively, which can be obtained from the process in Section 3.3.1. The NTLM of VTLM Ⅱ leads to negative linear temperature distribution, negative induced thermal linear slope, and downward deformation in bridges. Meanwhile, the results of PTLM of VTLM Ⅱ are opposite. This finding is consistent with the effects of VTLM Ⅰ.
Fig. 15
15displays the simplified schematic of VTLM Ⅱ, and the parameters of VTLM Ⅱ are given in
Fig. 14 .Fig. 15 .
1415Vertical thermal load model Ⅱ: (a) positive thermal load model and (b) negative thermal load model. Simplified schematic of vertical thermal load model Ⅱ: (a) positive thermal load model and (b) negative thermal load model. 18
Fig. 16
16Relationship between the thermal effects and thermal loads.
4
Thermal stress of the composite girder4.1 Calculation method of thermal stressTaking the centroid of the converted section of the composite girder as the coordinate origin, fiber constraint and the structural boundary constraint, we can express the secondary axial force and the secondary bending moment of the steel-concrete composite girder as con N and con M are the inertia moment of the concrete and steel girders related to the converted section axis.
m, and the sectional dimensions of the continuous steel-concrete composite girder are shown in Fig. 1. The profile 1 of VTLM Ⅰ and PTLM of VTLM Ⅱ are vertical 20 thermal load model for positive temperature effects, and the profile 2 of VTLM Ⅰ and NTLM of VTLM Ⅱ are profiles for negative temperature effects. The thermal stress under the thermal effect of VTLM and vertical temperature difference gradient in CS are also calculated. Fig. 17 displays the vertical distribution of thermal self-stress and secondary thermal stress in the mid-support section of the steel-concrete composite girder. The PTLM of VTLM Ⅱ and NTLM of VTLM Ⅱ calculates the stress from equivalent linear temperature gradient and equivalent nonlinear temperature gradient without considering the equivalent uniform temperature. As shown in Figs. 17 (a-b), the differences between thermal self-stress and secondary thermal stress under the effect of VTLM Ⅰ and VTLM Ⅱ are small, indicating that the thermal effects generated by VTLM Ⅰ and VTLM Ⅱ are consistent. For the profile 2 of VTLM Ⅰ and the NTLM of VTLM Ⅱ, the thermal self-stress at the top surface of the concrete bridge deck is 1.478 and 1.331 MPa, respectively, which are larger than the 1.183 MPa recommended in CS. For the profile 1 of VTLM Ⅰ and the PTLM of VTLM Ⅱ, thermal self-stress at the top of the bridge deck is −0.604 and −0.812 MPa, respectively,which are less than the −1.452 MPa recommended in CS. Large thermal self-stress is found in the position of the inflection part of VTLM, and the thermal self-stress caused by VTLM Ⅰ and VTLM Ⅱ is larger than that of the recommended value in CS for steel girder. The secondary thermal stress presents linear distribution (Fig. 9 (b)), and the secondary thermal stresses of the concrete deck and steel girder are larger than the recommended value in CS in VTLM Ⅰ and VTLM Ⅱ. If biased vertical temperature difference distribution in CS is applied for the composite girder, then the thermal secondary stress will deviate, which is unfavorable for the accurate design of the composite girder. Therefore, safety can be appropriately enhanced when thermal stress is calculated according to a single standard in the design stage.According to the above analysis, the thermal stress caused by the vertical temperature difference gradient in CS can hardly surpass the thermal stress caused by temperature loads in the design service life of the composite girder. Particularly, large deviations exist between VTLM and the vertical temperature difference gradient in CS, leading to the thermal deformations of the girder or the thermal stresses of the steel girder being greater than the design values. The VTLM Ⅰ and VTLM Ⅱ can replenished the thermal loads of composite girders in the design stage. Additionally, the proposed thermal load decomposition method and thermal stress calculation method can enrich the calculation theory of bridge temperature effects. This work provides a calculation method for the static effect of the bridge thermal loads and a calculation idea for the calculation of the bridge fatigue damage under temperature effects. Figs. 18 (a-b) show the time history of thermal self-stress of the bridge deck and steel girder roof (the position of the maximum stress value) under the effect of equivalent uniform temperature. The maximum and minimum 21 thermal self-stresses on the top surface of the bridge deck are 0.714 and −0.119 MPa, respectively, which exceed the 0.798 and −0.206 MPa calculated by the TT (PTLM) of VTLM Ⅱ and the TT (NTLM) of VTLM Ⅱ. The maximum/minimum thermal self-stresses on the bottom surface of the bridge deck are 1.124 and −0.187 MPa, respectively, which are smaller than the 1.256 and −0.323 MPa obtained in the TT (PTLM) of VTLM Ⅱ and the TT (NTLM) of VTLM Ⅱ. The maximum and minimum self-stresses of the steel girder are 2.099 and −12.623 MPa, respectively, which are less than the 3.631 and −14.094 MPa calculated by the TT (PTLM) of VTLM Ⅱ and the TT (NTLM) of VTLM Ⅱ, respectively. Hence, the TT (PTLM) of VTLM Ⅱ and the TT (NTLM) of VTLM Ⅱ can be considered a good method to calculate the thermal stress produced by uniform temperature.
Fig. 17 .Fig. 18 .Fig. 19 .
171819Thermal stress of the composite girder: (a) thermal self-stress and (b) secondary thermal stress. Time history of thermal self-stress: (a) stress of the bridge deck and (b) stress of the steel girder roof. Time history of thermal stress: (a) self-stress of the bridge deck, (b) self-stress of the steel girder roof, (c) secondary stress of the bridge deck, and (d) secondary stress of the steel girder roof.
( 2 )
2VTLM Ⅰ and VTLM Ⅱ were established carefully. The profile 1 of VTLM Ⅰ and PTLM of VTLM Ⅱ are positive temperature gradients, and the profile 1 of VTLM Ⅰ can be described with a three-segment linear function composed of TP1, TP2, and TP3. The PTLM of VTLM Ⅱ has TT, TL, and TNL with a positive temperature effect. Additionally, the profile 2 of VTLM Ⅰ and NTLM of VTLM Ⅱ are negative temperature gradients, and the profile 2 of VTLM Ⅰ can be expressed by a two-segment linear function with parameters TN1 and TN2. The NTLM of VTLM Ⅱ is composed of TT, TL, and TNL with a negative temperature effect. VTLM Ⅱ can clearly reflect the contribution of TT, TL, and TNL to the secondary thermal stress and thermal self-stress of the composite girders. (3) Extreme values of daily temperature differences TP1, TP2, TP3, TN1, and TN2 can be described by the normal distribution function, and the stand values of TP1, TP2, TP3, TN1, and TN2 are 16.8°C, 13.5°C, 4.2°C, −14.5°C, and −20.3°C, respectively, with a 50-year return period. Daily maximum and minimum values of TT and TL can be expressed by GMM. The maximum stand values of TT and TL are 52.4°C and 27.5°C, respectively, and the minimum are −13.5°C and −12.3°C, respectively, with a 50-year return period.
.7
Derivation of decomposition formula
Long-term temperature experiment
Determine the form of temperature difference gradient
Probability statistics of temperature difference
Standard value of temperature difference
Thermal loads model Ⅰ
1.Equivalent uniform temperature;
2.Equivalent linear temperature;
3.Equivalent nonlinear temperature;
Probability statistics of equivalent temperature
Calculation
Probabilistic limit-state design analysis
Standard value of equivalent temperature
Thermal loads model Ⅱ
Thermal stress formulas
Thermal stress calculation
The relationship between thermal effects
and thermal loads
1.Solar radiation
Sunshine
Diffuse
reflection
2.Ambient temperature
3.Strong cold air
Ground reflection
Thermal convection
Heat conduction
N
E
30º
Thermal stress of VTLM
Stress during monitoring period
and Table 1.8
700×50
1625
200
700×50
1095×30
1095×30
3300×55
1200
3300
W1
W8
E1
E8
Fig. 3 Arrangement of measuring points.
Table 1 Measure locations.
Sensor number
Distance from the top of the bridge deck (m)
W1
E1
0.0
W2
E2
0.12
W3
E3
0.20
W4
E4
0.25
W5
E5
0.35
W6
E6
0.50
W7
E7
0.95
W8
E8
1.40
Table 2 .
2The standard value of temperature difference of TP1-TP3 and TN1-TN2 are 16.8°C, 13.5°C, 4.2°C, −14.5°C, and −20.3°C.
Table 2 .
2Parameters of normal distribution and standard values within the 50-year return period.VTLM Ⅰ
Temperature difference
Parameters
Standard value/℃
Profile 1
TP1
7.471
1.905
16.8
TP2
8.566
1.764
13.5
TP3
1.497
0.712
4.2
Profile 2
TN1
−4.380
1.857
−14.5
TN2
−9.103
3.043
−20.3
Table 3 .
3Parameters of GMMType
a1
b1
1
A2
b2
2
A3
b3
3
a4
b4
4
a5
b5
5
+
T
T
1.54
8.88 18.03 −1.47 8.53 17.91 −0.02 5.17 27.03 0.04 3.61 0.11 0.004 7.09 36.66
+
L
Table . 4
.Parameters in vertical thermal load model Ⅱ.Positive thermal load model
Negative thermal load model
T1/℃ T2/℃ T3/℃ T4/℃ k/℃/m TT/℃ T5/℃ T6/℃ T7/℃ T8/℃ k/℃/m TT/℃
4.6
1.5
6.2
14.3
18.9
52.4
−8.9 −13.8
1.3
−6.7
−12.3 −13.5
Thermal load
Thermal effect
Bridge design
Statically indeterminate structure
Statically determinate structure
Axial deformation, non-
stress
Axial deformation, secondary
thermal stress
Axial deformation, bending
deformation, thermal self-
stress
Axial deformation, bending
deformation, thermal self-
stress, secondary stress
Axial deformation, non-
stress
Axial deformation, secondary
thermal stress
Bending deformation, non-
stress
Bending deformation,
secondary thermal stress
Non-deformation, thermal self-
stress
thermal self-stress, Non
secondary thermal stress
VTLM Ⅰ
Uniform
temperature
Vertical
temperature
difference gradient
VTLM Ⅱ
TT
Expansion joints,
supports
Stress checking
TL(y)
TNL(y)
, secondary thermal stress exhibits a cycle characteristic due to the daily and annual cycle of temperature. The secondary thermal stress is usually larger than the thermal self-stress (Figs. 19 (c-d)) in the composite girder. The maximum secondary thermal stress caused by TT, TL, and TNL for the top surface of the bridge deck is 0.328, 6.373, and 0.141 MPa, respectively, and the corresponding minimum value is −1.973, −5.177, and −0.126 MPa, respectively. The maximum secondary thermal stress caused by TT, TL, and TNL for the top surface of the steel girder is 13.909, 36.465, and 0.884 MPa, respectively, and the corresponding minimum value is −2.31, −44.899, and −0.993 MPa, respectively. The equivalent linear temperature TL is the main factor leading to the secondary thermal stress. Compared with that of TL, the influence of TNL on the secondary thermal stress can be ignored. Equivalent uniform temperature TT can also lead to the secondary thermal stress for the statically indeterminate structure. The thermal self-stresses caused by TT, TL, and TNL on the top surface of the bridge deck and steel girder are shown in Figs. 18 and 19 (c-d). The maximum thermal self-stress caused by TT, TL, and TNL for the top surface of the bridge deck is 0.715, 0.251, and 3.759 MPa, respectively, and the corresponding minimum value is −0.118, −0.205, and −2.794 MPa, respectively. For steel girder, the maximum thermal self-stress caused by TT, TL, and TNL is 2.099, 2.100, and 13.040 MPa, respectively, and the corresponding minimum value is −12.623, −2.586, and −32.589 MPa, respectively. Therefore, the equivalent nonlinear temperature TNL is the main factor causing the thermal self-stress. Compared with that of TNL, the influence of equivalent linear temperature TL and equivalent uniform temperature TT on thermal self-stress can be ignored.
TimeSepNov Jan Mar May Jul Sep Nov Jan MayAcknowledgementsThe authors gratefully acknowledge the financial support provided by the National Natural Science
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| sample_1024 | 0.9693 | arxiv | |
A CLUSTER-BASED APPROACH TO WEATHER FORECAST ACCURACY *
9 Mar 2023
Jill Lundell jlundell@ds.dfci.harvard.edu
Department of Data Science Dana-Farber Cancer Institute Department of Biostatistics Harvard T.H. Chan School of Public Health Boston
Department of Mathematics and Statistics
Department of Mathematics and Statistics
Utah State University Logan
Utah State University Logan
02215, 84322, 84322MA, UT, UT
Brennan Bean brennan.bean@usu.edu
Department of Data Science Dana-Farber Cancer Institute Department of Biostatistics Harvard T.H. Chan School of Public Health Boston
Department of Mathematics and Statistics
Department of Mathematics and Statistics
Utah State University Logan
Utah State University Logan
02215, 84322, 84322MA, UT, UT
Jürgen Symanzik juergen.symanzik@usu.edu
Department of Data Science Dana-Farber Cancer Institute Department of Biostatistics Harvard T.H. Chan School of Public Health Boston
Department of Mathematics and Statistics
Department of Mathematics and Statistics
Utah State University Logan
Utah State University Logan
02215, 84322, 84322MA, UT, UT
A CLUSTER-BASED APPROACH TO WEATHER FORECAST ACCURACY *
9 Mar 2023LET'S TALK ABOUT THE WEATHER
Improved understanding of characteristics related to weather forecast accuracy in the United States may help meteorologists develop more accurate predictions and may help Americans better interpret their daily weather forecasts. This article examines how spatio-temporal characteristics across the United States relate to forecast accuracy. We cluster the United States into six weather regions based on weather and geographic characteristics and analyze the patterns in forecast accuracy within each weather region. We then explore the relationship between climate characteristics and forecast accuracy within these weather regions. We conclude that patterns in forecast errors are closely related to the unique climates that characterize each region.Keywords Climate · Clustering · Data Expo 2018 · Glyph Plots · Random Forests · Visualization From the icy, wet winters along the Great Lakes, to the hot and dry summers in the Southwest, the United States (U.S.) experiences a wide range of climatic extremes. These extremes create unique challenges when forecasting the weather. Understanding forecast errors across such a diverse landscape is equally challenging, requiring multi-dimensional visualizations across space, time, and climate measurements. Better understanding of the nature and patterns in forecast errors across the U.S. helps meteorologists as they strive to improve weather forecasts. It can also help everyday Americans know how much faith to put in the weather forecast on the day of an important event.The 2018 Data Expo of the Sections on Statistical Computing and Statistical Graphics of the American Statistical Association (ASA) provided an opportunity to explore and compare weather forecast errors across the U.S. Our analysis focused on the question:How do weather forecast errors differ across regions of the U.S.?This motivating question prompted the subsequent questions:• Do U.S. weather stations cluster into regions based on weather characteristics?• How do error variables correlate and do these correlations change by region?• How do forecast errors change by region and by season? * Citation: JF Lundell, B Bean, and J Symanzik. Let's talk about the weather: A cluster-based approach to weather forecast accuracy.
[3,7422]
• Where are the best and worst forecast accuracies?
• Which variables are important in determining forecast errors?
Preliminary results of our analysis are published in the proceedings for the 2018 Joint Statistical Meetings [1].
This article is devoted to answering these questions. We use ensemble graphics to create an overall picture of weather forecast errors across different regions of the U.S. [2]. Ensemble graphics enhance traditional analyses by connecting several visualizations of the data with adjoining text. This presentation is able to tell a cohesive story of the data more effectively than would be possible with a few disjointed graphics. In Section 1, we summarize the data and then show that the U.S. can be clustered into six well-defined weather regions using the provided climate measurements, elevation, and distance to coast. These clusters, or weather regions, form the basis of our comparison of forecast accuracy across the U.S. through a series of multi-dimensional plots and variable importance analyses described in Section 2. in Section 3, we introduce the interactive application we created to enhance our data explorations. We conclude in Section 4 that the climate differences that distinguish the weather regions of the U.S. also create region-specific patterns and differences in forecast accuracy. Two appendixes are included at the end of this paper to explain data cleaning and how to create the glyphs used in this article.
Weather regions
The data contain measurements and forecasts for 113 U.S. weather stations from July 2014 to September 2017. These data can be obtained from our supplemental materials or at the following URL:
http://community.amstat.org/stat-computing/data-expo/data-expo-2018.
Daily measurements for eight different weather metrics were recorded for each location including temperature, precipitation, dew point, humidity, sea level pressure, wind speed, cloud cover, and visibility. Many notable weather events are also textually recorded such as thunderstorms and fog. Daily measurements of the minimum, maximum, and mean were recorded for each metric. Weather characteristics used in this article are listed in Table 1. Data were supplemented with some geographic information and carefully examined and cleaned. Details on data cleaning, obtaining additional data, and the justification behind our final variable selection are found in Appendix A.
Developing weather clusters
The U.S. has been divided into regions based on environmental characteristics such as watersheds and climate [3] [4]. We examined the set of existing environmental regions and were unable to find one that made sense in terms of weather in the context of this analysis. We created our own weather regions by clustering the weather stations based on the metrics in Table 1. Thus, clusters are defined by weather characteristics observed at each station. We use these clusters to determine how weather forecast error patterns are related to the unique climate measurements of a particular region. A review of existing weather regions and how they correspond to our weather regions is discussed in Section 1.2. Data were aggregated across each weather station by taking the mean and standard deviation of each variable in Table 1 for each of the 113 weather stations over the period of record.
Hierarchical clustering [5] with Euclidean distance and Ward's minimum variance clustering method [6] was used to identify clusters. The clusters were examined spatially to determine the performance of the clustering method and select the final number of clusters. We wanted to ensure the weather station clusters were of a sufficient size to be practical. Five clusters resulted in one cluster that included all of the stations from the Midwest to the East Coast which we think is too large because of the differences in coastal and inland climates. Seven clusters produced a cluster that contained only five weather stations which is too small. Thus, we chose six clusters to divide the U.S. into weather regions. Figures 1 and 2 show the results of the cluster analysis. Figure 3 shows a parallel coordinate plot of the characteristics for each weather region. The Z-score for mean and standard deviation for each of the variables in Table 1 was computed and plotted on the parallel coordinate plot. It is difficult to distinguish the six weather regions from each other so an interactive app was created that provides a better view of the features of each cluster. The app is discussed in Section 3.
The names and characteristics of each weather cluster are as follows:
• The National Oceanic and Atmospheric Administration (NOAA) developed climate regions that incorporate seasonal temperature and precipitation information [7]. These regions differ substantially from the North American ecological regions as they also have a lateral trend in addition to the longitudinal trend and are constrained by state boundaries. Spectral curves assessing drought and wet spells were used to define the NOAA regions [8]. The NOAA regions correspond roughly to our general weather regions despite region borders being defined by state boundaries. The north/south division in the eastern U.S. closely aligns with our cluster division in that area. The major east/west division in our clusters is in a similar location to the NOAA clusters as well.
The International Energy Conservation Code (IECC) climate clustering of the U.S. [4] and subsequent reclassification by Hathaway, et al. [9] divided the U.S. into fourteen regions based on temperature, dew point, wind speed, and radiation. Cluster methods included K-means clustering and Monte-Carlo sifting. Both sets of regions show a strong lateral trend in the Eastern U.S. These regions also show distinct separation of the West coast and Southwest deserts from the rest of the Western U.S. Similar trends are also seen in our clusters. The lateral trend in the Eastern U.S. is not as strong in our clusters, but this is likely because we chose a smaller number of weather clusters. The inclusion of additional variables insensitive to lateral trends such as distance to coast, elevation, and humidity, all serve to reduce the lateral separation in our clusters.
One key difference between our weather regions and the regions seen in other studies is that we combine Florida and the Pacific coast into a single weather region. This is likely a result of our choice to omit geographic proximity of weather stations in the cluster analysis calculations and consider only similarities in weather patterns. Both Florida and the Pacific coast experience less seasonality in their weather patterns than the rest of the country. This results in smaller than average standard deviations for many of the climate variables in both of these regions. These small standard deviations create a measure of closeness between Florida and the Pacific coast which likely explains why these Because we did not use spatial proximity as a clustering variable and we assigned all weather stations to one of our six weather clusters, Hawaii and Alaska are clustered with Cali-Florida and the Northeast respectively. Our clusters show that weather patterns typically have strong spatial correlations, with temperate coastal regions being a notable exception.
Forecast error explorations
Given the clear separation of the country into distinct weather regions, we seek to determine if there are clear differences in forecast error patterns among the regions. Forecasts were restricted to minimum temperature, maximum temperature, and the probability of precipitation. The forecast error for minimum and maximum temperature is calculated as the absolute difference between forecast and measurement. The forecast error for precipitation is measured using the Brier Skill Score (BSS), a well-known measure of probabilistic forecast accuracy [10]. It is defined for a particular weather station as Table 1. Each line in the plot represents one of the 113 weather stations. The color of the lines match the weather region to which the station belongs. An interactive app is available that allows for better identification of regional trends.The Southwest region is highlighted in this graph to emphasize its weather characteristics
BSS = 1 − N i=1 M j=0 (Y ij − O i ) 2 N i=1 M j=0 (P − O i ) 2 (1) where • Y ij ∈ [0, 1] is• O i ∈ {0,
1} is a binary variable with value 1 if any precipitation fell during the day and 0 otherwise. We define a precipitation event as a positive precipitation measurement or the inclusion of the words "rain" or "snow" in the event information;
• P ∈ [0, 1] is the average daily chance of precipitation over the period of interest, defined as P = 1
N N i=1 O i ;
• N denotes the number of days of recorded precipitation in the period of record and M ∈ {0, . . . , 5} denotes the number of forecast lags.
Note that the BSS ∈ (−∞, 1], with 1 indicating a perfect forecast skill and movement towards −∞ indicating worse forecasts. We chose to use 1 − BSS so all three error variables are consistent in orientation. The following subsections explore differences in forecast errors both between and within the previously defined weather regions visualized in Figure 1. Forecast errors are averaged over lag and in some cases averaged over month in each graph. The visualizations in the following subsections confirm our hypothesis that different weather regions experience distinctly different weather forecast error patterns.
Error correlations
Are the forecast errors for the three different measurements (i.e., minimum temperature, maximum temperature, and precipitation) correlated with each other? How do these relationships change between the different weather regions? We explore such correlations through the use of correlation ellipses [11] superimposed on a map of the U.S. in Figure 4. We calculated Spearman correlations between each pair of measurements for the locations within each cluster. The sign of the correlation coefficient is denoted by the slope of the ellipse and the strength of correlation is denoted by the width of the ellipse.
All of the correlations between error variables are positive except for correlations between minimum temperature and the other two variables in the Northeast. The strongest relationships are seen in the Midwest, the South and the Southwest. The weakest relationships are found in the Northeast. Only a few cluster-specific correlations are significant. This is likely due to the small number of stations in many of the weather regions. However, the overall correlations for the 113 weather stations are all positive and significant. This indicates that areas with good predictions for one forecast variable have generally good predictions for the other forecast variables as well. The weakest correlations are between minimum temperature and precipitation predictions. Although there are relationships between the three weather forecast variables, those relationships are not particularly strong and the strength differs within each region. The observations made using this correlation ellipse map illustrate how this plot style facilitates multi-dimensional comparisons across space. Information on the calculations and implementation of the correlation glyphs can be found in Appendix B.
Max Temp
Min Temp
Min Temp
Precip Combined Non−significant correlation (α = 0.05) −1 −0.5 0 0.5 1 Correlation | | | | | | | | | Cali−Florida Southeast Northeast Intermountain West Midwest Southwest
Error scatterplots
Scatterplots reveal outliers and overall trends within weather regions and across forecast lag. Forecast lag is defined as the number of days between the day of forecast and the day being forecast. Thus, same day forecasts would have a lag of 0, one day prior forecasts a lag of 1, and so on. Because we are comparing three variables spatially and temporally across the U.S., static graphs are not optimal for assessing all relationships of interest. We constructed an interactive scatterplot app that facilitates examination of trends between the three forecast error variables aggregated across all forecast lags or for individual forecast lags. Figure 5 (a-c) shows examples of plots from the interactive app. The figure shows the scatterplot for the data aggregated over all forecast lags, as well as the scatterplots for lags of 5, 3, and 1, to illustrate how forecast accuracy changes over forecast lag. Figure 5(a) compares minimum temperature forecast accuracy with precipitation accuracy. Weather stations with the worst predictions of minimum temperature are located in New England and the Intermountain West. New England is known for extreme winter weather and the frequency of extreme weather events seems to be increasing [12]. This likely contributes to the struggle these stations have predicting minimum temperature. The worst predictor of minimum temperature is Austin, Nevada. This location is addressed further in Figure 5(c). Cali-Florida uniformly has the best predictions of minimum temperature. However, Cali-Florida also has some of the greatest variability in precipitation prediction accuracy when examining individual lags. its weather measurements which were collected in Eureka, Nevada. The poor predictions for maximum and minimum temperature can be explained by the change in climate over such a large distance. This is reflected in a negative prediction bias of around 5 • F for maximum temperature and a positive bias of around 7 • F for minimum temperature. San Francisco has good predictions of minimum temperature and poor predictions for maximum temperature. This phenomenon is further explained in Section 2.3.
The interactive app developed in conjunction with this project allows for further investigation of forecast accuracy trends. The app is discussed in Section 3.
Seasonal trends
The position of the U.S. in the northern hemisphere makes most of the country subject to distinct weather seasons.
Seasons are most pronounced in the northern U.S. We hypothesize that the forecast error behavior is inextricably linked to this seasonality. We explore this through a series of space-time graphs. Modeling space and time simultaneously creates a three-dimensional problem usually visualized as small multiples. Small multiples are "a series of graphics, showing the same combination of variables [e.g., latitude and longitude], indexed by changes in another variable [e.g., time]" [14]. The issue with this approach is that it becomes difficult to visually comprehend all but the most drastic changes from graph to graph. One alternative that allows simultaneous visualizations of both space and time is through the use of glyphs, or symbols, that allow for multi-dimensional visualizations in a spatial context [15] [16]. In addition to highlighting forecasting asymmetries, Figure 6 reveals location-specific anomalies. For example, San Francisco, California, predicts minimum temperatures well all year, but only predicts maximum temperatures well in the winter months. This is likely due to chilling coastal fogs known to frequent the region throughout the year that can create sharp temperature differences over short distances [17]. The struggle to predict temperature seems reasonable in light of these facts as this measurement location is more than 11 miles inland from the forecast location. The issue is likely less pronounced in the winter because the contrast between inland and coastal temperatures is reduced.
Maximum temperature predictions are particularly poor in the summer months in Austin, Nevada. It is unclear why predictions are worse in the summer than in the winter.
Another location-specific anomaly of note is the drastic seasonality of precipitation forecasts for locations surrounding the Great Lakes, as observed in Figure 6. The error scatterplots in Figure 5(b) show that precipitation accuracy is poor in this region, but the seasonality of the predictions cannot be observed in the scatterplots. The unusually bad forecasting in the winter is likely due to lake-effect snow which is prevalent in the region. Up to 100% more snow falls downwind of Lake Superior in the winter than would be expected without the lake-effect [18]. This area has been previously identified as having the most unpredictable precipitation patterns in the nation [19]. The above examples demonstrate the ease with which comparisons can be made across space and time with these glyph-based plots. Information about how to generate the glyphs is included in Appendix B.
Variable importance
The differences in forecast error patterns across regions prompt identification of the most important climate measurements for predicting forecast error. We used random forests [20] to determine which weather variables had the greatest impact on the forecast errors. The data were aggregated over forecast lag and month. Three random forest models were generated for each weather region using the forecast error variables as the response. The means and standard deviations for each of the weather variables listed in Table 1 and the forecast lag were the predictor variables. Figure 7 contains three parallel coordinate plots that show the variable importance measures in each region for each forecast error variable. The importance measures obtained from random forests were recentered by subtracting the minimum importance measure and then rescaled to the interval (0, 100) by dividing by the maximum importance measure of the recentered values for each weather cluster and forecast error variable combination, and finally multiplying by 100. Thus, the most important variable within each weather region has a value of 100 and the least important has a value of 0 for each error measure. This allows direct comparisons of importance between weather regions and across error measures. Forecast lag is also the most important variable for the maximum temperature error for all weather regions except Cali-Florida. The standard deviation of maximum temperature and maximum wind speed (WS) are more important than lag in Cali-Florida. The variability in maximum temperature is also important for the Southeast, Northeast, and the Intermountain West. Distance to coast (Dist2Coast) and elevation are important for the maximum temperature error in the Intermountain West.
Variables that are important for the minimum temperature error varied substantially across weather regions. The variability in minimum temperatures is important for all regions, but other important variables differ widely from region to region. Minimum temperature is the most important for the Northeast and Intermountain West, but maximum temperature is important for the Southeast. Minimum dew point and the variability in the maximum sea level pressure (SLP) are important in the Southwest while variability in minimum sea level pressure is the most important for the Midwest, Southeast, and Southwest. Forecast lag is not particularly important for any of the regions except for the Midwest.
Interactive application
It is difficult to identify the patterns in climate measurements and forecast errors for all weather regions with static visualizations. We developed an interactive Shiny app to enhance our weather data explorations. This app can be accessed at https://jilllundell.shinyapps.io/finaldataexpoapp/.
The first tab of the app is an interactive version of the parallel coordinate plot introduced in Figure 3. The app allows the user to select a weather region which is highlighted on the graph. Characteristics of the selected region can be easily seen and compared to all other observations. The second tab of the app is an interactive scatterplot. Figure 5 (a-c) shows examples of the graphs generated in this tab. The user can select up to two of the three forecast error variables to be on the axes. The forecast lag can also be selected. Points on the scatterplot can be brushed or clicked and the selected points show up on a map of the U.S. Information about selected stations is listed in a table under the graph. The idea of linked brushing between scatterplots and maps was first introduced in Monmonier [21]. This app allows for a more complete exploration of outliers and trends in the data across forecast lags and between error variables than a static graph.
Conclusions
Climate patterns in the United States cleanly separate into six recognizable regions through a cluster analysis using the means and standard deviations of the weather variables provided in Table 1. We explored the relationship between the three weather forecast variables (i.e., minimum temperature, maximum temperature, and precipitation) using correlation ellipses shown in Figure 4. We found that all clusters show signs of positive correlations among the error variables with the exception of the Northeast cluster.
We visualized the pairwise relationship between forecast errors through a series of scatterplots across all forecast lags in Figure 5. These plots highlight the superiority of locations in the Cali-Florida region for predicting minimum temperature across all lags, and also show that the poor precipitation predictions of the Great Lakes region are mostly confined to forecasts greater than lag 2. Lastly, the abnormally high errors in Austin, Nevada, are likely a product of the large distance between forecast and measurement locations.
We explored seasonal differences of forecast errors in Figure 6 and observed that seasonal differences in forecast errors tend to be more pronounced in northern, inland clusters than southern clusters. We also showed that location specific anomalies, such as the asymmetry in seasonal maximum temperature forecast errors in San Francisco and the precipitation forecast errors near the Great Lakes, have plausible explanations in the literature.
Next, we compared the important variables in determining forecast errors across clusters using scaled random forest variable importance measures in Figure 7. These measures demonstrate that forecast lag is most important in determining the maximum temperature and the precipitation forecast errors, but not important in predicting the minimum temperature forecast errors. Many clusters place similar importance on a few variables, but there are some variables that are important only in a single cluster, such as the importance of maximum wind speed in predicting the maximum temperature forecast error in Cali-Florida.
For further insight regarding the nature of forecast errors across these six clusters, we refer readers to our R shiny app described in the previous section. A current version of the app can be found at the following URL:
https://jilllundell.shinyapps.io/finaldataexpoapp/ This app, in conjunction with the visualizations presented in this article, reinforces the idea that the U.S. cleanly clusters into well defined weather regions and patterns in forecast errors are closely related to the unique climates that characterize each region.
The visualizations in this paper, both interactive and static, were designed to be scalable for larger weather datasets. We anticipate illustrating this capability on an expanded set of stations in the future. An expanded analyses will also serve to validate the regional patterns observed and described in this paper. In addition, we anticipate adapting several of the static glyph plots presented in this paper for interactive use. Greater interactivity will allow for more detailed explorations of weather patterns in the United States across both time and space.
A Data cleaning
We primarily used the dataset provided by the Data Expo to perform the analyses described in the article. We supplemented the provided location information with elevation and distance to the nearest major coast. Elevation information was obtained for each location through Google's API server [35] via the rgbif R package [36]. Distance to coast was calculated as the closest geographical distance between each measurement location and one of the vertices in the U.S. Medium Shoreline dataset [37], which includes all ocean and Great Lakes coasts for the contiguous 48 states. Because this dataset does not include the coastlines of Alaska and Hawaii, distance to coast calculations for these locations used manually extracted shorelines from NOAA's Shoreline Data Explorer [38]. We acknowledge there are limitations to this method of distance calculation, as distances for some locations, such as Arizona (Flagstaff, Nogales, and Phoenix), are slightly longer than they would be had we used shoreline information for Mexico's Gulf of California. Nevertheless, these measurements effectively separate inland weather stations from coastal stations. Table 1 shows the weather variables included in our final analysis. We excluded mean daily measurements for temperature, precipitation, dew point, humidity and sea level pressure as these measurements were near perfect linear combinations of their corresponding minimum and maximum measurements. We also excluded maximum visibility from the analysis as this measurement was equal to 10 miles for more than 97% of all recorded measurements. Lastly, we combined the information provided by maximum wind speed and maximum wind gust by retaining only the lower of the two measurements after removing outliers. The decision to combine the information from these two wind variables was motivated by the fact that 13% of all maximum wind gust values were missing. In addition, it is difficult to separate unusually high, yet valid, maximum wind gust and wind speed measurements from true outliers.
Some stations did not record relevant climate variables. When possible, these missing observations were replaced with corresponding measurements obtained from the nearest National Weather Service (NWS) first order station as obtained through the National Climatic Data Center (NCDC) [39]. Missing values include wind speed in Baltimore, Maryland, precipitation in Denver, Colorado, and replacements of outlier precipitation measurements at multiple locations. When replacements were not readily obtained through the NCDC, systematic missing observations were replaced with corresponding observations from the nearest geographical neighbor within the dataset, as was the case for visibility and cloud cover in Baltimore, Maryland (replaced with Dover, Delaware, measurements) and Austin, Nevada (replaced with Reno, Nevada, measurements). Table 1 also shows the observation ranges for each of the included variables. These measurement ranges are either definitional, such as the bounds for humidity, or simply practical, such as the bounds for temperature. All measurements falling outside the bounds shown in Table 1 were removed prior to our analysis. Several individual outliers were also removed or replaced based on location-specific inconsistencies including • removal of one unusually low minimum temperature measurement in Honolulu, Hawaii, (< 10 • F) and two in San Francisco, California (< 20 • F);
• replacement of the following unusually high precipitation readings with precipitation readings at nearby weather stations [39]: Forecast variables were restricted to minimum temperature, maximum temperature, and the probability of precipitation. We found no obvious outliers in the weather forecasts. This is reasonable due to the fact that forecasts are not subject to inevitable sensor technology failures that occur when taking an actual measurement. Rather, the forecast data were replete with duplicate values for minimum temperature and precipitation. We retained the lowest forecast of minimum temperature and the highest forecast of precipitation probability for each forecast.
-
Forecast lags of six or seven days contained a large number of missing values. We removed all forecasts past lag 5. We also removed all forecasts containing negative lags (i.e., a forecast made after the actual observation).
B Polar coordinate considerations for geographic maps
The glyph plots in Figures 4 and 6 rely on proper conversions from polar to geographic or Cartesian coordinates. This allows the glyphs to be plotted directly on the underlying map, rather than embedding polar coordinate subplots in the image. Avoiding subplots allows for greater precision in the placement of the glyphs and avoids the computational burden of creating and embedding multiple figures. This direct plotting approach requires special considerations for geographical maps, as polar coordinate glyphs become distorted when projecting geographical coordinates to a Cartesian plane. For example, a perfect circle in geographical coordinates will appear elongated in the vertical direction when the circle is projected in the northern hemisphere. One solution to this issue is to project all geographical coordinates to a Cartesian plane prior to the glyph construction. This can be conveniently accomplished using the mapproject() function in the mapproj R package [26].
Polar coordinates are defined in terms of radius r and angle θ. Figure 6 defines r ∈ [0, 1] as the scaled average absolute error between predicted and actual temperature and θ = (4−m)π 6 where m represents the numeric month. We center each glyph at 0 with Cartesian coordinates (x, y) = (r cos θ, r sin θ)
Let (x i , y i ) represent the set of Cartesian coordinates centered at the origin that create the glyph associated with location i. These coordinates are defined using the same units as the underlying map projection. The final coordinates of the rendered glyph are defined as α · (x i + u x , y i + u y )
where (u x , u y ) represents coordinates of location i and α represents a global scaling parameter used to adjust the size of the rendered glyphs on the map. A point is drawn at location (u x , u y ) to serve as a reference for the glyph. Asymmetry about the point (u x , u y ) reveals seasonal patterns in the forecast errors.
We construct the correlation ellipses of Figure 4 with foci F 1 , F 2 located along the semi-major axis y = x (θ = π 4 ) for positive correlations and y = −x (θ = − π 4 ) for negative correlations. We fix F 1 at the origin and denote r as the radius extending from F 1 to the edge of the ellipse, as illustrated in Figure 8. This approach to ellipse creation is outlined in Knisley and Shirley [40] and adapted here where we define r for θ ∈ [0, 2π] as , where ρ ∈ (−1, 1)\{0} represents the desired correlation between forecast errors. In the event that ρ = −1, 1, or 0, we use ρ ± ( > 0) when creating the ellipse to avoid numerical precision errors. The ellipse is then converted to Cartesian coordinates and centered at the origin as r cos(θ) − |ρ|(2 − |ρ|) √ 2 , r sin(θ) − sign(ρ) |ρ|(2 − |ρ|) √ 2 .
Each ellipse is scaled to be circumscribed in the [−0.5, 0.5] × [−0.5, 0.5] square. This scaling makes it possible to create a matrix of ellipses using a common grid size. It also reduces the difference in areas between ellipses which facilitates comparisons of shape. This scaling is defined as
(x i , y i ) = x i 2 · max(|x i |)
, y i 2 · max(|y i |) .
Note that there are three ellipses for each location. We define a matrix of ellipses centered at the shared vertex of the lattice denoted by (u x , u y ). Let (x i , y i ) represent the coordinates of one of the three ellipses centered at this location. Each ellipse is centered and scaled on the map as
α · (x i + u x + o 1 , y i + u y + o 2 )
where o 1 and o 2 represent offset terms used to separate the centers of the three ellipses in the matrix defined for each location.
This direct plotting approach of the ellipses eases plot customization, as there is no need to reconcile formatting differences between independently created subplots. This approach can also be generalized to plot other geometric shapes on a geographic map. It is also helpful for interactive applications that require fast renderings of images in response to dynamic inputs.
Figure 1 :
1Map of the six weather regions. The color band at the bottom identifies each region by name and color two geographic areas all into a single cluster when working with six or fewer clusters. The Florida and Pacific stations separate into separate clusters when using seven clusters with exception of two stations from the Pacific Coast that cluster with the Florida stations. Hawaii and Alaska are either ignored in the literature or placed in their own regions.
Figure 2 :
2the predicted probability of rain on day i with forecast lag j; Dendrogram of weather clusters identified inFigure 1
Figure 3 :
3Parallel coordinate plot of the means and standard deviations of the weather variables listed in
Figure 4 :
4Spearman correlations between forecast error variables represented as ellipses superimposed on a map of the United States. The p-value for each correlation is compared against a 0.05 level of significance
Figure 5 (
5b) compares maximum temperature prediction accuracy with precipitation accuracy. Four weather stations in the Great Lakes region have the worst precipitation predictions in the dataset. Poor precipitation forecast accuracy in this region illustrates the difficulty in forecasting lake-effect snow. This phenomenon is discussed in greater depth in Section 2.3. Precipitation forecast accuracy for the Great Lakes region improves substantially as the forecast lag decreases and forecasts with lag 1 are as accurate as the rest of the nation.
Figure 5 (Figure 5 :
55c) shows the relationship between minimum and maximum temperature forecast accuracy. Three outliers stand out in these scatterplots, namely Key West, Florida, Austin, Nevada, and San Francisco, California. Key West predicts both minimum and maximum temperature more accurately then any other weather station. Key West also ranks in the top five for lowest variability in eight of the weather variables, which likely explains the accurate forecasts. Austin is the poorest predictor of both measures. Seventy miles along the "loneliest highway in America"[13] separate Austin from Scatterplots comparing the three forecast error variables. The scatterplot to the left of the map is aggregated over all forecast lags. Points of interest discussed in the text are highlighted in the respective plots
Figure 6
6shows glyph plots of seasonal forecast errors throughout time. The forecast error is visualized as the scaled distance from a center point to the edge of a polygon with twelve observations starting with January at the 12:00 position and proceeding clockwise. The asymmetry of the glyphs about their center points illustrates how forecast errors change across time and across space. For example, locations in the Northeast are worse at forecasting precipitation in the winter than in the summer, while locations in the Southeast forecast precipitation equally well throughout the year.
Figure 7 Figure 6 :
76shows that the most important variable for the precipitation error is forecast lag regardless of weather region. None of the other variables are very important relative to lag. The Southeast shows minimum dew point (DP) and the Glyph plots of weather forecast accuracy averaged by month. The error is represented as the scaled distance from a center point to the edge of a polygon beginning with January at the 12:00 position and proceeding clockwise
Figure 7 :
7Variable importance for each of the three forecast accuracy measurements. Variable importance measures have been rescaled to make the measures directly comparable between weather regions and accuracy measures standard deviation of maximum dew point as being somewhat important. Cloud cover is important for the precipitation error in the Northeast.
Oklahoma City, Oklahoma, on 8/10/2017 (38.33in → 0.8in) -Salmon, Idaho, on 4/21/2015, 5/2/2016, and 5/3-4/2017 (10.02in → 0in) -Flagstaff, Arizona, on 12/24/2016 (7.48in → 0.97in) -Indianapolis, Indiana, on 7/15/2015 (9.99in → 0in); • removal of one unusually low minimum dew point measurement in Honolulu, Hawaii (< 40 • F), two in Hoquiam, Washington (< 0 • F), four in Las Vegas, Nevada (< −15 • F), and two in Denver, Colorado (< −20 • F).
Figure 8 :
8Sample ellipse with F 1 located at the origin
Table 1 :
1List of weather variables included in our analysis. All observations outside the indicated ranges were removed prior to our analysis.Variable
Unit
Range
Min/Max Temperature
• F
[−37, 127]
Precipitation
in
[0, 12.95]
Min/Max Dew Point
• F
[−50, 90]
Min/Max Humidity
%
(0, 100]
Min/Max Sea Level Pressure inHg [28.2, 31.2]
Mean/Max Wind Speed
mph
[0, 70]
Min Visibility
mi
[0, 10]
Cloud Cover
okta {0, 1, · · · , 8}
Distance to Coast
mi
[0, 807]
Elevation
ft
Cali-Florida (13 stations): Warm and humid with high dew point and pressure. Low variability in almost all measurements. • Southeast (22 stations): Warm and humid with lots of rain. High variability in precipitation and low variability in temperature. • Northeast (39 stations): Cold, humid, and low visibility. High variability in temperature, dew point, and pressure. • Intermountain West (19 stations): Cold and dry, with high variability in temperature, wind speed, and pressure. Low variability in precipitation and dew point. • Midwest (13 stations): Landlocked with high wind speed and high variability in temperature, pressure, and wind speed. • Southwest (7 stations): Warm, sunny, and dry with little variation in temperature or precipitation. High variability in wind speed and humidity.1.2 Comparison to existing climate regionsEcological and climate regions have been developed for the U.S. in other studies. Many of these studies focused on smaller regions in the U.S., but a few have looked at the U.S. as a whole. Clustering methods and the variables used to identify clusters differ from study to study. The ecological regions of North America defined by the Commission for Environmental Cooperation[3] used ecosystems to develop regions. Air, water, land, and biota, including humans, were used to create the ecoregions. These ecoregions show a strong longitudinal trend that corresponds well with the longitudinal trends in our clusters. Clusters were not determined by statistical clustering methods, but by careful assessment of ecological properties across North America.
Albany, NY Amarillo, TX Anchorage, AK Atlanta, GA Atlantic City, NJ Austin, NV Baker, OR Baltimore, MD Bangor, ME Birmingham, AL Bismarck, ND Boise, ID Boston, MA Buffalo, NY Carlsbad, NM Charleston, SC Charleston, WV Charlotte, NC Cheyenne, WY Chicago, IL Cincinnati, OH Cleveland, OH Columbia, SC Columbus, OH Dallas, TX Denver, CO Des Moines, IA Detroit, MI Dover, DE Dubuque, IA Duluth, MN Eastport, ME El Paso, TX Eugene, OR Fargo, ND Flagstaff, AZ Fresno, CA Garden City, KS Grand Junction, CO Grand Rapids, MI Havre, MT Helena, MT Honolulu, HI Hoquiam, WA Hot Springs, AR Idaho Falls, ID Indianapolis, IN Jackson, MS Jacksonville, FL Kansas City, MO Key West, FL Klamath Falls, OR Knoxville, TN Lander, WY Las Vegas, NV Lewiston, ID Lincoln, NE Los Angeles, CA Louisville, KY Manchester, NH Memphis, TN Miami, FL Milwaukee, WI Minneapolis, MN Mobile, AL Montgomery, AL Montpelier, VT Nashville, TN Needles, CA New Haven, CT New Orleans, LA New York, NY Nogales, AZ North Platte, NE Oklahoma City, OK Philadelphia, PA Phoenix, AZ Pierre, SD Pittsburgh, PA Portland, ME Portland, OR Providence, RI Provo, UT Raleigh, NC Reno, NV Richfield, UT Richmond, VA Roanoke, VA Sacramento, CA Salmon, ID Salt Lake City, UT San Antonio, TX San Diego, CA San Francisco, CA Santa Fe, NM Sault Ste Marie, MI Savannah, GA Scranton, PA Seattle, WA Shreveport, LA Sioux Falls, SD Spokane, WA Springfield, IL Springfield, MA Springfield, MO St George, UT St Louis, MO Syracuse, NY Tampa, FL Trinidad, CO Watertown, NY Wichita, KS Wilmington, NC
AcknowledgementsThe authors would like to thank the Sections on Statistical Computing and Statistical Graphics of the ASA for providing the data used in this analysis. The primary analytical tool for this analysis was the R[22]. Additional data information regarding specific measurement locations were provided in the weatherData R package[23]. Distance and spatial calculations made use of the fields[24], geosphere[25], mapproj[26], rgdal[27], and sp[28]R packages. Other data manipulations and visualizations made use of the tidyverse[29], as well as the ggforce[30], latex2exp[31], RColorBrewer[32], and reshape2[33]R packages. Variable importance models made use of the randomForest[34]R package. also
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| sample_1027 | 0.6261 | arxiv | |
Biogéographie, évolution B. Soc. Zool. Fr
1274
Powers and limitation of the molecular approach for the study of biogeography and speciation : examples in tropical African mammalsWe attempted to test biogeographic hypotheses proposed for the evolution of tropical faunas (e.g. refuge, riverine barrier, and environmental gradient theories) by applying the most widely used molecular approach, i.e. mitochondrial DNA sequencing, to selected African mammalian taxa (Insectivora, Rodentia and Primates). First, we constructed a molecular phylogeny of taxa we intended to use for phylogeographic studies, in order to ascertain their monophyly and to calibrate a molecular clock for divergence time estimates.Second, we analysed and compared the phylogeographic patterns of four forest-dwelling small mammal species and one primate super-species. Third, we evaluated the evolutionary processes potentially involved in the speciation of cercopithecine Primates, by testing their geographic mode of speciation and reconstructing evolutionary scenarios of some life-history traits.Our phylogenetic results confirm that gene history is not necessarily the same as organism history. Thus, mitochondrial DNA should be studied in combination with other independent data, such as nuclear genes, morphology, ecology and behaviour. The obtained phylogeographic patterns all differ one from the other, which may be explained by differences in initial distributions, or by different responses to the same events. However, individual patterns present a certain degree of consistency with the faunal areas defined for the central African forest. They indicate a role of Plio-Pleistocene vicariance events in the intra-specific diversification of small mammals and suggest that genetic divergence would be much older than the last glacial cycles. In the case of cercopithecine Primates, speciation would have been predominantly allopatric and driven by Miocene and Pliocene vicariance events. Taken together, our results give support to the refuge hypothesis, without excluding the riverine barrier nor the paleogrographic hypotheses. They emphasize the role of paleoecological changes in generating diversity and that of the main riverine barriers in shaping the present distribution of that diversity.
INTERETS ET LIMITES DE L'APPROCHE MOLECULAIRE
Nos résultats phylogénétiques confirment que l'histoire des gènes n'est pas forcément celle des taxons et qu'il est important de prendre en compte plusieurs sources d'information indépendantes. Les analyses phylogéographiques révèlent des scénarios différents pour chacun des modèles, ce qui peut refléter soit des distributions initiales différentes, soit une réponse différentielle aux mêmes événements selon les taxons. Ces scénarios présentent une certaine concordance avec les régions fauniques définies pour les forêts d'Afrique centrale, mais suggèrent que les événements de divergence intra-spécifique seraient beaucoup plus anciens que les derniers cycles glaciaires. Nos résultats sont en accord avec la théorie des refuges et confirment le rôle de barrière joué par les principales rivières.
Introduction
Pour comprendre l'évolution du monde vivant, il est nécessaire de connaître la façon dont les organismes se diversifient dans le temps et dans l'espace. C'est l'objectif de la biogéographie, discipline qui étudie la distribution des taxons à l'échelle des peuplements, repère les caractères communs à ces distributions, et cherche à identifier les processus environnementaux, biologiques et historiques qui les ont façonnés (MYERS & GILLER, 1988).
Une approche plus récente, baptisée phylogéographie (AVISE et al., 1987), consiste à étudier l'évolution d'une lignée à la fois, en intégrant une dimension phylogénétique. CARCASSON, 1964 ;MOREAU, 1969 ;GRUBB, 1990 ;COLYN, 1991 Nous avons cherché quelles conclusions biogéographiques pouvaient être tirées de la comparaison des variations géographiques de la diversité génétique pour différents modèles.
Nous avons également tenté de savoir si certaines des prédictions associées aux théories évolutives formulées pour la faune tropicale étaient vérifiées. L'essentiel des analyses est basé sur un fragment d'ADN mitochondrial codant pour l'ARN-r 16S (ci-après appelé haplotype). . 2). Afin d'identifier les mécanismes impliqués, nous avons analysé la structuration géographique de la diversité génétique par une analyse des groupements emboîtés (TEMPLETON, 1998). La majorité des événements résulterait de la fragmentation passée de l'aire de distribution (vicariance). Il y aurait eu aussi plusieurs événements de dispersion et d'isolement par la distance.
Matériel et méthodes
Résultats et discussion
Choix des modèles
Les analyses phylogéographiques ont révélé quatre scénarios phylogéographiques différents pour les quatre modèles de petits Mammifères retenus, ce qui tendrait à confirmer que "la concordance entre schémas phylogéographique est l'exception plutôt que la règle" (ZINK, 1996 ;TABERLET et al., 1998 (ZINK, 1996 ;TABERLET et al., 1998). Toutes ces hypothèses font intervenir les caractéristiques écologiques et biologiques des espèces, or celles-ci sont peu connues dans le cas des modèles étudiés.
Synthèse biogéographique
Dans un premier temps, nous avons essayé de savoir si la diversité génétique intraspécifique a été affectée par l'histoire supposée des aires biogéographiques. Chaque schéma phylogéographique a été comparé avec un arbre théorique des aires correspondant aux régions fauniques mises en évidence pour la faune mammalienne (Fig. 1) (QUEROUIL et al., 2002). Les résultats ne nous ont pas permis de proposer de nouveaux scénarios biogéographiques pour l'Afrique centrale, mais suggèrent que ce but pourrait être atteint en analysant un nombre beaucoup plus élevé de modèles. Ils remettent en cause la prédiction que, s'il existe une histoire commune des aires, elle devrait être reflétée par la majeure partie des peuplements (NELSON & PLATNICK, 1981).
Ancienneté des événements de divergence
Les principaux événements de divergence ont été datés après calibration d'une horloge moléculaire propre à chaque taxon, en se basant sur les datations proposées pour les fossiles.
La diversité génétique intra-spécifique semble remonter au Pliocène pour au moins deux des modèles (S. johnstoni et S. longicaudatus), l'événement de divergence le plus ancien ayant été estimé à 3,2 +/-0,6 millions d'années (MA). Les phénomènes à l'origine de la différenciation intra-spécifique seraient donc bien antérieurs aux derniers cycles glaciaires supposés avoir modelé les régions fauniques (contra GRUBB, 1990 ;COLYN, 1991), lesquels peuvent par contre expliquer la distribution géographique actuelle des lignées, en conjonction avec les conditions écologiques, géomorphologiques et climatiques (cf. ENDLER, 1982 Mammifères, il ne semble pas que les caractéristiques de l'habitat aient induit une différentiation intra-spécifique car la diversité génétique n'est pas corrélée avec les assemblages floristiques.
Nous avons également abordé la question de la permanence des préférences écologiques au cours de l'évolution, qui est un postulat implicite à la théorie des refuges. Pour paléo-environnementales. La théorie paléogéographique pourrait être éliminée a priori en raison de la rareté des événements géologiques ayant affecté la zone d'étude (bien que la formation du rift Est Africain puisse avoir eu des répercussions morphogénétiques et climatiques en Afrique centrale). La théorie des refuges est la théorie le plus souvent invoquée pour expliquer la distribution actuelle de la faune dans les forêts de plaine africaines (e.g. CARCASSON, 1964 ;MOREAU, 1969 ;GRUBB, 1990 ;COLYN, 1991). Il est généralement admis que la forêt tropicale africaine a effectivement été fragmentée durant des périodes de forte aridité du Terciaire et surtout du Quaternaire (MALEY, 1996 ;LINDER, 2001). En revanche, la théorie des refuges est controversée dans le cas de l'Amérique du Sud, faute de preuve de la fragmentation de la forêt amazonienne (MORITZ et al., 2000 ;PATTON et al., 2000). Ainsi, alors que le principal moteur de l'évolution pourrait être d'origine paléo-climatique en Afrique tropicale, il serait probablement d'origine morphogénétique en Amérique tropicale.
Conclusion et perspectives
La zone principale d'étude correspond à une région de l'Afrique centrale pour laquelle nous disposons d'un échantillonnage conséquent et qui semble présenter à elle seule toute la complexité qui peut être observée à plus large échelle (Fig. 1). Cependant, certaines questions ont été abordées à l'échelle de l'ensemble des forêts de plaine africaines, ainsi qu'à l'interface forêt-savane. Les modèles biologiques ont été choisis parmi trois Ordres de Mammifères : Insectivores, Rongeurs et Primates. Les Primates, moins bien représentés dans nos collections, ont été beaucoup plus étudiés que les petits Mammifères sur le plan biologique et écologique, ce qui nous a permis d'aborder plus en détail les mécanismes de la spéciation. Les méthodes utilisées pour obtenir des séquences d'ADN et reconstruire des phylogénies sont décrites ailleurs (QUEROUIL, 2001). Les principales méthodes de phylogéographie et de biogéographies utilisées seront mentionnées au fur et à mesure.
cela, nous avons construit une phylogénie des Cercopithecini en utilisant l'ensemble des données génétiques, morpho-anatomiques et écologiques disponibles, puis pisté l'évolution de différentes caractéristiques éco-éthologiques sur cette phylogénie. En dépit de la plasticité écologique et comportementale de certaines espèces, il y aurait eu un nombre limité de changements d'habitat et de mode de locomotion chez les Cercopithecini. Dans l'ensemble, nos résultats tendent à exclure les théories faisant intervenir les pressions environnementales comme moteur principal de l'évolution, i.e. la théorie des gradients environnementaux et celle des perturbations (Tab. 1). Ils confortent surtout les prédictions associées à la théorie des refuges et à la théorie paléogéographique, sans exclure la théorie des barrières fluviales, dont l'effet pourrait s'être additionné à celui des fluctuations
REMERCIEMENTS
Je tiens à remercier tous ceux qui par leur soutien scientifique et moral ont contribué à l'achèvement de cette thèse, et en particulier Annie Gautier-Hion, Marc Colyn et Erik Verheyen. RÉFÉRENCES AVISE, J.C. (2000).-Phylogeography. Harvard University Press, Cambridge, MA. AVISE, J.C., ARNOLD, J., BALL, R.M., BERMINGHAM, E., LAMB, T., NEIGEL, J.E., REEB, C.A. & SAUNDERS, N.C. (1987).-Intraspecific phylogeography: The mitochondrial DNA bridge between population genetics and systematics. Annu. Rev. Ecol. Syst., 18, 489-522. AYRES, J.M. & CLUTTON BROCK, T.H. (1992).-River boundaries and species range size in Amazonian primates. Am. Nat., 140, 531-537.
Figure 2 .
2Mise en correspondance des groupements phylogénétiques obtenus pour les quatre modèles petits Mammifères avec les régions fauniques. Les pointillés rassemblent les localités dont les haplotypes se groupent lors des analyses phylogéographiques. Les flèches indiquent des événements probables de dispersion sur longue distance. Les surfaces grisées représentent des régions génétiquement homogènes, dont les limites hypothétiques sont adaptées des travaux de DELEPORTE & COLYN (1999).
Figure legends
Figure legends
Figure 1 .
1Map of mammalian faunal areas in Central Africa, after DELEPORTE & COLYN (1999). The regions and sub-regions are shaded in grey, and the intergradation areas are dashed. The main collection sites are indicated by a three-letter code, and the main study area is delimited by a square box.
Figure 2 .
2Comparison of haplotype clusters revealed by phylogeographic analyses of four small mammal species with the faunal areas. Dashed lines circle localities sharing closely related haplotypes. Arrows represent potential dispersal events. Shaded areas delineate genetically homogenous regions, which are hypothetically delimited according to DELEPORTE & COLYN (
environnementaux...), en appliquant l'approche moléculaire la plus employée, le séquençage d'ADN mitochondrial, à quelques taxons de Mammifères africains (Insectivora, Rodentia, Primates). Nous avons d'abord tenté d'obtenir une phylogénie moléculaire d'espèces potentiellement intéressantes pour la phylogéographie, dans le but de vérifier leur monophylie et de calibrer une horloge moléculaire. Puis, nous avons recherché et comparé les schémas phylogéographiques de quatre espèces de petits Mammifères et d'une superespèce de Primates, dans le but d'en tirer des conclusions biogéographiques. Enfin, nous avons évalué les processus évolutifs potentiellement impliqués.POUR ABORDER LA BIOGEOGRAPHIE ET LA SPECIATION :
L'EXEMPLE DE QUELQUES MAMMIFERES
D'AFRIQUE TROPICALE
par
Sophie QUÉROUIL
Dans cette étude, nous nous sommes proposés de tester les hypothèses
biogéographiques formulées pour la faune tropicale (refuges, barrières fluviales, gradients
La comparaison de scénarios obtenus pour différentes lignées, ou phylogéographie comparée, tend à rejoindre les objectifs de la biogéographie.Les études biogéographiques et phylogéographiques réalisées dans diverses régions du monde ont permis de proposer des hypothèses évolutives concernant la flore et la faune. La plupart des modèles évolutifs attribuent un rôle majeur à la fragmentation des aires de distribution (allopatrie). Plusieurs de ces modèles font intervenir les changements paléoenvironnement floristique pourraient être suffisantes pour initier une diversification des taxons par sélection naturelle (théorie des gradients environnementaux -ENDLER, 1982).La grande diversité de la faune des régions tropicales a suscité de nombreux travaux et hypothèses. Cependant, l'essentiel des travaux récents qui ont permis d'alimenter le débat sur les modes de spéciation en milieu tropical se sont focalisés sur l'Amérique du Sud(MORITZ et al., 2000). La plupart des études réalisées en Afrique tropicale ne sont basées que sur la distribution actuelle des taxons et la reconnaissance de zones d'endémisme et de diversité élevée (e.g.environnementaux liés aux mouvements tectoniques (théorie paléogéographique -Emsley,
1965) et aux oscillations climatiques (théorie des refuges -HAFFER, 1969, qui attribue un rôle
majeur aux zones de stabilité environnementale, et théorie des perturbations -COLINVAUX,
1993, BUSH, 1994, qui considère au contraire les modifications de l'habitat dans les zones
d'écotone). Un autre modèle évolutif met l'accent sur la notion de barrière physique à la
dispersion (théorie des barrières fluviales -CAPPARELLA, 1991, AYRES & CLUTTON-BROCK,
1992). Des études récentes ont réhabilité le concept de diversification en présence de flux
génique (sympatrie). Notamment, en ce qui concerne la faune, les variations locales de
l'
autres modèles ont été choisis parmi des taxons ne présentant pas de difficulté taxinomique particulière : Stochomys longicaudatus, une espèce de Rongeurs appartenant à un genre monospécifique, et Cercopithecus cephus, une super-espèce de Primates. Les analyses phylogéographiques réalisées pour la super-espèce C. cephus mettent en garde contre les limites de l'utilisation de l'ADN mitochondrial pour reconstruire des phylogénies. Ils confirment que l'histoire des gènes n'est pas forcément celle des taxons (e.g. MOORE, 1995) et qu'il est important de prendre en compte plusieurs sources d'information indépendantes, telles que des gènes non liés sur la même molécule, la morphologie, l'écologie et le comportement (e.g. GRANDCOLAS et al., 2001). Les schémas phylogéographiques obtenus pour S. johnstoni et S. longicaudatus présentent une ségrégation géographique marquée des haplotypes qui serait due à des événements de vicariance anciens (Fig. 2). Les schémas obtenus pour S. ollula et H. stella font apparaître une expansion récente dans la zone d'étude (FigLe choix des modèles a nécessité un travail de révision taxinomique et phylogénétique
préliminaire. Les analyses phylogénétiques réalisées pour les musaraignes africaines
(QUEROUIL et al., 2001) et pour le genre de Rongeurs africains Hylomyscus ont permis de
retenir deux espèces d'Insectivores (Sylvisorex johnstoni et S. ollula) et une espèce de
Rongeurs (Hylomyscus stella) comme modèles pour les analyses phylogéographiques. Deux
Analyses phylogéographiques
). Contrairement à ce qui apparaît dans d'autres études comparatives portant sur les Rongeurs du bassin amazonien (PATTON et al., 2000) ou sur des régions géographiques limitées d'Amérique du Nord et d'Australie (TABERLET, 1998), les schémas phylogéographiques obtenus ne sont concordants ni dans le temps ni dans l'espace, et ceci même pour des espèces phylogénétiquement proches. Ce résultat pourrait s'expliquer par des différences dans le cadre spatial et temporel de l'évolution des espèces. Le paramètre temporel ne semble pas prédominant car au moins trois des quatre espèces seraient apparues vers la fin du Pliocène ou le début du Pléistocène (c'est-à-dire à la charnière entre Terciaire et Quaternaire). En revanche, comme les distributions géographiques des espèces au cours du Pléistocène ne sont pas connues, il est possible que les différences phylogéographiques observées résultent, au moins en partie, de différences d'extension et de localisation des aires de distribution passées.Une autre possibilité est que toutes les espèces aient bien été sympatriques et soumises à
des événements similaires durant la majeure partie du Pléistocène, mais n'aient pas répondu
de la même façon aux fluctuations paléo-environnementales. La variabilité des réponses aux
changements paléo-environnementaux pourrait être liée à la survie différentielle des espèces
dans différents refuges, à leur sensibilité aux barrières et aux pressions environnementales,
leurs capacités de colonisation et leur pouvoir compétiteur, ainsi qu'à différents paramètres
liés à la dynamique des populations
. Il est apparut que les arbres donc pas exactement les régions fauniques ni les relations présumées entre aires. Cependant, certains groupements d'haplotypes coïncident avec les régions fauniques (Fig. 2). Nos résultats tendent à confirmer l'identité des régions Ouest Congo (à l'exception de la localité Odzala) et Sud Ogooué, tout en mettant en évidence des échanges entre ces deux régions. La localité Odzala semble avoir eu une histoire particulière, fonctionnant comme une zone de convergence pour S. ollula et H. stella, et comme une zone génétiquement isolée pour S. johnstoni et S. longicaudatus. La région supposée d'intergradation pourrait avoir été colonisée à partir de différentes régions pour trois des modèles, mais apparaît comme une région génétiquement distincte dans le cas de S. johnstoni. Les donnés sont insuffisantes pour confirmer l'hypothèse d'un corridor savanicole ayant existé pendant la majeure partie du Pléistocène, où se serait produit un mélange des faunes lors des phases d'expansion récente de la forêt (cf. DELEPORTE & COLYN, 1999).Dans un second temps, nous avons essayé de reconstruire l'histoire biogéographique de la région à partir de nos données phylogéographiques. La plupart des méthodes classiques de biogéographie cladistique ne sont pas applicables pour un nombre aussi limité de modèles, aussi avons nous choisi la méthode de HOVENKAMP (1997) qui présente en outre l'avantage de ne pas nécessiter la prédéfinition des aires biogéographiques. Cette méthode, améliorée en tenant compte des temps de divergence estimés, nous a permis de conforter deux événements de vicariance, observés dans deux cladogrammes et dont les datations concordentobtenus étaient significativement différents de l'arbre théorique des aires pour trois des quatre
espèces (pour la quatrième espèce, H. Stella, le non-rejet de l'hypothèse nulle résulterait
d'une faible différentiation génétique). La ségrégation géographique des haplotypes ne suit
Ces datations sont plus anciennes que celles qui ont été envisagées à partir des fossiles, mais sont en accord avec les datations moléculaires réalisées pour de nombreux taxons de). Au niveau
inter-spécifique, trois des espèces de petits Mammifères seraient apparues vers la fin du
Pliocène, il y a au moins 2 MA (S. johnstoni et S. longicaudatus), ou au début du Pléistocène,
il y a environ 1,8 MA (S. ollula). La quatrième espèce, H. stella, pourrait être apparue plus
tard (quelque part entre 1,9 et 0,6 MA). De même, chez les Primates de la tribu des
Cercopithecini, les événements de divergence entre espèces soeurs remonteraient pour la
plupart au Pliocène.
Mammifères. En effet, près d'un tiers des événements de divergence intra-spécifique et deux-
tiers des événements de divergence entre espèces soeurs seraient antérieurs au Pléistocène
(Avise, 2000). Les événements de spéciation conduisant aux espèces actuelles seraient donc
aussi anciens en Afrique tropicale que dans d'autres régions tropicales et tempérées.
Recherche des processus évolutifs impliqués
Nous avons tenté de savoir si certaines des prédictions associées aux théories
évolutives qui ont été formulées pour la faune forestière tropicale étaient vérifiées. Nous
avons notamment évalué l'importance de la vicariance et de l'allopatrie, principes sur lesquels
reposent la plupart des méthodes biogéographiques et des théories évolutives, à l'aide d'un
test du mode géographique de spéciation appliqué aux Primates de la tribu des
Cercopithecini. Les résultats indiquent une prédominance de l'allopatrie et des événements de
vicariance du Miocène et du Pliocène dans l'évolution de ce taxon. Ils sont en accord avec ce
qui a été observé chez les petits Mammifères, chez qui la différentiation intra-spécifique
résulterait essentiellement d'événements de vicariance ayant eu lieu au Plio-Pléistocène.
Nous avons aussi essayé de déterminer si les pressions environnementales pouvaient
avoir favorisé la spéciation. Chez les Cercopithecini, chacune des espèces occupe une gamme
d'habitats variés et les espèces soeurs occupent des habitats semblables, ce qui tend à
minimiser le rôle de l'habitat comme cause initiale de la spéciation. Dans le cas des petits
Portugal. squerouil@dop.horta.uac.pt Ces travaux peuvent être considérés comme une étude exploratoire permettant d'évaluer
les intérêts et les limites des analyses phylogéographiques dans l'étude de l'évolution des
faunes forestières d'Afrique tropicale, et de mettre en évidence des pistes qui mériteraient
d'être explorées à l'avenir. Dans l'optique de tester des hypothèses biogéographiques d'ordre
général, telles que l'influence de la latitude, l'impact de barrières biogéographiques
prédéfinies ou l'importance du mode de dispersion, il apparaît nécessaire d'étudier un grand
nombre de modèles diversifiés. Cependant, une analyse "en profondeur" privilégiant
quelques modèles semble nécessaire pour évaluer les processus mis en jeu. Nous suggérons
de multiplier les points de collecte en Afrique centrale et d'adopter une approche
multidisciplinaire, de façon à déterminer avec précision le statut taxinomique et l'aire de
distribution des espèces étudiées, et à pouvoir trier les espèces selon un filtre écologique.
Cette perspective ne peut être envisagée que comme un travail d'équipe et sur le long terme.
Université de Rennes I, CNRS -U.M.R. 6552, Laboratoire Ethologie -Evolution -Ecologie,
Station Biologique, 35380 Paimpont, France.
Adresse actuelle : Instituto do Mar (IMAR), Departamento de Oceanografia e Pescas, Cais
Santa Cruz, 9901-862 Horta,
Tableau 1 :
1Prédictions associées aux différentes théories de l'évolution. Caractères gras : prédiction vérifiée par nos résultats, soutenant la théorie concernée. Caractères soulignés : prédiction non vérifiée, fournissant un argument contre la théorie.Figure 1. Carte des régions fauniques observées pour la faune mammalienne en Afrique centrale, d'après DELEPORTE & COLYN (1999). Les régions et sous-régions fauniques sont délimitées par différents niveaux de gris. Les régions appartenant à une même unité faunique sont regroupées par une ligne pointillée. Les zones hachurées représentent les régions d'intergradation, dans la limite du bloc forestier. Les principales localités de collecte sont indiquées sous forme abrégée et la zone principale de l'étude est encadrée en gras.Prédictions
Gradients Perturbations Barrières
fluviales
Paléo-
géographie
Refuges
mode géographique de
spéciation
sympatrie allopatrie
allopatrie
allopatrie
allopatrie
spéciation par différentiation
écologique
oui
oui
non
non
non
ancienneté des divergences
entre espèces
fin IV
IV
fin IV
III-IV
III-IV
concordance géographique
entre taxons
(et par rapport aux ...)
non
non
oui
(rivières)
oui
(événements
géologiques)
oui
(régions
fauniques)
concordance temporelle
entre taxons
(et par rapport aux ...)
non
oui
(périodes
froides)
non
oui
(événements
géologiques)
oui
(périodes
arides)
phases de contraction /
expansion des populations
non
oui
non
oui
oui
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| sample_1036 | 0.7688 | arxiv | |
Deep Learning for bias-correcting comprehensive high-resolution Earth system models
16 Dec 2022
Philipp Hess
Earth System Modelling
School of Engineering & Design
Technical University of Munich
MunichGermany
Potsdam Institute for Climate Impact Research
Member of the Leibniz Association
PotsdamGermany
Stefan Lange
Potsdam Institute for Climate Impact Research
Member of the Leibniz Association
PotsdamGermany
Niklas Boers
Earth System Modelling
School of Engineering & Design
Technical University of Munich
MunichGermany
Potsdam Institute for Climate Impact Research
Member of the Leibniz Association
PotsdamGermany
Global Systems Institute and Department of Mathematics
University of Exeter
ExeterUK
Deep Learning for bias-correcting comprehensive high-resolution Earth system models
16 Dec 2022
Key Points:• A generative adversarial network is shown to improve daily precipitation fields from a state-of-the-art Earth system model. • Biases in long-term temporal distributions are strongly reduced by the generative adversarial network. • Our network-based approach can be complemented with quantile mapping to further improve precipitation fields.-1-arXiv:2301.01253v1 [physics.ao-ph]AbstractThe accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming. The complex cross-scale interactions of processes that produces precipitation are challenging to model, however, inducing potentially strong biases in ESM fields, especially regarding extremes. State-of-the-art bias correction methods only address errors in the simulated frequency distributions locally, at every individual grid cell. Improving unrealistic spatial patterns of the ESM output, which would require spatial context, has not been possible so far. Here, we show that a post-processing method based on physically constrained generative adversarial networks (GANs) can correct biases of a state-of-the-art, CMIP6-class ESM both in local frequency distributions and in the spatial patterns at once. While our method improves local frequency distributions equally well as gold-standard biasadjustment frameworks it strongly outperforms any existing methods in the correction of spatial patterns, especially in terms of the characteristic spatial intermittency of precipitation extremes.
Introduction
Precipitation is a crucial climate variable and changing amounts, frequencies, or spatial distributions have potentially severe ecological and socioeconomic impacts. With global warming projected to continue in the coming decades, assessing the impacts of changes in precipitation characteristics is an urgent challenge (Wilcox & Donner, 2007;Boyle & Klein, 2010;IPCC, 2021). Climate impact models are designed to assess the impacts of global warming on, for example, ecosystems, crop yields, vegetation and other land-surface characteristics, infrastructure, water resources, or the economy in general (Kotz et al., 2022), using the output of climate or Earth system models (ESMs) as input. Especially for reliable assessments of the ecological and socioeconomic impacts, accurate ESM precipitation fields to feed the impact models are therefore crucial.
ESMs are integrated on spatial grids with finite resolution. The resolution is limited by the computational resources that are necessary to perform simulations on decadal to centennial time scales. Current state-of-the-art ESMs have a horizontal resolution on the order of 100km, in exceptional cases going down to 50km. Smaller-scale physical processes that are relevant for the generation of precipitation operate on scales below the size of individual grid cells. These can therefore not be resolved explicitly in ESMs and have to included as parameterizations of the resolved prognostic variables. These include droplet interactions, turbulence, and phase transitions in clouds that play a central role in the generation of precipitation.
The limited grid resolution hence introduces errors in the simulated precipitation fields, leading to biases in short-term spatial patterns and long-term summary statistics. These biases need to be addressed prior to passing the ESM precipitation fields to impact models. In particular, climate impact models are often developed and calibrated with input data from reanalysis data rather than ESM simulations. These reanalyses are created with data assimilation routines and combine various observations with high-resolution weather models. They hence provide a much more realistic input than the ESM simulations and statistical bias correction methods are necessary to remove biases in the ESM simulations output and to make them more similar to the reanalysis data for which the impact models are calibrated. Quantile mapping (QM) is a standard technique to correct systematic errors in ESM simulations. QM estimates a mapping between distributions from historical simulations and observations that can thereafter be applied to future simulations in order to provide more accurate simulated precipitation fields to impact models (Déqué, 2007;Tong et al., 2021;Gudmundsson et al., 2012;Cannon et al., 2015).
State-of-the-art bias correction methods such as QM are, however, confined to address errors in the simulated frequency distributions locally, i.e., at every grid cell individually.
Unrealistic spatial patterns of the ESM output, which would require spatial context, have therefore so far not been addressed by postprocessing methods. For precipitation this is particularly important because it has characteristic high intermittency not only in time, but also in its spatial patterns. Mulitvariate bias correction approaches have recently been developed, aiming to improve spatial dependencies (Vrac, 2018;Cannon, 2018). However, these approaches are typically only employed in regional studies, as the dimension of the input becomes too large for global high-resolution ESM simulations. Moreover, such methods have been reported to suffer from instabilities and overfitting, while differences in their applicability and assumptions make them challenging to use (François et al., 2020).
Here, we employ a recently introduced postprocessing method based on a cycle-consistent adversarial network (CycleGAN) to consistently improve both local frequency distributions and spatial patterns of state-of-art high-resolution ESM precipitation fields. Artificial neural networks from computer vision and image processing have been successfully applied to various tasks in Earth system science, ranging from weather forecasting (Weyn et al., 2020;Rasp & Thuerey, 2021) to post-processing (Grönquist et al., 2021;Price & Rasp, 2022), by extracting spatial features with convolutional layers (LeCun et al., 2015). Generative adversarial networks (Goodfellow et al., 2014) in particular have emerged as a promising architecture that produces sharp images that are necessary to capture the high-frequency variability of precipitation (Ravuri et al., 2021;Price & Rasp, 2022;Harris et al., 2022). GANs have been specifically developed to be trained on unpaired image datasets (Zhu et al., 2017). This makes them a natural choice for post-processing the output of climate projections, which -unlike weather forecasts -are not nudged to follow the trajectory of observations; due to the chaotic nature of the atmosphere small deviations in the initial conditions or parameters lead to exponentially diverging trajectories (Lorenz, 1996). As a result, numerical weather forecasts lose their deterministic forecast skill after approximately two weeks at most and century-scale climate simulations do not agree with observed daily weather records. Indeed the task of climate models is rather to produce accurate long-term statistics that to agree with observations. We apply our CycleGAN approach to correct global high-resolution precipitation simulations of the GFDL-ESM4 model (Krasting et al., 2018) as a representative ESM from the Climate Model Intercomparison Project phase 6 (CMIP6). So far, GANs-based approaches have only been applied to postprocess ESM simulations either in a regional context (François et al., 2021), or to a very-low-resolution global ESM . We show here that a suitably designed CycleGAN is capable of improving even the distributions and spatial patterns of precipitation fields from a state-of-the-art comprehensive ESM, namely GFDL-ESM4. In particular, in contrast to rather specific existing methods for postprocessing ESM output for climate impact modelling, we will show that the CycleGAN is general and can readily be applied to different ESMs and observational datasets used as ground truth.
In order to assure that physical conservation laws are not violated by the GAN-based postprocessing, we include a suitable physical constraint, enforcing that the overall global sum of daily precipitation values is not changed by the GAN-based transformations; essentially, this assures that precipitation is only spatially redistributed (see Methods). By framing bias correction as an image-to-image translation task, our approach corrects both spatial patterns of daily precipitation fields on short time scales and temporal distributions aggregated over decadal time scales. We evaluate the skill to improve spatial patterns and temporal distributions against the gold-standard ISIMIP3BASD framework (Lange, 2019), which relies strongly on QM.
Quantifying the "realisticness" of spatial precipitation patterns is a key problem in current research (Ravuri et al., 2021). We use spatial spectral densities and the fractal dimension of spatial patterns as a measure to quantify the similarity of intermittent and unpaired precipitation fields. We will show that our CycleGAN is indeed spatial context-aware and strongly improves the characteristic intermittency in spatial precipitation patterns. We will also show that our CycleGAN combined with a subseqeunt application of ISIMIP3BASD routine leads to the best overall performance.
Results
We evaluate our CycleGAN method on two different tasks and time scales. First, the correction of daily rainfall frequency distributions at each grid cell locally, aggregated from decade-long time series. Second, we quantify the ability to improve spatial patterns on daily time scales. Our GAN approach is compared to the raw GFDL-ESM4 model output, as well as to the ISIMIP3BASD methodology applied to the GFDL-ESM4 output. We compute global histograms of relative precipitation frequencies using daily time series (Fig. 1a). The GFDL-ESM4 model overestimates frequencies in the tail, namely for events above 50 mm/day (i.e., the 99.7th percentile). Our GAN-based method as well as ISIMIP3BASD and the GAN-ISIMIP3BASD combination correct the histogram to match the W5E5v2 ground truth equally well, as can be also seen in the absolute error of the histograms (Fig. 1b).
Comparing the differences in long-term averages of precipitation per grid cell ( Fig. 2 and Methods), large biases are apparent in the GFDL-ESM4 model output, especially in the tropics. The double-peaked Intertropical Convergence Zone (ITCZ) bias is visible. The double-ITCZ bias can also be inferred from the latitudinal profile of the precipitation mean in Fig. 3. Table 1 summarizes the annual biases shown in Fig. 2 as absolute averages, and additionally for the four seasons. The GAN alone reduces the annual bias of the GFDL-ESM4 model by 38.7%. The unconstrained GAN performs better than the physically constrained one, with bias reductions of 50.5%. As expected, the ISIMIP3BASD gives even better results for correcting the local mean, since it is specifically designed to accurately transform the local frequency distributions. It is therefore remarkable that applying the ISIMIP3BASD procedure on the constrained GAN output improves the post-processing further, leading to a local bias reduction of the mean by 63.6%, compared to ISIMIP3BASD with 59.4%. For seasonal time series the order in which the methods perform is the same as for the annual data.
Besides the error in the mean, we also compute differences in the 95th percentile for each grid cell, shown in Fig. S1 and as mean absolute errors in Table 1. Also in this case of heavy precipitation values we find that ISIMIP3BASD outperforms the GAN, but that combining GAN and ISIMIP3BASD leads to best agreement of the locally computed quantiles. Table 1: The globally averaged absolute value of the grid cell-wise difference in the longterm precipitation average, as well as the 95th percentile, between the W5E5v2 ground truth and GFDL-ESM4, ISIMIP3BASD, GAN, unconstrained GAN, and the GAN-ISIMIP3BASD combination for annual and seasonal time series (in [mm/day]). The relative improvement over the raw GFDL-ESM4 climate model output is shown as percentages for each method.
Season Percentile GFDL- ESM4 ISIMIP3- BASD % GAN % GAN (unconst.) % GAN- ISIMIP3- BASD % Annual - 0.
Spatial patterns
We compare the ability of the GAN to improve spatial patterns based on the W5E5v2 ground truth, against the GFDL-ESM4 simulations and the ISIMIP3BASD method applied to the GFDL-ESM4 simulations. To model realistic precipitation fields, the characteristic spatial intermittency needs to be captured accurately.
We compute the spatial power spectral density (PSD) of global precipitation fields, averaged over the test set for each method. GFDL-ESM4 shows noticeable deviations from W5E5v2 in the PSD (Fig. 4). Our GAN can correct these over the entire range of wave- Table 1 as the average is taken here over the longitudes without their absolute value. The GAN-ISIMIP3BASD approach shows the lowest error.
lengths, closely matching the W5E5v2 ground truth. Improvements over ISIMIP3BASD are especially pronounced in the range of high frequencies (low wavelengths), which are responsible for the intermittent spatial variability of daily precipitation fields. Adding the physical constraint to the GAN does not affect the ability to produce realistic PSD distributions. After applying ISIMIP3BASD to the GAN-processed fields, most of the improvements generated by the GAN are retained, as shown by the GAN-ISIMIP3BASD results.
For a second way to quantifying how realistic the simulated and post-processed precipitation fields are, with a focus on high-frequency spatial intermittency, we investigate the fractal dimension (Edgar & Edgar, 2008) of the lines separating grid cells with daily rainfall sums above and below a given quantile threshold (see Methods). For a sample and qualitative comparison of precipitation fields over the South American continent see Fig. S2. The daily spatial precipitation fields are first converted to binary images using a quantile threshold. The respective quantiles are determined from the precipitation distribution over the entire test set period and globe. The mean of the fractal dimension computed with boxcounting (see Methods) (Lovejoy et al., 1987;Meisel et al., 1992;Husain et al., 2021) for each time slice is then investigated (Fig. 5). Both the GFDL-ESM4 simulations themselves and the results of applying the ISIMIP3BASD post-processing to them exhibit spatial patterns with a lower fractal dimension than the W5E5v2 ground truth, implying too low spatial intermittency. In contrast, the GAN translates spatial fields simulated by GFDL-ESM4 in a way that results in closely matching fractal dimensions over the entire range of quantiles.
Discussion
Postprocessing climate projections is a fundamentally different task from postprocessing weather forecast simulations . In the latter case, data-driven postprocessing methods, e.g. based on deep learning, to minimize differences between paired samples GANs and W5E5v2 ground truth agree so closely that they are indistinguishable. In contrast to ISIMIP3BASD, the GAN can correct the intermittent spectrum accurately over the entire range down to the smallest wavelengths.
of variables such as spatial precipitation fields . Beyond time scales of a few days, however, the chaotic nature of the atmosphere leads to exponentially diverging trajectories, and for climate or Earth system model output there is no observation-based ground truth to directly compare to. We therefore frame the post-processing of ESM projections, with applications for subsequent 195 impact modelling in mind, as an image-to-image translation task with unpaired samples.
To this end we apply a recently developed postprocessing method based on physically constrained CycleGANs to global simulations of a state-of-the-art, high-resolution ESM from the CMIP6 model ensemble, namely the GFDL-ESM4 (Krasting et al., 2018;O' Neill et al., 2016). We evaluate our method against the gold-standard bias correction framework ISIMIP3BASD. Our model can be trained on unpaired samples that are characteristic for climate simulations. It is able to correct the ESM simulations in two regards: temporal distributions over long time scales, including extremes in the distrivutions' tails, as well as spatial patterns of individual global snap shots of the model output. The latter is not possible with established methods. Our GAN-based approach is designed as a general framework that can be readily applied to different ESMs and observational target datasets. This is in contrast to existing bias-adjustment methods that are often tailored to specific applications.
We chose to correct precipitation because it is arguably one of the hardest variables to represent accurately in ESMs. So far, GANs have only been applied to regional studies or low-resolution global ESMs (François et al., 2021; to improvements even when postprocessing global high-resolution simulations of one of the most complex and sophisticated ESMs to date. In the same spirit, we evaluate our approach against a very strong baseline given by the state-of-the-art bias correction framework ISIMIP3BASD, which is based on a trend-preserving QM method (Lange, 2019).
Comparing long-term summary statistics, our method yields histograms of relative precipitation frequencies that very closely agree with corresponding histograms from reanalysis data (Fig. 1). The means that the extremes in the far end of the tail are accurately captured, with similar skill to the ISIMIP3BASD baseline that is mainly designed for this task. Differences in the grid cell-wise long-term average show that the GAN skillfully reduces biases (Fig. 2); in particular, the often reported double-peaked ITCZ bias of the GFDL-ESM4 simulations, which is a common feature of most climate models (Tian & Dong, 2020), is strongly reduced (Fig. 3). The ISIMIP3BASD method -being specifically designed for this -produces slightly lower biases for grid-cell-wise averages than the GAN; we show that combining both methods by first applying the GAN and then the ISIMIP3BASD procedure leads to the overall best performance.
Regarding the correction of spatial patterns of the modelled precipitation fields, we compare the spectral density and fractal dimensions of the spatial precipitation fields. Our results show that indeed only the GAN can capture the characteristic spatial intermittency of precipitation closely (Figs. 4 and 5). We believe that the measure of fractal dimension is also relevant for other fields such as nowcasting and medium-range weather forecasting, where blurriness in deep learning-based predictions is often reported (Ravuri et al., 2021) and needs to be further quantified.
Post-processing methods for climate projections have to be able to preserve the trends that result from the non-stationary dynamics of the Earth system on long-time scales. We have therefore introduced the architecture constraint of preserving the global precipitation amount on every day in the climate model output . We find that this does not affect the quality of the spatial patterns that are produced by our CycleGAN method. However, the skill of correcting mean error biases is slightly reduced by the constraint. This can be expected in part as the constraint is constructed to follow the global mean of the ESM. Hence, biases in the global ESM mean can influence the constrained GAN. This also motivates our choice to demonstrate the combination of the constrained GAN with the QMbased ISIMIP3BASD procedure, since it can be applied to future climate scenarios, making it more suitable for actual applications than the unconstrained architecture.
There are several directions to further develop or approach. The architecture employed here has been built for equally spaced two-dimensional images. Extending the CycleGAN architecture to perform convolutions on the spherical surface, e.g. using graph neural networks, might lead to more efficient and accurate models. Moreover, GANs are comparably difficult to train, which could make it challenging to identify suitable network architectures. Using large ensembles of climate simulations could provide additional training data that could further improve the performance. Another straightforward extension of our method would be the inclusion of further input variables or the prediction additional high-impact physical variables, such as near-surface temperatures that are also important for regional impact models.
Methods
Training data
We use global fields of daily precipitation with a horizontal resolution of 1 • from the GFDL-ESM4 Earth system model (Krasting et al., 2018) and the W5E5v2 reanalysis product (Cucchi et al., 2020; WFDE5 over land merged with ERA5 over the ocean (W5E5 v2.0), 2021) as observation-based ground truth. The W5E5v2 dataset is based on the ERA5 (Hersbach et al., 2020) reanalysis and has been bias-adjusted using the Global Precipitation Climatology Centre (GPCC) full data monthly product v2020 (Schneider et al., 2011) over land and the Global Precipitation Climatology Project (GPCP) v2.3 dataset (Huffman et al., 1997) over the ocean. Both datasets have been regridded to the same 1 • horizontal resolution using bilinear interpolation following (Beck et al., 2019). We split the dataset into three periods for training (1950-2000), validation (2001-2003), and testing (2004-2014). This corresponds to 8030 samples for training, 1095 for validation, and 4015 for testing. During pre-processing, the training data is log-transformed withx = log(x + ) − log( ) with = 0.0001, following Rasp and Thuerey (2021), to account for zeros in the transform. The data is then normalized to the interval [−1, 1] following (Zhu et al., 2017).
Cycle-consistent generative adversarial networks
This section gives a brief overview of the CycleGAN used in this study. We refer to (Zhu et al., 2017; for a more comprehensive description and discussion. Generative adversarial networks learn to generate images that are nearly indistinguishable from real-world examples through a two-player game (Goodfellow et al., 2014). In this set-up, a first network G, the so-called generator, produces images with the objective to fool a second network D, the discriminator, which has to classify whether a given sample is generated ("fake") or drawn from a real-world dataset ("real"). Mathematically this can be formalized as
G * = min G max D L GAN (D, G),(1)
with G * being the optimal generator network. The loss function L GAN (D, G) can be defined as
L GAN (D, G) = E y∼py(y) [log(D(y))] + E x∼px(x) [log(1 − D(G(x)))],(2)
where p y (y) is the distribution of the real-world target data and samples from p x (x) are used as inputs by G to produce realistic images. The CycleGAN (Zhu et al., 2017) consists of two generator-discriminator pairs, where the generators G and F learn inverse mappings between two domains X and Y . This allows to define an additional cycle-consistency loss that constraints the training of the networks, i.e.
L cycle (G, F ) = E x∼px(x) [||F (G(x)) − x|| 1 ](3)+ E y∼py(y) [||G(F (y)) − y|| 1 ].
It measures the error caused by a translation cycle of an image to the other domain and back. Further, an additional loss term is introduced to regularize the networks to be close to an identity mapping with,
L ident (G, F ) = E x∼px(x) [||G(x) − x|| 1 ](4)+ E y∼py(y) [||F (y) − y|| 1 ].
In practice, the log-likelihood loss can be replaced by a mean squared error loss to facilitate a more stable training. Further, the generator loss is reformulated to be minimized by inverting the labels, i.e.
L Generator = E x∼px(x) [(D X (G(x)) − 1) 2 ] + E y∼py(y) [(D Y (F (y)) − 1) 2 ](5)+ λL cycle (G, F ) +λL ident (G, F ),
where λ andλ are set to 10 and 5 respectively following (Zhu et al., 2017). The corresponding loss term for the discriminator networks is given by
L Discriminator = E y∼py(y) [(D Y (y) − 1) 2 ] + E x∼px(x) [(D X (G(x))) 2 ](6)+ E x∼px(x) [(D X (x) − 1) 2 ] + E y∼py(y) [(D Y (F (y))) 2 ].(7)
The weights of the generator and discriminator networks are then optimized with the ADAM (Kingma & Ba, 2014) optimizer using a learning rate of 2e −4 and updated in an alternating fashion. We train the network for 350 epochs and a batch size of 1, saving model checkpoints every other epoch. We evaluate the checkpoints on the validation dataset to determine the best model instance.
Network Architectures
Both the generator and discriminator have fully convolutional architectures. The generator uses ReLU activation functions, instance normalization, and reflection padding. The discriminator uses leaky ReLU activations with slope 0.2 instead, together with instance normalization. For a more detailed description, we refer to our previous study . The network architectures in this study are the same, only with a change in the number of residual layers in the generator network from 6 to 7.
The final layer of the generator can be constrained to preserve the global sum of the input, i.e. by rescalingỹ
i = y i N grid i x i N grid i y i ,(8)
where x i and y i are grid cell values of the generator input and output respectively and N grid is the number of grid cells. The generator without this constraint will be referred to as unconstrained in this study. The global physical constraint enforces that the global daily precipitation sum is not affected by the CycleGAN postprocessing and hence remains identical to the original value from the GFDL-ESM4 simualtions. This is motivated by the observation that large-scale average trends in precipitation follow the Clausius-Clapeyron relation (Traxl et al., 2021), which is based on thermodynamic relations and hence can be expected to be modelled well in GFDL-ESM4.
Quantile mapping-based bias adjustment
We compare the performance of our GAN-based method to the bias adjustment method ISMIP3BASD v3.0.1 (Lange, 2019(Lange, , 2022 that has been developed for phase 3 of the Inter-Sectoral Impact Model Intercomparison Project (Warszawski et al., 2014;Frieler et al., 2017). This state-of-the-art bias-adjustment method is based on a trend-preserving quantile mapping (QM) framework. It represents a very strong baseline for comparison as it has been developed prior to this study and used not only in ISIMIP3 but also to prepare many of the climate projections that went into the Interactive Atlas produced as part of the 6th assessment report of working group 1 of the Intergovernmental Panel on Climate Change (IPCC, https://interactive-atlas.ipcc.ch/). In QM, a transformation between the cumulative distribution functions (CDFs) of the historical simulation and observations is fitted and then applied to future simulations. The CDFs can either be empirical or parametric, the latter being a Bernoulli-gamma distribution for the precipitation in this study. The CFDs are fitted and mapped for each grid cell and day of the year separately. For bias-adjusting the GFDL-ESM4 simulation, parametric QM was found to give the best results, while empirical CDFs are used in combination with the GAN.
To evaluate the methods in this study we define the grid cell-wise bias as the difference in long-term averages as,
Bias(ŷ, y) = 1 T T t=1ŷ t − 1 T T t=1 y t ,(9)
where T is the number of time steps,ŷ t andŷ t the modelled and observed precipitation respectively at time step t.
Evaluating spatial patterns
Quantifying how realistic spatial precipitation fields are is an ongoing research question in itself, which has become more important with the application of deep learning to weather forecasting and post-processing. In these applications, neural networks often achieve error statistics and skill scores competitive with physical models, while the output fields can at the same time show unphysical characteristics, such as blurring or excessive smoothing. Ravuri et al. (2021) compare the spatial intermittency, which is characteristic of precipitation fields, using the power spectral density (PSD) computed from the spatial fields; in the latter study, the PSD-based quantification was complemented by interviews with a large number of meteorological experts. We propose the fractal dimension of binary precipitation fields as an alternative to quantify how realistic the patterns are.
We compute the fractal dimension via the box-counting algorithm (Lovejoy et al., 1987;Meisel et al., 1992). It quantifies how spatial patterns, for example coastlines (Husain et al., 2021), change with the scale of measurement. The box-counting algorithm divides the image into squares and counts the number of squares that cover the binary pattern of interest, N squares . The size of the squares, i.e. the scale of measurement, is then reduced iteratively by a factor s. The fractal dimension D fractal can then be determined from the slope of the resulting log-log scaling, i.e., D fractal = log(N squares ) log(s) .
(10)
Supporting Information for "Deep Learning for bias-correcting comprehensive high-resolution Earth system models" Figure S1. Bias maps as in Fig. 2 but with the 95th percentile instead of the mean.
Figure 1 :
1Histograms of relative precipitation frequencies over the entire globe and test period(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014). (a) The histograms are shown for the W5E5v2 ground truth (black), GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), unconstrained GAN (orange), and the constrained-GAN-ISIMIP3BASD combination (blue). (b) Distances of the histograms to the W5E5v2 ground truth are shown for the same models as in (a). Percentiles corresponding to the W5E5v2 precipitation values are given on the second x-axis at the top. Note that GFDL-ESM4 overestimates the frequencies of strong and extreme rainfall events. All compared methods show similar performance in correcting the local frequency distributions.
Figure 2 :
2Bias in the long-term average precipitation over the entire test set between the W5E5v2 ground truth (a) and GFDL-ESM4 (b), ISIMIP3BASD (c), GAN (d), unconstrained GAN (e) and the GAN-ISIMIP3BASD combination (f).
Figure 3 :
3Precipitation averaged over longitudes and the entire test set period from the W5E5v2 ground truth (black) and GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), unconstrained GAN (orange) and the GAN-ISIMIP3BASD combination (blue). To quantify the differences between the shown lines, we show their mean absolute error w.r.t the W5E5v2 ground truth in the legend. These values are different from the ones shown in
Figure 4 :
4The power spectral density (PSD) of the spatial precipitation fields is shown as an average over all samples in the test set for the W5E5v2 ground truth (black) and GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan, dashed), unconstrained GAN (orange, dashed-dotted) and the constrained-GAN-ISIMIP3BASD combination (blue, dotted). The
Figure 5 :
5The fractal dimension (see Methods) of binary global precipitation fields is compared as averages for different quantile thresholds. Results are shown for the W5E5v2 ground truth (black) and GFDL-ESM4 (red), ISIMIP3BASD (magenta), GAN (cyan), unconstrained GAN (orange, dashed), and the GAN-ISIMIP3BASD combination (blue). The GAN can accurately reproduce the fractal dimension of the W5E5v2 ground truth spatial precipitation fields over all quantile thresholds, clearly outperforming the ISIMIP3BASD basline.
Figure S2 .
S2Global mean absolute errors (MAEs) are given in the respective titles. Combining the GAN with ISIMIP3BASD achieves the lowest error compared to the other methods. Qualitative comparison of precipitation fields at the same date (December 21st 2014) over the South American continent. The region is used for a comparison of the fractal dimension in binary precipitation patterns.
). The GFDL-ESM4 model simulations are hence chosen in order to test if our CycleGAN approach would lead
Philipp Hess 1,2 , Stefan Lange 2 , and Niklas Boers 1,2,3 Earth System Modelling, School of Engineering & Design, Technical University of Munich, Munich, Germany Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Potsdam, Germany Global Systems Institute and Department of Mathematics, University of Exeter, Exeter, UK Contents of this file 1. Figure S1 to S2 January 4, 2023, 1:33am arXiv:2301.01253v1 [physics.ao-ph] 16 Dec 20221 2 3 X -2
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January 4, 2023, 1:33am
AcknowledgmentsNB and PH acknowledge funding by the Volkswagen Foundation, as well as the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research.Competing interestsThe authors declare no competing interests.Data availabilityThe W5E5 data is available for download at https://doi.org/10.48364/ISIMIP.342217. The GFDL-ESM4 data can be downloaded at https://esgf-node.llnl.gov/projects/ cmip6/.Code availabilityThe Python code for processing and analysing the data, together with the PyTorch Lightning(Falcon et al., 2019)code is available at https://github.com/p-hss/earth system model gan bias correction.git. The ISIMIP3BASD code in(Lange, 2022)is used for this study.
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| sample_1039 | 0.9523 | arxiv | |
Green Hydrogen Cost-Potentials for Global Trade
D Franzmann
IEK-3)
Forschungszentrum Jülich GmbH
Institute of Energy and Climate Research -Techno-economic Systems Analysis
52425JülichGermany
Faculty of Mechanical Engineering
Chair for Fuel Cells
RWTH Aachen University
52062Aachen, German
H Heinrichs
IEK-3)
Forschungszentrum Jülich GmbH
Institute of Energy and Climate Research -Techno-economic Systems Analysis
52425JülichGermany
F Lippkau
Institute of Energy Economics and Rational Energy Use (IER)
University of Stuttgart
70565StuttgartGermany
T Addanki
Chair of Renewable
Sustainable Energy Systems -TU Munich
C Winkler
IEK-3)
Forschungszentrum Jülich GmbH
Institute of Energy and Climate Research -Techno-economic Systems Analysis
52425JülichGermany
Faculty of Mechanical Engineering
Chair for Fuel Cells
RWTH Aachen University
52062Aachen, German
P Buchenberg
Chair of Renewable
Sustainable Energy Systems -TU Munich
T Hamacher
Chair of Renewable
Sustainable Energy Systems -TU Munich
M Blesl
Institute of Energy Economics and Rational Energy Use (IER)
University of Stuttgart
70565StuttgartGermany
J Linßen
IEK-3)
Forschungszentrum Jülich GmbH
Institute of Energy and Climate Research -Techno-economic Systems Analysis
52425JülichGermany
D Stolten
IEK-3)
Forschungszentrum Jülich GmbH
Institute of Energy and Climate Research -Techno-economic Systems Analysis
52425JülichGermany
Faculty of Mechanical Engineering
Chair for Fuel Cells
RWTH Aachen University
52062Aachen, German
Green Hydrogen Cost-Potentials for Global Trade
(max 6): Green hydrogencost-potentialsLH2greenhouse gas- neutralenergy systemenergy security
Green hydrogen is expected to be traded globally in future greenhouse gas neutral energy systems. However, there is still a lack of temporally-and spatially-explicit cost-potentials for green hydrogen considering the full process chain, which are necessary for creating effective global strategies. Therefore, this study provides such detailed cost-potential-curves for 28 selected countries worldwide until 2050, using an optimizing energy systems approach based on open-field photovoltaics (PV) and onshore wind. The results reveal huge hydrogen potentials (>1,500 PWhLHV/a) and 79 PWhLHV/a at costs below 2.30 EUR/kg in 2050, dominated by solar-rich countries in Africa and the Middle East. Decentralized PV-based hydrogen production, even in wind-rich countries, is always preferred. Supplying sustainable water for hydrogen production is needed while having minor impact on hydrogen cost. Additional costs for imports from democratic regions are only total 7% higher. Hence, such regions could boost the geostrategic security of supply for greenhouse gas neutral energy systems.
Introduction
Green hydrogen has been advocated by various studies as a key element in the transformation of the energy system towards greenhouse gas-neutrality [1]. The main reasons for this are that it can serve as seasonal bulk storage to counteract the volatility of wind and solar energy technologies [2] and can be used as a material to support the decarbonization of challenging sectors like the chemical industry [3]. Although hydrogen can be produced in various ways, green hydrogen produced via water electrolysis powered by renewable energy technologies is preferred in most scenarios thanks to its minimal carbon footprint [4]. Hence, the regional conditions for renewable energy sources (RES) determine a large portion of the achievable hydrogen production costs [5], [6]. As wind speeds, solar irradiation, and suitable locations for both renewable sources vary largely across the world, the idea arose to make use of this difference by trading green hydrogen internationally [7]. In this context, different transport options for green hydrogen are currently being discussed [8] and various bilateral agreements have been signed or are under consideration [9]. Against this background, knowledge about spatially-resolved costs and potentials for green hydrogen production as a potential globallytraded energy carrier is mandatory.
However, recent studies have primarily focused on the local or national production of hydrogen [10], [11], [12], such as for Niger in Bhandari [13] or Turkey in Karayel et al. [14]. On the other hand, most global studies focus on electricity potentials from renewable energy sources, rather than considering the potential for hydrogen export or import [15,16]. Only a few studies have investigated the potentials for green hydrogen on a global scale as well for carriers based on hydrogen. One common approach is to divide the world into evenly spaced gridded cells based on latitude and longitude coordinates and to calculate green hydrogen cost based on cost optimizations for each grid cell [6][17] [18].The IRENA Green Hydrogen Report [6] calculates the costs and potentials for green hydrogen globally, but does not take into account the total system necessary for exporting it. Instead, its approach only considers time series for the sizing of photovoltaics (PV), onshore wind, and electrolysis for 1x1km² stand-alone systems. The study of Sens et. al. [18] uses a similar approach based on grid cells to calculate country specific hydrogen potentials within Europe and the North African / MENA region as well as import costs for gaseous hydrogen transport to Germany via pipeline. They find that North Africa can provide gaseous green hydrogen below 2 EUR/kgH2 in 2050 based on hybrid generation from onshore wind and PV. Also, they notice a high curtailment rate of the renewable energy production within the energy system in general, which drops substantially as soon as large scale hydrogen storage like salt caverns become available resulting in parallel to decreasing hydrogen cost . Fasihi et. al [17] uses the grid cell approach for a global evaluation of baseload hydrogen production. For each 0.45°x0.45° cell, a cost-optimal energy system including batteries and underground salt cavern hydrogen storages are utilized, leading to gaseous hydrogen cost of 1.18 EUR/kg in 2050 in Africa and South America. Though, the energy system does not include costs for transportation and effects from spatial compensation via grids within the countries. A similar approach from Fasihi [19] is applied for calculating global ammonia production costs. All gridded approaches neglect synergies with spatial compensations via grid and often temporal compensations via storage units. In addition, the approach does not consider costs for the transportation of hydrogen to a location of export.
In contrast to the gridded approach, a study from Janssen et. al. [20] shows cost prognoses for different European countries. The expected costs for gaseous hydrogen in 2050 are as low as 1.7 EUR/kg in 2050 in Ireland. Yet, the approach does not consider energy potentials for RES and hydrogen, as only average capacity factors for onshore wind and PV are applied at each country. Brändle [21] proposes a green hydrogen import cost tool, and considers a similar country wise approach as Janssen et. al. [20] . He utilizes a cost optimization of generation and electrolysis units, which is based on average capacity factors and synthetic time series optimizing the sizing country wide. Therefore, this approach does not take the entire hydrogen export energy system into account and , hence, neglects possible impacts of storage and gridbalancing needs. The approach was also used by Moritz et. al [22] to calculate export costs for other hydrogen based energy carriers. Buchenberg et. al. [23] considers a more complex energy system designs for synfuel exports, but does not model spatially resolved transportation. Also, studies based on integrated assessment models exist like a study from van der Zwaan et. al [24], which shows an positive economic impact of energy imports on the European and North African energy system. Yet, these studies lack a detailed spatial and temporal resolution.
Hence, there remains a gap in knowledge regarding the impact of the full green hydrogen process chain design on hydrogen production costs for export needs. Therefore, this paper attempts to close this gap by investigating highly temporally-and spatially-resolved green hydrogen production costs in countries around the world, including the full infrastructure necessary for exporting liquid hydrogen. By this, the impact of the full export infrastructure on cost distributions across a selected set of suitable countries will be revealed. Liquid hydrogen is chosen as the exported energy carrier for hydrogen, as it is expected that this option will result in the lowest shipping costs in the long term [5]. Also, it has the least environmental impacts [25][26][27]. The latter is especially advantageous, as liquid hydrogen is not toxic, in contrast to, for example, ammonia [28]. As renewable energy sources, wind turbines and openfield photovoltaics (PV) are selected, as both are expected to play a crucial role in future energy systems due to their comparably low costs and abundant global potential [1,15,29]. In addition, they avoid some of the severe environmental impacts that can occur with renewable energy sources such as hydropower and bioenergy [30][31][32]. The obtained information regarding potentials and full infrastructure costs for green hydrogen exports around the world can serve as a basis for developing import strategies for various countries and, hence, is provided as open data in the Appendix of this paper.
For this purpose, the utilized methodology is shown in full detail in Section 2. In Section 3, the obtained results are presented, and a special focus is given to the distribution of global green hydrogen potentials and energy system characteristics that support low hydrogen production costs. In Section 4, the paper is complemented by a discussion of the obtained results and conclusions are drawn therefrom.
Methodology
For this study, an approach is utilized that calculates the liquid hydrogen export cost based on volatile renewable energy sources for a given set of countries, including all process steps along the production chain. The goal is to calculate the export cost-potential curves for countries with the most beneficial renewable energy potentials across the world to determine differences in export cost to serve as a basis for developing strategies for reliable green hydrogen imports.
An overview of the applied approach is shown in Figure 1. It consists of five steps along the process chain, starting with volatile renewable energy sources and ending within an export harbor. Each step is described in more detail in the upcoming subsections. In the first step, countries with high solar and wind resources are selected. For these, a land eligibility analysis is conducted. Based on the available areas for renewable energy technologies, the electricity time series of these renewable energy technologies are simulated hourly from Merra-2 weather data for open-field PV and onshore wind. Afterwards, the results are clustered to serve as an input for the energy system optimizations to design the respective hydrogen export infrastructures.
To determine the cost-potential curves for liquid hydrogen exports, for each considered country 36 discrete energy systems are optimized with nine varying expansion degrees of renewable energy technologies for four different years, ranging from 2020 to 2050. The chosen approach is based on the energy system framework FINE [33,34] and uses a holistic optimization to minimize the total system costs, which is equal to the liquid hydrogen costs in the harbor. Subsequent to the energy system optimization, the utilized renewable energy potentials are allocated to specific locations and clustered into parks. The parks are connected by designing a local transmission grid for the hydrogen export to account for sub-regional infrastructure costs as well. Finally, the obtained single cost-potentials for liquid hydrogen exports are merged into full cost-potential curves for each exporting harbor.
Deriving the potentials of volatile renewable energy sources
The selection of the considered countries for renewable energy potentials was based on the Global Wind Atlas [35] for wind energy and on the Global Solar Atlas [36] for solar energy. This analysis focuses on wind turbines and open-field PV, as both are perceived to be cornerstones of a global energy transformation [1,37] and bear the comparable lowest environmental and social impacts amongst renewable energy technologies [38]. To achieve a good and wellbalanced global coverage, the country selection is based on the world regions utilized in the global energy system model TIAM [39], which aims to represent the full global energy system and transformation pathways most properly. Hence, for each region in TIAM, at least one promising country in terms of volatile renewable energy potentials is selected. This results in 28 selected countries, as shown in Figure 2. For the technical electricity potentials of open-field PV and onshore wind turbines, results calculated using the open-source tool pyGRETA [40] from Buchenberg et al. [23] are utilized. Those potentials are derived by converting historical weather data for 2019 from MERRA-2 [2] and the Global Wind Atlas [35] at any location into hourly capacity factors of electricity generation [40]. This results in time series with a spatial resolution at the equator of 250 m x 250 m for wind energy and 50 km x 50 km for solar energy allocated to 250m x 250m cells for those areas, which are assumed to be suitable or available for the installation of renewable energy technologies. The applied identification of suitable areas is based on a land eligibility approach by Ryberg et al. [41]. For this study, 38 different exclusion types for land areas with specific buffer distances for each generation technology are considered (see Table 5). The exclusions consist of physical limitations like slopes, sociopolitical constraints such as distances to settlements, land use conflict with croplands and natural conservation. Finally, this results in the total technical electricity potential of open-field PV and onshore wind turbines for the considered countries as listed in Table 1 and described in more detail in Buchenberg et al. [23]. These renewable energy potential data serve as the energy source within the hydrogen export model. As the model bears a spatial aggregation at the GID-1 level (see section 2.2), the energy potentials and their time series are clustered. All available placements for renewable energy technologies within a GID-1 region are split into 11 clusters each for open-field PV and onshore wind based on their full load hours. These quantiles split the full potentials per region first into ten evenly spaced renewable energy potentials in terms of their full load hours, with an additional cluster being added representing the best 5% of the potentials to account for more details amongst the best potentials. Finally, this results in 13,376 overall clusters across the 28 considered countries, describing the total technical potential for each country.
Designing the infrastructure for green liquid hydrogen exports
The aim of the liquid hydrogen export models is to find the cost-optimal solution to convert renewable electricity from onshore wind and open-field PV to liquid hydrogen at an export harbor. Several types of carriers for transporting hydrogen like gaseous hydrogen (GH2), ammonia (NH3), or liquid organic hydrogen carriers (LOHCs) can be considered [42][43][44].
Based on a study from Heuser et al. [5], liquid hydrogen (LH2) is chosen as the hydrogen carrier for exporting hydrogen in future global hydrogen markets for this study, due to its low shipping and reconversion cost in the long term. Liquid hydrogen needs most part of its energy for conversion at the location of export, where the process can utilize low cost renewable energy of the exporting country, whereas ammonia and LOHC both have a high demand for high temperature heat occurring within the importing country, which imports hydrogen or hydrogen carrier mostly due to limits in local renewable energy expansion at sufficiently low cost. Hence, this could result in a barrier for ammonia and LOHC depending on the use in the importing country [6]. Additionally, liquid hydrogen has higher conversion efficiencies and lower investment costs compared to LOHC and ammonia [45].
The entire structure of the underlying energy system model is shown in Figure 3. It consists of the renewable energy sources on the left. The generated electricity can be converted via PEMelectrolysis and distributed via hydrogen pipelines (hydrogen path) or can also be stored in batteries and transported within an electrical grid to a harbor to supply liquefaction (electricity path). In the harbor, the hydrogen is liquefied and stored to be readied for the export of green hydrogen. As the spatial resolution of the model highly impacts the generation and infrastructure in terms of cost and design [46], each considered country is modeled on a GID-1 level, which roughly equates to federal states and varies between 85 regions for Russia and four for Great Britain.
A higher spatial resolution would result in excessively challenging computational efforts. The respective export port for each country is considered as an additional region within the model. The assumed hydrogen demand for export is allocated within this separate region. In all countries apart from Turkmenistan, the industrial port with the highest freight handling capacity based on data from marineinsight [47] and worldshipping [48] is assumed as the export location. For Turkmenistan, which has no access to an ocean for global shipping, the Pre-Caspian gas pipeline highlighted in Balkanabat [49] is assumed as the point of export. For all points of export, no capacity restrictions are applied.
The onshore wind turbines and open-field PV are modeled as electricity sources within the model. Their temporally-resolved maximum feed-in is determined by the hourly time series from the renewable energy potential analysis (see Section 2.1). As the time series, especially for wind energy, vary strongly even within GID-1 sub-regions, eleven clusters for both technologies based on their full load hours are considered within each of these. Based on these clusters, the optimization can choose which to utilize first from an energy systems perspective.
The electricity of the renewable energy technologies is partially converted into green hydrogen by means of PEM electrolysis within the region of the renewable electricity generation (decentralized) or at the export location (centralized). As the aim of this study is to derive the maximum technical liquid hydrogen potential associated with its costs based on renewable potentials, restrictions for ramp up and material use etc. are not considered and the model is allowed to expand electrolysis infinitely if required. The water usage for the hydrogen production is assumed to be from groundwater and costs are therefore already included in the techno-economic assumptions (see Table 2). In the future, groundwater will most probably not be available as an unlimited resource [50]. Yet, the additional cost of seawater desalination on hydrogen production is marginal, as Yates et al. [51] and Heinrichs et. al. [52] showed. For the grid, the model can choose between an AC electric grid and gaseous hydrogen pipelines (see Table 2). Based on the fact that in most cases, decentralized hydrogen production and transport via hydrogen pipeline is expected to be the comparably cheaper option in accordance with Reuß et al. [53], the electric grid primarily serves the purpose of supplying the electricity demand of the liquefaction of about 0.205 kWhel/kWhH2,LHV [53] within the harbors. Both grids are modeled using a greenfield approach due to the vast required infrastructure expansions, allowing grid connections between neighboring sub-regions from centroid to centroid with a detour factor of 1.3 [54] and connecting remote parts to the nearest locations on the mainland.
The hydrogen is liquefied and stored in the export location. As was shown in Reuß et al. [53], the cost of liquefaction greatly depends on the system size. Currently, there are only plants available at a capacity below 100 tons per day [44,55,56]. For the large-scale applications in this study, higher capacities are needed. Therefore, the investment costs are modeled as a function of the liquefaction plant size (see Table 2). As there are currently no large-scale liquefaction plants available, the limitation of scaling effect is set as the largest LNG liquefaction train at about 20,000 tons per day [57]. As hydrogen export via ship is assumed to be constant throughout the entire year, the storage is needed to account for fluctuations in hydrogen generation.
The hydrogen energy system model is formulated and solved using the open energy system model framework FINE [33, 34] as a holistic linear optimization, taking into account all of the design and operation of the export process chain in one approach. The optimization itself is carried out with the gurobi solver [58], and is solved for one year. As the model itself only considers spatial differences for transport on the GID-1 level, all transport costs below that spatial resolution are not accounted for within the optimization. Therefore, this is considered through a post-processing step following the optimization. In this step, the local transmission grid to connect the wind turbines and PV modules first to the parks and second to the electrolysis units is calculated. This is done by deriving the actual used placements by choosing the best placements from the potentials in terms of full load hours until the capacity from the optimization is reached. All placements within a 5 km radius are clustered to wind or PV parks. Subsequently, each park is connected to the electrical grid on the GID-1 level obtained within the optimization using a minimum spanning tree [59]. Figure 4 depicts this step for a random example in which all parks are connected to the electrolysis units of the respective GID-1 region. Finally, the cost for the local transmission grid is calculated assuming the parameter from Table 2. The resulting hydrogen export costs are calculated as:
2 = + 2 ,
where is the total annual energy system costs from the optimization, the cost for the local transmission grids, and 2 , the exported amount of hydrogen for the simulated year.
Hydrogen cost-potential curve generation
Based on the derived hydrogen export costs as described above, the export cost-potential curves for liquid hydrogen are calculated. This is done for the years 2020, 2030, 2040, and 2050 based on the techno-economic assumptions from Table 2. For each year and country, nine different hydrogen export amounts are calculated to discretize the hydrogen costpotential-curve. The export amounts are evenly spaced to 95% of the maximum exportable hydrogen. Above this threshold the optimization is limited in flexibility options like curtailment and storage capacities due to energy losses, which would lead to artificial system designs. By this, the most expensive 5% of the technical potential are neglected due to the effects above. The maximum is derived by applying the conversion efficiencies for electrolysis and liquefaction to the maximum electrical potential from Table 1. For each country, the combination of exported hydrogen amount and total system cost across all export variations form the cost-potential curve. In this study, from the 1008 possible configurations (28 countries, 9 export demands, 4 years), 957 combinations are calculated to derive a detailed cost-potential curve for each considered country. 51 energy systems achieved only suboptimality by the used optimization problem solver gurobi and, hence, were dropped. As these costs account for all energy system costs for each discrete assumed hydrogen export, the cost-potential curves are based on the absolute costs and not the marginal cost, which are often seen in economic evaluations of price models [64].
Results
This section presents the cost-potential curves for the liquid green hydrogen export of all considered countries. The countries are categorized into three groups based on different characteristics of their hydrogen export energy systems. Subsequently, these energy systems are analyzed in terms of their specific designs obtained within the optimization and their cost development through 2050 is shown.
Global green liquid hydrogen cost-potential curves
The obtained hydrogen cost-potential curves are shown Figure 5. In total, the exportable amount of liquid hydrogen for the considered 28 countries sums up to over 1540 PWhLHV/a, which is about nine times the world primary energy consumption for 2019 (173 PWhLHV) [65].
Investigating the resulting energy system designs in greater detail reveals three distinct country groups, as displayed in Figure 5. Group I comprises countries with comparably cheap large-scale solar energy potentials. The hydrogen energy systems of those countries are dominated by solar energy, which leads to nearly stable hydrogen costs for the entire hydrogen potential (see the typical country of Oman in Figure 6). The small cost increase over the exported hydrogen stems mainly from transport, especially hydrogen grid costs, whose impact is constrained by decreasing liquefaction cost from scaling effects. The cost share of open-field PV and electrolysis as the main cost factors account for 53-65% for these countries. With high full load hours of open-field PV of up to and over 2000 h/a and minimal electricity generation costs of 1.63 EURct/kWhel in 2050 in Oman, a hydrogen cost of 2.07 EUR/kgH2 can be achieved. In total, 79 PWhLHV/a of liquid hydrogen for export can be produced at a hydrogen cost below 2.30 EUR/kg in 2050 within group I.
Group II includes the medium-to high-cost, large potential countries between 2.50 and 7,50 EUR/kgH2. For some countries of this group, the effects of stable potential costs as described in group I also applies for the first part of their cost-potential curve (India, Turkmenistan and Australia with PV, and Argentina with wind). These parts sum up to 129 PWhLHV/a hydrogen production and represent roughly 12% of the total potential of group II. Additionally, all of them exhibit a steep increase in their costs at a certain point (see Figure 6 for the typical country of Canada). This is primarily due to an increase of storage and grid costs with increasing exploitation of hydrogen potentials from 0.84 to 2.52 EUR/kgH2 and an increase in electricity cost due to uneven distributed potentials with higher needs for comparably longer grid distances from 4.70 to 5.29 EURct/kWhel .
Group III describes countries with smaller generation potentials below 1 PWhLHV/a. As the 11 renewable energy clusters per GID-1 region are distributed over smaller potentials, more details can be observed. One example of this is the impact of scaling liquefaction costs, leading to a drop with increasing exploitation of the hydrogen potential for countries with steady potentials at low export rates such as South Korea and Bulgaria. In general, these countries see a substantial increase in costs with increasing hydrogen exports (see Figure 6 for South Korea) resulting from a reduction in wind full load hours from, e.g., over 2600 to below 1300
hours per year in South Korea. Iceland shows the same effect but resulting, in contrast, from constant high wind full load hours and low full load hours for PV placements. Only Germany and Ireland exhibit steady costs for green hydrogen because of their more constant RES full load hours. The distribution and storage costs exhibit a share of about 17% and are therefore the lowest of all the groups.
Impact on optimal energy system design
Analyzing the resulting energy system designs in more detail reveals further patterns across the three country groups, as can be seen in Table 3. From the three available flexibility options (battery usage, grid balance, and curtailment) within the model, the option preferred by the model is curtailment of solar power combined with decentralized hydrogen production in the GID-1 regions for group I. The only countries utilizing batteries to a larger extent are from group II, resulting in a cost share of ca. 12% compared to less than 4% in the other country groups. In contrast, the larger countries of groups I and II require larger grid connections to exploit their full potentials stretched over their entire areas, resulting in a cost share for grids of roughly 18% and 24%, respectively, for groups I and II and only for 10% for the small countries of group III. Although the interpretation of high grid costs for large countries is fairly trivial, the high utilization of batteries in group II derives from a combination of high transport costs due to long distances and comparably low full load hours of renewable energy technologies. This implies that the usage of batteries to decrease green hydrogen costs is only beneficial in comparable uneconomical hydrogen energy systems with hydrogen costs above 2.50 EUR/kg. Therefore, they will probably not be part of an optimal global solution for hydrogen supply, as other regions most likely offer a sufficient amount of potential green hydrogen. Moreover, the hydrogen energy systems from groups II and III typically utilize a combination of wind and solar power (see Figure 6) to make use of synergies in the different feed-in time series, ultimately leading to higher full load hours of the electrolysis (3140 h/a for group I and over 4000 h/a for groups II and III). Yet, the impact on the PEM cost reduction from the full load hour increase is minor, at only 0.02 to 0.09 EUR/kgH2. Figure 7 shows the impact of the share of PV utilization on the electricity generation costs. Firstly, it can be seen that all low-cost solutions (group I) only utilize solar energy primarily as a result of the higher costs of wind turbines. The average electricity generation cost in the considered regions results in roughly 0.062 EUR/kWhel for wind turbines and 0.026 EUR/kWhel for open-field PV. This difference mainly stems from the assumed cost of wind turbines and open-field PV and the different weather conditions. Secondly, all countries, even those with the best onshore wind placements in the world, utilize a higher capacity of PV than wind power in their hydrogen energy systems. This explains why some countries with high wind full load hours, such as Norway, still have high hydrogen generation costs due to comparably low full load hours of PV.
In addition, it must be noted that the lowest supporting points of the derived cost-potential curves in this study are at 10% of the maximum hydrogen export of each country, which already represent large-scale hydrogen production. Hence, smaller competitive wind energy potentials might be overlooked, which could contribute to local small-scale hydrogen production. However, the focus of this study is on the global exchange of hydrogen, for which large scale production units will be required to make use of scaling effects.
Cost development
In this study, the optimal energy systems were derived for 2020 to 2050. The results are shown in Figure 8. It can be seen that in most cases, costs homogeneously drop. The only difference observed is between countries with rich solar and wind resources, where the average electricity costs between 2020 and 2050 drop by 52% for PV and 20% for onshore wind. This stems from assumptions regarding cost developments for onshore wind and solar PV, with solar countries experiencing a larger drop compared to wind countries between 2020 and 2030. Apart from that, the results do not indicate region-specific preferences for cost digressions for the observed countries. The biggest drop in costs for green liquid hydrogen of about 1.40 EUR/kgH2 is expected to happen between 2020 and 2030. The first time that costs for green hydrogen production drop below 2.50 EUR/kg occurs in Oman and Namibia in 2040. Other countries only follow between 2040 and 2050 (see also Figure 5). It must be noted that these costs are still export costs in the harbor. Hence, the final hydrogen cost for local supply within the considered regions will not include the liquefaction cost, whereas imported hydrogen will bear additional shipping costs.
Cost Sensitivity Analysis
As the cost parameters for future technologies are forecasted, the assumptions from Table 2 underlie uncertainties. To tackle the impact of uncertainty in these costs a sensitivity analysis concerning the investment costs for PV, onshore wind, electrolysis, and liquefaction costs is conducted. The results for three exemplary countries, Oman for group I, Argentina for group II and Germany for group III are shown in Figure 9, where the investment cost for PV, onshore wind and PEM are varied by +-30% for an exemplary expansion rate of 10% of the countrywise maximum export in 2050. This expansion rate was chosen as it allows for most freedom in system design while already representing a global hydrogen market beyond a ramp-up. For the liquefaction, the maximum plant size is compared to a minimum of 700 t/d as a derived future plant capacity used by IRENA [66] and a theoretical unlimited scaling of the liquefaction costs.
There is a significant impact on liquid hydrogen export costs in Oman, particularly regarding liquefaction costs, which have an average impact of 19%. Oman's large export amounts result in the largest drop of hydrogen costs across all sensitivities, when infinite liquefaction scaling is applied, as the liquefaction plant is scaled from 20 kt/d to 808 kt/d. The corresponding cost are reduced by -0.22 EUR/kgH2 to 1.85 EUR/kgH2. However, Oman utilizes only solar resources which have lower full load hours than the wind resources of countries in groups II and III. As a result, limiting liquefaction to 700 t/d leads to the highest increase in liquefaction costs, making Oman and other countries in group I more sensitive to liquefaction costs than the other groups. Also, because Oman solely relies on solar resources, it shows the highest dependency on PV costs among all groups as seen in Table 4. Argentina shows the lowest dependency of all countries on specific changes in costs (below 11% for all sensitivities). This is due to the utilization of solar and wind resources, allowing the energy system to change the primary source of energy with changes in renewable costs without a significant change in electricity costs. In addition, the higher full load hours of the electrolysis and liquefaction due to the utilization of wind turbines make the energy system more robust to cost changes in electrolysis and liquefaction investments. In Germany, the largest change in hydrogen costs occurs with varying onshore wind costs (13% change), as the energy system mainly utilizes onshore wind resources for electricity generation. Consequently, it shows the lowest change in hydrogen costs when PV costs change (6%). Because of the high full load hours of wind turbines in Germany, the change of electrolysis and liquefaction costs is low compared to the other countries, with the same reasoning as in Argentina. Furthermore, due to the small hydrogen export amount of Germany, as well as all countries in group III, infinite scaling of the liquefaction plant does not affect the hydrogen costs because the liquefaction plant is already below the maximum scaling of 20 kt/d in the reference case. Countries from group II and group III show lower dependency of hydrogen export cost on costs assumptions compared to countries from group I apart from the dependency due to high shares of wind in Germany. Another notable finding is that all energy systems tend to exhibit a high increase in batteries in the case of small and expensive liquefaction plants. This is due to the higher costs of liquefaction for smaller plant sizes, which favors higher full load hours of the liquefaction, which can be achieved by utilizing batteries. In the reference case without batteries, the full load hours of the liquefaction are at 2996 h/a, which rise to 4250 h/a in the case for higher liquefaction costs. In this case, the system purpose of batteries is balancing the diurnal fluctuations of electricity supply.
Geostrategic security of hydrogen supply and water risk levels
Although the results presented before focus on cost and potentials, other aspects can impact future global hydrogen exchange. In this context, the diversification of supply and water risk levels in particular are important. As the considered export countries exhibit all types of political regimes, the question can arise of whether this might impact the security of supply. By sorting all cost-potential curves in accordance with the underlying political regime of each export country, cumulative curves revealing the impact of sourcing liquid hydrogen from different regime types becomes apparent. For this sorting, the State of Democracy map of Lauth et al. [67] is utilized in its most recent version from 2019. The map classifies political regimes into five types (namely working and deficient democracies, hybrid regimes, moderate and hard autocracies). The resulting cumulative cost-potential curves (see Figure 10) show that the export costs of autocratic countries are cheapest up to 500 PWhLHV/a, whereas the export cost premiums of democratic countries account for roughly 7% at a hydrogen expansion equal to the global primary energy supply in 2019 [65]. However, differences in transport cost are likely to further increase this difference; especially for Germany and Europe more widely, this can increase the cost premium to ~20-24%. It must be noted that the assumed political situation might change until 2050, as this study only evaluates the political situation based on 2019.
In addition to the diversification aspects, the water supply for hydrogen must also be considered in terms of sustainability and security of supply. This is especially true, as water electrolysis consumes water instead of using it, as do many other types of water demands. Water stress scenarios from the World Resources Institute [68] reveal that even under the optimistic water stress scenario for 2040, most green hydrogen potential, and especially cheap solar-based hydrogen potential, is concentrated in regions that are already water-stressed, without imposing further burdens on water through hydrogen production ( Figure 11). Water stress is assumed to start at the latest with a high water risk level [69].
As each kg of hydrogen roughly requires 9 liters of water [50], the water demand for hydrogen production only in regions with high and extreme water risk alone adds up to more than 1.8 times Europe's water withdrawal in 2019 [70]. However, utilizing seawater desalination in countries with sufficient coastal access can offer an alternative if installed in accordance with best practices so as to avoid environmental issues in coastal regions. Nevertheless, the impact of this additional process step on costs is only around 0.01 EUR/kgH2, as a study by Heinrichs et al. [52] showed that utilizing sea water desalination for water for hydrogen energy systems adds little to no cost surplus to green hydrogen costs.
Discussion and conclusions
The conducted analysis shows that the global green liquid hydrogen potentials of more than 1,540 PWhLHV/a in 28 countries exceed the world primary energy consumption by a factor of 9 [65]. Over 79 PWhLHV/a of this green liquid hydrogen will be available at costs below 2,30 EUR/kg in 2050. Therefrom, the highest cost contributors will be the renewable energy sources and electrolysis, amounting to about 65% of the total hydrogen costs. Hence, future hydrogen costs are highly sensitive to the decreasing costs of such technologies.
Compared to the results from IRENA [6], the costs reported in this study are generally higher. For example, in Australia, IRENA [6] estimates a cost of 0.8 EUR/kg in 2050, whereas this report projects over 2.6 EUR/kg. This is mainly explicable due differences in cost assumptions for CAPEX, WACC, and electrolysis efficiency (electrolysis: CAPEX = ~0.4 EUR/kg, efficiency = ~0.15 EUR/kg), as well as additionally considered energy system components in this study such as liquefaction, grids, and storage (~1.2 EUR/kg). Furthermore, Brändle et al. [21] calculates a lower cost for liquid hydrogen generation with, e.g., 1.8 EUR/kg in Australia for the same reason of not accounting for transportation and storage costs. Looking at hydrogen costs for Australia minus such costs for transportation and storage, the liquid hydrogen costs of this study would result in 1.74 EUR/kg, which is even below the estimates of Brändle et al. [21]. The study from Janssen et. al. [20] shows cost for gaseous hydrogen starting from 1.66 Figure 11. Global hydrogen potentials in 2050 by water stress level, according to [54].
EUR/kg in Ireland in 2050, whereas this study projects 2.79 EUR/kg. As Janssen does not include the costs for a complex transport infrastructure, the hydrogen costs from this study for only RES and electrolysis account to 2.09 EUR/kg. The residual difference in costs is arising from higher assumptions of the lifetime of 30 years in Janssen et. al. [20] for onshore wind, PV and PEM resulting in lower total hydrogen costs. This shows the high impact of considering the full process chain in high temporal and spatial resolutions on the resulting hydrogen cost in addition to differences in cost assumptions.
For 2050, the IEA [71] states that the costs for hydrogen from natural gas with carbon capture and storage (CCS) technology will be between 1. 15 The lowest cost for hydrogen potentials will be available from PV-rich countries. Additionally, countries with good wind resources also depend on having good PV resources to achieve competitive hydrogen costs. This strong tendency towards PV-utilization facilitating low hydrogen costs can be seen in the literature [6], [21] as well. In accordance with this study, IRENA [6] found PV to be the dominant electricity source for green hydrogen over onshore wind sources. However, the results in this study go even further and suggest that even countries with high wind potentials will need to utilize at least 57% of the build capacity from PV to achieve low-cost green hydrogen production. Contrary to this, Janssen et. al [20] found, that the cheapest hydrogen in Europe can be produced from wind turbines and not PV. The main difference lies in the average full load hours for PV and onshore wind. This study calculates 1000 h/a for PV and 3575 h/a for onshore wind in Ireland including endogenously optimized curtailment, while Janssen et al. uses 788 for PV and 3942 h/a for onshore wind. This comparison indicates that there are tipping points in energy systems for favoring wind or solar generation for green hydrogen based on the cost prognosis of PV-modules, wind turbines and electrolysis as well as variations of RES input full load hours. As this study showed, capacity results for Oman and Germany are robust against costs variations, whereas Argentina shows a larger shift in capacity utilization with cost variations. Therefore, the implied tipping points in energy systems are country specific and not occurring in every country. Future work could be done in further examining these tipping points for green hydrogen production.
Moreover, for the PV-rich countries, the model actively chooses an optimal curtailment with direct and decentral electrolysis over storing and distributing electricity. The studies from IRENA [6] and Brändle et al. [21] show the same utilization of curtailment of renewable energy sources to increase the full load hours of electrolysis and, hence, decrease hydrogen costs. In contrast, this study finds a utilization of storage systems for wind-rich regions that has not been used in other studies [6], [21] due to their chosen approaches.
In general, the presented results are heavily dependent on the techno-economic assumptions from Table 2. The expansion of hydrogen-and renewable-based energy systems will foster decreasing costs due to learning effects. This learning effect can be endogenously modeled, as in Brändle et al. [21], but still depends on exogenous assumptions regarding expansion scenarios containing their own type of uncertainty. Although the focus of this study is on the impact of PV and onshore wind potentials, in some regions renewables like offshore wind and hydropower have an impact on hydrogen generation costs. Given the focus of this study on the large-scale export of hydrogen, all statements are only valid for such large-scale deployment of green liquid hydrogen generation. Based on the discretization of the models used, there might still be some small-scale applications for hydrogen generation that exhibit different characteristics, such as smaller wind farms with high full load hours with direct electrolysis utilization. Further, the local demand for hydrogen and electricity is not considered in this study, as only the exportable amount of hydrogen is calculated. While this will have an impact on some smaller countries from group 1 with an average electricity demand of 35% of the renewable potentials, the impact of local demands is significantly lower in larger countries of group 1 (<0.3%) or countries from group 2 (<3%) [72], as seen in Table 7.
Future green hydrogen will be needed to decarbonize the shipping and aviation sectors in particular, as well as the ammonia, methanol, and iron industries, as shown in Lippkau et al. [73]. Those demand centers are usually geographically separated from the sun-rich regions that can produce hydrogen at a low cost, as presented in this study. Based on the supply curves, global trading with sun-poor regions would be conceivable and cost-optimal [73]. LH2 shipping would be a suitable technology for both long and short distances if gaseous pipeline transport is not an option [53]. In addition, LH2 shipping could be possible starting at 0.52 EUR/(PJ 1000km) in 2030 and could decrease to 0.26 EU/(PJ 1000km) in 2100 [52]. The results of a TIMES-based energy system analysis with TIAM from Lippkau et al. [73] show that the main oil-exporting nations (e.g., Middle Eastern, Asian, African, and South American countries) could shift their economies towards a hydrogen basis. Yet, as stated in the analysis above, aspects of geostrategic security of supply should be taken into consideration.
Figure 1 .
1Visualization of the main steps for calculating hydrogen export costs.
Figure 2 .
2TIAM regions (colored) and selected countries (striped).
Figure 3 .
3Overview of the elements of the energy system model.
Figure 4 .
4Geospatial design of the energy system, including local transmission grids and the export harbor.
Figure 5 .
5Green liquid hydrogen export cost-potential curves for each considered country in 2050.
Figure 6 .
6Cost share per technology for the liquid hydrogen costs for typical countries of each group (Oman: group I; Canada: group II; South Korea: group III).
Figure 7 .
7Impact of PV and wind combinations on hydrogen production costs for each country at 20% export in 2050.
Figure 8 .
8Liquid hydrogen cost development from 2020 to 2050 at 20% of the maximum export.
Figure 9 :
9Investment cost sensitivity analysis for Oman (group I), Argentina (group II) and Germany (group III) exemplarily for 10% of the country-wise maximum export in 2050.
Figure 10 .
10Global hydrogen supply in 2050 by government type, based on[52].
Table 1 .
1Aggregated country potentials for open-field PV and onshore wind [23].TIAM region
Open-field PV
Onshore Wind
Capacity
[TWel]
Energy
[PWhel]
Capacity
[TWel]
Energy
[PWhel]
Libya
139.49
292.93
10.45
15.41
Namibia
16.32
35.75
3.22
4.33
Australia
350.32
734.41
36.61
67.93
Canada
109.45
96.25
39.66
46.16
China
137.74
240.15
40.99
45.89
Argentina
102.49
177.90
14.39
26.84
Chile
22.49
48.75
2.83
2.48
Peru
12.19
27.28
5.10
0.74
Germany
0.34
0.39
0.28
0.56
Bulgaria
0.14
0.22
0.28
0.19
Poland
0.26
0.32
0.41
0.86
Estonia
0.12
0.13
0.16
0.37
Lithuania
0.12
0.13
0.21
0.29
Latvia
0.18
0.20
0.26
0.44
Russia
88.95
73.84
82.49
80.54
Turkmenistan 29.44
50.25
2.79
3.75
India
17.41
31.61
11.12
8.69
Japan
0.27
0.40
0.80
0.83
South Korea
0.05
0.08
0.18
0.19
Oman
25.00
52.11
1.86
2.00
Table 2 .
2Assumed techno-economic parameters for the considered green hydrogen export chain process steps. EUR refers to EUR2022. The cost assumptions are calculated as total annual costs with an interest rate of 8%.CAPEX [EUR/kW]
OPEX[% Efficiency Lifetime Source
2020
2030 2040 2050 capex/a] [%]
[years]
Onshore wind 1,257 1,137
987
923
3.0
100
25
[60]
PV
703
395
340
326
1.0
100
25
Battery
277
147
124
102
2.5
95
15 [61]
LH2 storage
0.85
0.85 0.85 0.85
2.0
100
20 [53]
PEM
electrolysis
900
700
575
450
1.5
2020:64
2030:69
19 [62]
Table 3 .
3Technology cost per hydrogen generation and curtailment for each group.Group
Total
[EUR/
kg]
Absolute costs [EUR/kg]
Table 4 :
4Average impact of sensitivities on liquid hydrogen export costs by technology for exemplary countriesPV
Onshore wind
PEM
Liquefaction
Oman (group I)
12%
1%
8%
19%
Argentina (group II)
8%
5%
5%
11%
Germany (group III)
6%
13%
4%
7%
and 2.02 EUR/kg based on a price assumption of 2 EUR/MWh for natural gas and for coal gasification with carbon capture and storage at about 2.12 to 2.4 EUR/kg. Compared to the costs for green hydrogen, starting at 2.07 EUR/kg in this study, it can be concluded that green hydrogen could become costcompetitive with hydrogen from coal with CCS in 2040, whereas hydrogen from natural gas with CCS heavily depends on the price developments of natural gas. Yet, another important point for both technologies is the availability of cheap and secure CO2 storage, as well as acceptance of such storage capacities.
AcknowledgementsA major part of this work has been carried out within the framework of the ETSAP-DE project (03EI1032B) funded by the German Federal Ministry for Economic Affairs and Climate Action (BMWK). In addition, parts of this work have been carried out within the framework of the H2 Atlas-Africa project (03EW0001) funded by the German Federal Ministry of Education and Research (BMBF).Author contributions
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| sample_1067 | 0.8726 | arxiv | |
Deep learning of systematic sea ice model errors from data assimilation increments
7 Apr 2023
William Gregory
Atmospheric and Oceanic Sciences Program
Princeton University
NJUSA
Mitchell Bushuk
Geophysical Fluid Dynamics Laboratory
NOAA
PrincetonNJUSA
Alistair Adcroft
Atmospheric and Oceanic Sciences Program
Princeton University
NJUSA
Yongfei Zhang
Atmospheric and Oceanic Sciences Program
Princeton University
NJUSA
Laure Zanna
Courant Institute of Mathematical Sciences
New York University
New YorkNYUSA
Deep learning of systematic sea ice model errors from data assimilation increments
7 Apr 2023manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES)Corresponding author: Will Gregory, wg4031@princeton.edu -1-
Key Points:• We show that sea ice data assimilation increments closely reflect the systematic bias patterns of a global ice-ocean model • Convolutional neural networks can make skillful predictions of sea ice data assimilation increments, using only model state variables • The skillful predictions suggest the network could be used as a parameterization to reduce sea ice biases in free-running model simulationsAbstractData assimilation is often viewed as a framework for correcting short-term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short-term corrections, or analysis increments, can closely mirror the systematic bias patterns of the dynamical model. In this study, we use convolutional neural networks (CNNs) to learn a mapping from model state variables to analysis increments, in order to showcase the feasibility of a data-driven model parameterization which can predict state-dependent model errors. We undertake this problem using an ice-ocean data assimilation system within the Seamless system for Prediction and EArth system Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory, which assimilates satellite observations of sea ice concentration every 5 days between 1982-2017. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are states and tendencies of sea ice concentration, sea-surface temperature, ice velocities, ice thickness, net shortwave radiation, ice-surface skin temperature, sea-surface salinity, as well as a land-sea mask. We find the CNN is able to make skillful predictions of the increments in both the Arctic and Antarctic and across all seasons, with skill that consistently exceeds that of a climatological increment prediction. This suggests that the CNN could be used to reduce sea ice biases in free-running SPEAR simulations, either as a sea ice parameterization or an online bias correction tool for numerical sea ice forecasts.
Plain Language Summary
To make predictions of the Earth's climate system we use expensive computer simulations, called climate models. These models are not perfect however, as we often need to approximate certain physical laws in order to save on compute time. On the other hand we have observational climate data, however these data have limited space and time coverage and also contain errors because of noise and assumptions about how our measurements relate to the quantity we are interested in. Therefore we often use a process called data assimilation to combine our climate model predictions together with observations, to produce our 'best guess' of the climate system. The difference between our best-guessmodel and our original climate model prediction then gives us clues as to how wrong our original climate model is. In this work we use some fancy statistics, called machine learning, where we show a computer algorithm lots of examples of sea ice, atmosphere and ocean climate model predictions, and see if it can learn its own inherent sea ice errors. We find that it can do this well, which means that we can hopefully incorporate the machine learning algorithm into the original climate model to improve its future climate predictions.
Introduction
The influence of structural errors within climate models due to missing physics, imperfect parameterizations of subgrid-scale processes, as well as errors in the underlying numerics, leads to systematic biases across the atmosphere, land, sea ice, and ocean. Subsequently, our ability to diagnose and correct these biases ultimately governs the accuracy of numerical weather and climate predictions on different time scales (Stevens & Bony, 2013). In the context of sea ice for example, much effort has been afforded to the improvement of model physics and subgrid parameterizations through the development of e.g., ice thickness distribution (Thorndike et al., 1975;Bitz et al., 2001) and floe-size distribution theory (Rothrock & Thorndike, 1984;Horvat & Tziperman, 2015), surface melt-pond (Flocco et al., 2012), ice drift (Tsamados et al., 2013) and lateral melt parameterizations (M. Smith et al., 2022), as well as sea ice rheology (Hibler, 1979;Dansereau et al., 2016;Ólason et al., 2022). Such studies have shown how the improved represen-tation of sea ice physics produces model simulations which more closely reflect observations in terms of either their mean sea ice volume, drift, or ice thickness distribution. Despite this, however, biases will often persist due to the fact that physical processes must be approximated in order to meet computational restraints, and that parameterizations are often based on sparse observations which were collected under a climate regime which may not generalize to future conditions (Notz, 2012). Sea ice is also strongly coupled to both the atmosphere and ocean via mechanical and thermodynamic forcing, thus sea ice biases can also manifest from biases in these components.
Many previous studies have leveraged data assimilation (DA) as a way to either assess model error or better understand model physics within numerical weather prediction (NWP) systems (Leith, 1978;Klinker & Sardeshmukh, 1992;Dee, 2005;Rodwell & Palmer, 2007;Palmer & Weisheimer, 2011;Carrassi & Vannitsem, 2011;Mitchell & Carrassi, 2015;Crawford et al., 2020;Laloyaux et al., 2020). Generally, DA can be considered a Bayesian framework for combining a model forecast with observations in order to produce an optimal estimate of a given set of climate state variables, often called the analysis state. The difference between this analysis state and the model forecast prior to assimilation is then the analysis increment, which represents our 'best guess' as to the appropriate correction to the model forecast when taking into account both model and observational uncertainty. One caveat to this is that many DA systems do not formally account for systematic model biases, and so these systems often produce non-zero values in the time-mean of their analysis increments; indicating consistent discrepancies between the model and observations. Attributing such errors to their correct source is also non-trivial (Dee, 2004(Dee, , 2005, as model biases can manifest non-locally in space and time (Palmer & Weisheimer, 2011;C. Wang et al., 2014) and involve non-linear interactions across different model components (Large & Danabasoglu, 2006;Kim et al., 2022). Observations themselves may also contain systematic errors, such as the design of weather filters in satellite-derived sea ice area retrievals (Kern et al., 2019) and uncertainties related to summer ice surface properties (Kern et al., 2020). While some studies have shown relative success in separating systematic errors between observations and models (Auligné et al., 2007;Dee & Uppala, 2009), many assimilation systems simply assume that the observational errors are uncorrelated and Gaussian, and subsequently any systematic patterns within the analysis increments can largely be considered a manifestation of the various model biases. Under this assumption, the increments can be seen as a reflection of model error growth associated with missing or imbalanced physical processes occurring over short time scales, often called fast physics errors, however such errors ultimately have an impact on the model's bias patterns over climate time scales as well (J. M. Murphy et al., 2004;Rodwell & Palmer, 2007).
The analysis increments therefore provide useful information on model deficiencies, which could inform new parameterizations to reduce systematic model biases. Indeed, variational schemes such as weak-constraint 4D-Var (Wergen, 1992;Zupanski, 1993;Trémolet, 2007;Laloyaux et al., 2020) already aim to account for systematic model error during DA, and while this is invaluable in NWP, the underlying model physics remains unchanged, meaning that a free-running model simulation invariably remains biased. An alternative approach which has been explored in the ocean modeling community (Chepurin et al., 2005;Balmaseda et al., 2007;Lu et al., 2020) is to use DA to first derive the climatological components of the systematic model biases, and then incorporate these components back into the model as an adjustment to the model state tendencies. Lu et al. (2020) for example designed an ocean DA system which assimilates temperature and salinity profile data into version 6 of the Modular Ocean Model (MOM6), and from this they derived analysis increments of temperature and salinity at each model grid cell location and vertical level. They subsequently computed the daily climatology of the increments, which represent the systematic component of model error for each field on any given day of the year, and incorporated these as a three-dimensional adjustment to the model temperature and salinity tendencies for subsequent MOM6 ocean simulations. This 'ocean ten-dency adjustment' was found to reduce ocean model bias and improve the skill of coupled model seasonal predictions of the El Niño Southern Oscillation.
More recently, machine learning (ML) has been put forward as a data-driven framework for targeting model biases. ML, in particular deep learning (DL), algorithms have become increasingly popular in climate research for a variety of applications ranging from NWP (Pathak et al., 2022;Bi et al., 2022) to satellite altimetry data processing (Dawson et al., 2022;Landy et al., 2022). In the context of dynamical climate models, DL algorithms have proven effective tools for deriving model parameterizations directly from numerical simulations. For example, many past studies have focused on learning subgrid parameterizations from high resolution experiments and/or observations of the ocean (Bolton & Zanna, 2019;Zanna & Bolton, 2020;Zhu et al., 2022), atmosphere (Brenowitz & Bretherton, 2018;Gentine et al., 2018;Rasp et al., 2018;O'Gorman & Dwyer, 2018;Yuval & O'Gorman, 2020;P. Wang et al., 2022), and sea ice (Finn et al., 2023). In the context of DA-based approaches, some recent studies have relied on iterative sequences of DA and ML to infer unresolved scale parameterizations from sparse and noisy observations (Brajard et al., 2021), or to learn state-dependent model error from analysis increments (Farchi et al., 2021) and nudging tendencies (Watt-Meyer et al., 2021;Bretherton et al., 2022), while others have combined DA with equation discovery to extract interpretable structural model errors (Mojgani et al., 2022). Many of these studies have relied on idealized models to showcase the feasibility of various DA-ML methodologies, however recently Bonavita and Laloyaux (2020) used ML to learn state-dependent model errors from atmospheric analysis increments produced from a 4D-Var simulation within the the Integrated Forecasting System (IFS) model at the European Centre for Medium-range Weather Forecasts (ECMWF), and similarly, Laloyaux et al. (2022) attempted to learn atmospheric temperature errors within the same IFS model using the model bias directly, as a way to a-priori define the bias model within subsequent 4D-Var simulations. This latter approach however was unable to outperform the current operational weak-constraint 4D-Var system at ECMWF.
In this study, we present a DA-based ML approach to learn the systematic biases of a large-scale sea ice model used for climate simulations. We learn state-dependent sea ice errors within the Seamless system for Prediction and EArth system Research (SPEAR) model , developed at the Geophysical Fluid Dynamics Laboratory (GFDL), by constructing convolutional neural networks (CNNs) which learn a functional mapping from model state variables to sea ice DA increments. Somewhat different to previous studies which have been centered around DA and ML in idealized model contexts (Brajard et al., 2021;Farchi et al., 2021;Mojgani et al., 2022), our application here is, to our knowledge, the first example of using ML to learn systematic model error from DA increments in a global ice-ocean model (though similar approaches have previously been explored within large-scale atmospheric models Chen et al., 2022)). We also choose to learn sea ice errors from DA increments as opposed to learning the model bias directly (e.g., Laloyaux et al. (2022)), as the increments have inherently accounted for model and observational uncertainty, and they also provide a full spatio-temporal record of errors for model state variables which are not direct observables, such as subgrid ice thickness distribution category concentrations. It is also worth noting that while we present this article in the context of using ML to make offline predictions of sea ice DA increments, we are ultimately working towards an ML model which can be implemented as an online sea ice parameterization within SPEAR. Similar to previous works (Grundner et al., 2022;P. Wang et al., 2022), this article is therefore an initial evaluation into the feasibility of this task, based on offline performance. This paper is structured as follows: Section 2 provides a brief overview of the SPEAR ice-ocean model configuration, as well as the sea ice DA setup. Section 3 then highlights how the climatological sea ice concentration (SIC) bias of a SPEAR ice-ocean model experiment maps closely onto the SPEAR SIC DA increments, motivating the idea of learn-ing systematic model error from analysis increments. Section 4 describes the ML problem setup and documents the CNN architectures and hyperparameter settings. Section 5 then showcases the predictive performance of the CNN, and provides an assessment of the CNN sensitivity and generalization ability. Section 6 presents a discussion on the results and outlines considerations for future work relating to sea ice parameterizations and climate prediction. A final summary is then given in section 7, as well as an outlook on the broader implications of this work within the climate modeling community.
2 Model configuration 2.1 SPEAR ice-ocean model SPEAR is a fully coupled ice-ocean-atmosphere-land model, with nominal 1 • horizontal resolution in the ice and ocean components . The SPEAR ocean component is based on MOM6, with 75 vertical layers, and the sea ice component on version 2 of the Sea Ice Simulator (SIS2; see Adcroft et al. (2019) for details on both MOM6 and SIS2). In this work, we consider an ice-ocean model configuration of SPEAR forced by atmospheric conditions and river runoff from the Japanese 55-year Reanalysis for driving ocean-sea-ice models (JRA55-do; Tsujino et al. (2018)).
The SIS2 ice dynamics are solved using a elastic-viscous-plastic rheology on a tripolar Arakawa C-grid (Bouillon et al., 2009), with advection performed with a modified upwind scheme (Adcroft et al., 2019). The energy-conserving thermodynamics of the ice follows that of Bitz and Lipscomb (1999), and uses a vertical structure consisting of four ice layers and a single snow layer. Following Bitz et al. (2001), five ice thickness distribution categories are implemented in a Lagrangian scheme, with thickness boundaries of 0.1, 0.3, 0.7, 1.1 metres. The coupling between ice and ocean occurs at a frequency of 60 minutes, with a temperature coupling coefficient of 240 Wm −2 K −1 , while faster coupling with the atmosphere occurs through a surface skin temperature every 20 minutes. The model does not contain melt-pond, subgrid ridging, lateral melt, or land-fast ice parameterizations.
Sea ice data assimilation and model experiments
An experimental ice-ocean DA system within SPEAR was recently developed by Y. Zhang et al. (2021), whereby satellite-derived SIC from the National Snow and Ice Data Center (NSIDC; Cavalieri et al. (1996)) NASA Team algorithm is assimilated into SIS2 via the Ensemble Adjustment Kalman Filter (EAKF; Anderson (2001)), and MOM6 sea-surface temperatures are nudged towards observations from version 2 of the 1 • gridded Optimum Interpolation Sea-Surface Temperature (OISSTv2) data set (Reynolds et al., 2007;Banzon et al., 2016). In this section we give a brief overview of this DA setup, although the reader is referred to Y. Zhang et al. (2021) for further details.
A single SPEAR ensemble member is initialised in 1958 with World Ocean Atlas ocean conditions, and a prescribed atmosphere from JRA55-do reanalysis. This single member is then integrated forward to 1979 in order to 'spin up' the ocean and sea ice, which then provides the initial ice and ocean conditions for a set of 30 ensemble members, each with individual perturbed sea ice physics. These perturbations correspond to independent random draws from a uniform distribution for sea ice model parameters including the ice strength parameter (Hibler, 1979), as well as the ice, snow, and pond albedo parameters (Briegleb & Light, 2007). The distribution for ice strength spans 20,000-50,000 Nm −1 , while the distribution for albedo parameters spans -1.6-1.6 standard deviations (Y. Zhang et al., 2021). The 30 perturbed physics ensemble members are then integrated forward from 1979 to 1982 in order to spin up the sea ice and generate sufficient spread across the ensemble. After which, the first sea ice DA update is made on January 6 th 1982 and continues every 5 days until December 27 th 2017, providing a total of 2618 as-similation cycles. This corresponds to 73 cycles per year except for 1982, 1987 and 1988, which contain 71, 68 and 70 cycles, respectively. There are 71 cycles in 1982 because the first cycle begins after the initial update on January 6 th , and 68 and 70 in 1987 and 1988 due to missing satellite observations between December 3 rd 1987 and January 13 th 1988 (Cavalieri et al., 1996). Note that, for convenience, the model is run with a 'no leap' calendar which excludes leap-year days.
During each assimilation cycle, a model forecast is run until 00:00 hours UTC on the assimilation day (e.g., Jan 6 th ), at which point the ice concentration from each of the model's five individual ice thickness distribution categories (hereafter SICN; note that SIC = 5 k=1 SICN k ) are passed to the EAKF, along with the satellite SIC observations, and subsequently the SICN forecasts are updated by the filter to produce their analysis states. Given that the aggregate SIC analysis state corresponds to the sum of the SICN analysis states, it is necessary to post-process SICN after each DA cycle in order avoid non-physical values in SIC, which is bounded between 0 and 1. This is achieved by appropriately scaling each of the SICN states when SIC is greater than 1, and setting SICN to 0 when SIC is negative. After post-processing, the analysis increments are then computed for each of the five category concentrations (∆SICN), and for each of the 30 ensemble members. State variables for each ensemble member are saved as daily mean fields during model integration, giving 365 days × 36 years = 13140 daily forecasts for each variable. For the remainder of this article we consider only the ensemble mean fields for both the model state variables and the analysis increments.
In order to understand the inherent SIC bias patterns within SPEAR, the next section includes a comparison of the SIC DA increments (∆SIC) to an additional model experiment without SIC DA, referred to here as FREE. This experiment corresponds to the same JRA-forced ice-ocean model configuration with sea-surface temperature nudging, as well as the same perturbed sea ice physics, and initial conditions from the spinup run as the SIC DA experiment. Therefore the FREE experiment configuration is identical to the SIC DA run, except for the assimilation of SIC observations.
Analysis increments and model bias in SPEAR
Learning systematic model error from DA increments, with the goal of an eventual sea ice parameterization which reduces climate model bias, relies on the assumption that the fast physics errors captured within the DA increments reflect the long-term systematic biases of the free-running model (Rodwell & Palmer, 2007). In this section, we examine whether this necessary condition is satisfied, making comparisons of ∆SIC to the climatological bias of the FREE experiment. The model bias is computed relative to NSIDC NASA Team satellite SIC observations. Figure 1 shows seasonal climatologies of the SPEAR FREE SIC model bias and ∆SIC between 1982-2017, for both the Arctic and Antarctic. Here we notice that the free-running model is, on average, positively biased in both hemispheres, with larger magnitude biases in the Antarctic. Crucially, we find largely consistent patterns between the model bias and ∆SIC. In the Arctic for example, the large positive biases in the Greenland, Iceland, Norwegian (GIN) and Barents seas (east Atlantic) are mirrored by overall negative increments, hence the DA is acting to remove sea ice in this region. The winter Arctic SIC biases appear to be related to systematic biases in the sea ice edge position, which is apparent when noticing that the increments in the fully covered ice pack (north of the 75% observed SIC contour) are relatively small compared to the marginal ice zones in DJF and MAM. The presence of larger increments in the central ice pack in JJA and SON are then likely a reflection of local SIC errors in the ice-covered zone in addition to ice edge position errors. The only notable discrepancy between model bias and ∆SIC in the Arctic appears to be in the Kara and Laptev shelf seas in JJA, where both the model bias and increments are positive. This suggests that the assimilation fore- casts are negatively biased in this region, which may be related to a residual overshooting problem in the DA experiment, as highlighted in the original SPEAR sea ice DA study by Y. Zhang et al. (2021).
Turning to the Antarctic, despite largely positive biases across all seasons, negative biases dominate many of the coastal regions in the austral summer (DJF), including the Weddell Sea, whereby many of these biases become lower in magnitude or even positive by austral winter (JJA). Interestingly, the isolated negative bias towards the north- 7 t h D e c 1 2 t h D e c 1 7 t h D e c 2 2 n d D e c 2 7 t h J a n 1 s t J a n 6 t h J a n 1 1 t h J a n 1 6 t h J a n 2 1 s t J a n 2 6 t h J a n 3 eastern edge of the Ross Sea is a persistent feature from MAM through to SON, reaching its largest magnitude in SON. This may be related to strong deep ocean convection in this region (Adcroft et al., 2019), which manifests as positively biased sea-surface temperatures which are co-located with the negatively biased SIC zone (see Figure S1 in Supporting Information S1). Overall, the strong spatial and seasonal agreement between the free-running model bias and ∆SIC supports this study's plan to use DA increments to learn a parameterization of sea ice model error.
1 s t F e b 5 t h F e b 1 0 t h F e b 1 5 t h F e b 2 0 t h F e b 2 5 t h M
Visualising the time evolution of the sea ice DA forecasts ( Figure 2) shows the relationship between systematic biases and analysis increments more clearly. In the GIN Sea (Figure 2a), we can see that the model forecasts in each DA cycle (black dots) are drifting towards the positively-biased free-running model state (dark blue dots) over the 5-day forecast period, and as such the analysis increments (dashed black lines) are systematically negative to account for this. Similarly, in the Weddell Sea ( Figure 2b) the forecasts are drifting towards the negatively-biased free-running model state, resulting in systematically positive increments. The forecast drift that is observed in either case can be quantified by the assimilation forecast tendencies, which for a given assimilation cycle i, corresponds to the time-derivative of the forecast c at time t, or more simplyċ
i (t) = c i (t) − c i (t − 1).
The total forecast tendency for a given assimilation cycle is then the sum of the individual daily tendencies:ċ i (1) +ċ i (2) + ... +ċ i (5). Klinker and Sardeshmukh (1992) showed that the mean total tendencies across a large number of assimilation cycles, referred to as the systematic forecast tendency, is approximately equal to the negative of the analysis increments, which is also the case in our SPEAR DA experiments (see Figure S2). Building on this, Rodwell and Palmer (2007) then later described how the forecast tendencies can be broken down into tendencies associated with the model's representation of various resolved and parameterized physical processes, and subsequently used them to make assessments of model physics errors after a model change had been made. In our study here, we utilize this inherent link between forecast tendencies and analysis increments to construct CNNs which use inputs of both state variables from the DA forecasts, as well as their associated forecast tendencies, in order to predict ∆SICN.
Convolutional neural networks
CNNs are a specific class of DL algorithms which are well-suited to problems where inputs contain local correlation structure in space and/or time (K. Murphy, 2022). For this reason they have historically been successful in the domains of image recognition and segmentation (Simonyan & Zisserman, 2014;Zeiler & Fergus, 2014;Dong et al., 2015;Ronneberger et al., 2015;Krizhevsky et al., 2017), where the aim is to e.g., classify objects or isolate features within medical images. In Earth system modeling CNNs have subsequently been utilized for their ability to exploit the two-dimensional structure associated with turbulent fluids, and hence learn subgrid parameterizations of ocean mesoscale (Bolton & Zanna, 2019;Zanna & Bolton, 2020) and cloud moisture convection (Han et al., 2020). For this reason, we use them here to learn sea ice model errors, which also inherently exhibit two-dimensional structure.
Architecture
Generally speaking, a CNN can be seen as a series of linear weighted sums in which a rectangular weight matrix, or kernel, slides over an input image in order to produce a new feature representation of that same input. By sequentially repeating this procedure on each new feature map, and adding nonlinear activation functions between network layers, the network is then able to extract increasingly complex behaviour from the inputs, before a final operation which maps the last set of features to each pixel of the output image. Figure 3 shows this procedure in the present context of learning 'images' of sea ice DA increments. In this case we develop two independent CNNs, where each can be classified as a 'fully CNN' as the outputs of each layer are produced only by convolution operations. Network A is used to learn the aggregate (∆SIC) increments from various atmosphere, ocean and sea ice model states and forecast tendencies, while network B uses the predictions of ∆SIC from network A in order to learn a mapping from ∆SIC to ∆SICN. We find this two-step approach yields significantly lower prediction error than using a single network to predict ∆SICN directly. Table 1 summarizes the architectural choices made for Networks A and B.
Each of the inputs of a given CNN have independent kernels that connect to every feature map in the subsequent layer of the network, hence with 3×3 kernels in each layer, 17 input variables, and features per layer of 32, 64, 128, and 1, network A has a total number of weights given by (3×3×17×32)+(3×3×32×64)+(3×3×64×128)+ (3 × 3 × 128 × 1) = 98, 208. Meanwhile, with 1×1 kernels in each layer, 12 input variables, and features per layer of 32, 64, 128, and 5, network B has a total number of weights given by (1 × 1 × 12 × 32) + (1 × 1 × 32 × 64) + (1 × 1 × 64 × 128) + (1 × 1 × 128 × 5) = 11, 264. An advantage of the CNN approach is that a single kernel matrix is used for the entire spatial domain of a given input, meaning that structures which exhibit similar characteristics, but occur at different locations within the input, will be equally resolved. This property of translational invariance is not guaranteed in e.g., typical feedforward (artificial) neural networks which use the whole domain at once as input (Gardner & Dorling, 1998). Non-linearities within the system can also be exploited by passing each feature map through a non-linear activation function, such as the rectified linear unit (ReLU) function, which is the identity function for positive values and zero for negative values. In both networks in our application, the first three convolution operations are followed by ReLU activation functions, while the final convolution to the output layer is simply linear.
The inputs to network A correspond to the 5-day means of the model states and 5-day forecast tendencies from each DA cycle, for each of SIC, sea-surface temperature (SST), zonal and meridional components of ice velocities (SIU and SIV, respectively), sea ice thickness (SIT), net shortwave radiation (SW), ice-surface skin temperature (TS), sea-surface salinity (SSS), and finally a land-sea mask containing zeros over land grid cells and ones over ocean grid cells. Note that SIU and SIV are vector fields with values located at C-grid cell edges, while the other scalar fields have values centered within each grid cell (see e.g., Griffies et al. (2004)). This means that SIU and SIV contain one additional matrix column and row, respectively, compared to the scalar fields. We therefore compute a 2-point average along the columns of SIU and rows of SIV, so that the these variables are defined on the same tracer grid as the scalar fields. The inputs to network B correspond to the ∆SIC predictions from network A, along with the model states and forecast tendencies of SICN, as well as a land-sea mask. It should also be noted that the inputs of each network (excluding the land-sea mask) are standardized by subtracting their respective mean and normalizing by their respective standard deviation, where both mean and standard deviations are computed over ocean grid cells poleward of 40 • latitude, across all training samples (see section 4.2). This provides a single value of the mean and standard deviation for each network input. Furthermore, given that, in our network architecture, each convolution operation in network A reduces the size of the input image by 2 pixels in both matrix dimensions, the final outputs are 8 pixels smaller than the original inputs (hence a 9×9 centered stencil is required to make a local prediction at any grid point). To ensure we utilize the appropriate information at the image boundaries, we therefore pad the input data by 4 pixels on each side in the following way: the last 4 columns of the image are padded in front of the first column (zonal periodicity), the original first 4 columns are padded to the last column (zonal periodicity), a copy of the first 4 rows is flipped 180 • counter-clockwise and padded in front of the first row (symmetry across the model's Arctic bipolar fold, see Griffies et al. (2004); the sign of the ice velocities in the first 4 rows is also flipped during this process), and finally the last row is padded with 4 rows of zeros (the final row corresponds to the Antarctic continental land mass).
Training
In order to generate accurate predictions, the weights of each CNN must be optimized. This is typically achieved by minimizing an appropriate loss function L which describes the similarity between the final outputs of the network and the target variable (i.e., the analysis increments). For network A the loss function (L A ) is the mean-squared error (MSE) of the ∆SIC predictions, while for network B the loss function (L B ) is the sum of the MSE of each of the five ∆SICNs, as well as an additional term to impose a soft constraint that the sum of the five ∆SICNs are equal to ∆SIC:
L A = 1 N S N S i=1 ∆SIC CNN i − ∆SIC True i 2 ,(1)L B = 5 k=1 1 N S N S i=1 ∆SICN CNN ki − ∆SICN True ki 2 + λ 1 N S N S i=1 5 k=1 ∆SICN CNN ki − 5 k=1 ∆SICN True ki 2 .
(2)
Here, N = 320 × 360 = 115, 200 is the number of model grid points, which corresponds to the entire globe. S = 10 is the batch size (randomly shuffled temporal samples), and λ = 5 is a scaling constant. The loss function is minimized using the Adam stochastic gradient descent method (Kingma & Ba, 2014) within the PyTorch Python library (Paszke et al., 2019), which accommodates graphical processing unit (GPU) and batch processing facilities for significant computational speed-ups and efficient memory handling, respectively. Recall Table 1 for a full list of the details of each CNN.
As well as optimizing the weights of each CNN, there are other factors which influence the predictive performance that also need to be considered. For one, there is the physical architecture of each CNN, which includes e.g., the number of layers within each network, the type of activation function, and the size of the convolution kernels. Then there are also specific hyperparameters, which include e.g., the learning rate of the Adam optimizer, and the number of training epochs. Choosing the optimal architectures and hyperparameters is referred to as model selection and is generally approached by selecting the model which produces the lowest error score on unseen validation data (i.e., data that were not used to optimize the CNN weights). In order to ensure that the validation error is representative of the model's predictive performance across all samples it is often necessary to perform K-fold cross-validation, where the data are split into K equalsized temporally contiguous chunks. The model is then trained on K − 1 chunks, and predictions are validated on the remaining chunk. We opt for temporally contiguous chunks here, as opposed to random sampling of training and validation points, due to inherent temporal auto-correlation within the data, which would likely lead to data leakage issues during the validation stage. In any case, this process is repeated K number of times where each time a different chunk is chosen to be the validation set. The average validation error across all K tests is then the generalization error of that particular CNN model. To arrive at the final CNN architectures and hyperparameters detailed in Table 1, we performed 5-fold cross-validation at each model selection step, hence for a given architecture and set of hyperparameters the model was trained 5 times, where each time the 2618 temporal samples were split into different combinations of 2094 training and 524 validation points. Specific architectures and hyperparameters were subsequently chosen based on the model which showed the lowest average 5-fold cross-validation score. Ideally, one would perform model selection by scanning all possible combinations of hyperparameters and CNN architectures and finding which combination produces the lowest cross-validation score. For large data sets however, this is computationally impractical and as such we proceeded with model selection by testing one hyperparameter and/or architecture at a time and taking the model with the lowest 5-fold cross-validation score forward to the next test (see Figure S3 for example learning curves from various model selection tests). The results in the next section are based on predictions on validation data from the final CNN models, as described in Table 1. Note that, for convenience, hereafter we refer to networks A and B together as our final network architecture.
Results
Before presenting the results of the CNN predictions, we first introduce the error metrics which are used to evaluate the model's performance. For a given spatial map of the SIC increments on any given day, ∆SIC True , and the equivalent CNN prediction on the same day, ∆SIC CNN , the regional uncentered spatial pattern correlation (Barnett & Schlesinger, 1987) between these two fields is given as:
ρ = n i=1 ∆SIC CNN i ∆SIC True i ∆SIC CNN 2 ∆SIC True 2 ,(3)
where · 2 is the 2 vector norm, and n = 100×360 = 36, 000 for either pan-Arctic or pan-Antarctic regions (approx. 45 • N and 30 • S, respectively). We opt for this metric over the standard (centered) linear correlation coefficient as the subtraction of the mean to compute the covariance in the centered case may result in differences between ∆SIC True and ∆SIC CNN at open-ocean grid cells (e.g., Legates and Davis (1997)). Similar to the centered pattern correlation, an uncentered pattern correlation value of 1 represents a perfect agreement between the true and predicted increments on day t, while a value of −1 represents a perfect out-of-phase agreement. A value of 0 subsequently represents no agreement.
We also introduce the regional root-MSE (RMSE) as:
RMSE = 1 n n i=1 ∆SIC CNN i − ∆SIC True i 2 .(4)
This metric captures the average deviation of the predictions from the true increments, hence an RMSE value of 0 represents perfect predictions.
Predictions
In this section we show the predictions of ∆SIC as the sum of the five predicted ∆SICNs, on the held-out data that were not used to optimize the network weights during training. We therefore generate 2618 predictions spanning the 1982-2017 period, which correspond to combining the 5 individual held-out chunks from the cross-validation experiment of the final model, into a continuous time series record. We focus on ∆SIC here, as opposed to ∆SICN, as the former is the direct observable quantity and as such lends to more intuitive interpretation of the results, although the reader is referred to Figures S4-S8 for comparable versions of Figure 4 for each ∆SICN. Figure 4 shows the seasonal climatologies of the ∆SIC predictions, where we notice that, in both hemispheres, the CNN is able to predict the average spatial pattern of the increments very well. In the Arctic, the network performs best in DJF, with average daily spatial pattern correlations of 0.73, and a spatial pattern correlation of 0.98 between the climatologies of the daily DJF predicted and true increments. The poorest predictions in the Arctic are in JJA and SON with average daily spatial pattern correlations of 0.64 and 0.62, respectively, and correlations of 0.96 and 0.98, respectively between the climatologies. In JJA for example, while the network reproduces the average spatial pattern well, the magnitude of the increments to the north of Greenland and in the Canada basin is generally too low. Similarly, in the Antarctic, the CNN also performs best in DJF with average daily spatial pattern correlations of 0.80, however the average magnitude of the predicted increments is generally too low in regions such as the Weddell Sea. The poorest predictions in the Antarctic are in MAM with average daily spatial pattern correlations of 0.64, perhaps owing to the network's inability to fully resolve the relatively small-scale heterogeneities in e.g., the Ross and Weddell seas. The largescale patterns are generally in good accordance however. These initial results suggest that the network is able to learn the mean bias patterns of the model with considerable skill. Moving beyond assessments of climatologies, Figure 5 shows randomly sampled snapshots of the predictions for individual days across each season, as a way to assess how the CNN performs at capturing the fast physics errors (for an animation of the CNN performance on additional daily snapshots, see Supporting Information S2). Broadly speaking, we find that the CNN is able to capture the large-scale structure of the increments, but often fails to capture smaller-scale features. The February prediction in the Arctic (Figure 5e) shows high skill with a spatial pattern correlation of 0.74, however at this time of year the increments are primarily associated with sea ice edge errors, while the increments in the central ice pack (i.e., the majority of the Arctic domain) are effectively zero. Nonetheless, the CNN is able to predict these ice edge errors very well, particularly in the Labrador, GIN, Barents, Okhotsk, and Bering seas. As the melt season progresses, the prediction skill generally drops, where it is lowest in September (Figure 5h), with a spatial pattern correlation of 0.43. The true July and September increments (Figures 5c and 5d, respectively) exhibit significant variability within the core ice pack which, in some regions, the network is unable to reproduce. For example, the large negative increments in the Beaufort and Chukchi seas in July. The CNN does however manage to capture some amount of the variability in July, such as the large positive increments in the Kara and Laptev shelf seas.
The prediction skill in the Antarctic is generally higher than in the Arctic, and comparing Figures 5i and 5m, we can see that the CNN accurately predicts a significant amount of the variability in summer, with a spatial pattern correlation of 0.84. The subsequent predictions in April, July and November (Figures 5n-p) show slightly lower skill than in January, with the lowest skill in April with a spatial pattern correlation of 0.62. At these times the increments are largely related to sea ice edge errors, and the CNN is generally able to capture the large-scale patterns, as well as some of the localized features, such as the positive increments at the north-eastern edge of the Ross Sea in November (Figure 5p), and the band of positive increments along the northern edge of the Weddell Sea in April (Figure 5n).
From the daily snapshots we can infer that the CNN captures large amounts of the fast physics errors, although there is some seasonal variation to the skill, where the predictions in the Arctic are generally best over the winter period and poorest in the summer. Meanwhile in the Antarctic the predictions appear most skillful in the summer and poorest in the early growth season (April). In the next section we provide an assessment of the CNN's sensitivity to various inputs, as well as its sensitivity to the geographic training domain. In doing so, we subsequently highlight this seasonal skill variation in more detail.
Sensitivity analysis
Network inputs
In this section we perform sensitivity tests to determine which model states and forecast tendencies contribute most to the prediction skill of ∆SIC (again, as the sum of the five predicted ∆SICNs on held-out samples), at different times of the year. The sensitivity analysis is performed by training a series of initial networks which each con-tain a single variable as inputs (e.g., SIC states and forecast tendencies), and assessing which of these networks results in the highest prediction skill of ∆SIC in both hemispheres. The input variable of this network is then assumed to be the most physically-relevant predictor of ∆SIC. The testing then continues by training a second series of networks which contain two input variables: the best predictor from the first test, as well as any one of the remaining input variables. The network which results in the largest improvement in skill relative to the best network from the first test is then taken forward, and so on. For 7 network input variables (classifying SIU and SIV as a single input), we therefore trained 28 independent network configurations in order to establish a hierarchy of predictors. Figure 6 shows daily 36-year climatologies of spatial pattern correlation and RMSE error metrics, for sensitivity tests in both the Arctic and Antarctic domains. The hierarchy of predictors in terms of largest skill contribution proceeds as: SIC, SST, SIU and SIV, SIT, SW, TS, and finally SSS. Hence for the SIC curves, the network inputs to generate these predictions are only SIC states and forecast tendencies, while for the SST curves, the network inputs are SIC and SST states and forecast tendencies, and so on. The SSS curve then represents the predictions from the final model (i.e., the network architecture presented in section 4.1). The climatology prediction (black dashed curve) refers to using the daily 36-year climatology of the true ∆SIC increments to predict the true ∆SIC increment on any given day. This is an offline-equivalent to the 'ocean tendency adjustment' approach by Lu et al. (2020), as discussed in section 1, and as such serves as our benchmark here, where we can see that each sensitivity test provides improvement in skill over this climatological tendency benchmark. From this analysis we can also see that, relative to the benchmark climatology, SIC is responsible for a significant fraction of the overall network skill (approx. 66% in both hemispheres). SST, SIU and SIV then account for an additional 20%, with the remaining variables SIT, SW, TS and SSS making up the last 14%. Furthermore, while SIC, SST, SIU and SIV are essential inputs in all months of the year, the contributions from other variables such as SW and TS are generally limited to the summer months.
In terms of spatial pattern correlation, the maximum skill of the final network in the Arctic occurs at the beginning of March, after which the skill declines somewhat continuously until the end of July, and then more rapidly to its minimum in early September. Meanwhile in the Antarctic, the points of maximum and minimum skill are separated by approximately 1.5 months, with the maximum occurring at the end of January, and the minimum at the beginning of March. Although the skill variation in the Arctic appears to somewhat correlate with the climatological sea ice area, the rate of change in sea ice area in the melt and growth season is generally not consistent with that of the CNN prediction skill. Furthermore, in the Antarctic the skill is increasing between November and January, while the sea ice area is decreasing. This therefore suggests that the skill variation is not directly tied to the seasonal cycle of sea ice area. When also considering the standard deviation of the increments, we can see that the low spatial pattern correlation scores coincide with times when the standard deviation of the increments, and hence the RMSE, are relatively low. This may initially suggest that the lower spatial pattern correlation at these times is either a consequence of low signal variance, or that the network training does little to optimize these points as they inherently have lower MSE than e.g., the winter months. If however the spatial pattern correlation scores were a direct reflection of the increment standard deviation, we would expect to see similarly low spatial pattern correlations in e.g., April in the Arctic or November in the Antarctic, however this is not generally the case. What is noticeable, is that the climatology benchmark also exhibits the same seasonal variation in spatial pattern correlation and RMSE as the CNN predictions, highlighting that the lower skill in the late summer in both hemispheres is not likely due to any shortcomings in the ML model, but rather a feature of the increments themselves. In particular, the climatological prediction is less skillful in the low-CNN-skill months, suggesting that these months are inherently more challenging to predict.
Training domain
The network in this study is trained on data from the entire globe, meaning that it must find the optimal set of weights which generalize to make accurate predictions of the analysis increments in both the Arctic and the Antarctic. Given that the bias patterns, and hence characteristics of the increments, are somewhat different between the two hemispheres, we conduct further sensitivity tests to determine how well the network has generalized. As before, error metrics are shown in terms of the sum of the five predicted ∆SICNs on held-out samples that were not used to train the model. Figure 7 shows daily climatologies of spatial pattern correlation and RMSE error metrics, for three variations of the network training setup. One where the network is trained on the entire globe (i.e., our proposed network in section 4.1), one where the network is trained on just the Arctic domain, and one where the network is trained on just the Antarctic domain. Here we notice that the network which is trained on global data is able to make just as skillful predictions of ∆SIC in the Arctic, as the network which is trained only on Arctic data. The same is also true for the Antarctic case. Interestingly, we can also see that the network which is trained only on the Arctic are still able to make relatively skillful predictions of the Antarctic increments, even performing better than the benchmark climatology predictions between the months of December and February. Meanwhile, the network which is trained on Antarctic data is not able to generalize as well to the Arctic, although still shows some small amount of skill between July and August. This analysis therefore confirms that training on global data is vital for generalizing across domains while still matching the skill of networks trained on each individual domain.
Final validation
Due to the fact that we perform model selection by choosing specific CNN architectures and hyperparameters which minimize the average cross-validation score on data that were not used to optimize the CNN weights, there is an inherent risk of over-fitting the model to these validation data. As such, it is often necessary to retain an additional data set which has not been used for validation at any point during the model selection process. For this, we extend the Y. Zhang et al. (2021) sea ice DA experiment from December 27 th 2017, through to December 27 th 2021, providing an additional 291 validation data points. We subsequently evaluate the performance of our CNN model by training on all 2618 samples between 1982-2017, and validating on the extended data period between 2018-2021. It should be noted that this extended DA experiment is identical in configuration to that which was outlined in section 2.2, except that in this extended case the atmospheric forcing from JRA55-do reanalysis corresponds to version 1.5, while previously it was version 1.3. This version change relates to a correction in the sign and rotation of tropical cyclones, and as such we do not expect this to result in significant differences in the representation of sea ice in the extended DA simulations. Figure 8 shows daily spatial pattern correlation and RMSE error metrics over the 2018-2021 period for both the Arctic and Antarctic domains (black curves). We also overlay the daily climatology skill of the final network architecture from the cross-validation experiments between 1982-2017, hence the blue curves here are identical to the 'Train global' curves in Figure 7, and are simply repeated for each of the 4 validation years presented. The predictions appear to generalize well to the future data, where spatial pattern correlation values are generally in accordance with the 1982-2017 period, particularly in the Antarctic, and are still out-performing the climatology prediction in both hemispheres. On average, the RMSE over the 2018-2021 period is slightly higher than the 1982-2017 climatology, which is due to the fact that there is a non-stationary com-ponent to the increments, whereby the variance increases over the course of the time series record (see Figure S9). Therefore naturally the climatological RMSE of the CNN predictions increases over time as well (see Figure S10). In any case, the generalization ability of the predictions suggests that the CNN has not simply over-fitted to the training and/or validation data during model selection.
Discussion
The ability of the proposed CNN to make skillful predictions of the sea ice concentration analysis increments, using only information on local model state variables and their tendencies, provides interesting avenues for future work. The fact that the predictions show improvements in skill relative to a daily increment climatology (e.g., Lu et al. (2020)), generalize well to each hemisphere, and show skill on a separate validation data set, strongly suggests that the CNN could be used to reduce sea ice biases within SPEAR, either as an online sea ice model parameterization, or as a bias correction tool for numerical sea ice prediction. Ultimately, one could argue that there is still room for improvement in the CNN performance, particularly in the late summer months. Considering the inherent complexity of the problem at hand, and the likely influence of both non-linear and non-local processes, it is conceivable to push the limit of predictive skill further by increasing the complexity of the network, both in terms of the total number of weights, and the 9×9 grid cell domain of influence on a local prediction. Indeed, such changes could be implemented through increasing the width and/or depth of the network, as well as incorporating non-local connections (in space) through e.g., fully-connected layers. On the other hand, the architectures here been developed specifically with the goal of a sea ice model parameterization in mind, and as such, factors including computational cost and practicality of implementation in parallelized high-performance computing environments have been considered throughout the development. In the following sections we provide a discussion on the directions for future work relating to both sea ice parameterization and seasonal sea ice prediction.
Considerations for parameterization
ML models have been shown to be successful at parameterizing subgrid-scale processes within dynamical models, including ocean mesoscale eddies (Guillaumin & Zanna, 2021), atmospheric convection (Yuval & O'Gorman, 2020), and sea ice dynamics (Finn et al., 2023). Common to each of these studies is that the ML models target specific physical processes, with the aim of replacing pre-existing knowledge-based parameterizations, or deriving new parameterizations for physical processes which are not currently represented. On the other hand, our proposed CNN is trained to predict sea ice increments which reflect numerous interacting model errors across various model components. To subsequently disentangle these coupled model physics errors a-posteriori and then apply them as parameterizations to their respective components, is not straightforward. In our goal of constructing a sea ice model parameterization, it is critical to ensure that the parameterization is not acting to correct coupled model errors that originate in other model components (e.g., an ocean heat transport bias or atmospheric circulation bias that imprints upon the sea ice). Our DA-ML methodology attempts to mitigate this possibility, as the ice-ocean DA system is driven by atmospheric reanalysis and also nudges SST and SSS towards observed values. These observational constraints on the atmosphere and ocean allow us to interpret the DA increments as isolated sea ice model physics errors, however this assumption is not perfect as the ocean component of the DA system can still imprint some errors on the sea ice state (e.g., Figure S1). Future investigation will be required to determine how the CNN generalizes in a fully coupled setting with fully-interactive atmosphere-ice-ocean feedbacks (see section 6.2).
Another major consideration for a sea ice parameterization is how to appropriately conserve mass, heat, and salt. In the context of the ocean, Lu et al. (2020) achieved global conservation of heat and salinity when implementing the climatological ocean DA increments into MOM6 by ensuring that the global integral of the correction to each variable was zero. In the case of sea ice, assuming the parameterization enters the thermodynamic solver, then appropriately coupling this parameterization with the upper ocean would mean that a predicted negative sea ice concentration increment would remove sea ice (columnwise) by adding mass and salt to the ocean mixed layer, while also removing heat. This step is likely to come in the form of a mass, heat, and salt budget assessment between the ice and ocean after evaluating the amount of local sea ice mass change associated with a given predicted SIC increment, rather than adapting the CNN architectures themselves to respect conservation.
Although we have considered implementation cost in the design of our network, some investigation will be required to quantify this cost in terms of both matrix computations and additional memory load. Regarding memory load, our parameterization will not require any additional memory in terms of the number of grid cells stored on any one central processing unit (CPU), as our 9×9 network stencil requires the same number of 'halo' grid points as the default SPEAR configuration, which uses a halo size of 4. There will be some small amount of memory cost for storing the network weights on each CPU however. Looking to similar studies, Guillaumin and Zanna (2021) found that implementing a fully CNN with 8 convolutional layers as a stochastic parameterization into an idealized shallow water model resulted in a 25% increase in the run time, compared to an unparameterized simulation. C. Zhang et al. (2023) also found that the cost of doing inference with this same network as a parameterization in MOM6 was 10 times more expensive than the CPU cost of the simulation itself. Although we effectively have 8 convolutional layers when considering both networks A and B, we can still expect much lower computational overheads given that ours is a deterministic model (i.e., we predict a single output at each grid point for each ∆SICN, rather a, potentially larger, number of parameters which describe a distribution of values), and that our kernel size for network B is 1×1 in each layer, while the Guillaumin and Zanna (2021) network uses variable size kernels throughout, ranging from sizes 3×3 to 5×5. Like in this study, they also did not use zero-padding, though in their case given the larger kernel sizes, they required a stencil of 21×21 grid points to make a local prediction.
Finally, the increments in this study represent error growth over a 5-day period, and the input states and tendencies of the CNN are given as 5-day means. After implementation, the CNN predictions will need to produce a correction which reflects error growth over a given model timestep, and similarly the input states and tendencies will need to be adjusted accordingly. This will therefore require further sensitivity tests to determine how to appropriately perform this scaling.
Considerations for sea ice forecasting
Some of the initial concerns over implementation of the CNN as a sea ice model parameterization can be alleviated by assessing how the network performs as an online bias correction tool within the context of seasonal sea ice forecasting. In previous work, Y. showcased the benefits of using SIC assimilation to initialize the sea ice conditions for SPEAR retrospective forecasts (hereafter reforecasts) of the Arctic sea ice cover between 1992-2017. In Y. , the same ice-ocean SPEAR model configuration and initial conditions as outlined here in section 2.2, were used to perform DA between 1982 and the first day of each month, for all years between 1992 and 2017. Whereby the first day of each month represented the initialization point, after which the model would run in fully coupled mode to generate forecasts out to 1-year lead time. Assimilation in Y. Zhang et al. (2021 was performed by passing the prior model state variables and observations to the Data Assimilation Research Testbed (DART; Anderson et al. (2009)), which then computes the set of analysis states offline, providing the new set of initial conditions with which to begin the next assimilation cycle. Given that our CNN is inherently independent of the observations, we propose that it would be relatively straightforward to bias correct the sea ice within the fully coupled reforecast period by replacing the standard call to DART with our CNN. In this scenario, we could perform seasonal reforecasts (up to 12-month lead times) to assess how the network generalizes to the fully coupled SPEAR model, while not requiring strict conservation properties due to the shorter time scales. Furthermore, we could continue in the same 5-day cycle configuration so that the network predictions would not need to be scaled for different temporal sampling. If the reforecasts then have improved skill relative to the SPEAR DA-initialized reforecasts from Y. , they may be fit-forpurpose as a model parameterization.
7 Concluding remarks 7.1 Summary In this study we have shown that deep learning (DL), specifically convolutional neural networks (CNNs), can be used to make skillful predictions of sea ice model errors, in the form of data assimilation (DA) increments, using only information from model state variables and tendencies (the time derivative of the model state variables). We developed a CNN using an ice-ocean DA system which assimilates satellite observations of sea ice concentration (SIC) into the Seamless system for Prediction and EArth system Research (SPEAR) model every 5 days between 1982-2017. SPEAR has a 5-category ice thickness distribution, hence concentration increments are produced for each subgrid category, where the observable (aggregate) SIC increment corresponds to the sum of 5 categories. We therefore developed a two-step CNN architecture, in which the first step learns the physical mapping from various local sea ice, ocean and atmosphere state variables and forecast tendencies to the aggregate SIC increments. The second step then learns the mapping from the aggregate concentration error to each of the subgrid terms. We subsequently showed that our DL architecture is able to make skillful predictions of the SIC increments in both the Arctic and the Antarctic and across all seasons. Spatial pattern correlations between the climatologies of the observed and predicted increments are high, with values of at least 0.96 for both the Arctic and Antarctic, demonstrating that the CNN is able to skillfully capture the mean model bias. The CNN also has skill at predicting the state-dependent model errors, with daily pattern correlation values ranging from 0.64-0.80 and 0.62-0.73 in the Antarctic and Arctic, respectively. This shows that the CNN is able to predict the fast physics errors and systematic bias patterns of the SPEAR model with considerable skill, which is also confirmed by the fact that the predictions show improved skill over a model which simply predicts the climatological mean increment on any given day of the year. Sensitivity analysis revealed that SIC as an input to the network is responsible for approximately 66% of the overall network skill, followed by sea-surface temperature (SST) and ice velocities which account for 20%, and finally ice thickness, net shortwave radiation, ice-surface skin temperature and sea-surface salinity which account for the remaining 14%.
Outlook
Recent studies have highlighted how DA provides a unique opportunity to leverage sparse and/or noisy observations, in order to facilitate machine learning of structural model errors Brajard et al., 2021;Farchi et al., 2021;Mojgani et al., 2022;Chen et al., 2022). Building on this, we have shown here how DA also provides the ability to learn errors within unobserved model state variables, and hence provides a new framework for learning subgrid-scale parameterizations for climate models. In section 6 we subsequently outlined how the strong predictive performance of the CNN and its generalization ability suggests that the network has the potential to reduce sea ice biases in free-running climate simulations, as a sea ice model parameterization within SPEAR. Irrespective of this eventual goal however, the findings in this work ultimately have wider implications for the climate modeling and numerical weather prediction (NWP) community in general. With regards to NWP, previous studies have already shown that ML techniques can be used to learn state-dependent fast physics errors within large-scale atmospheric models, subsequently leading to improved online predictions by using the ML model as a bias correction tool Chen et al., 2022). In our study, we have shown that the concept of learning state-dependent fast physics errors is transferable to a global ice-ocean model, which could further aid NWP when considering that coupling the atmosphere with an ice-ocean model has previously shown to improve short-term weather predictions (G. Smith et al., 2018).
Turning to longer-term simulations, the fact that the systematic errors are also predictable suggests that a parameterization built from DA increments has the potential to reduce persistent climate model biases and improve the fidelity of climate change projections. On the other hand, while we have shown that state variables such as SIC and SST explain a significant fraction of the variance in the analysis increments, our current framework does not allow us to attribute these correlations to a specific model deficiency, for example an incorrectly parameterized or missing physical process. One additional avenue for future work could therefore involve designing a perfect model experiment in which a single ensemble member is run with a specific parameterization that has been tuned or turned on (e.g., sea ice ridging or melt-pond formation). This member would then be treated as the ground truth and assimilated into the original model. The resultant analysis increments would then be a manifestation of the systematic bias within the original model, associated with this specific incorrect/missing parameterization, and hence one could more confidently isolate which state variables within an ML model contribute most to predicting this particular structural error.
Open Research
All data for training each CNN are openly available at the following locations: Python code to pre-process the input data and train the CNNs can also be found at https:// github.com/m2lines/seaice DA-ML. The optimized weights of the CNNs and standardization statistics for the inputs are also saved within the same repository.
Supporting Information S1: Deep learning of systematic sea ice model errors from data assimilation increments are the spatial pattern correlations between the respective climatologies of the true and predicted increments. are the spatial pattern correlations between the respective climatologies of the true and predicted increments. are the spatial pattern correlations between the respective climatologies of the true and predicted increments. are the spatial pattern correlations between the respective climatologies of the true and predicted increments. Antarctic 1982-1989 1989-1996 1996-2003 2003-2010 2010-2017
Figure 1 .
1Seasonal climatologies of SPEAR free-running model bias (model minus observations) and sea ice concentration analysis increments, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Dashed and solid contours denote the observed climatology marginal ice zone boundaries over the same period (15 and 75% SIC contours, respectively). Yellow markers in (a) and (i) are example grid-point locations used for analysis in Figure 2.
Figure 2 .
2SPEAR sea ice concentration data assimilation example, shown for one grid cell as daily climatologies. Examples are presented for the Arctic (a) and Antarctic(b) through the period December-February. The grid cells for both the Arctic and Antarctic examples correspond to locations in the GIN Sea and Weddell Sea, respectively (see the yellow markers inFigures 1a and 1i).
Figure 3 .
3Schematic of the CNN architectures used to learn functional mappings from state vectors to analysis increments. The yellow and purple squares represent 3×3 and 1×1 kernels over which the convolution operations are performed in each layer, respectively, where there is one kernel for every feature map in each layer. The white pixel is then the sum of convolution outputs from all features in the previous layer, which has subsequently been passed through a ReLU activation function. The activation function after the last convolution operation to the output layer is the identity function.
Figure 4 .
4Seasonal climatologies of the (true) SPEAR aggregate sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SIC True and ∆SIC CNN in each respective season, while values with [2] are the spatial pattern correlations between the respective climatologies of the true and predicted increments.
Figure 5 .
5Daily snapshots of the (true) SPEAR aggregate sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show random days in DJF, MAM, JJA, and SON over the period 1982-2017. Spatial pattern correlations are reported for each prediction.
Figure 6 .
6Prediction skill metrics for independent sensitivity tests to network inputs, presented as daily climatologies of predictions on held-out samples, computed over the period 1982-2017, for the Arctic (left column) and Antarctic (right column). The shaded region reflects the improvement in skill of the final network (solid black curve) over the benchmark climatology prediction (dashed black curve).
Figure 7 .
7Prediction skill metrics for independent sensitivity tests to the network training domain, presented as daily climatologies of predictions on held-out samples, computed over the period 1982-2017, for the Arctic (left column) and Antarctic (right column).
Figure 8 .
8Generalization performance of CNN predictions for the extended period between January 2018 and December 2021. Error metrics for the black curves are shown at the frequency of the data assimilation system (5-daily), while the blue curve is the daily climatology skill of the final network over the 1982-2017 period.
•
Inputs (DA forecast states and tendencies): ftp://sftp.gfdl.noaa.gov/perm/ William.Gregory/seaice DA-ML inputs 1982-2017.nc • Outputs (DA increments): ftp://sftp.gfdl.noaa.gov/perm/William.Gregory/ seaice DA-ML outputs 1982-2017.nc
Figure S1 .Figure S2 .Figure S3 .
S1S2S3Seasonal climatologies of the SPEAR free-running model bias. Inside the climatological sea ice extent contour (black dashed line) are the aggregate sea ice concentration biases (model minus observations). Outside the contour are the sea-surface temperature biases (model minus observations). a) Arctic biases (December-February), b) Antarctic biases (Comparisons of the climatological aggregate sea ice concentration analysis increments (a,c), and the aggregate sea ice concentration forecast tendencies (b,d). The spatial pattern correlation between panels a) and b) is -0.99. Similarly, the spatial pattern correlation between panels c) and d) is also -0.99. SIC, SST, SIU, SIV, SIT, SW, TS, SSS) tendencies (SIC, SST, SIU, SIV, SIT, SW, TS, SSS) states + tendencies (SIC, SST, SIU, SIV, SIT, SW, TS, SSS) Learning curve examples for various CNN model selection tests. Each curve is the mean 5-fold cross-validation error on ∆SIC predictions (solid lines = error on training samples, transparent curves = error on validation samples). (a) Tests of the network sensitivity to the inputs (i.e., using just state variables, or just tendencies, or both). (b) Tests of the network depth (number of convolutional layers). (c) Tests of the network width (features per convolutional layer). (d) Tests of the optimizer learning rate. (e) Tests of the activation function used after each convolution operation. (f) Tests of the size of the convolution kernel used in each layer.
Figure S4 .
S4Seasonal climatologies of the (true) SPEAR category 1 sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SICN True and ∆SICN CNN in each respective season, while values with [2]
Figure S5 .
S5Seasonal climatologies of the (true) SPEAR category 2 sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SICN True and ∆SICN CNN in each respective season, while values with [2]
Figure S6 .
S6Seasonal climatologies of the (true) SPEAR category 3 sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SICN True and ∆SICN CNN in each respective season, while values with [2]
Figure S7 .
S7Seasonal climatologies of the (true) SPEAR category 4 sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SICN True and ∆SICN CNN in each respective season, while values with [2]
Figure S8 .
S8Seasonal climatologies of the (true) SPEAR category 5 sea ice concentration analysis increments and the equivalent CNN predictions, for both the Arctic (a)-(h) and Antarctic (i)-(p). Columns from left to right show DJF, MAM, JJA, SON climatologies, computed over the period 1982-2017. Values with the superscript [1] are the average of daily spatial pattern correlations between ∆SICN True and ∆SICN CNN in each respective season, while values with [2]are the spatial pattern correlations between the respective climatologies of the true and predicted increments.
Figure S9 .
S9The standard deviation of the true aggregate sea ice concentration analysis increments (∆SIC True ), computed over each of the 5 cross-validation periods used for validating the CNN predictions. Shown as daily climatologies.
Table 1 .
1Details of the convolutional neural networks (CNNs) inputs, outputs, architecture, and hyperparameters used during training.Network A
Network B
Inputs (* states & tenden-
cies)
SIC*, SST*, SIU*,
SIV*, SIT*, SW*,
TS*, SSS*, Land-
sea mask
∆SIC CNN , SICN*,
Land-sea mask
Outputs
∆SIC
∆SICN
Size of input data set
2094×17×328×368 2094×12×320×360
Size of output data set
2094 × 1 × 320 × 360 2094 × 5 × 320 × 360
Normalization
Inputs standard-
ized (see main
text)
Inputs standard-
ized (see main
text)
Convolution layers
4
4
Features per layer
32, 64, 128, 1
32, 64, 128, 5
Activation function(s)
ReLU, ReLU,
ReLU, Linear
ReLU, ReLU,
ReLU, Linear
Kernel size(s)
3 × 3
1 × 1
Kernel stride(s)
1
1
Bias parameters
False
False
Zero-padding
None
None
Total weights
98,208
11,264
Batch size
10
10
Optimizer
Adam
Adam
Learning rate
0.001
0.001
Weight decay
1 × 10 −7
1 × 10 −7
Epochs
150
125
Seed
711
711
eddies
William Gregory 1 , Mitchell Bushuk 2 , Alistair Adcroft 1 , Yongfei Zhang 1 , LaureZanna 3 Atmospheric and Oceanic Sciences Program, Princeton University, NJ, USA 2 Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, NJ, USA 3 Courant Institute of Mathematical Sciences, New York University, New York, NY, USA1
Analysis increments (% per day)True
SON
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(e)
CNN
0.27 [1]
0.76 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(f)
CNN
0.25 [1]
0.72 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(g)
CNN
0.25 [1]
0.52 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(h)
CNN
0.2 [1]
0.27 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)True
SON
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(e)
CNN
0.13 [1]
0.5 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(f)
CNN
0.2 [1]
0.53 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(g)
CNN
0.21 [1]
0.27 [2]
−0.4 −0.2
0.0
0.2
0.4
Analysis increments (% per day)
(h)
CNN
0.1 [1]
0.23 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)True
SON
−0.4 −0.2
0.0
0.2
0.4
Analysis increments (% per day)
(e)
CNN
0.19 [1]
0.62 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(f)
CNN
0.27 [1]
0.72 [2]
−0.2 −0.1
0.0
0.1
0.2
Analysis increments (% per day)
(g)
CNN
0.24 [1]
0.35 [2]
−0.50 −0.25 0.00
0.25
0.50
Analysis increments (% per day)
(h)
CNN
0.33 [1]
0.53 [2]
−0.4 −0.2
0.0
0.2
0.4
AcknowledgmentsWilliam Gregory, Mitchell Bushuk, Alistair Adcroft and Laure Zanna received M 2 LInES research funding by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program. This work was also intellectually supported by various other members of the M 2 LInES project, as well as being supported through the provisions of computational resources from the National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Laboratory (GFDL). We also thank Spencer Clark and Zachary Labe for their invaluable feedback on this article.ReferencesAdcroft, A., Anderson, W., Balaji, V., Blanton, C., Bushuk, M., Dufour, C. O., . . .
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| sample_1082 | 0.9392 | arxiv | |
Monitoring the Impact of Wildfires on Tree Species with Deep Learning
Wang Zhou wang.zhou@ibm.com
IBM T.J. Watson Research Center IBM Research Yorktown Heights
IBM T.J. Watson Research Center IBM Research Yorktown Heights
10598, 10598New York, New York
Levente Klein kleinl@us.ibm.com
IBM T.J. Watson Research Center IBM Research Yorktown Heights
IBM T.J. Watson Research Center IBM Research Yorktown Heights
10598, 10598New York, New York
Monitoring the Impact of Wildfires on Tree Species with Deep Learning
One of the impacts of climate change is the difficulty of tree regrowth after wildfires over areas that traditionally were covered by certain tree species. Here a deep learning model is customized to classify land covers from four-band aerial imagery before and after wildfires to study the prolonged consequences of wildfires on tree species. The tree species labels are generated from manually delineated maps for five land cover classes: Conifer, Hardwood, Shrub, ReforestedTree and Barren land. With an accuracy of 92% on the test split, the model is applied to three wildfires on data from 2009 to 2018. The model accurately delineates areas damaged by wildfires, changes in tree species and regrowth in burned areas. The result shows clear evidence of wildfires impacting the local ecosystem and the outlined approach can help monitor reforested areas, observe changes in forest composition and track wildfire impact on tree species.
Introduction
In the last decades the frequency, the intensity and the damage caused by wildfires is increasing in the Pacific Northwest [1]. While wildfires can cause tremendous economic and social losses, one of their prolonged consequences is the resulting change of the vegetation species [2,3,4]. With climate change, the temperature and soil moisture create unfavorable conditions for vegetation regrowth in areas that were devastated by wildfires. The higher temperatures and lesser soil moisture impact the germination of seeds in locations where in the past they could strive. For example, multiple studies [5,6] have demonstrated that rose pines and blue oaks may not regenerate in their traditional locations. The climate change may affect the variety and density of trees in areas affected by wildfires, and thus it is important to systematically monitor the long-term tree species distributions in fire-prone regions.
Classification of tree species is often carried out by forest agencies based on visual inspection of aerial imagery [7]. These kinds of vegetation identification campaigns are sparse in time with irregular updates, which may not be sufficient to register the changes in vegetation caused by wildfires happening almost yearly.
Here we propose a deep learning based classification method to monitor the impact of wildfires on tree species. Large-scale image classification on multispectral images to detect tree species before and after wildfires can quantify the impact of wildfires on vegetation species. We apply the method to three historical wildfire regions in California and the results show clear changes in vegetation. With high resolution images readily available from aerial or satellite observations, tracking tree species across large areas over extended period of time is possible. Monitoring vegetation in near real time can be used by forest services and environmental agencies to better plan for forest management after natural disaster events and quantify ecological disasters. The impact of climate change on vegetation shift in North West USA has been studied since 1990s [6,8]. Droughts, wildfires and pests inflicted noticeable impact on trees health in Sierra Nevada Mountains, California [9]. To quantify the impact of wildfires on tree regeneration, field surveys [2,10,11] are often conducted but limited to only a few sample sites. Hansen et al. [12] plant small plots of trees in areas with significant environmental differences and observe that some of the tree species cannot germinate or survive under changed climate with increased ambient temperature and soil moisture, which suggests that climate change will rearrange certain tree species habitat. However, the controlled planting studies are labor intensive and rely on continuous supervision on the plots, which restricts the scale of such studies.
Quick classification of trees from aerial and satellite imagery can enable large-scale survey of tree species and track climate impact on their survival in their traditional habitats. Convolutional neural networks have been used to identify forests/trees in satellite snapshots [13,14,15], dense time series of imagery [16], and hyperspectral imagery [17]. Tracking tree species before and after wildfires was not pursued in any of the above studies. Additionally Lidar point clouds are classified to recognize tree species [18] or combination of hyperspectral data and Lidar [19], but access to high resolution Lidar scans is not readily available for most of the locations on the globe.
Datasets and Method
Datasets. The National Agricultural Imagery Program (NAIP) collects high resolution aerial imagery in four spectral bands (Red, Green, Blue and Near Infrared) every other year for the last decades [20]. The spatial resolution for the most recent acquisitions is 0.6 m while older images are acquired at 1 m resolution. The imagery is collected in full leaf season, offering a consistent way to compare the vegetation status year to year. In this study, NAIP images from 2009, 2012, 2014, 2016 and 2018 are analyzed. All the data are resampled to the same spatial resolution (0.6 m) as part of the data processing.
Labels. Labeled vegetation data is extracted from manual labels created in 2011 for the Sierra Nevada mountains [7]. Manually delineated polygons contain vegetation classes Conifer, Hardwood, Shrub and urban areas. For the tree covered regions the density of each tree class is specified. The classes were filtered based on the coverage density to identify locations with a specific tree species. Additionally, two more classes were grouped, ReforestedTree, where newly planted trees were sampled to identify the characteristics of reforested regions, and Barren, where all the identified tree classes of [7] were small. Each polygon was then separated in non-overlapping areas of the size of 32 × 32 pixels and signed with the label from the annotated polygons. The associating NAIP data within the identified areas were extracted from PAIRS Geoscope platform [21]. The data were further filtered by eliminating samples which had low Normalized Difference Vegetation Index (NDVI) [22] values and were most likely not encapsulating vegetation information for Conifer and Hardwood [23]. Table 1 lists the number of samples for the curated dataset. In total, 93,849 samples are collected for training, and two sets of 5,000 samples for validation and testing, respectively.
Networks.
A modified version of ResNet34 [25] is used for the classification of tree species. The network was specially changed to accommodate the four-channel input data compared to regular three-channel RGB images. Since the training data is noisy and limited, smoothed labels y LS k [26,27,28] were used to compute a CrossEntropy loss instead of hard one-hot labels y k ,
y LS k = y k (1 − α) + α/K,(1)
where K = 5 is the total number of classes and α is the label smoothing factor, in order to mitigate over-fitting and extreme gradients from wrong labels.
Experiments
Configurations. Our experiment setup is as follows. For training, an SGD optimizer with a momentum of 0.9 and a weight decaying of 0.0005 is used. The learning rate is set to be 0.1 and divided by 10 every 100 epochs, and the model is trained for 300 epochs in total with a mini-batch size of 512. Label smoothing factor α is set to be 0.1. Random horizontal/vertical flipping, rotation and random cropping is applied at training, while for testing no data augmentation is used. For large areas of interest, the data are diced into 32 × 32 pixel tiles, and fed batch by batch to the network for classification at testing. The classification results are then assembled to recreate a classification map. A 3 × 3 majority filter is applied on the classification map to reduce noise. Our implementation is based on Pytorch.
Results. The model is first evaluated on the test split of the curated dataset. The overall classification accuracy is 92.2% on the test data. The model is then applied to three wildfire regions to generate the classification maps in order to study the changes in tree species in those affected regions. Figures 1 and 3 depict the tree species maps across different years, and in Figure 2 the bar plots illustrate the area distributions of each class normalized by the total area. trees, Shrub expanded by almost three times. It is evident from Figure 1 and Figure 2a that frequent wildfires hurt the regrowth of trees, and forest areas may be permanently removed and covered by grass and shrubs, which are more prone to potential fires.
Interestingly, there is a consistent trend of decline of Conifer in this area, which is captured by the decline of area percentage of Conifer in Figure 2a over the years. This may reflect the slow decline of conifer trees at the foothill of Sierra Nevada, as is also observed in [9]. Our approach can serve as a tool to study long-term changes in tree species at large scales. While this study covers only the last decades of forest composition change due to data availability, it reveals some consistent trends that can be observed by the current climate impact on California's forests.
Since the 2007 Fletcher Fire took place before any of the NAIP data were collected, there are no abrupt changes in the species in this area ( Figure 3). Due to the fire, half of the land remained bare in 2009. However, there has been uninterrupted regrowth of trees across the area, with an increasing distribution of ReforestedTree observed in Figure 2b. The area of Barren is decreasing as being converted to trees and shrub regrowth. The trend suggests that if there were no further wildfires, this area can recover and sustain the vegetation on long term.
Conclusion
A deep learning model is trained to classify tree species from aerial imagery and track the changes in tree species before and after three wildfires in California over a 9 year period. The model tracks multiple major tree species and validates that some tree species vanish from the areas affected by the wildfire. The model accurately recognizes long-term changes in areas that were reforested to preserve forest composition. This approach can be used to monitor the forest composition across large geographical areas in response to climate change, enabling foresters and environmental groups to make more informed decisions to preserve ecosystem balance.
Broader Impact
Climate change is increasing the frequency and the intensity of wildfires across the globe, causing tremendous loss of lives and economic damages. Besides larger areas being burned, the climate change is impeding tree regrowth in areas that were covered prior to wildfire, which in turn accelerates the climate change. Deep learning techniques are used to classify tree species in remote sensing images and track forest composition changes. Quantitative evaluation of tree density and tree species detection can help forest services, ecological organization and environmental groups to carry out comprehensive studies to preserve current forests and ensure the carbon reduction through reforestation.
Figure 1 :
1Tree species classification of burned regions of 2013 Swedes Fire (blue outline) and 2017 Wall Fire (red outline) in Butte County, CA. In Figure 1, two of the wildfires were studied, 2013 Swedes Fire marked with blue outline and 2017 Wall Fire marked with red outline 1 . Comparing the map for the blue-bordered region between 2012 and 2014, a large patch of the vegetated areas was cleared by the Swedes Fire and turned into bare land as indicated by the Barren class. The bar plot (Figure 2a) shows a sudden expansion of Barren land areas after 2012, with 18% of the region converting to no vegetation covered land. In 2016, half of the bare land area from 2014 was covered by new vegetation and Hardwood coverage is doubled by extending into the previously Shrub area. A new disruption occurred in 2017, caused by the Wall Fire. Most of the Hardwood as well as ReforestedTree disappeared, and without the regrowth of 1 In November 2018, the disastrous Camp Fire started in the same region. NAIP data of 2018 were acquired before the wildfire, and therefore it reflects the vegetation status before the Camp Fire.
Figure 2 :
2Land cover distribution of (a) 2013 Swedes Fire and 2017 Wall Fire together and (b) 2007 Fletcher Fire (incomplete bar for 2018 is due to missing data in Oregon State in 2018).
Figure 3 :
3Tree species classification of burned regions of 2007 Fletcher Fire in Modoc County, CA. The missing part of the 2018 classification is due to missing data in Oregon State in 2018.
34th Conference on Neural Information Processing Systems (NeurIPS 2020) Workshop, Vancouver, Canada.arXiv:2011.02514v2 [cs.CV] 12 Nov 2020
2 Related Work
Table 1 :
1Dataset statistics of the tree species.Tree type
Label # points
Conifer
0
18,708
Hardwood
1
19,873
Shrub
2
24,430
ReforestedTree
3
21,701
Barren
4
19,137
Total
103,849
Wildfires. Wildfire boundaries were obtained from California [24] and analyzed to investigate the
variability of tree species before and after wildfires. Specifically, Swedes Fire in 2013 and Wall Fire
in 2017 both of which happened in Butte County, CA, and Fletcher Fire from 2007 in Modoc County,
CA were reported. These regions are not covered by the training samples.
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| sample_1101 | 0.9951 | arxiv | |
In this article, we propose two-stage planning models for Electricity-Gas Coupled Integrated Energy System (EGC-IES), in which traditional thermal power plants (TTPPs) are considered to be retrofitted into carbon capture power plants (CCPPs), with power to gas (PtG) coupling CCPPs to gas system. The sizing and siting of carbon capture, utilization and storage (CCUS)/PtG facilities, as well as the operation cost of TTPPs/CCPPs/gas sources/PtG, are all considered in the proposed model, including penalty on carbon emissions and revenue of CCUS. With changing policy on climate change and carbon emission regulation, the uncertainties of carbon price and carbon tax are also analyzed and considered in the proposed planning model. The stochastic planning, and robust planning methods are introduced to verify mutually through economic and carbon indices. The proposed methods' effectiveness in reducing carbon emissions, increasing CCUSs' profit from EGC-IES are demonstrated through various cases and discussions.Index Terms-Carbon capture, utilization and storage, Electricity-Gas Coupled Integrated Energy System, Carbon tax and price uncertainty, Two-stage stochastic planning, Two-stage robust planning.
Matrixes:
A Gas node-gas source incidence matrix B Gas node-gas pipeline incidence matrix C Bus-generator incidence matrix
A. Background and Motivation
HE emission of greenhouse gas which gives priority to carbon dioxide (CO 2 ), is a primary driver of global climate change and one of the most pressing challenges nowadays [1]. In response to global climate change, the Paris Agreement was adopted by 196 parties at the 21st Conference of the United Nations Framework Convention on Climate Change in Paris on 12 Dec., 2015 and entered into force on 4 Nov., 2016. Its longterm goal is to keep the rise in global average temperature to well below 2°C above pre-industrial levels, and to pursue efforts to limit the increase to 1.5°C [2].
It has already sparked various low-carbon solutions since the Paris Agreement entered into force, more and more countries, regions and cities all over the world are establishing zerocarbon targets. Carbon capture, utilization and storage (CCUS) is the key technology that reduces and removes CO 2 after emission, which is a critical part of zero-carbon goals [3]. According to Special Report on CCUS [4] released by International Energy Agency (IEA), the next decade will be critical to the zero-carbon emission goal via retrofitting existing power and industrial facilities. Thus carbon capture power plant (CCPP), which is altered from traditional thermal power plant (TTPP), its carbon reduction performance in Gas Network, Electricity Network and even Electricity-Gas Coupled Integrated Energy System (EGC-IES) are worth investigating urgently.
Encouragingly, as more ambitious climate pledges are taken, many programs and strategies are factoring in the role and potential for carbon pricing and carbon markets [5]. How to translate commitment into reality in ensuring we can confine global warming to below 2°C, the careful planning for EGC-IES considering the global changing and divergent carbon price policy will be critical.
B. Literature Review
Several scholars have carried out related researches in developing planning models considering CCUS. In CCUS and its applications, research [6] introduced a scalable infrastructure model to determine where and how much CO 2 to capture and store, where to build and connect pipelines. A mixed integer linear programming (MILP) model was developed [7] to describe a general modeling approach for optimal planning of energy systems subject to carbon and land footprint constraints. Several literatures addressed the retro fitment [8], expansion ([9], [11]), transition [10] pipeline networks ( [12], [13]) planning problems considering CCUS.
Later in 2016, literature [14] presented a planning framework considering CO 2 supply, production, transportation, and emission costs . literature [15] developed a two-step linear optimization to make a trade-off between the cost of network modification and CO 2 emissions considering the network revamp. In recent years, CO 2 utilization has attracted more and more attention from scholars to industry. Review [16] and [17] summarized the existing and under-development technologies for CO 2 utilization in the world. The exact applications in gas field [18], oil field [19], and chemical products [20] were gradually studied in depth. CCUS is often planned with particular actual cases to observe performance. For example, a multi-stage mixed integer programming (MIP) model for CCUS planning was developed and tested in Beijing-Tianjin-Hebei, China [21], the United States [22] and the United Kingdom [23].
Specializing on CCUS's application in retrofitting existing T facilities, early research [24] presented linear models of the most common components in the CCPP. A post-combustion and solvent/sorbent separation technology based CCPP model is established in [25], the authors investigated the performance of CCPP in the carbon emission market [26] in 2012. The TTPP was equipped with nuclear units, renewable energy units, and different fossil fuel-fired units in [27] to form MINLP and solve using particle swarm optimization algorithm. Table I categories these researches by topics and mathematical method for CCUS planning in detail. MILP [6]- [8], [12], [14], [15], [24], [
C. Problem Identification and Main Contributions
Due to the long time horizons involved in CCUS planning, it is necessary to include uncertainties. Several literatures have studied relevant researches on uncertainties such as load and renewable generation uncertainties [28], generation and demand side uncertainties [29], user behavior uncertainty [30], etc. However, as the significant contents of low-carbon development, the volatilities of carbon price and carbon tax are essential sources of uncertainties that cannot be ignored.
Besides, gas-fired power generation units are considered as the coupling point of gas and electricity systems [31] for a long time. The development of power to gas (PtG) technology could be a new coupling point [33] in the future. However, related research in EGC-IES is still very few.
In this paper, two-stage planning methods for EGC-IES with CCUS considering carbon price uncertainty are proposed. Main contributions of the paper are therefore three-fold:
(1) A CCPP planning model retrofitted from TTPP, with PtG in EGC-IES for CO 2 utilization is proposed, in which the methane produced by PtG is transported to the gas network to relieve the gas supply pressure.
(2) The carbon penalty and carbon revenue are introduced in the objective function considering carbon tax and carbon price uncertainties globally.
(3) Three planning models aim at finding out a balance point where the external revenue and reduced penalty to cover the investment cost. The effectiveness of the proposed model is also verified.
The remainder of this paper is organized as follows: Section II would outline the CCUS business model under carbon market and carbon policy. Model formulation is displayed in Section III where the detailed objective function and constraints are described. Section IV discusses the proposed four models. Case studies and conclusions are given in Section V and VI.
II. PRELIMINARY OF CCUS AND ITS BUSINESS MODEL
CCUS is a crucial emissions reduction technology that can be applied across the energy system [3]. Fig. 1 illustrates the significant profits method of CCUS currently. Its business model can be summarized as follows [4]: CCUS involve CO 2 capture from fuel combustion or industrial processes, uncaptured CO 2 is subject to the mandatory penalty in the form of carbon tax; captured CO 2 is transported via vehicles or pipeline or permanently stored deep underground, CO 2 could be utilized as a resource to create valuable products and services such as CO 2 enhanced oil recovery, CO 2 enhanced coal bed methane, chemical and biological products; in an emission trading system, captured CO 2 can also be traded, as predicted in The New York Times that carbon will be the world's biggest commodity market [32]. Nowadays, there are 22 CCUS facilities worldwide with the capacity to capture more than 40 Mt CO 2 every year. Report [4] pointed out three aspects that summarize the growth trends in CCUS projects over the following decades: 1) Retrofitting of existing power and industrial facilities that significantly reduce emissions.
2) The scale-up of low-carbon hydrogen production with CCUS.
3) The rapid adoption of CCUS technologies and applications that are not yet widely used.
According to the technical development level, the current focus of CCUS is on retrofitting fossil fuel-based power and industrial plants.
Due to the vast differences in the economic and technological development levels and resource endowments around the world, this article uses the technical parameters published by IEA and related literatures to build a general planning model for TTPP retrofitting into CCPP, other than focus on one or several specific CCUS technologies; at the same time, based on the consideration of carbon policies are influenced by politics, culture and other factors, carbon price and carbon tax are regarded as uncertainties, the business models like carbon penalty and carbon revenue are adopted to form the planningoperation two-stage model.
III.MODEL FORMULATION
In Section III, the objective function, gas network model, electricity network model, CCPP and PtG coupling model, and constraints on facility investment and siting are elaborated separately.
A. Objective function
The objective function is to minimize the total cost (1)
B. Gas network model
A typical gas network model comprises natural gas transmission pipelines, natural gas sources and gas loads. The Weymouth equation [34] is adopted in (6) to describe natural gas transmission flow in this model, in which the gas flow is expressed as a quadratic equation of nodal gas pressure, , a b denote the input end and output node respectively, in accordance with the specified direction. Formula (7a) introduces the variable I to replace nodal pressure to avoid the nonconvexity.
2 2 2 , ,, , , , 1,gas gas GP p t p t p a t b t f f W p t T (6) 2 ,
, ,
gas gas GP p t p t p a t b t f f W I I p t T (7a) 2 2 , , , 1, GN m m m t I m t T (7b), , , 1,
Piecewise linearization are listed as constraints (8a)-(10), adopted from [35] with continuous variable and binary variable : the former indicating the proportion occupied in a specific segment and the latter indicating the selected status of the segment (the value of changing from 1 to 0 means the segment is selected). ,
, ,, , , , 1, , 1, 1GP p t k p t k p t T k seg (8a) , , 0 1, , 1, , 1, GP p t k p t T k seg (8b) , , 1 , , , , 1, , 1, 1 GP p t k p t k p t T k seg (8c) ,,1 , , , 1 , 1 , , 1, , 1,f F F F p t T k seg (9) 2 , ,,1 ,1 , , , 1 , 1 , , 1 , 1, , 1,W I I F F F F F F p t T k seg (10)
Natural gas source production is limited by output constraints (11a) and ramp constraints (11b). Eq. (12) is the power balance constraint in gas network model among gas source, gas flow, and gas load, where on right-hand side , m t L is the gas load at node m to be balanced, , mi A is the element of gas node-gas
source incidence matrix A , , 1 m i A if gas source i is connected to gas node m , ,GS i i i t P P P i t T (11a) ,, 1,GS i i i t i t P P P P i t T (11b) , ,, 1 , , 2,gas m i i t m p p t m t GN GS GP P f L m i p t T A B (12) min GS GEN PtG inv ope ope ope CC CS pen tra C C C C obj C C C C , , , , , , 1, (1 ) , ,(1 )1 L L dr dr PtG siting dr t (2b) , ,, 1,GS GS ope i i t i t C r P i t T (3a) , ,, 1,GEN GEN ope j j t j t C r P j t T (3b) , ,, 1,PtG PtG ope q q t q t C r P q t T (3c) , ,, 1,CC CC CC CCPP j t j t C r Q j t T (4a) , ,, 1,CS CS CS CCPP j t j t C r Q j t T (4b) , ,, , 1,tax EMI CC CCPP pen j t j t j t C r Q Q j t T (5a) ,, 1,pr CS CCPP tra j t j t C r Q j t T ， (5b)
C. Electricity network model A typical electricity power system comprises electricity transmission lines, generators, and electricity loads. The DC power flow model in eq. (13a)-(13b) can be adopted to estimate steady state for the distribution system, (14) is constraint for power flow on transmission line.
, , , / , , 1, ele TL l t a t b t l f X l t T (13a) , ,, 1,EB n t n t T (13b) , ,, 1,ele ele ele TL l l l t F f F l t T (14)
Generators' output constraints (15) and ramp constraints (16) of
GEN j j j t j t j t u P P u P j t T (15) ,, , 1,GEN j j j t j t P P P P j t T (16) , , 1 , , , on j t GEN on j tt j t j tt t T v u j t T T (17a) , , 1 1 , , , off j t GEN off j tt j t j tt t T w u j t T T (17b) ,, 1 , , 2,GEN j t j t j t j t u u v w j t T (18) ,, 1 , , , , 2,GEN j t j t v w j t T , 1, , 1,
Eq. (20) is the power balance constraint in electricity network among generator, power flow, and load, similar to eq. (12).
, ,, , , , , 1,ele n j j n l l t n t EB GEN TL P f L n j l t T C D(20)
D. CCPP and PtG coupling model A coupling model combined TTPP, CC, CS and PtG technology to retrofit into CCPP is illustrated below, where exhaust emission from TTPP is flowed into CCUS, then captured CO2 is provided to Sabatier reactor to react with H 2 electrolyzed to produce CH 4 . The external characteristics are adopted in planning problem instead of the internal chemical reaction process [36], Fig. 2 shows the flow chart retrofitting TTPP to CCPP with CCUS.
,, , , , , 1,CCPP PtG CC GEN j t j t j t j t P P P P j t T (21) , , , , 1, emi GEN j t j t Q emi P j t T (22) , , / , , 1, CC CC CC GEN j t j t Q P W j t T (23)
Eq. (21) denotes the TTPP output power supply for the external grid, PtG, and carbon capture device. In (22), considering that the CO 2 emissions of power plants changed with loads, the CO 2 emission volume accounts for a fixed proportion emi of output power based on statistical data from U.S. DOE [39]. The relationship between the captured CO 2
CH CH GN CCPP j t m j t m V V m j t T , , , 1,
Natural gas generated by PtG can be delivered to the gas network to relieve gas supply pressure. , m j s is the binary variable indicating the investment statue of transmission pipeline between gas node m and PtG j , which is equal to 1 if they are connected, otherwise it is 0. j PtG y is integer variable denoting the number of PtG module to be invested, with each module assumed to be 1MW. Constraint (28) means that every pipeline can only be invested after PtG was chosen to be expanded on CCPP due to investment logic, where M is a very large number used in the Big-M method. Similarly in (29), the transmission volume of natural gas between gas node m and PtG j at any time is bound by decision variable , m j s . (30) implicates the coupling relationship between natural gas produced by PtG and transmitted in pipeline. Fig. 3 illustrates the sketch on facility sizing and siting in EGC-IES.
CH G gas m i i t m p p t m j t m t j GN GS GP CCPP P f V L m i p j t T A B (31) , ,, , , , , , , , 1,CCPP ele n j j t n l l t n t EB CCPP TL P f L n j l t T C D, , , , , , 1,
After retrofitting TTPP to CCPP with CCUS and PtG, the original power balance functions in (12) and (20) are converted into (31) and (32) by adding an external gas source from PtG and replacing generator as CCPP.
IV.METHODOLOGY
In Section IV, three models are formulated based on previous constraints and objective function, and the effectiveness of proposed models are verified through case studies in Section V.
A. Without CCUS planning
Without CCUS planning is the original circumstance, in which it does not exist additional investment in CCUS equipment. The CO 2 generated by TTPP is directly emitted into the atmosphere, and the utilities have to pay the carbon penalty. Correspondingly, there is no carbon revenue due to the absence of CCUS.
The objective function in (28) consists of operation costs of gas sources, generators, and carbon penalty due to CO 2 emission. It could be put into a compact form:
, ,, 2 minC P C P C P i j t T s t (33)
B. Deterministic planning with CCUS
Deterministic planning with CCUS considers investment cost, operation cost, carbon capture/storage cost and carbon penalty/revenue in a specific value of carbon price and carbon tax. Different planning results can be obtained since the carbon price and carbon tax fluctuations along with policy changes. It could be put into a compact form:
, ,
,
c y c s C P C P C P C P C P C P C P s t b a i j q , 1, t T (34)
C. Two-stage stochastic planning with CCUS
There are over 61 carbon pricing initiatives in place or scheduled for implementation until 2020 [4], meanwhile, the carbon price level of the implemented carbon pricing mechanism varies greatly around the world. Therefore, it is essential to consider the carbon price and carbon tax uncertainty based on the implemented carbon pricing mechanism globally. In the two-stage stochastic planning model, the first-stage decisions include the PtG capacity and its siting, while the second-stage considers the operation cost, e. g. carbon capture & storage cost, carbon penalty & trading in all scenarios.
, ,
,
min ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) (, , , , , ( ) ( )C P s C P s C P s C P s s t b P 3 19 ,32 , , , 1,21 GS CCPP PtG a i j q t T (35)
D. Two-stage robust planning with CCUS Unlike the method using probabilistic weights of uncertainties in stochastic planning, two-stage robust planning further considers the robustness of uncertainty set in the second stage. Box uncertainty set is adopted to illustrate the uncertainty of policy considering carbon price and carbon tax, the boundaries of uncertainty set are obtained from recent Prices in implemented carbon pricing initiatives in [5].
,, , , , , , , , ( ) ( , . . 6 11 ,13 19 , 32 , , , , 21 , 1,
pr pr
GS CCPP PtG GN EN r r s t b a i j q m n t T (36)
V. CASE STUDIES An updated IEEE 24-bus electric system with the Belgian 20node natural gas system are employed to verify the effectiveness of the proposed models. A sketch map indicating sources of key parameters of PtGs and their siting planning is shown in Appendix Table. All the datasets are available in [40]. The investment cost of PtG is set as 3 M$/MW, the siting costs of PtG to gas system are set to different values according to distance. The MILP is modeled by MATLAB 2019b with YALMIP toolbox and solved by Gurobi 9.1 on a laptop with Intel® Core™ i7-6700U 3.40 GHz processor and 8GB RAM.
A. Analysis of planning results
Four cases are developed to observe corresponding planning and operation results based on the proposed models as follows: Table II summarizes the problem identifications of the proposed four cases. The detailed planning results are shown in Table III.
Overall, the investment cost increased from Case 2 to Case 4. The reasons can be traced back to the second stage, the second stage of Case 2 is calculated in a specific scenario ( ta x r =50 $/ton, pr r =40 $/ton); while the second stage of Case 3 is the weighted average based on 25 equal-probabilistic scenarios extracted from the current carbon price and carbon tax range globally, with more scenarios simulated, the planning result is likely to get closer to the average value ( ta x r =60 $/ton, pr r =40 $/ton); as for Case 4, the planning result reflects the optimal decisions in the worst scenario of the current global carbon policy ( ta x r =120 $/ton, pr r =1 $/ton), where the extreme situation probably won't happen in practice. The siting planning of CCUS obtained the same results, gas node #17 is selected as the connection node of gas network and electricity network due to joint optimization based on sitting cost and load conditions of gas network node. More detailed analysis of investment costs can be found in Section V.B.
As for the operation cost, the gradual rise of generators' and PtGs' indicate their outputs increased along with the carbon capture process and PtGs' increasing investment. The operation costs of gas sources decreased slightly while the generators generate more power (174.60 in Case 1 →334.62 in Case 4), revealing that gas sources' supply pressure is eased with the coupling PtGs producing gas from CCUS in EGC-IES.
Carbon-related indices are also our key concerns. Case 1 (without CCUS planning) accounted for maximum carbon emission volume and carbon penalty except for Case 4 (robust planning with the highest carbon tax), the carbon emission volume increases from Case 2 to Case 4 since outputs of generators to supply for CCUS is also increased to avoid more penalty due to higher carbon tax, while the carbon capture and storage volume of Case 2 and Case 3 varied little. In Case 4, with the highest carbon tax and lowest carbon price, we obtained the worst circumstance with maximum carbon penalty (1588.40M$) and minimum carbon revenue (15.04M$) of the EGC-IES.
In summary, for the global average carbon price and carbon tax level, the business model of installing CC-CS-PtG CCUS for TTPP and transmitting produced gas to the gas network is economically feasible. However, for those countries or regions with high carbon taxes and low carbon prices, the business model of retrofitting such kind of CCUS for policy arbitrage is still not applicable. The next subsection analyzed the approximate range of carbon prices and carbon taxes that have economic advantages in terms of the total cost.
B. Sensitivity analysis of carbon price and carbon tax
The investment decisions in different carbon prices and carbon taxes are simulated in Fig. 4 changed in steps of $10. It can be concluded from the figure that the investment tends to rise as carbon price decreases and carbon tax increases. It is reasonable under the current business model: the optimal choice is to sell the captured CO 2 for income when the carbon price is rather high; with relatively low carbon price, it is not costeffective to sell the captured CO 2 and it would be better to produce methane to reduce gas supply pressure. Furthermore, it can be observed from Fig. 4 that when carbon price is higher than carbon tax (lower right corner of Fig. 4), no more CCUS investment is preferred; on the contrary, when carbon price is lower than carbon tax, CCUS investment is adopted, and the investment increases with difference increases. The results depict that CCUS retrofitting is an investment strategy sensitive to the carbon emission policy, i.e., carbon tax and carbon price. 5 is to further analyze the trend of total cost along with carbon price and carbon tax compared to circumstance without CCUS planning, in which surface in pink color represents the total cost without CCUS. Generally speaking, the total cost presents a downward tendency along with the carbon price increases and carbon tax decreases. It can be seen from the figure that while the value of carbon price is larger than 40 $/ton, the business model of CCUS retrofitting with CC, CS and PtG for TTPP is approachable globally. This retrofit planning has achieved economically better for some high-carbon tax areas while the carbon price equals 30 $/ton.
It is worth mentioning that, despite carbon prices increasing in many jurisdictions all over the world, the carbon prices in most parts of the world are still below 40$/ton at present. Report [5] has pointed out that the carbon price level of 50$/ton-100$/ton by 2030 is required to cost-effectively reduce emissions in line with the temperature goals in the Paris Agreement, this is also consistent with the intersecting line shown in Fig. 5. Facing the policy foundation of a gradual increase in carbon prices, the retrofit planning could have great potential in the future.
C. Analysis of daily carbon indices
The effectiveness of the proposed models can be verified further by comparing daily carbon emission, capture, storage, and utilization volume in Appendix Fig. Case 1 in blue color can be regarded as a benchmark without CCUS planning, it results in vast amounts of carbon emissions and simultaneously wastes policy dividends. Case 2 and Case 3 can be compared and analyzed together, in which more sampled scenarios can lead closer to the global average level in Case 3. Case 4 in purple line reflects the "worst case" in robust optimization: compared with Case 2 and Case 3, the robust planning result is more inclined to carbon emission and averse to carbon capture/storage due to the extremely low carbon price, even when carbon tax is also high; at the same time, the planning result adopted maximum carbon emissions volume and minimum carbon capture/storage volume in the worst circumstance. Moreover, captured carbon is used for storage or utilization, they made a tradeoff with each other. Because of the minimum operating power constraint with the planned capacity of PtG (Constraints (27)), the carbon utilization volume in Case 4 still achieved the highest among all cases.
Carbon-related volume is also consistent with the load conditions. During the morning and evening load valley moment (1:00-6:00, 22:00-24:00), CCUS is sufficient to achieve zero carbon emissions; the changing trend of carbon capture and carbon storage curves is basically in accordance with load conditions for Case 2 and Case 3. During non-valley periods (7:00-22:00), abnormal changes of carbon capture and storage happened due to the worst carbon price in Case 4.
On the whole, it can be observed that the effectiveness of the proposed models (deterministic planning, two-stage stochastic planning & two-stage robust planning) in reducing carbon emissions, increasing carbon capture and utilization by making use of carbon policy dependent on carbon tax and prices.
VI.CONCLUSIONS
This paper presents a gas-electricity coupled integrated energy system planning model with CCUS, in which carbon price and tax uncertainties are included. With proper carbon tax and price range, the proposed model effectively reduces carbon emissions, increases carbon capture and usage, and makes use of policy to profit. In the proposed model, the capacity and siting of PtG are included in the objective function to optimize the first-stage investment cost, and the economic indices on operation cost of generator, gas source and PtG, carbon capture and storage cost, as well as carbon penalty and revenue are optimized by IES operation strategy in the second stage.
Moreover, carbon price and carbon tax were considered in the model as the key sources of the uncertainties under the changing carbon policy. Stochastic and robust planning methods are introduced to verify mutually through economic indices and carbon indices. The case studies demonstrate the effectiveness of the proposed gas-electricity coupled models by PtG and illustrated the benefits of CUSS installation. Future work could further consider gas turbine and power to gas to form bi-direction energy flows and renewable energy and load uncertainties in EGC-IES.
F
Lowest boundary point of gas flow in segment k on pipeline p , Maximum/minimum outputs power of gas source i , Mm 3 /h i P Maximum ramp up power of gas source i , Mm 3 /h , m t L Gas load of gas node m in hour t , Mm 3 Student Member, IEEE, Xinwei Shen, Senior Member, IEEE, Qinglai Guo, Senior Member, IEEE, Hongbin Sun,
Gas flow on pipeline p in hour t , Nodal pressure of gas node m in hour t , bar , , p t k Continuous variable of segment k on pipeline p in hour t indicating the proportion occupied in a specific segment , , p t k Binary variable of segment k on pipeline p in hour t indicating the selected status of Power flow on transmission line l in hour t , MW , n t Phase angle of electric node n in hour t
Fig. 1
1CCUS business model flow chart
of gas source i , generator j and PtG q , power of gas source i , generator j and PtG q in hour t, Q are CO 2 volume indicating emission, capture and storage of CCPP j in hour t, respectively.
F
represents the lowest boundary point of gas flow in segment k on pipeline p .
are similar to those of natural gas sources, in which u indicating the start-stop status, the value of u keeps 1 if the generator is in operation, otherwise being 0. The unit commitment constraints in formulas (17a)-(19) are employed to accurately describe generator output characteristics. v and w are binary variables to reflect startup and shutdown actions, the value of v is 1 if the generator started up from the prior moment, and the value of w is 1 if the generator shut down from the prior moment, otherwise they remain 0.
Fig. 3
3Sketch on facility investment and siting of EGC-
Deterministic planning results with CCUS( ta x r =50 $/ton, pr r =40 $/ton);3) Case 3Two-stage stochastic planning results with CCUS in 25 scenarios (the value of ta x r and pr r are selected as five-segment points on average within their range to form 5*5 equalprobabilistic scenarios, the range of ta x
Fig. 4
4Investment cost in different carbon tax and carbon price Fig.
Fig. 5
5Total cost in different carbon tax and carbon price
APPENDIX Appendix Fig. Daily carbon emission, capture, storage, and utilization volume (a). carbon emission volume. (b). carbon capture volume. (c). carbon storage volume. (d). carbon utilization volume. Appendix
Set of gas pipelinesAngXuan and Xinwei Shen are with Tsinghua-Berkeley Shenzhen Institute, Tsinghua Shenzhen International Graduate School, Tsinghua University. Qinglai Guo and Hongbin Sun are with Dept. of Electrical Engineering, Tsinghua University. This work is supported by the National Natural Science Foundation of China (No. 52007123) (Corresponding author: Xinwei Shen, email: sxw.tbsi@sz.tsinghua.edu.cn; Hongbin Sun, email: shb@tsinghua.edu.cn).NOMENCLATURE
Abbreviations:
CCUS
carbon capture, utilization and storage
CC
carbon capture
CS
carbon storage
IEA
International Energy Agency
TTPP
traditional thermal power plant
CCPP
carbon capture power plant
EGC-IES
Electricity-Gas Coupled Integrated Energy
System
PtG
Power to gas
Sets:
GN
Set of gas nodes
GP
Table I
ISummary of Planning Model Considering CCUSCategory
Literature
Carbon capture & storage
[6]-[11]
Carbon transportation
(pipeline planning)
[12]-[15]
Topics
Carbon utilization
[16]-[23]
Decision tree method
[13]
1 seg
gas
gas
gas
gas
p t
p
p t k
p k
p k
k
GP
1 p
a t
b t
seg
gas
gas
gas
gas
gas
gas
p
p
p t k
p k
p k
p k
p k
k
GP
volume by carbon capture device, i. e.(unit: MWh/ton) is the energy consumption of capturing per ton CO 2 by carbon capture device adopted from[37]. MWh) is CO 2 consumed volume of PtG to generate unit work CH 4 adopted from[38]. Constraints (26) denote CH 4 production character of PtG, volume by PtG in CCPP j during hour t . Constraints(27) limits the output power of PtG in CCPP j during hour t withCC
Q , and unit work by
carbon capture device operation power
CC
P is approximated by
linear correlation with C C
W
in (23), C C
W
,
,
, ,
,
1,
CC
CS
CU
CCPP
j t
j t
j t
Q
Q
Q
j
t
T
(24)
Fig. 2 Framework of CCPP and PtG coupling in EGC-IES
The captured CO 2 is either used for PtG to produce methane
(
CU
Q ) as separated form or stored to sell to carbon market (
CS
Q
) in compressed form, which can be modeled by (24).
2
,
, ,
,
1,
CO
CU
PtG PtG
CCPP
j t
j t
Q
P
j
t
T
(25)
4
4
,
,
/
,
,
1,
CH
CH
PtG PtG
CCPP
j t
j t
V
P
H
j
t
T
(26)
,
,
,
1,
j
j
PtG
PtG
PtG
PtG
PtG
CCPP
j t
y P
P
y P
j
t
T
(27)
The total CO 2 volume consumed by PtG during time period
t can be calculated as (25), where
PtG
is the conversion
efficiency of PtG from electricity to CH 4 ,
2
C O
(unit:
ton/4
CH
H
is the calorific value of
methane, usually takes 36MJ/m 3 ,
4
,
CH
j t
V
signifies produced CH 4
boundaries
PtG
P
and
PtG
P
multiplied by planned module
j
PtG
y .
E. Constraints on Facility Investment and Siting
,
0
,
j
PtG
m j
m GN
s
y M j CCPP
(28)
4
, ,
,
0
,
,
,
1,
CH
GN
CCPP
m j t
m j
V
s M m
j
t
T
(29)
4
4
,
, ,
Table II
IISummary of Compared Cases
Case
With
CCUS
Deterministic
planning
Stochastic
planning
Robust
planning
Case 1
×
×
×
×
Case 2
√
√
×
×
Case 3
√
×
√
×
Case 4
√
×
×
√
Table III .
IIIPLANNING RESULTS Contains CC, CS and PtG deviceCategory
Indices
Case 1
Case 2
Case 3
Case 4
CCUS *
-
36.61
72.58
428.69
CCUS sittings
-
50.74
50.74
50.74
Annualized
Investment Cost
(M$)
Total
-
87.35
123.32
479.43
Gas Sources
4809.61 4761.19 4760.28 4751.27
Generators
174.60
288.44
292.56
334.62
PtGs
-
0.90
1.79
10.58
Capture
-
723.68
705.26
470.37
Storage
-
120.34
117.00
75.22
Penalty
967.89
110.55
186.31
1588.40
Revenue
-
962.74
936.05
15.04
Operational Cost
(M$)
Total
5952.10 5042.37 5127.17 7215.44
Total Cost (M$)
5952.10 5129.72 5250.49 7694.87
Emission
19.36
2.21
3.10
13.23
Capture
-
24.12
23.51
15.68
Storage
-
24.06
23.40
15.04
Carbon-related
Volume (Mt)
Utilization
-
0.06
0.11
0.64
*
Table .
.Source of Key ParametersCCPP energy consumption of capturing per ton CO 2Parameter
Value
Source
CO 2 emission factor of TTPP emi
1005 g/KWh
Website [39]
Carbon capture cost
≤30 USD/ton
Carbon storage cost
≤10 USD/ton
Website [4]
Carbon tax
1~120 USD/ton
Carbon prize
1~80 USD/ton
Report [5]
C
W
0.269 MWh/ ton
CO 2 consumed volumn of PtG per unit output
2
C O
0.2 ton /MWh
Conversion efficiency of PtG PtG
0.6
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| sample_1104 | 0.9938 | arxiv | |
Understanding the Loss in Community Resilience due to Hurricanes using Facebook Data Tasnuba Binte Jamal (Corresponding author)
Ph.DStudent
Department of Civil
Department of Civil, Environmental, and Construction Engineering
Environmental, and Construction Engineering University of Central Florida
12800 Pegasus Drive32816OrlandoFLUSA
Ph.DSamiul Hasan samiul.hasan@ucf.edu
University of Central Florida
12800 Pegasus Drive32816OrlandoFLUSA
Understanding the Loss in Community Resilience due to Hurricanes using Facebook Data Tasnuba Binte Jamal (Corresponding author)
1Community ResilienceDisruptions on RoadsPower OutageHurricaneSocioeconomic DisparityGeneralized linear mixed model 3
Significant negative impacts are observed in productivity, economy, and social wellbeing because of the reduced human activity due to extreme events. Community resilience is an important concept to understand and quantify the impacts of an extreme event to population activity. Resilience is generally defined as the ability of a system to manage shocks and return to a steady state in response to an extreme event. In this paper, we analyze aggregate location data from Facebook in response to Hurricane Ida. Using changes in the number of Facebook users before, during, and after the disaster, we empirically define and quantify community resilience as a function of the magnitude of impact and the time to recover from the extreme situation. We measure resilience and the transient loss of resilience in population activity for the affected communities in Louisiana. The loss in resilience of the affected communities were explained by three types of factors, including disruption in physical infrastructures, disaster conditions due to hurricanes, and a community's socio-economic characteristics. We find that a greater loss in community resilience is associated with factors such as disruptions in power and transportation services and disaster conditions. We also find socioeconomic disparities in loss of resilience with respect to a community's median income.Understanding community resilience using the decreased population activity levels due to a disaster and the factors associated with loss in community resilience will allow us to improve hazard preparedness, enhance disaster management practices, and create better recovery policies towards strengthening infrastructure and community resilience.
INTRODUCTION
Many countries in the world are now facing major disasters such as wildfire, tornado, hurricane, tropical storm, and flooding. In the USA, total cost of the damages due to weather and climate disasters exceeded $ $2.295 trillion since 1980 (National Centers for Environmental Information, NCEI). From 2000 to 2021, there are a total of 28 major hurricanes in the USA (NOAA) and the induced damages have significantly increased due to major landfalls in recent years (3). For instance, Hurricane Irma caused a damage of about $50 billion in Florida (4). Damages by such extreme events cause a change in regular human activities. Compared to regular periods, human activities in disaster periods go through a significant amount of perturbation. People are less likely to work or move the same way in disaster situations as they do in normal conditions. Since a decrease in human activity is an indication of drop in business, recreation, and health services (5) (Fig. 1), understanding the changes in human activities is a key factor to analyze the hardships to the daily life of disaster affected communities.
In general, resilience indicates the ability of a system to return to its normal state or situation after a disruption due to an extreme event (6,7). At the onset of a hurricane, human activities start to decrease in the affected area, reach maximum drop after a certain time, and then start to recover. Since human activities are not at usual level, the amount of decrease in activities compared to regular periods can be termed as the loss of resilience for the disaster affected community. To quantify community resilience in human activity, different types of location data (Twitter and mobile phone location data) have been used previously (7,8).
Technological advancements provide researchers the access to high-fidelity location data. Such highresolution location data including taxi data (9,10), GPS data (11,12), cell phone call recordings (13), Wi-Fi (14), and mobile phone datasets (15,16) were used previously to understand human mobility and activity following an extreme event. However, these datasets are not always available; they are often proprietary, and sometimes confined to some specific point of interests (POIs) only (e.g., shopping mall, restaurants, etc.). To effectively quantify community resilience, data must be easily accessible and usable (17). These data unavailability issues can be avoided if location data from a widely used service are made accessible.
Some studies have utilized post-disaster survey data to understand population activity due to natural disasters (18)(19)(20)(21)(22)(23). However, such survey data are not reliable because they cannot capture the dynamic patterns of recovery and respondents may not remember everything. So, it is challenging to collect longitudinal data from disaster-affected regions through post-disaster surveys (15,24).
To this end, Facebook Data for Good platform is sharing aggregate data of the Facebook users following a crisis event to help humanitarian organizations (25). Data from 'Facebook Data for Good' (now 'Data for Good at Meta') platform are free and easily available. This platform shares aggregate data on where people are located before, during, and after a crisis event. It shares the counts of Facebook users who enable location services on their mobile device (25). Whenever there is a disaster, such data of Facebook users are globally available from the affected regions. Facebook population data is a great source to identify crisis events over a certain time window and investigate the impacts of these events to population activity.
Worldwide, 2.9 billion monthly active Facebook users are reported in 2022. About 240 million users were found in the USA in 2021 (26). According to Pew Research Center's national survey (2019), Facebook usage rates are high in USA (27). For example, 69% of U.S. adults use Facebook as a social media platform (27), indicating the applicability and reliability of Facebook data in research.
In this paper, we study community resilience in population activity against a hurricane utilizing Facebook data before, during and after Hurricane Ida. We define community resilience as the ability of an affected community to return to its regular activity (in terms of social activity). So, the loss of resilience is equivalent to the amount of disruption in population activity. A resilient community can withstand an extreme situation while a non-resilient or vulnerable community undergoes a significant and prolonged disruption. Therefore, a resilient community loses a small amount of resilience and a vulnerable community on the other hand loses a significant amount of resilience due to disasters. In general, resilience indicates a community's long-term property in reaction to all potential crisis events. We refer to this loss as the "transient loss of resilience" because it is determined in reaction to a single disaster (7). This paper is a first step towards developing methodologies to determine the loss in community resilience from Facebook data with the following specific contributions:
1. We demonstrate the use of a large-scale macroscopic location dataset collected from Facebook to quantify community resilience. While data from this source have been used in the field of ubiquitous computing and research on migration and evacuation, we add a new dimension to this type of data by quantifying resilience for the affected community due to an extreme event such as a hurricane.
2. We further develop a statistical model to investigate the association between multiple types of infrastructure disruptions (transportation and electricity services) and the transient loss of resilience in population activity due to hurricanes, while accounting for hazard characteristics. While previous studies investigated the disparities in community resilience from varying socioeconomic and demographic attributes, we add a new domain by looking at multiple types of infrastructure disruptions and disaster condition aspects.
When a disaster occurs, the socio-infrastructure systems of a community might be significantly disrupted such as disruptions in electricity services, transportation networks' functionality, business activities, delayed and inequal assistances from Govt. and non-Govt. organizations. Such disruptions preclude population activity to come back to normal state and prevent communities from being resilient to disasters (Fig. 2). It is important to investigate which factors are associated with the transient loss of resilience of an affected community. Understanding the drop in population activity levels due to a disaster, its gradual recovery processes, and the factors associated to such processes will allow us to improve hazard preparedness, enhance disaster management practices, reduce economic losses, and create better recovery policies. The findings of this study provide insight into effective identification of less resilient communities to hurricanes from large-scale, real-time, free, and easily accessible Facebook data, as well as the correlates of transient loss of community resilience. We focus on how disruption in multiple physical infrastructures, and disaster condition are associated with the transient loss of community resilience from the Generalized Linear Mixed Model (GLMM). We highlight the disparities in recovery patterns associated with socioeconomic community attributes as well.
LITERATURE REVIEW
Previous research analyzed location-based data to understand recovery patterns and quantify the losses to the lifestyle of an affected community due to disasters. Analyzing large-scale location-based datasets (cell phone call recordings and social media posts), studies found that recovery patterns are not random, they follow some specific patterns (10,11,16,28,29). High-resolution location data including taxi data (9,10), GPS data (11,12), cell phone call recordings (13), Wi-Fi (14), and mobile phone datasets (15,16) were used previously to understand human mobility and activity following an extreme event. We can now measure the recovery trajectories using big data at previously unheard-of high frequency, granularity, and scale. Such big data enabled us to further quantify the fundamental resilience features of communities utilizing data driven complex systems modeling (30). For a more effective, inclusive, and responsive disaster response and recovery; mobile phone location data holds enormous potential (31).
Through the use of mobile phones, it is now possible to collect spatio-temporally detailed observations of individual mobility throughout a vast region (32,33) and it was discovered that human trajectories exhibit a high degree of temporal and spatial regularity. Guan et al. (34) developed methods to track changes in social interaction using Twitter data and in two transportation networks (subway and taxi) using subway ridership and taxi data on daily basis due to a major disaster. Juhasz et al. (35) investigated the effect of Hurricane Irma on visitation numbers in Florida considering six different point of interest (POI) provided by SafeGraph platform. They identified factors associated with increased or decreased distance between home and a specific POI category. Sudo et al. (12) proposed a particle filter method to predict human mobility several hours ahead of an event using real-time location data. Yabe et al. (16) focused on population recovery patterns during post-disaster periods, by observing human mobility trajectories of mobile phone users. They explained the heterogeneity in displacement rates and the speed of recovery across communities at local government units (LGU) level (LGUs correspond to counties in the USA).
Overall, previous studies focused on recovery trajectories, human mobility and activity, displacement rates (e.g., percentage of population impacted by a disaster) and recovery time of the affected community from different types of location datasets. Despite such progress, the current body of literature needs a general 'term' for understanding the population displacement rate and recovery patterns after disasters with easily accessible, free, and representative longitudinal data. For example, displacement rates or recovery speed separately may not reveal the extent of disruptions to the activities of an affected community by a disaster because despite having small rate of displacement, it may take longer time for them to recover or vice-versa. So, to better understand the impacts of a disaster to an affected community, we need to consider 'resilience' which involves both systemic impact (e.g., percentage of population impacted by a disaster) and duration of impacts (7,8,15,36). In general, resilience indicates the ability of a system to return to its normal state after a disruption (6,7). For community resilience, it is usually defined as the ability of the disaster affected community to come back to the normal life. Hong et al. (8) and Roy et al. (7) quantified community resilience in population activity and mobility using geo-located mobile device and social media data, respectively. However, these studies are limited to only quantifying community resilience. They did not investigate the factors associated with the loss of resilience of a community due to disasters and how recovery patterns vary across affected communities despite facing similar levels of shocks.
Several studies investigated the disparities in disaster response and recovery patterns associated with varying socioeconomic, demographic, and geophysical community attributes (8,37,38). (15) showed the relationship between inundation with hazard impact and the restoration time for community to get back to their regular activity in Houston, Texas due to Hurricane Harvey. Again, these studies focused either on recovery time or percentage of population impacted due to disaster instead of considering a general single term (e.g., the loss in community resilience). Moreover, the impact of major infrastructure systems (e.g., transportation network) and the severity of hazard (e.g., wind speed) on community resilience were not investigated in these studies. After an extreme event, infrastructure systems are critical to recover to maintain the well-being of a community (40). As such, how infrastructure disruptions are associated with community resilience needs to be understood to enhance recovery policies. For instance, Yabe et al. (41) studied the socio-physical interdependencies in urban systems and their effects on disaster recovery for Puerto Rico due to Hurricane Maria. They found that expanded centralized infrastructure systems of the cities enhance the recovery efficiency of critical services. (42) found that resilience rises as facilities are distributed more fairly, boosting effective embeddedness by 10% to 30% for various facilities and counties. According to study focusing on 20 parishes hit by Hurricanes Katrina and Rita between August and September 2005, governments looking to rebuild their infrastructure should invest in locally engaged community development to achieve a stronger overall recovery and that soft and local policy toolkits can speed up the process (43).
Besides recovery process after disasters, location datasets were used to study migration, evacuation and disease spread. Mobile phone datasets are being used for inferring migration patterns (44)(45)(46), and disease spread (47)(48)(49). Facebook data was previously used to study migration and evacuation. Fraser (52) showed by comparing evacuation patterns from 10 different hazards in the US and Japan from 2019 to 2020 that some disasters have more similar evacuation patterns than others. Large, widespread disasters, such as some storms, fires, and power outages, cause both clustered and scattered evacuation networks, but smaller, more concentrated disasters primarily cause dispersed networks. Yabe et al., (53) discover that an individual's likelihood of evacuating is strongly correlated with the seismic intensity they experience through a cross-comparison analysis between four major earthquakes tracking mobile phone users' positions for a period of two months prior to and after the disaster instances in Japan. They demonstrated that the evacuation probabilities in all earthquakes collapse into a common pattern, indicating that evacuation behavior is equally dependent on seismic intensity despite the diversity of earthquake profiles and urban characteristics.
From the discussions above, in summary, following observations can be made. First, different types of location datasets including retrospective survey data, mobile phone data, social-media data, call recordings have been used in previous studies. Second, these datasets were used for various purposes: recovery trajectories, human mobility and activity, displacement rates (e.g., percentage of population impacted by a disaster), recovery time, resilience, evacuation, and migration pattern. Third, population displacement and recovery patterns after disasters were explained by power outage, household damage, flood, social capital, and socioeconomic community attributes. From the literature, it is evident that it is challenging to collect longitudinal data from disaster-affected regions through post-disaster surveys, and mostly these datasets are proprietary. But, to effectively quantify community resilience, data must be free, easily accessible, and usable (17) by urban decision makers and emergency officials. These data unavailability issues can be avoided if location data from a widely used service are made accessible. To better identify the negatively impacted community, we need to consider 'resilience' with easily accessible, free, and representative longitudinal data which involves both percentage of population impacted by a disaster and time to recover (7,8,15,36). Loss of community resilience should be explained by multiple types of infrastructure disruptions rather than confining to power outage only. For example, the importance of transportation networks' recovery of the regions and disaster condition were understudied in the current literature, despite having significant implications on policymaking for community resilience. More specifically, the following research questions are yet to be answered: Can we quantify loss of community resilience from a more easily accessible, free, and representative longitudinal data? Can we explain the heterogeneity in loss of community resilience using different types of infrastructure disruptions, disaster condition while accounting for socioeconomic attributes?
To answer these questions and bridge the gaps in the current literature, we show how Facebook users' population dataset can be used to explore how affected communities' social activities are coming back to the normal state after a disruption. We apply the concept of resilience for understanding population activity under Hurricane Ida at county-subdivision level. This paper defines the practical terms of population-resilience parameter and use it effectively to identify less resilient communities to hurricanes from real-time, free, and easily accessible Facebook data. In this regard, the population-resilient parameter could be used to evaluate the capacity of disaster-mitigation system to manage shocks and return to a normal state in response to an extreme event such a high-intensity Hurricane. Since this study analyzes the data at county subdivision level, which is finer geographical level than LGU (in Louisiana 64 parishes are divided into 579 county subdivisions), the findings ensure better understanding of community resilience as well as the association between loss of community resilience and physical infrastructure disruptions, disaster condition and economic aspects. The paper's findings could aid policy makers and emergency officers to identify and strengthen less resilient communities to hurricanes and thus to support their disasterpreparedness activities.
DATA DESCRIPTION
Facebook Population Data
In this study, we used Facebook population data at an administrative region level collected from Facebook's Data for Good platform. Facebook Population data shares the aggregate number of Facebook mobile app users who enable location services in their mobile devices (25). It is to be noted that this dataset does not depend on Facebook usage by the users. That is, even if people do not use Facebook after coming back to the original home location after the hurricane, as they will be distressed and burdened with all kinds of recovery activities, Facebook can still track users' location. This dataset provides the average number of users present in a region during the baseline period (90 days before the day the data was generated), the number of users during a crisis event, and the difference between these two quantities. Additionally, a z score is provided to highlight the areas with the most significant differences between what is being observed during an extreme event and what is typically seen when there is no extreme situation. It is obtained by [(users during crisismean baseline users)/ variance of baseline users]. The range of z-score is -4 to 4. Rouge, Acadia, Jefferson all these counties have county-subdivision named District 1. To identify the county that a county-subdivision belongs to, we used Facebook user movement data at an administrative region level 4 collected from the same platform. We used Facebook movement dataset because this dataset has the latitude and longitude of the center of the boundary polygon shape (e.g., county subdivisions) which is not available in the Facebook population datasets. Using the censusgeocode package in Python, we determined the corresponding county of a county-subdivision from the latitude and longitude of the center of a county-subdivision. Then we merged the county names with the Facebook population datasets based on polygon ID and obtained the unique county subdivisions. A polygon ID is a unique identifier for a county subdivision provided in these datasets (since the polygon ID is same for a county subdivision in both datasets).
The collected dataset for Hurricane Ida had data for 442 county subdivisions from 73 different counties across Alabama, Mississippi, and Louisiana states. In this study, we have focused only on Louisiana state because decreased population activity was observed mostly in Louisiana. People might have evacuated to Alabama and Mississippi and increased activity was observed. Since our focus is only on decreased activity, which causes loss of community resilience, we did not consider Alabama, Mississippi states. We found data for 327 county subdivisions from 39 parishes in Louisiana. In Louisiana a parish is equivalent to a county of other states in the USA.
Representativeness of Facebook population data
In this study, we use the number of Facebook users as a sample of the population. This requires validating whether the Facebook data is a representative sample of the actual population. Pew Research Center's national survey in 2019 reported high Facebook usage rates in USA. For example, 69% of US adults use Facebook as a platform or messenger app, and 74% of the Facebook users visit it once a day.
Facebook usage is also high among men (63%) and women (75%), among White, Black, and Hispanic population (each 69-70%) (27).
To further validate this, we adopted an approach introduced in Yabe et al. (16) for macroscopic/aggregate location data. We calculated the Pearson's correlation between the number of Facebook users and population in 39 parishes of Louisiana and found it to be 0.98 (Fig. 3). We also calculated the Pearson's correlation between the number of Facebook users and population from 327 county (parish) subdivisions of Louisiana and found it to be 0.964 (Fig. 3). Fig. 3 also indicates that the number of Facebook users is linearly proportional to the population both at county subdivision level and parish level. As such, Facebook users can be used as a proxy/sample of total population in this study. In Louisiana state, parish is equivalent to county in other states of the USA.
Physical Infrastructure Data
Disruption on roads
We collected disruptions on roads data from Regional Integrated Transportation Information System (RITIS) website. We considered duration of disruption on roads in hours in each county subdivision within our considered time window (from 25 th August 2021 to 30 th September 2021). RITIS provides event data from three different agencies with each agency having their own definitions of categorizing different events. In this study, we mainly considered weather hazard, weather closures, road closed, closures and obstruction agency-specific event types. The county subdivision of an event is not provided in this dataset, but latitude and longitude of the event are available. So, we identified the corresponding county subdivision from the latitude and longitude of the event.
Power service restoration time
To investigate how disruptions in power services are impacting community resilience, we included restoration time from power outage of the parishes. We collected power outage data from Bluefire Studios LLC. for Hurricane Ida. From this dataset, we obtained the total number of electricity customers in a parish of Louisiana and the number of customers faced power outages during Hurricane Ida in 1-hour time intervals from 20 th August 2021 to 30 th September 2021. We used the duration between the time when 10% customers or more of a particular county first lost their electricity services and the time when 10% customers or less were yet to restore their power services (Fig. 4). It was observed that the counties where less than 10% customers lost power services, did not take long time to get their electricity services back.
Due to data unavailability, we assumed that restoration time of power outages for all the county subdivisions under a parish is same. On average, it took same time for all the county subdivisions under a parish to restore the power services.
Property damage data
To explore if property damages have an impact on community resilience, we included property damage in terms of average inspected damage (based on Federal Emergency Management (FEMA)'s inspection guidelines). It is available for valid registrations from households within the state, county, zip that had a complete inspection, collected from FEMA's housing assistance datasets for Hurricane Ida. We determined the corresponding county subdivision of an observation based on city, zip code, parish, and state. For some county subdivisions no damage data was found in the FEMA dataset; we assumed that there was no FEMA inspected damage in those subdivisions.
Age of the houses
Since old houses are prone to be damaged by natural disasters, county subdivisions with a greater number of older houses might be less resilient to hurricane. To indicate this variable, we considered the percentage of houses that are built before 2000 (more than 21 years old when Hurricane Ida occurred in 2021) in each county subdivision. We collected this data from American Community Survey (ACS).
Disaster Condition
Distance to hurricane path
We collected hurricane path for Hurricane Ida from National Hurricane Center (NHC). We used haversine formula (Equation 1) to calculate the distance between the center of a county subdivision and hurricane path and considered minimum distances from the center of county subdivision to hurricane path. This formula is used to calculate geographic distance on earth between two different latitudelongitude values of two different points on earth. This is considered as the shortest distance between two points on earth surface (7). We considered hurricane path from 26 th August to 4 th September because hurricane was dissipated after 4 th September 2021.
= 2 ( √ 2 ( 2 − 1 2 ) + 1 2 2 ( 2 − 1 2 ))(1)
where, 2 , 1 are the latitude of point 1 and latitude of point 2, λ1, λ2 are the longitude of point 1 and longitude of point 2, and r is the radius of earth.
As disaster conditions, other variables such as the type of evacuation orders issued (mandatory and voluntary) and flood depth could be used. However, these variables are likely to be correlated with the distance from hurricane path because the regions close to the hurricane path are likely to issue a mandatory or voluntary evacuation order for their residents. Besides, these variables are difficult to obtain at a county subdivision level.
Socio-economic characteristics
As socio-economic characteristics, we included the median household income, the percentage of The list of candidate variables for the model and their descriptive statistics are provided in Table 1. The correlations between these candidates were tested using Pearson correlation coefficient measure ( Fig. 5). According to Pearson correlation coefficient, no highly correlated variables were identified but moderately correlated variables: restoration time of power outage and distance to hurricane path were identified (55). For the housing age variable, the variance inflation factor (VIF) was 11. For rest of the variables, VIF was less than 7. The multicollinearity condition number is 3.013 is below 30 which indicates that collinearity should not an issue with statistical models.
METHODS
Quantifying Community Resilience
To quantify community resilience, we first calculated transient loss of resilience using Equation 2
proposed by Bruneau et al. (36) in the context of infrastructure resilience due to an earthquake and later used by Roy et al. In this study, we used Facebook population data to quantify community resilience against hurricanes. First, for a community, we assume population activity rate available from Facebook data as a measure of its quality function ( ). We define population activity rate on a given day as the rate of Facebook users who were found in a given county-subdivision out of all the affected users on that day. The population activity rate on a given day was calculated by dividing the number of users observed in a particular county-subdivision on that day by the total number of typical users represented by the number of average Facebook users observed 90 days prior to that day.
We all of them, the minimum Z-score was less than -1.82 (>45% of -4) for more than 1 day out of our considered 37 days.
To obtain resilience of an affected community (see Table 3 and 4 in Appendix), we subtracted the transient loss of resilience from 37 which is the area under horizontal line (Fig. 6). The duration from 25 th August ( 0 ) to 30 th September ( 0 ) is of 37 days, giving the area as (1 × 37) = 37.
Statistical modeling approach
To determine the effects of different factors on the transient loss of community resilience, we Table 1 and random intercept for every county (parish). We have introduced parish as a random effect in the model. We included the random effects in the model since we expect that the loss of resilience values of the county subdivisions of a parish to be correlated with each other. We fitted the GLMM using the Gamma family with log link function in R and all the variables were standardized before fitting the model.
RESULTS
We present the results in two parts. First, we show the visualization of our datasets and the quantified resilience and transient loss of resilience. Second, we present the results of the Generalized Linear Mixed model (GLMM). Fig. 7 and 8) was: at the starting of a hurricane, human activities start to decrease in the affected area, reach maximum drop after a certain time (mostly on the day and the next day when the landfall occurred), and then start to recover. Distance to hurricane path was found to be significant and positively associated with loss of community resilience. In addition, median household income was found to be significant among the socioeconomic characteristics of the communities. The percentage of Black and Hispanic population and the percentage of houses built before 2000 had negative association with loss of resilience, but those were not found to be statistically significant.
Population Activity Trajectories
Power Outage Trajectories
Community Resilience
Spatial Distribution of Community Resilience
Result from the GLMM Model
The variance for parishes (random effects) was found to be 0.1185 and 0.325 for residuals. The random effects are important as they explain a significant amount of variation. We can take the variance for the parishes and divide it by the total variance: [0.1185/ (0.1185 + 0.3250)] = 27%. So, the differences between parishes explain ~27% of the variance that has been left after explained by the fixed effects. The R 2 (marginal), representing the proportion of variance explained by the fixed effects, has a value of 0.44.
The R 2 (conditional), representing as the proportion of variance explained by the entire model, including both fixed and random effects, has a value of 0.61. Therefore, due to introducing parishes as random effects, the proportion of variance explained by the model increased.
DISCUSSIONS
In this study, we used large-scale Facebook population datasets for Hurricane Ida occurred at
Louisiana, USA to explore how population activity before, during and after a disaster can quantify the Hurricanes Irma and Maria (16).
The described approaches and findings of the study can aid policy makers and emergency officials in following ways: i) To better understand the negative impacts of a disaster to an affected community, our proposed method to quantify 'transient loss of resilience' using Facebook data can be used rather than considering displacement rates and recovery speed separately. Because it involves both systemic impact (e.g., percentage of population impacted by a disaster) and time to recover. ii) Since Facebook data is globally available for the affected region, can be collected in real-time, is free and easily available; it can be reliably used by policy makers and emergency officials to understand the negative impact on the affected community by quantifying the loss of community resilience. iii) Since this study analyzes the data at county subdivision level, which is finer geographical level than county, the findings ensure better understanding of community resilience as well as the association between loss of community resilience and physical infrastructure disruptions, disaster condition and economic aspects. iv) The findings of this study suggest that the association between social and physical systems should be considered by the policymakers to achieve resilient cities. Due to the association between community resilience in terms of population activity and physical infrastructure systems, infrastructure disruptions caused by disasters can exacerbate the hardship experienced by the affected population. v) The findings suggest that better and fast recovery policies, and better infrastructure systems should be given emphasis by the policy makers in less wealthier communities to make them resilient to hurricanes
CONCLUSIONS
This study first quantifies transient loss in community resilience and uses it effectively to identify less resilient (more negatively impacted) communities to hurricanes from large-scale, real-time, free, and easily accessible Facebook data. The use of large-scale location data enables proactive monitoring of population activity before, during, and after a disaster such that the impact to affected community can be evaluated in real-time. This study can be used as a reference for local governments and policymakers to decide equitable spatio-temporal allocation of resources and services like food, utilities, and optimized shelter locations by rapid impact assessment based on observed loss of resilience in real-time. Performance of transportation systems should be enhanced before and after hurricanes to ensure fast evacuation as well as fast come back to the original home location after the dissipation of hurricanes. We also found that for regions facing same restoration time of power outage but located at different distances from hurricane path, the region, which is located far away from the hurricane path, suffered more due to
Hurricane probably because regions far from hurricane path received less financial and logistical support during recovery process. So, disaster preparedness programs and support during recovery process should not be confined only to the communities who are close hurricane path rather across all communities according to their need. Moreover, this study found a disparity issue, that is, communities with lower income were more impacted. While it is often assumed that poor, minority communities are less prioritized, and inequality was previously found in terms of community resilience and experienced hardship in Texas during Hurricane Harvey (8, 23), we found disparity issue to be consistent in Louisiana during Hurricane Ida as well. This emphasizes accelerated recovery activities, and better infrastructure systems in less wealthier communities.
Loss in community resilience indicates drop in regular population activity. A decline in population activity has a ripple effect on many aspects of society, from banking and finance to academia and healthcare.
So, policy makers and emergency officials should effectively identify the disaster-impacted communities in real-time and accelerate the recovery process in transportation and power infrastructures, provide equal recovery services and pre-disaster preparedness trainings across all communities without considering the economic characteristics. As a result, this will help make cities more resilient to hurricanes.
The study has some limitations. We assumed all county subdivisions under a parish on average had undergone same time of power disruption because power companies do not reveal the postal code and city name in the provided datasets. There could be slight differences from the assumption. As an indication of housing damage information, we used FEMA housing assistance datasets. Even if FEMA did not provide housing assistance due to Hurricane Ida, there could be housing damages in some parishes. So, alternative datasets can be used to better reflect the property damage estimates caused by hurricanes in future research.
Since maximum sustained wind speed or gust speed at each county subdivisions can better reflect the hurricane characteristics, it should be included in future research along with distance from to hurricane path. Our research can be expanded to forecast power outage curves due to hurricanes by predicting the recovery pattern of population activity on social media in conjunction with hurricane-related data (e.g., wind speed, wind duration, hurricane path, flood depth). Due to the intimate interaction between infrastructure systems and population engagement on social media, these anticipated post-disaster mobility curves can be used by emergency personnel and policymakers as an indicator of the spatio-temporal pattern of electrical disruption.
DATA AVAILABILITY STATEMENTS
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. All data sources have been mentioned in Data Description chapter.
ACKNOWLEDGMENTS
The authors are grateful to the U.S. National Science Foundation for the grant CMMI-1832578 to support the research presented in this paper. However, the authors are solely responsible for the findings presented here.
DECLARATIONS
Conflict of interest:
The authors declare no competing interests.
Ethical statement: All procedures were carried out in conformity with the necessary rules and guidelines.
This study uses aggregated data provided by Facebook rather than any individual-level user data from Board protocol was required for this analysis because it was an observational study of aggregate-level data. Significance level: 0-'***', 0.001-'**', 0.05-'*', 0.1-'', 1
TABLES
However, few studies focused on the effects of multiple infrastructure disruptions and disaster conditions on community resilience in population activity. Yabe et al. (16) considered the effects of median income, population size, housing damage rates, connectedness to cities, and durations of power outage on the recovery speed and displacement rates after Hurricane Maria in Puerto Rico. Sadri et al. (39) focused on the effects of physical infrastructure damage, social capital, household characteristics, and recovery assistance on recovery time of a household due to tornados using survey data in southern Indiana. The importance of transportation networks' recovery and disaster conditions of the regions were understudied in the current literature, despite they have significant implications on policymaking for disaster affected communities. Podesta et al.
Acosta et al. (50) estimated population changes due to migration over the course of a year after Hurricane Maria in Puerto Rico using Facebook data and found a 17% decrease in population in 2017. Fraser (51) used trajectories of Facebook users' movement dataset to analyze evacuation pattern: where people go when they have left disaster zones at county subdivision level due to Hurricane Dorian in Florida. He found that linking social capital and soft community-focused preparation strategies increased evacuation across cities.
For our considered time window (from 25 th August 2021 to 30 th September 2021), we were able to collect data at administrative region level 4 which is equivalent to county-subdivisions. This platform provides data at 8-hour intervals (12 am to 8 am, 8 am to 4 pm, and 4 pm to 12 am) (25). We have considered only 4 pm to 12 am interval since people are more likely to stay at their home locations during this time period compared to other time periods. People are more likely to stay at their workplace at 8 am to 4 pm and may disable their location service on mobile after 12 am before sleeping. Facebook population dataset provides only the names of the county-subdivisions (if administrative region level is 4) without the names of the counties associated with each county-subdivision. For Louisiana, it is not possible to identify a unique county-subdivision because several county subdivisions under different parishes (equivalent to a county in other states) have the same names. For example, East Baton
Black population, and the percentage of Hispanic population in each county subdivision. We collected the percentage of Hispanic population and poverty information for the county subdivisions from the demographic and economic characteristics of American Community Survey (ACS) 5-Year Data Profile for 2020. About 33% of the populations in Louisiana are Black which is the 2 nd highest population group and about 5.6% of the populations in Louisiana are Hispanic which is 3 rd highest population group (54).
( 7 )
7for quantifying transient resilience loss (TRL) in human mobility. denotes transient resilience loss, ( ) denotes a quality function of a system at time , and ( 1 − 0 ) is the recovery time.Fig. 6shows a conceptual diagram to illustrate these terms. The area between the horizontal dashed line (baseline value) and decreased quality function (solid line) from 0 to 1 is defined as transient loss of resilience of a system. The horizontal dashed line indicates that the performance of a system is supposed to follow this line if the system does not experience any disruption.The solid curved line within 0 to 1 indicates system performance follows this trend due to the occurrence of an extreme event. So, the resilience is the area under the quality function curve from time 0 to 1 . It can be obtained by subtracting the transient loss of resilience from the area under horizontal line from 0 to 1 .
calculated transient resilience loss (TRL) (Equation 2) by a numerical integration method. For analysis we considered the time period from 25 th August 2021 to 30 th September 2021. We selected this time window because most of the activity fluctuation curves for the affected county subdivisions returnedto the normal state within this time. Since we are concerned with loss of community resilience, we did not consider any increase in activities from the base period (if there was any within this time window). Among the given 327 county subdivisions in this data source, we did not consider the county subdivisions that did not have any drop in population fluctuations curves. We did not consider the county subdivisions for which population activity rate did not fall below the 90% (100% means population activity did not decrease at all). In other words, we considered the county subdivisions where 10% or more Facebook users were missing at least for one day within 29 th August to 5 th September compared to the baseline Facebook users.Hurricane Ida had its landfall on 29 th August 2021, and we considered county subdivisions where significant drop in Facebook users was observed within 7 days of landfall. In this way, we obtained observations for 166 county subdivisions out of 327. To validate that there was extreme situation in the selected 166 county subdivisions, we further checked the clipped Z-scores provided in Facebook population datasets and for
developed a Generalized Linear Mixed Model (GLMM) with Gamma family. We used GLMM for two reasons: (i) it is likely that the observations used in this study are not independent since the transient loss of resilience values for the subdivisions under a county might be similar to each other; in GLMM, to account for the non-independence issue, a random effect is introduced into the linear predictor of a regression model (Equation 3 and 4); (ii) Fig. 11 shows that the transient loss of resilience is not normally distributed and it ranges between 0 and 37. So, community loss of resilience is skewed and always positive (TRL > 0). In GLMM, it is possible to account for any distribution (e.g., Gaussian, Beta, Poisson, Gamma etc.is a × 1 column vector of continuous dependent variable, is a × matrix of the predictor variables; is a × 1 column vector of the fixed-effects regression coefficients; is the × matrix for the random effects; is a × 1 vector of the random effects (the random complement to the fixed ); and is a × 1 column vector of the residuals. Here, the dependent variable can follow any distribution. Also, is not actually estimated; instead, is assumed as normally distributed with a zero mean and variance [i.e., ~ (0, )]. Since the fixed effects are directly estimated, including the intercept, random effect complements are modeled as deviations from the fixed effect, so they have zero means. The random effects are just deviations around the value in . In our study, we have =166 observations from 36 parishes over 37 days. Since our dependent variable, transient loss of community resilience is continuous, always positive, and not normally distributed, for in (Equation 4), we used the Gamma family of distribution with a log link function (58). Further, we have 8 fixed effects as predictor variables showed in
Fig. 7
7shows how population activity (in terms of activity on Facebook) fluctuated due to Hurricane Ida for 11 county subdivisions under 11 parishes. It shows that the population activity rate started to decrease from 25 th August 2021. The highest decrease in population activity was observed on 29 th and 30 th August 2021 (the day and the next day when the landfall occurred). The red vertical line in Fig. 7 and indicates the day when landfall occurred due to Hurricane Ida. Within 30 th September, all the county subdivisions (apart from county subdivision under Terrebonne) recovered. However, recovery time varies across the county subdivisions. Some county subdivisions recovered fast (e.g., District 9 of East Baton Rouge parish), for some county subdivisions, it took longer time to return to a typical level of population activity (e.g., New Orleans). Similarly, maximum impact varied across county subdivisions. For example, in District 9 of Plaquemines parish, maximum magnitude of impact dropped below 0.2, on the other hand, in District 9 of East Baton Rouge, it dropped to 0.8 only. Population activity rate at county subdivision level for Jefferson, Lafourche, Assumption and Plaquemines parishes are shown in Fig. 8. Population activity pattern under Hurricane Ida was homogeneous for Jefferson Parish. Population activity fluctuation curves in subdivisions under Jefferson parish followed very closely to each other. On the other hand, population activity fluctuation curves for subdivisions under Lafourche, Assumption and Plaquemines parishes were not exactly same but subdivisions under a parish followed a certain pattern most of the time. Similar to Fig. 7, the highest decrease in population activity was observed on 29 th and 30 th August 2021 in subdivisions under these parishes. Recovery time and maximum impact varied across subdivisions. Despite the differences in recovery time and maximum impact, the common property of the population activity fluctuation curves (
Fig. 9
9shows the percentage of customers in different parishes who faced power outages due to Hurricane Ida. It shows that customers started to lose electricity supply after 28 th August 2021. Most of the customers lost electricity services on 29 th and 30 th August 2021, the day, and the next day when landfall occurred. Similar to Fig. 7, the red vertical line in Fig. 9 indicates the landfall day. In some counties (for example, Jefferson, St. Charles, Lafourche, Plaquemines, Terrebonne, St. John the Baptist, Orleans), about 100% customers lost power services. On the contrary, few customers from Iberia and Cameron lost their power services. It took long time for the customers in Terrebonne (28 days), Lafourche (29 days), and St. John the Baptist parishes (27 days) to restore the power services. Restoration time was shorter for the customers in St. Mary (3 days).
Fig. 10
10shows the spatial distribution of transient loss of resilience over county subdivisions. It shows that county subdivisions in South-East Louisiana suffered higher transient loss of resilience. Transient losses of resilience were higher in the county subdivisions under Terrebonne, St. John the Baptist, Plaquemines, Lafourche, and St. Charles. At the time of landfall (29 th August 2021), these places were close to the hurricane path. Since wind speed of hurricane path fell to 65 mph from 130 mph when it was over Livingston, some of the county subdivisions under this parish did not have higher transient loss of resilience, despite being close to hurricane path. Most of the county subdivisions from North (e.g., county subdivisions under St. Helena and Washington parish) and North-Western (e.g., county subdivisions from East Baton Rouge to far north Calcasieu parish) side of hurricane path resulted in lower loss of resilience (between 0 to 1). Although district 4 of Vernon parish and some of the county subdivisions from Cameron parish are far from hurricane path, they had moderate transient loss of resilience (between 4 and 6).
Fig. 11
11shows the distribution of the values of transient loss of resilience. Among 166 county subdivisions, about 60 county subdivisions' transient loss of resilience value varied between 0.1 to 1 and for 46 county subdivisions, the value was 4.
2 presents the results of the GLMM model. Among multiple types of physical infrastructure disruption related predictor variables, disruption to transportation systems and power outage were found to be significant and positively associated with transient loss of resilience. A positive association means that an increase in a predictor variable will increase the loss in resilience and a negative association indicates the opposite. The exponentiated coefficient of duration of disruptions on roads (e^ {0.141} = 1.1514) is the factor by which the mean transient loss of resilience increases by 1.15 times with one hour increase in duration of disruptions to transportation network. One day increase in restoration time for power outage (e^ {0.632} = 1.88) increases the mean transient loss of resilience by 1.88 times. Housing damages had positive association with transient loss of community resilience too, but this predictor variable was not found to be significant.
resilience and transient loss of resilience of the affected communities. Since Facebook population datasets provide data at county subdivision level (in Louisiana 64 parishes are divided into 579 county subdivisions), this work quantifies loss of community resilience focusing on finer geographical unit, whereas most of current literature are confined to county level macroscopic analysis. It was found that subdivisions under Plaquemines, Lafourche, St. John the Baptist, Orleans, Terrebonne, St. Charles, and Jefferson parishes were more negatively impacted (e.g., less resilient to) by Hurricane Ida. We also studied how disruption in multiple physical infrastructures, disaster condition, and socioeconomic characteristics are associated with the transient loss of community resilience from the Generalized Linear Mixed Model (GLMM). A positive coefficient for duration of disruption on roads indicates that the transient loss of resilience was higher in places having a longer duration of road blockage.This implies that people who evacuated could not come back to their home locations within shortest time.As a result, people's regular social activity was also not observed shortly after Hurricane Ida. The importance of transportation networks' recovery of the regions was understudied in the current literature, despite having significant implications on policymaking for community resilience. This study suggests that performance of transportation systems should be enhanced before and after hurricanes to ensure fast evacuation as well as fast come back to the original home location after the dissipation of hurricanes. Similar to duration of disruption on roads, the positive coefficient for the restoration time of power outage indicates that a longer restoration time in power services causes a higher loss of resilience. This implies that people might have connectivity issue in their area that prevented their normal social activity which resulted in a higher loss of resilience. Therefore, to enhance community resilience against an extreme event, faster restoration from power outages should be a necessary recovery effort.We found a positive coefficient between the distance to hurricane path and the transient loss of resilience. This may appear counterintuitive as it indicates that regions farther from the hurricane path would suffer a higher loss of resilience. However, this is probably because of the presence of the variable indicating the power outage restoration time in the model. The positive coefficient for the distance to hurricane path implies that if two regions faced same restoration time of power outage but located at different distances from hurricane path, the region which is located far away from the hurricane path, suffers a higher transient loss of resilience(59). A possible reason for this could be that places which were close to hurricane path were given priority including financial and logistical support during recovery process fromdifferent humanitarian and relief organizations or those communities might have better disaster preparedness because those places are prone to hurricanes. To further investigate this issue, we explored data from Community Emergency Response Team (CERT) Dataset (60). This Program educates people about disaster preparedness for hazards that may impact their area and trains them in basic disaster response skills. Among our considered 36 parishes for Hurricane Ida, CERT has programs only in 12 parishes in Louisiana and majority of those parishes (10 out of 12) are located close to the Hurricane Ida's path. This implies that disaster preparedness programs can be expanded among communities who live far away from the hurricane path to educate and train them about the basic disaster response skills about team organization, and medical operations.Median household income had negative effects on transient loss of community resilience, implying that communities with a lower median income had a higher loss in resilience. This might happen as poorer communities might take a longer time for recovery and resulted in population activity drop for a longer time. Furthermore, regions with poorer communities might have poor infrastructure systems causing more populations to lose their regular social activity. The negative relationship between median household income and loss of community resilience indicates an equity issue, that is, communities with lower income are disproportionately impacted. This necessitates accelerated recovery activities, and better infrastructure systems in less wealthier communities to make them resilient to hurricanes. While it is often assumed that poor, minority communities are less prioritized, and inequality was previously found in terms of community resilience and experienced hardship in Texas during Hurricane Harvey (8, 23), we found disparity issue to be consistent even in Louisiana during Hurricane Ida.Studies on Hurricanes Katrina and Rita show that median income, and built environment contribute to migration (61) and evacuation(62).(23) found inequity in experienced hardship due to infrastructure disruptions during Hurricane Harvey for various vulnerable subpopulations. Power service restoration time and housing damage are associated with recovery speed of the communities as found in disasters including
Facebook . "
.Facebook Data for Good" (now known as "Data for Good at Meta") platform collected any user information in accordance with Facebook's Data Use Policy, then aggregated it to the neighborhood level to protect people's privacy so that researchers never came into contact with individual-level information. All other data like Power outage data from Bluefire Studios LLC., disruptions on roads data from Regional Integrated Transportation Information System (RITIS), and socio-economic data from American Community Survey (ACS) are aggregate data and do not contain any individual-level information. They do not contain any sensitive information or user information. No Institutional Review
FIGURE CAPTIONS Fig. 1 .
CAPTIONS1Influence of decreased human activity on daily life.
Fig. 2 .
2Factors associated with decreased population activity.
Fig. 3 .
3Facebook users vs population in 327 parish subdivisions and 39 parishes of Louisiana.
Fig. 4 .
4Power outage for Livingston Parish due to Hurricane Ida and considered restoration time in this study.
Fig. 5 .Fig. 6 .
56Correlations among variables Conceptual definition of resilience and transient loss of resilience for the affected communities.
Fig. 7 .
7Population activity curves from Facebook population datasets in Louisiana due to Hurricane Ida.
Fig. 8 .Fig. 9 .
89Population activity curves for subdivisions under four different parishes Power outage curves due to Hurricane Ida.
Fig. 10 .
10Transient loss of resilience for 166 county subdivisions along with hurricane path.
Fig. 11 .
11Distribution plot of transient loss of community resilience.
Fig. 2 .
2Factors associated with decreased population activity.
Fig. 3 .
3Facebook users vs population in 327 parish subdivisions and 39 parishes of Louisiana.
Fig. 4 .
4Power outage for Livingston Parish due to Hurricane Ida and considered restoration time in this study.
Fig. 5 .Fig. 6 .
56Correlations among variables Conceptual definition of resilience and transient loss of resilience for the affected communities.
Fig. 7 .
7Population activity curves from Facebook population datasets in Louisiana due to Hurricane Ida.
Fig. 8 .Fig. 9 .
89Population activity curves for subdivisions under four different parishes Power outage curves due to Hurricane Ida.
Fig. 10 .
10Transient loss of resilience for 166 county subdivisions along with hurricane path.
Table 3
3and 4 present the results of resilience calculation for Hurricane Ida. The highest transient loss of resilience was found 12.88 for District 8 in Plaquemines parish. We also calculated the ratio between transient loss of resilience and resilience (Transient loss of resilience/Resilience). The highest ratio of resilience loss over resilience has been found as 0.53 for the same county subdivision. During Hurricane Ida, among the 36 parishes in Louisiana considered here, the county subdivisions of Plaquemines suffered the highest transient loss of resilience followed by the county subdivisions of St. John the Baptist, Terrebonne, Lafourche, St. Charles, and Orleans (Table 3). Most of the county subdivisions under Plaquemines had the highest transient resilience loss and transient loss of resilience over resilience ratio.On the contrary, the county subdivisions under East Baton Rouge parish had the highest community resilience followed by the county subdivisions under Vermilion, Iberville, Iberia, and Lafayette parishes due to hurricane Ida (Table 4). These metrics indicate significant disruptions in population activity after Hurricane Ida in Louisiana state.
Table
physical infrastructure disruptions, disaster condition as well as socioeconomic characteristics. This study found that activity of Facebook users tended to drop more in communities with longer time of infrastructure disruptions. The importance of transportation networks' recovery of the regions was understudied in the current literature, despite having significant implications on policymaking for community resilience.Secondly, this study investigated why some communities (in terms of Facebook users) are more
impacted. Transient loss in community resilience was examined for Hurricane Ida for 37 days of time
window from August 25, 2021, to September 30, 2021, using generalized linear mixed models at county
subdivision level. Using models, descriptive statistics, and geospatial analytics, this study identified
consistent relationships between transient loss of community resilience and key factors: multiple types of
Table 1 .
1Descriptive StatisticsSocio-economic characteristics and social vulnerabilityTable 2. Results of the generalized linear mixed model Socio-economic characteristicsVariables
Mean
Std
Min
Median
Max
Transient loss of resilience (activity
ratio-day)
3.19
2.81
0.101
2.278
12.882
Physical infrastructure data
Duration of disruption on roads (hr)
490.07
1202.94
0.5
76.55
11441.32
Restoration time for power outage
(Day)
12.49
9.13
0
13
29
Property damage
4051.81
7045.78
0
1539
45117.71
% of Households built before 2000
72.5
17.95
0
75.45
96.4
Disaster condition
Distance to hurricane path (km)
67.6
55
5.734
49.067
287.38
Median household income (USD)
53791.48 19837.67 16583
52085
133056
% of Black population
29.7
23.73
0
23.8
93.4
% of Hispanic population
3.91
3.73
0
2.90
20.7
Table 3 .
3Transient loss of resilience and resilience values of 20 least resilient county subdivisionsParish Name
County subdivision
Transient loss of
resilience
Resilience
Transient loss or
resilience/
Resilience
Plaquemines
District 8
12.88
24.12
0.53
District 9
12.22
24.72
0.49
District 7
11.62
25.39
0.46
District 6
9.61
27.39
0.35
St. John the Baptist
District 5
11.07
25.93
0.43
District 7
8.63
28.37
0.30
Terrebonne
District 7
10.94
26.06
0.42
District 1
9.72
27.28
0.36
District 8
8.57
28.44
0.30
District 9
8.52
28.48
0.29
Lafourche
District 9
10.07
26.93
0.37
District 5
7.84
29.16
0.27
St. Charles
District 3
8.72
28.28
0.31
District 2
7.72
29.28
0.26
District 6
7.70
29.30
0.26
Sabine
District 1
8.28
28.72
0.29
Orleans
New Orleans
8.28
28.72
0.29
Livingston
District 8
6.87
30.13
0.23
Cameron
District 1
6.80
30.20
0.22
Jefferson
District 5
6.76
30.24
0.22
Table 4 .
4Transient loss of resilience and resilience values of some resilient county subdivisions FIGURES Fig. 1. Influence of decreased human activity on daily life.Parish Name
County (Parish)
subdivision
Transient loss of
resilience
Resilience
Transient loss
or resilience/
Resilience
East Baton Rouge
District 4
0.10
36.9
0.002
District 3
0.15
36.85
0.004
District 12
0.30
36.7
0.008
District 7
0.49
36.51
0.013
District 9
0.53
36.47
0.014
District 8
0.61
36.39
0.017
Vermilion
District 13
0.26
36.74
0.007
Ascension
District 8
0.29
36.71
0.008
District 10
0.36
36.64
0.009
Iberville
District 13
0.30
36.70
0.008
District 10
0.30
36.70
0.008
Iberia
District 5
0.34
36.66
0.009
District 13
0.52
36.48
0.014
St. Tammany
District 8
0.36
36.64
0.010
District 9
0.50
36.50
0.013
Washington
District 3
0.39
36.41
0.011
Livingston
District 3
0.34
36.66
0.009
District 5
0.40
36.60
0.010
District 7
0.46
36.54
0.013
Lafayette
District F
0.43
36.57
0.011
St. Martin
District 6
0.45
36.55
0.012
District 2
0.50
36.50
0.014
Assumption
District 8
0.53
36.47
0.015
St. Mary
District 5
0.53
36.47
0.015
St. Landry
District 3
0.57
36.43
0.016
Fig. 11. Distribution plot of transient loss of community resilience.
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| sample_1109 | 0.9342 | arxiv | |
Data-driven competitive facilitative tree interactions and their implications on nature-based solutions
Aristides Moustakas
Institute for Applied Data Analytics
Universiti Brunei Darussalam
Jalan Tungku Link
1410Gadong, BruneiBE
Ioannis N Daliakopoulos
Department of Agriculture
Technological Educational Institute of Crete
HeraklionGreece
Tim G Benton
School of Biology
University of Leeds
LS2 9JTLeedsUK
Aris Moustakas arismoustakas@gmail.com
Data-driven competitive facilitative tree interactions and their implications on nature-based solutions
10.1016/j.scitotenv.2018.09.349Journal paper published in: Science of the Total Environment Corresponding author:Environmental informaticsecological facilitationeco-hydrologydensity effectssoil moistureland surface temperaturesavannas
Spatio-temporal data are more ubiquitous and richer than even before and the availability of such data poses great challenges in data analytics. Ecological facilitation, the positive effect of density of individuals on the individual's survival across a stress gradient, is a complex phenomenon. A large number of tree individuals coupled with soil moisture, temperature, and water stress data across a long temporal period were followed. Data-driven analysis in the absence of hypothesis was performed. Information theoretic analysis of multiple statistical models was employed in order to quantify the best data-driven index of vegetation density and spatial scale of interactions. Sequentially, tree survival was quantified as a function of the size of the individual, vegetation density, and time at the optimal spatial interaction scale. Land surface temperature and soil moisture were also statistically explained by tree size, density, and time. Results indicated that in space both facilitation and competition co-exist in the same ecosystem and the sign and magnitude of this depend on the spatial scale. Overall, within the optimal data-driven spatial scale, tree survival was best explained by the interaction between density and year, sifting overall from facilitation to competition through time. However, small sized trees were always facilitated by increased densities, while large sized trees had either negative or no density effects. Tree size was more important predictor than density in survival and this has implications for nature-based solutions: maintaining large tree individuals or planting species that can become large-sized can safeguard against tree-less areas by promoting survival at long time periods through harsh environmental conditions. Large trees had also a significant effect in moderating land surface temperature and this effect was higher than the one of vegetation density on temperature.
Highlights
(i)
Data-driven approaches may provide new insights into understanding facilitation (ii) Facilitation & competition coexist depending on the spatial scale.
(iii) Within a spatial scale there are competitive years and facilitative years.
(iv) Tree size is more important predictor than density in tree survival (v) Large trees moderate surface temperature more than vegetation density
Introduction
With the rapid development of smart sensors, social networks, as well as digital maps and remotely-sensed imagery, spatio-temporal data are more ubiquitous and richer than ever before (Fayyad et al., 1996;Gupta et al., 1997;Moustakas, 2017). The volume of such (big) data creates great challenges in the handling, visualizing, and analysing (Chen and Zhang, 2014;Jagadish et al., 2014;. These challenges have generated the necessity of new interdisciplinary fields between statistics, computer science, and the field of the data domain, potentially providing a paradigm shift in science (Kitchin, 2014), with data-driven approaches (Deluigi et al., 2017;Hong et al., 2018;Levi et al., 2018;Yin et al., 2018).
Since its advent, remote sensing has provided important coverage, mapping and classification of land-cover features, such as vegetation, soil, and water (Lillesand et al., 2014). Remote sensing is giving us unprecedented access to data between ecosystems and climate (Kerr and Ostrovsky, 2003;Reichstein et al., 2007), allowing us to explore ecological effects which are weak at the individual scale but important in determining ecosystem-level properties. Within the field of ecology, the availability of remotely sensed imagery has huge potential for addressing ecological questions at scales unimaginable in the past (Xu et al., 2015). One area is the ability to look at patterns of survival between plants over large scales and multiple time steps (Moustakas et al., 2010). This is important because the way trees interact and survive determines a range of ecosystem services and thus has implications for nature-based solutions (Baró and Gómez-Baggethun, 2017).
Often under-recognised in the past, positive (facilitation) and negative (competition) density plant interactions are now considered to have serious implications for population dynamics and ecosystem function (Brooker et al., 2008). There are several definitions of facilitation (Wright et al., 2017) as well as interactions occurring between different types of plant, such as tree-tree, shrub-tree, tree-grass or woody species-grass, grass-seedling, and seedling-adult trees. Here, our focus is on tree survival, so we use the term 'facilitation' as increased chance of woody species survival (tree-tree and shrub-tree, i.e. among woody species only, thereafter tree) with increasing number of individual neighbours or canopy cover within a defined neighbourhood. Facilitative-competitive interactions have often been investigated in terms of the stress gradient hypothesis (Bertness and Callaway, 1994), which predicts an increase of positive interactions (facilitation) with increasing environmental stress (Bertness and Callaway, 1994;Blaser et al., 2013;Dohn et al., 2013). Apart from the interest that facilitation exhibits from the perspective of basic biological knowledge, it has serious implications for soil surface water, degraded land restoration (Antonio et al., 2018;Víctor et al., 2017), as well as for agriculture and food security (Li et al., 2014;Moschitz et al., 2015). To that end, understanding the interplay between trees and the way they ameliorate their biotic and physical environment (Yu and D'Odorico, 2017) as well as climate and soil, is critical for ecosystem management, agricultural planning, and water management (Davis et al., 2017).
Negative density effects on plant life-histories have been reported to switch to positive effects along a stress gradient, with precipitation as the most commonly reported stress (Noemí et al., 2016). However, there are several other key stressors that can include, among others, elevation (Cavieres et al., 2006;Choler et al., 2001), grazing (Smit et al., 2007), fire (Moustakas, 2015), and temperature (Callaway and King, 1996). In addition, the strength and sign of density effects depends on both on the spatial and temporal scales. Regarding spatial scales, there are cases where competition and facilitation coexist in the same ecosystem (Staver, 2018), with finer scale facilitation and coarser scale competition (Riginos et al., 2009), or the inverse (van de Koppel et al., 2006).
In terms of temporal scales it has been documented that depending on the daily environmental conditions the same individual plants can compete or facilitate depending on water availability and temperature (Wright et al., 2015). These relationships can change over time, in some years facilitation or competition may dominate. Even in years, where, on average, facilitation may dominate, there may be days that competition prevails. Thus, this provides a challenge in selecting the temporal scale for analysis. Adding to the complexity of the problem, positive or negative density effects depend also on the density per se as a stress gradient with studies reporting that facilitation peaking at intermediate densities (Dickie et al., 2005) and other studies reporting that higher densities would increase both competition and facilitation determined by the environmental stress gradient (Wright et al., 2015). Part of the complexity (Veblen, 2008;Wright et al., 2013) and lack of a clear picture may derive from the fact that the definition of the spatial scale (neighbourhood) of local interactions becomes a crucial determinant of the power to detect effects at different scales (Bradter et al., 2013;Gunton and Pöyry, 2016); (Fig. 1).
In this study we employ hypothesis-free big data analytics of the impact on tree survival by other tree individuals across 61 years. We integrate a previously published tree dataset with a large number of tree individuals across a long temporal replicate (Moustakas et al., 2006;Moustakas et al., 2008) with temperature, soil water, and water stress data. All data are derived by remote sensing. Doing so we retrospectively integrate tree data with hydrological and climatic data that were not previously available, as the first two time replicates of the tree data were derived in periods when satellites were not available (aerial photos were used instead), and thus the hydrological and temperature data could not be extracted. Past studies in facilitation have mainly been hypothesis-driven. The problem is that when we make a hypothesis, we become attached to it (Chamberlin, 1897;Platt, 1964). We explicitly refrained from formulating any hypotheses; instead we performed data-driven analysis, making the implicit hypothesis that an underlying dependence between collected data can be objectively mined (van Helden, 2013). Data-driven approaches are not competitive to hypothesis-led studies in scientific knowledge discovery but are complementary and iterative with them (Kell and Oliver, 2004). To that end, we initially perform data-driven selection of the best index of tree density as well as the spatial scale of interactions. We then study survival as a function of density, size of the individual, and year as well as their interactions. We sought to quantify the data-driven index of density as well as scale of spatial interactions. We sequentially investigated the spatio-temporal patterns of density effects.
Methods
Study area
Plots (N=7) are located in semi-arid savanna in the Southern Kalahari near the city of Kimberley, South Africa, covering a total area of ~700 ha. A satellite view of the plots is provided in Fig. 1a, and a ground view in Fig. 1b. Plots extend between 28°55"00' S, 24°77"40' E and 28°65"00' S, 24°88"90' E. Rain is seasonal, falling mainly between December -February (summer months) (Moustakas et al., 2006). Mean annual precipitation is 411 mm (St.Dev = 132), while summer mean maximum daily temperature is 32 o C, and winter mean minimum daily temperature is 3 o C (Moustakas et al., 2006). The soil consists of mainly Hutton (haplic arenosol) type soil and its depth exceeds 2 m (Moustakas et al., 2006). The main tree species present in the plots are Acacia erioloba, Acacia hebeclada, Acacia tortilis, Grewia flava, and Tarchonanthus camphorate, with A. erioloba being by far the most dominant species, as precipitation is scarce and the sandy soil in the area allows deep rooted species to access permanent deep-soil aquifers (Moustakas et al., 2006). In general the study plots had grazing and some browsing, whereas anthropogenic disturbances and land-uses were minimal (Moustakas et al., 2006).
Normalized Difference Vegetation Index (NDVI)
The Normalized Difference Vegetation Index (NDVI) ( (Deering and Haas, 1980;Tucker, 1979) is commonly used to represent the level or intensity of vegetation activity. It is based on a simple ratio between the near infrared (NIR) and red (R) spectral bands, which characterize leaves development and photosynthesis, respectively (Daliakopoulos et al., 2009). The MODIS satellite data with a ground resolution of 250 m was used over the plots.
(1)
where ρ i is the reflectance for the red and near infrared bands, denoted by subscripts R and NIR, respectively.
Land Surface Temperature (LST)
Land surface temperature (LST) is a significant parameter in exploring the exchange of surface matter, surface energy balance and surface physical and chemical processes and is currently widely used in soil, hydrology, biology and geochemistry (Deng et al., 2018;Hao et al., 2016;Tomlinson et al., 2011). Landsat 4 and its successors have one or two thermal bands, and they offer the possibility of obtaining LST estimates at 30 m resolution. Emissivity data must be estimated or alternatively obtained from secondary sources (Muro et al., 2016). A common way of estimating emissivity is the NDVI threshold method, which is based on the statistical relationship existing between thermal and visible and near-infrared bands ((Deng et al., 2018;Sobrino et al., 2004)Deng et al., 2018Sobrino et al., 2004). The relationship has also been reported to yield higher accuracies in arid areas (Sobrino et al., 2008), therefore its use in the case study is ideal. Here we estimate LST from a single thermal channel using the generalized SC algorithm proposed by (Jiménez-Muñoz et al., 2009;Jiménez-Muñoz and Sobrino, 2003) that is applicable to the TIR channel of Landsat 5 relying on the estimation of the so-called atmospheric functions (AFs), which were assumed to be dependent only on atmospheric water vapor content and land surface emissivity.
Soil Moisture Index (SMI)
Soil moisture retained a great deal of attention during recent years, with several relevant indicators being proposed using a wide range of completely different methods and sensors (Kerenyi and Putsay, 2000;Vlassova et al., 2014). Given the NDVI and the Land Surface Temperature Ts [ o K] of each pixel, one can define the SMI index for a large enough land dataset (i.e. an entire satellite scene). Ts/NVDI values can be used to derive
(2) (3) (4)
where Ts is the Land Surface Temperature [°K] of each pixel, and a [°K] and b [°K] are the slope and intercept values of the dry and wet edge as denoted by subscripts d and w. On a conceptual level, the scatter plots of the Ts/NDVI space can be enveloped in a triangular (Carlson et al., 1994) or a trapezium shape (Moran et al., 1994) where the upper sloping edge is defined as the dry edge ( ), and the lower sloping edge is defined as the wet edge ( ), since they represent extreme conditions of soil moisture and evapotranspiration.
Tree data
A previously published (Moustakas et al., 2006;Moustakas et al., 2008) long-term (1940 to 2001 over 5 time snapshots) tree data set covering over 20,000 individuals within the study area plots was used. The study species are evergreen and thus their NDVI reflectance has very low inter-annual variation . Hence, the fact that the aerial photos have not been taken during the same month each year does not introduce significant bias in the projected tree size . There was negligible browsing, anthropogenic disturbances, or tree diseases in the study plots (Moustakas et al., 2006). As a result, the tree canopy size (as estimated from remote sensing) is not biased by these causes (Moustakas et al., 2006;Moustakas et al., 2008).
For the identification and multi-temporal analysis of the trees, black-and-white aerial photographs of the area taken in 1940, 1964, 1984, and 1993, and an IKONOS satellite image taken in 2001 were used. Every individual tree was identified and followed from 1940 to the next available photo till 2001. The spatial resolution of the aerial photos was 2 m, whereas that of the IKONOS satellite image was 1 m. Since both satellite and aerial photos are used in the tree database, the spatial resolution was set to 2 m; as a result, trees with canopy diameter of minimum 2 m are clustered. Thus, assuming a cyclical projected canopy, the minimum projected canopy area (tree size) recorded is approximately:
(6)
In order to avoid the tree delineation error, we excluded from the analysis all trees appearing to have canopy area larger than 350 m 2 , which was the maximum recorded and verified during fieldwork (Moustakas et al., 2006). The study area analyzed in this paper contained 16,331 tree individuals in total across years. Field work for comparing patterns in the classification and easily visible ground-truth landmarks, as well as comparing remotesensing classified and actual tree canopy sizes of tree individuals was also performed; for further details concerning the remote-sensing methods see (Moustakas et al., 2006;Moustakas et al., 2008).
Spatio-temporal tree dataset
The classification conducted populated a database containing the X, Y coordinates of each tree, the year, the canopy surface area in m 2 , a unique tree number ID, the year that the tree was first seen and last seen, and whether the tree survived (survival) or not (death) as binary events. Processing further with spatial statistical analysis, we clustered spatial neighbourhoods in terms of circles with increasing radii spanning from 4, 8,16,32,64,128,256, and 512 (focal neighbourhood) m around each tree individual (focal individual) replicated across all tree individuals in the data base, for each available time step. We then calculated (i) the number of tree individuals, (ii) the total canopy cover, and (iii) the percentage of canopy cover within each focal neighbourhood [4, … , 512] m.
Data integration
We sought to integrate the spatial tree data set with NDVI, temperature, and soil moisture of neighbouring areas in a grid-based classification of 30 x 30 m. The USGS Landsat 5 Collection 1 Tier 1 Raw Scenes with a resolution of 30 m were processed using a Google Earth Engine (GEE) script (see Supplementary material, Appendix 1). Among the high resolution optical sensors, Landsat-5 is considered as one of the better calibrated sensors for NDVI extraction and it is thus often used as a benchmark for other products (Beck et al., 2011). These data were not available for the two first time snapshots (1940 and 1964) since satellite records became available much later. Nevertheless, they were available for the last 3 snapshots (June 1984(June , 1993(June , and 2001 dates and scenes shown in Table S1)). Indexes discussed here were used without further calibration since (a) the aggregation level of the satellite image information (30 x 30 m) would not allow direct ground-truthing with conventional ground measurements, and (b) the results we later draw upon don't pertain absolute values but rather a comparative assessment among the scenes. NDVI and LST were extracted from the respective Landsat scene enveloping the study area and values were plotted for each scene pixel (Fig. S1). To get an estimate of the wet and dry edges of the conceptual trapezoid, data was binned in intervals of 0.05 NDVI and for each interval minimum and maximum values are identified. Then, linear regression was applied to the resulting minimum (wet edge) and maximum (dry edge) temperatures. From the regression equations, the slopes (a) and intercepts (b) were obtained and applied to Eq. 4. Table S1 shows the resulting values (see Supplementary material). The R code for the estimation of SMI from NDVI and LST values is given in Supplementary material, Appendix 2. The final resulting dataset comprised of all the tree data described above plus values of NDVI, temperature, and soil moisture index for each tree individual.
Standardised Precipitation Index (SPI)
Standardised Precipitation Index (SPI); (McKee et al., 1993) is widely used to access meteorological drought occurrence as cumulative precipitation deviation from the norm on a variety of timescales (Daliakopoulos et al., 2017). On short timescales, SPI relates well to stress on soil moisture, while at longer timescales, it can depict water stress on slower processes such as groundwater and reservoir storage (Keyantash, 2018). SPI is obtained by fitting a gamma or a Pearson Type III distribution to monthly precipitation values. The default implementation employed here uses a 2-parameter gamma distribution fit where the shape and scale parameters are maximum likelihood estimates as described in (Thom, 1958). Here, SPI-48 (the cumulative precipitation deviation from the norm over 48 months) corresponding to long duration events (Daliakopoulos et al., 2017) was estimated using monthly precipitation data from the nearest (distance ~35 km) weather station at Kimberley, South Africa, and the 'SPI' package in R (R Development Core Team, 2018) for the period 1940-2003. Missing monthly precipitation values (about 13% of the dataset) were infilled based on an unbroken dataset of annual values , considering the monthly average for the given month M and the long-term annual average according to:
SPI-48 allowed us to define periods of long-term water stress or availability that could have an impact on deep-rooted vegetation. SPI values between [-1, 1] consist 68% of the total values, while values between [1.5, 2.0] define severely wet periods and values between [-2.0, -1.5] severely dry periods, while values > 2 or < -2 extremely wet or dry cases, respectively (Keyantash, 2018;McKee et al., 1993).
Survival Analysis
We employed Generalised Linear Models with logistic regression with tree death as dependent variable (an event occurring at most once for each tree in the data and thus avoiding temporal autocorrelation). We initially sought to quantify the most parsimonious data-driven index of neighbourhood density which included (a) number of tree individuals within each focal neighbourhood, (b) percentage of canopy cover within each focal neighbourhood, (c) total cover within each focal neighbourhood by selecting the model that exhibited the lowest Akaike (AIC) value (Burnham and Anderson, 2002;Gunton and Kunin, 2007;. Sequentially sought to quantify the most parsimonious datadriven index of focal neighbourhood (i.e. define the best scale of competitive-facilitative tree interactions) by selecting the focal neighbourhood (scale) that exhibited the lowest AIC. Having quantified the optimal index of neighbourhood density and the optimal index of spatial scale of interactions, we then sought to quantify tree survival (dependent variable) as a function of the size of tree individual, density, and year and all their two-way and threeway interactions. In particular, the three-way interaction between tree size, density and year can provide spatio-temporal information regarding potential switching from competition to facilitation through time (negative to positive density effects on survival) for different levels of density and how is this modulated by tree size. Year refers to the last seen year of a tree. Analysis of heteroscedasticity of the best model indicated that the model fit assumptions were fulfilled.
Explaining temperature or SMI with tree size, density, and year Linear models were fitted between SMI or LST as dependent variables (analysis repeated twice, once for each dependent variable) and the best data-driven index of density, scale of interactions and tree size (independent variables), in order to predict soil moisture or land surface temperature on each location based on those variables. Analysis of heteroscedasticity of each of the two models, indicated that the model fit assumptions were fulfilled each time.
Results
Data-driven index of density and of spatial scale
The number of tree individuals increased exponentially across the examined scales of 4 to 512 meters around each tree (Fig. 2a); this pattern was very similar to the total cover around each tree across scales (Fig. 2b). However, the inverse pattern was recorded with the percentage of cover around each tree across scales, where the percentage of cover decreased exponentially across scales (Fig. 2c). The best data-driven index of density was total cover across scales ( Fig. 2d and Table S3, S4, S5 in Supplementary material S2). The best data-driven scale of interactions was 512 m, the coarsest scale from the ones explored, followed by 4 m the finest scale from the ones explored ( Fig. 2d and Table S4). We therefore proceeded throughout the analysis by counting within a circle of 512 m around each individual tree (scale) the total tree canopy cover in m 2 (density). Examining the best model fit between tree death and density (total cover within 512 m from each tree), size of the individual tree, and year indicated that all three variables were significant and their marginally significant three-way interaction between them was not justified (Table 1); the removal of the three-way interaction between size-density-year resulted in a model with >2 AIC difference than the full model (Burnham and Anderson, 2002). The interaction between year and size explained the largest amount of deviance (696.66) followed by tree size alone (543.27), and density alone (345.41); (Table 1). The interaction between size and density (1.37), size and year (17.77), the three-way interaction between size density and year (7.47) explained relatively small amounts of the total explained model deviance, and year alone was also not among the most informative predictors of survival (125.01); (values of explained deviance in parentheses here and Table 1).
Size had a negative effect on death indicating that larger individuals had lower chance of death and thus a higher chance of survival (negative model coefficient for size alone, Table 2), and this was consistent across years: the size-year interaction was negative across all years with negative coefficients for size :1964, size:1984, and size:1993; Table 2. Increasing densities always resulted in increased chance of survival (facilitation) for smallsized trees across all years (bin size=0, Fig. 3). Increasing densities had no effect on the mean chance of survival for large-sized trees (bin size=350, Fig. 3); however, increased densities resulted in increased the confidence intervals for the survival of big trees indicating larger variance and potentially negative density effects on big trees (bin size=350, Fig. 3). In 1940, the interaction between density and size is negative with increasing densities across all tree sizes (i.e. there was facilitation) except the largest trees (bin size=350) were there was no effect between density and survival (neither facilitation or competition) (Fig. 3). In 1964, there were positive density effects on survival (facilitation) for all tree sizes except the largest trees (bin size=350) where negative density effects were found (competition); (Fig. 3). In 1984, there were increased deaths with density across all tree sizes (competition) except the smallest sized trees (bin size=0) that the relationship is positive i.e. facilitation (Fig. 3). In 1993 there is decreased chance of death with increasing density (facilitation) for small and intermediate tree sizes and increased death chance with density (competition) for the largest sized trees (bin sizes of 200 and 350); (Fig. 3).
Water stress (SPI)
In terms of water stress (SPI index), there were periods of severe draught (SPI < 1.5) as well as severe humidity (SPI > 1.5) across all available time intervals (Fig. 4). Exceptional draught (SPI ≤ -2) was recorded during the 1964-1984period (in 1967Fig. 4) as well as during the 1984-1993period (in 1986Fig. 4). Exceptional humidity (SPI ~ 3) was also recorded in the 1964-1984period (in 1978Fig. 4).
Soil moisture (SMI)
Tree size, year, and density were highly significant predictors of SMI (all interactions significant; Table 3). The interaction between year and density and year alone explained the majority of deviance (8.29), but overall the values of deviance explained were low (all values of deviance explained in Table 3 are smaller than 10). SMI increased with tree size, and with canopy cover (positive model coefficients in Table 4). SMI also increased in time during the study as indicated by the positive coefficients for years 1993 and 2001 (the coefficient for year 1984 is in the intercept; Table 4). SMI always decreased with increased densities for large sized trees (Fig. 5). In 1984 SMI increased with density for small sized trees (Fig. 5). In 1983, SMI increased with density for small and middle sized trees (Fig. 5). In 2001 SMI decreased with density across all tree sizes (Fig. 5).
Land Surface Temperature (LST)
Tree size, year, and density were highly significant predictors of LST (all covariates and their interactions significant; Table 5). Overall, year explained the vast majority of deviance in LST (deviance explained 62390 in Table 5), followed by tree size (455), and the interaction between density and year (359; Table 5). LST decreased with increasing tree size and density (negative model coefficients in Table 6). LST decreased in 1993 and increased in 2001 in comparison with 1984 (the coefficient for 1984 is within the intercept; Table 6). In 1984 LST decreased with increasing density for small and middle sized trees, while it increased with increasing density for large sized trees ( Fig. 6; Table 6). In 1993, LST decreased with density for all tree sizes except the largest trees (bin size=350); (Fig. 6). In 2001, LST increased with density for all tree sizes (Fig. 6).
Discussion
Overall, death (the reciprocal of survival) was best explained (in terms of model deviance) by the interaction between density and year, shifting from facilitation to competition through time. It is important to note that it is the same tree individuals that facilitated that end up competing (Wright et al., 2015). Thus, when seen form a dynamic spatio-temporal perspective, in space there are both scale-dependent positive and negative density effects coexisting in the same ecosystem as described in other studies (Riginos et al., 2009;Staver, 2018;van de Koppel et al., 2006) -see also Table S5 & S6 in Supplementary analysis S3 for reporting the same result here. In time there is a shifting of positive to negative density effects at shorter time scales (Wright et al., 2015) as well as through years as shown here. However, one of the major findings reported here is that the survival of small sized trees was always facilitated by increased densities (i.e. always facilitation), while the survival of large sized trees was never facilitated by increased densities (i.e. either competition or no density effects).
It is often considered that within the stress gradient, it is the arid end (i.e. lack of water) that generates stress and thereby promotes facilitation (Dohn et al., 2013;Noemí et al., 2016). However even in an arid ecosystem such as the one examined here there is severe or exceptional water stress from humidity too -see SPI graph, Fig 4. While we cannot causally link water stress temporal conditions with survival and facilitation (we are unaware in which year/point within each interval of the data each tree died), we conclude that experimental stress gradients should include both the arid end as well as the humid end stress. Will facilitation occur in the high end of severe or exceptional humid conditions? Tree death due to prolonged wet conditions is well recorded in humid ecosystems (Assahira et al., 2017;Tzeng et al., 2018) and to that end extreme humidity can act as a stressor. Nevertheless our understanding of the use of surface vs. groundwater by deep rooted trees in more arid ecosystems is limited (Steggles et al., 2017).
The second best explanatory variable of the death was tree size alone while density alone was the third best predictor. During 1940-1964 facilitation was recorded across densities and tree sizes. However, large sized trees exhibited higher variance in the confidence intervals of the positive effects of density, implying that the level of facilitation varied. During 1964-1984 higher densities facilitated small sized trees but resulted in competition for large sized tree individuals. During 1984-1993 higher densities resulted in competition across all tree sizes but competition was higher for larger sized trees. During 1993-2001, density did not show any effects on small sized tress but exhibited negative effects on large sized ones. It is therefore not only the effects of density (Dickie et al., 2005;Wright et al., 2015) but also the size of the individual that play an important role -some earlier work has been briefly mentioning the role of tree size in terms of height in tree-grass interactions (Blaser et al., 2013;Moustakas and Evans, 2013). The role of tree size is important because large trees have a longer rooting system (Jackson et al., 2000) and are thus more likely to up-lift water via hydraulic lift (Ludwig et al., 2003) with vertical roots or to sustain rain water through their horizontal roots (Caldwell et al., 1998;Caldwell and Richards, 1989;Schenk and Jackson, 2002). In addition, tree size is a good predictor of survival (Colangelo et al., 2017;Coomes and Allen, 2007;Moustakas and Evans, 2015) with large trees having a higher probability of survival.
The fact that tree size was more important predictor than density has also serious implications for nature-based solutions (Keesstra et al., 2018;Nesshöver et al., 2017): maintaining large tree individuals or planting species that can become large-sized can safeguard against desertification or tree-less areas (Aba et al., 2017;Lindenmayer and Laurance, 2017;Runnström, 2000) by promoting survival at long time periods through harsh environmental conditions. The role of scattered trees (Prevedello et al., 2018) and, complementarily, the effects of declining old large tress (Jones et al., 2018) on biodiversity conservation have also been highlighted. In addition, species that can grow fast or become large-sized can facilitate ecological restoration of degraded areas (Rawlik et al., 2018). Assuming that large trees are likely to be old (Harper, 1977), in agricultural systems old individuals have been reported to prevent soil erosion to a considerable larger extend than younger ones (Rodrigo-Comino et al., 2018) and to that end old large tress are likely to efficiently act against soil erosion. Large trees are keystone species both in natural ecosystems (Munzbergova and Ward, 2002) as well as in urban parks (Stagoll et al., 2012).
In terms of soil moisture (SMI) the interaction between year and density explained the majority of deviance implying that the effect of density on soil moisture depends on the levels of density. Within this effect, large tree individuals exhibited a negative relationship with SMI for high densities. It has been reported that SMI may be peaking at intermediate densities (Ilstedt et al., 2016). Our results show no support for this but this could be a limitation of the linear assumptions of our analysis (Berk, 2004).
In terms of temperature, LST depended mainly on year meaning that overall it is the physical conditions that define the LST and the role of vegetation is relatively small (the deviance explained by year is two levels of magnitude higher than the one explained by biotic characteristics, size, or density). However, within this effect, both tree size (Breshears et al., 1998) and density (Kawashima, 1994;Song et al., 2013) had an effect in moderating temperature, with tree size having a level of magnitude stronger effect in temperature moderation than density. Again this highlights the importance of large trees on ecosystems (Jones et al., 2018;Lindenmayer and Laurance, 2017). In addition it has implications for nature based solutions in moderating urban temperatures (Gill et al., 2007;Nielsen et al., 2017), water use (Lin et al., 2018), energy saving (Kliman and Comrie, 2004;McPherson and Simpson, 2003;Morakinyo et al., 2018), as well as climatic-efficient agroforestry (Sida et al., 2018). While these effects can be quantified via remote sensing, they may often pass unnoticed as high resolution data are needed (Zhou et al., 2018).
Defining the spatial scale of interactions is critical (Génin et al., 2018) for defining density and this in return can have direct effects on positive or negative density effects. Often the 'local' interactions or fine scale is measured as e.g. distance to the nearest plant neighbours (Li et al., 2017;Meyer et al., 2008). However, the nearest neighbours in an arid ecosystem will be more distant than the nearest neighbours in a humid ecosystem. In addition if for example the four nearest neighbours were measured, the fifth nearest neighbour (not accounted for) may be a large-sized individual with strong interactions with the focal individual . In designed experimental studies (e.g. planting or manipulating plant individuals (Roush et al., 2017)), setting up quadrats also requires an, often subtly taken, decision regarding the scales of interaction. We suggest that a datadriven definition of scale of local interactions (Gunton and Kunin, 2007) may be a step forward for better understanding positive and negative density effects (Bradter et al., 2013;Gunton and Kunin, 2009), as well as their implications for agriculture , soil water availability (Zhang et al., 2018), and potential temperature amelioration (Soliveres et al., 2011;Wright et al., 2015). Note that the results derived here regarding competitivefacilitative interactions and tree survival would be notably different at different spatial scales across the ones examined (Supplementary analysis S3) and the relationship between scale and survival is spatio-temporal (Soliveres et al., 2010) and to that end, complex.
Going a step further, the data-driven scale of interactions (found to be here 512 m), would not hold true when calculated for each available year individually; partitioning the data for each available year and calculating the best data driven scale of interactions in 1940, 1964, 1984, 1993, and 2001 would not yield the same optimal scale of 512 m for each year. However using a dynamic (i.e. changing with time) year-specific spatial scale (circle) of interactions would introduce the statistical problem of multi-collinearity (Arturs, 2018;Fox and Monette, 1992): any scale found to be optimal for at least one time period would need to be included in the model that contains all the data and therefore densities e.g. at 4 m and at 512 m circles would need to be included in a full model across years. However, all individuals at 4 m are also within the 512 m circle generating multi-collinearity (Fox and Monette, 1992). While we chose a 'mean-field-approach' in defining the spatial scale of interactions across the time span of the study, in reality the scale of interactions is shorter than 512 m in some years (results not shown here).
Conclusions
Defining the spatial scale of interactions has substantial effect on density and reciprocally on whether density interactions will be positive or negative. The data-driven scale of interactions can change between years. Within the best data-driven spatial interaction scale, the best explanatory covariates of tree survival is the interaction between density and year shifting from facilitation to competition through time. Small sized trees are always facilitated by increased densities while large sized trees had either negative or no density effects. Tree size (alone) is a more important predictor than density (alone) in tree survival. This has serious implications for nature-based solutions, as maintaining large tree individuals or planting species that can become large-sized can act against tree-less areas by promoting survival at long time periods through harsh environmental conditions. Large trees have also a significant effect in moderating land surface temperature thereby creating a cool microclimate, and this effect is higher than the one of vegetation density on temperature. Therefore, an equal total cover consisted of several small-sized or middle-sized trees will not moderate the temperature as the same total cover comprised by large-sized trees. Table 1. ANOVA results of a logistic generalised linear model between tree death (dependent variable), and tree size in terms of canopy surface area in m 2 , tree density in terms of total canopy cover within a circle of 512 m 2 around each tree, and year as explanatory variables. Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0. -3.516 10 -2 1.004 10 -2 -3.502 0.0005 *** size:Year1993 -6.734 10 -3 8.906 10 -3 -0.756 0.4496 s512:Year1964 -4.790 10 -5 5.283 10 -5 -0.907 0.3646 s512:Year1984 3.822 10 -4 4.098 10 -5 9.326 <0.0001 *** s512:Year1993 3.572 10 -4 4.114 10 -5 8.683 <0.0001 *** size:s512:Year1964 1.822 10 -6 1.388 10 -6 1.312 0.1893 size:s512:Year1984 1.421 10 -6 1.160 10 -6 1.226 0.2203 size:s512:Year1993 4.155 10 -7 1.144 10 -6 0.363 0.7164 Table 3. ANOVA results of a generalised linear model between Soil Moisture Index (SMI; dependent variable), and tree size in terms of canopy surface area in m 2 , tree density in terms of total canopy cover within a circle of 512 m around each tree, and year as explanatory variables. Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0. -3.246 10 -8 3.307 10 -9 -9.815 <0.0001 *** size:Year1993 -6.327 10 -4 6.862 10 -5 -9.220 <0.0001 *** size:Year2001 -6.619 10 -4 7.521 10 -5 -8.800 <0.0001 *** s512:Year1993 -3.202 10 -6 2.124 10 -7 -15.079 <0.0001 *** s512:Year2001 -8.411 10 -6 2.061 10 -7 -40.819 <0.0001 *** size:s512:Year1993 2.625 10 -8 4.413 10 -9 5.950 <0.0001 *** size:s512:Year1993 2.689 10 -8 4.809 10 -9 5.591 <0.0001 *** Table 5. ANOVA results of a generalised linear model between Land Surface Temperature (LST; dependent variable), and tree size in terms of canopy surface area in m 2 , tree density in terms of total canopy cover within a circle of 512 m around each tree, and year as explanatory variables. Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0. -2.144 10 -7 3.481 10 -8 -6.160 < 0.0001 *** size:s512:Year2001 -2.362 10 -7 3.794 10 -8 -6.226 < 0.0001 *** Figure 1. a. Examples of potential interaction scales around a tree individual that can be used to define tree densities, and sequentially positive or negative density effects, from a detail of the remote sensing imagery in the study plots. The spatial extent of neighbourhood is used to define density as it is the denominator of the number of individuals or cover within the defined space. This is critical because based on the definition of the scale of interactions (neighbourhood) facilitation can be recorded in one scale while competition can be recorded on the nearest available used. In other words what is the local scale of tree-tree interactions? In addition, in order to investigate the potential existence of local scale facilitation and landscape scale competition one needs to define what is 'local' and what is landscape' as these often derive from the availability and scale of the data used and the terms are arbitrary. More often than not scales of interactions are taken as a silent presupposition. In this example densities are considerably higher (more trees and higher canopy cover) at finer spatial scales. b. A detail of the study plots as seen from the ground (photo A. Moustakas). . Three-way interactions between tree death explained by year, tree size (m 2 ), and density in 512 m circles around each tree. The vertical axis indicates probability of tree death (%). The horizontal axis indicates density in terms of total canopy cover in m 2 within a circle of 512 m around each tree. Panels indicate different years. Lines within panels indicate levels of the size of the tree individual that died across years with confidence intervals. Results are also reported in Table 1 and Table 2. 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 Figure 5. Three-way interactions between Soil Moisture Index (SMI) explained by year, tree size (m 2 ), and density in 512 m circles around each tree. The vertical axis indicates SMI values. The horizontal axis indicates density in terms of total canopy cover in m 2 within a circle of 512 m around each tree. Panels indicate different years. Lines within panels indicate levels of the size of the tree individual that died across years with confidence intervals. Results are also reported in Table 3 and Table 4. Figure 6. Three-way interactions between Land Surface Temperature (LST) explained by year, tree size (m 2 ), and density in 512 m circles around each tree. The vertical axis indicates LST in K 0 values. The horizontal axis indicates density in terms of total canopy cover in m 2 within a circle of 512 m around each tree. Panels indicate different years. Lines within panels indicate levels of the size of the tree individual that died across years with confidence intervals. Results are also reported in Table 5 and Table 6.
Supplementary material
Data-driven competitive-facilitative interactions and their implications for nature based solutions
Supplementary information regarding the Land Surface Temperature (LST)see methods. 1984, 1993, and 2001, and respective linear regression lines to identify dry edge (red line) and wet edge (blue line).
Selecting of the best data-driven index of neighbourhood density and the optimal scale of interactions. The potential neighbourhood density indices explored were (i) number of tree individuals denoted with d in the model structure below, (ii) the total tree canopy cover denoted s in the model structure below, and (iii) the percentage of tree canopy cover denoted with p in the model structure below. Each density index was tested across spatial scales of 4, 8, 16, 32, 64, 128, 264, 512 meters (focal neighbourhoods). Years examined are 1940Years examined are , 1964Years examined are , 1984Years examined are , and 1993. Year refers to the last seen year of a tree (i.e. if a tree was seen in 1940 but not in 1964 death year is 1940). Tree deaths were analyzed (the reciprocal of survival) an event occurring maximum once in the dataset as time series. The Generalised linear model (glm) with a binomial family (logistic regression) quantified tree deaths as a function of density within in scale-specific neighbourhood, size in terms of canopy surface area in m 2 of the tree individual, and year. The notation * between two variables A* B denotes the effects of variable A, the effects of variable B, and the interaction effect between A and B.
Number of individual trees across scales >
> q1<-glm(death~size*Year*d4, family="binomial") > q2<-glm(death~size*Year*d8, family="binomial") > q3<-glm(death~size*Year*d16, family="binomial") > q4<-glm(death~size*Year*d32, family="binomial") > q5<-glm(death~size*Year*d64, family="binomial") > q6<-glm(death~size*Year*d128, family="binomial") > q7<-glm(death~size*Year*d256, family="binomial") > q8<-glm(death~size*Year*d512, family="binomial") > > AIC(q1,q2,q3,q4,q5,q6,q7,q8) Total canopy cover across scales a1<-glm(death~size*Year*s4, family="binomial") a2<-glm(death~size*Year*s8, family="binomial") a3<-glm(death~size*Year*s16, family="binomial") a4<-glm(death~size*Year*s32, family="binomial") a5<-glm(death~size*Year*s64, family="binomial") a6<-glm(death~size*Year*s128, family="binomial") a7<-glm(death~size*Year*s256, family="binomial") a8<-glm(death~size*Year*s512, family="binomial") > AIC(a1,a2,a3,a4,a5,a6,a7,a8) Table S3. AIC scores of logistic regression with total tree canopy cover as density indicator a cross scales. The bolded italicised value corresponds to the minimum recorded AIC score deri ved from deaths at scales of 512 m with total canopy cover as a neighbourhood index. Percentage of canopy cover across scales > v1<-glm(death~size*Year*p4, family="binomial") > v2<-glm(death~size*Year*p8, family="binomial") > v3<-glm(death~size*Year*p16, family="binomial") > v4<-glm(death~size*Year*p32, family="binomial") > v5<-glm(death~size*Year*p64, family="binomial") > v6<-glm(death~size*Year*p128, family="binomial") > v7<-glm(death~size*Year*p256, family="binomial") > v8<-glm(death~size*Year*p512, family="binomial") > > AIC (v1,v2,v3,v4,v5,v6,v7,v8) Results from the second best (data-driven) optimal scale of interactions. Basel on the results of Table S3 the optimal spatial scale of interactions is a circle of 512 m around each tree, which was used throughout the analysis. The second best scale as deduced from results in Table S3 is the one of 4 m (the finest scale from the ones examined here). The results from the scale of 4 m do not match the ones of 512 m and in many years there is an inverse result regarding the effects of density on survival (death), showing that both positive and negative effects coexist on the same location at the same time depending on the scale. Table S5. ANOVA results of a logistic generalised linear model between tree death (dependent variable), and tree size in terms of canopy surface area in m 2 , tree density in terms of total canopy cover within a circle of 4 m 2 around each tree, and year as explanatory variables. 16.54 10560 8321.9 0.0008767 *** ---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Table S6. Summary of model coefficients of the ANOVA results from Table S5 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) 6.737e-01 1.214e-01 5.551 2.84e-08 *** size -1.352e-02 3.885e-03 -3.479 0.000504 *** s4 -4.227e-02 4.012e-03 -10.537 < 2e-16 *** Year1964 -6.042e-01 1.670e-01 -3.618 0.000297 *** Year1984 -1.028e+00 1.419e-01 -7.240 4.49e-13 *** Year1993 -1.235e+00 1.453e-01 -8.505 < 2e-16 *** size:s4 2.440e-04 3.440e-05 7.093 1.31e-12 *** size:Year1964 -7.441e-03 5.903e-03 -1.261 0.207469 size:Year1984 -7.894e-03 5.231e-03 -1.509 0.131231 size:Year1993 -1.146e-02 5.032e-03 -2.277 0.022773 * s4:Year1964 -2.414e-02 7.022e-03 -3.438 0.000585 *** s4:Year1984 -1.174e-02 6.005e-03 -1.955 0.050592 . s4:Year1993 1.198e-02 5.612e-03 2.134 0.032810 * size:s4:Year1964 1.520e-04 5.173e-05 2.939 0.003297 ** size:s4:Year1984 2.826e-05 4.140e-05 0.683 0.494867 size:s4:Year1993 -1.467e-05 3.972e-05 -0.369 0.711948
Figure 2 .
2Indices of neighbourhood density across spatial scales in terms of boxplots: The solid line is the median, and the boxes are defined by the upper and lower quartile (25th and 75th percentiles). The whiskers extend up to 1.5 times the inter-quartile range of the data. Spatial scales include circles with radii of 4, 8, 16, 32, 64, 128, 256, 512 meters around each tree individual. (a) Number of tree individuals within each circle. (b) Total tree canopy in m 2 within each circle. (c) Percentage of tree canopy cover (%) within each circle. (d) AIC values of the statistical models explaining survival as a function of tree size, density, year, and their 2-way and 3-way interactions across scales, and indices of neighbourhood density. Neighbourhood density indices included number of trees within each scale, total canopy surface area cover, and percentage of canopy surface area cover within each scale. The statistical models fitted were 24 = 8 scales x 3 indices of neighbourhood. The most parsimonious model (lowest AIC) included total canopy cover as an indicator of neighbourhood and a spatial scale of a circle of 512 m around each tree individual.
Figure 3
3Figure 3. Three-way interactions between tree death explained by year, tree size (m 2 ), and density in 512 m circles around each tree. The vertical axis indicates probability of tree death (%). The horizontal axis indicates density in terms of total canopy cover in m 2 within a circle of 512 m around each tree. Panels indicate different years. Lines within panels indicate levels of the size of the tree individual that died across years with confidence intervals. Results are also reported in Table 1 and Table 2.
Figure 4 .
4Monthly precipitation (in mm; upper panel) and the corresponding Standardised Precipitation Index (SPI; lower panel). Monthly precipitation values derive from the nearest available weather station in Kimberley, South Africa ranging from January 1940 to December 2003. Missing monthly precipitation values (plotted with grey colour on the upper panel) were interpolated (see methods for details). The SPI is calculated from the monthly precipitation time series, it defines periods of humidity and drought, and SPI values are universally comparable. Negative SPI values indicate draught (plotted in red) while positive indicate humidity (plotted in black). Values close to ±1.5 indicate severe conditions while values ±2 indicate exceptional conditions. Grey dotted vertical lines indicate the year when the aerial photos/satellite images are available.
1 ' ' 1Predictor
Df Deviance
Residual
Df
Residual
Deviance
Significance
None
10575
9846.5
size
1
543.27
10574
9303.2
<0.0001
***
s512
1
345.41
10573
8957.8
<0.0001
***
Year
3
125.01
10570
8832.8
<0.0001
***
size:s512
1
1.37
10569
8831.4
0.2419
size:Year
3
17.77
10566
8813.7
0.0005
***
s512:Year
3
696.66
10563
8117.0
<0.0001
***
size:s512:Year
3
7.47
10560
8109.5
0.05837
Table 2. Summary of model coefficients of the ANOVA results from Table 1
Coefficients
Estimate
Std. Error z value
Significance
(Intercept)
3.034
30.08
10.087
<0.0001
***
size
-2.155 10 -2 7.818 10 -3
-2.756
0.0058
**
s512
-4.082 10 -4 4.031 10 -5
-10.127
<0.0001
***
Year1964
-6.283E 10 -1 3.820 10 -1
-1.645
0.01
Year1984
-3.663 3.244 10 -1
-11.291
<0.0001
***
Year1993
-3.444 3.272 10 -1
-10.525
<0.0001
***
size:s512
1.952 10 -7 1.113 10 -6
0.175
0.8608
size:Year1964
-1.443 10 -2 1.023 10 -2
-1.411
0.1582
size:Year1984
Table S1 :
S1Slopes ( ) and intercepts ( ) for the regression equations of Land SurfaceTemperature ofFigure S1.Figure S1: NDVI versus Land Surface Temperature [ o K] scatterplots (black dots) for JuneDataset
Slope
[ o K]
Intercept
[ o K]
June 20, 1984
LT05_L1TP_172080_19840620_20170220_01_T1
Minimum
5.39
279.35
Maximum
-7.04
290.15
June 13, 1993
LT05_L1TP_172080_19930613_20170118_01_T1
Minimum
13.20
272.8
Maximum
-9.61
288.65
June 3, 2001
LT05_L1TP_172080_20010603_20161210_01_T1
Minimum
4.24
283.73
Maximum
-5.94
292.57
Table S2 .
S2AIC scores of logistic regression with number of individual trees as density indicat or across scalesdf
AIC
q1 16 9050.053
q2 16 8919.362
q3 16 9027.675
q4 16 9096.016
q5 16 9008.763
q6 16 8874.196
q7 16 8679.175
q8 16 8302.611
Table S4 .
S4AIC scores of logistic regression with percentage of canopy cover as density indica tor across scales.df
AIC
v1 16 8353.873
v2 16 8353.873
v3 16 8353.873
v4 16 8353.873
v5 16 8353.873
v6 16 8353.873
v7 16 8353.873
v8 16 8353.871
>
Df Deviance Resid. DfResid. Dev Pr(>Chi) NULL
10575
9846.5
size
1
543.27
10574
9303.2 < 2.2e-16 ***
s4
1
274.92
10573
9028.3 < 2.2e-16 ***
Year
3
251.50
10570
8776.8 < 2.2e-16 ***
size:s4
1
399.49
10569
8377.3 < 2.2e-16 ***
size:Year
3
19.00
10566
8358.3 0.0002733 ***
s4:Year
3
19.88
10563
8338.4 0.0001794 ***
size:s4:Year 3
AcknowledgementsWe thank the organizers of the first TerraEnVision conference, Barcelona, 2018 that lead to this special issue. The authors would like to acknowledge Dr. George Azzari from the Centre on Food Security and the Environment, Stanford University, for developing and sharing his thermal analysis GEE script based on Jimenez-Munoz et al. (2009). AM acknowledges a 2017-2018 Conference Grant funding from Universiti Brunei Darussalam..set({'system:time_start':img.get('system:time_start')}); }); } // Return a Landsat 5 TOA collection with only thermal (brightness temp) // and cloud score band. Collection is filtered by given dates and // by given polygon. function getLandsatTOA(startdate, enddate, poly){ var l5toas = filterCollection(ee.ImageCollection('LANDSAT/LT5_L1T_TOA'), startdate, enddate, poly).map(ee.Algorithms.Landsat.simpleCloudScore) .select([5,7], ["B6_BRT","CLOUDSC"]); return ee.ImageCollection(l5toas); } //Return a Landsat 5 SR collection of surface reflectance and //quality bands. Collection is filtered by given dates and //by given polygon. function getLandsatSR(startdate, enddate, poly){ var bnames = ["B1","B2","B3","B4","B5","B7","AO","QA"]; var bnumbers = [0,1,2,3,4,5,6,7]; var l5s = filterCollection(ee.ImageCollection('LEDAPS/LT5_L1T_SR'), startdate, enddate, poly).select(bnumbers, bnames); return ee.ImageCollection(l5s); } //Stick atmospheric metadata to image as bands. function addAtmosBands(srimg){ // var ozone = ee.Image(srimg.get('ozone')).select([0], ['OZONE']); var tair = ee.Image(ee.List(srimg.get('surface_temp')).get(0)) .select([0], ['SRTAIR00']) .addBands(ee.Image(ee.List(srimg.get('surface_temp')).get(1))) .addBands(ee.Image(ee.List(srimg.get('surface_temp')).get(2)) .select([0], ['SRTAIR12'])) .addBands(ee.Image(ee.List(srimg.get('surface_temp')).get(3)).select([0], ['SRTAIR18'])); var wv = ee.Image(ee.List(srimg.get('surface_wv')).get(0)) .select([0], ['SRWVAP00']) .addBands(ee.Image(ee.List(srimg.get('surface_wv')).get(1)).select([0], ['SRWVAP06'])) .addBands(ee.Image(ee.List(srimg.get('surface_wv')).get(2)) .select([0], ['SRWVAP12'])) .addBands(ee.Image(ee.List(srimg.get('surface_wv')).get(3)).select([0], ['SRWVAP18'])); return srimg.addBands(tair).addBands(wv); } //Join Landsat collections based on system:time_start function joinLandsatCollections(coll1, coll2){ var eqfilter = ee.Filter.equals({'rightField':'system:time_start', 'leftField':'system:time_start'}); var join = ee.Join.inner(); var joined = ee.ImageCollection(join.apply(coll1, coll2, eqfilter)); //Inner join returns a FeatureCollection with a primary and secondary set of //properties. Properties are collapsed into different bands of an image. return joined.map(function(element){ return ee.Image.cat(element.get('primary'), element.get('secondary')); }) .sort(var ndvi_max = ee.Image(ee.Number(NDVImax)); var ndvi = reflimg.normalizedDifference(["B4", "B3"]); var fvc = ndvi.subtract(ndvi_min) .divide(ndvi_max.subtract(ndvi_min)) .pow(ee.Image(2)); var e = ee.Image(Esoil).multiply(ee.Image(1).subtract(fvc)).add(ee.Image(Eveg).multiply(fvc)); return e.select([0], ['emissivity']); } //Convenience function for mapping emissivity computation over collection function getEmissivity(reflimg){ return coreEmissivity(reflimg, 0.18, 0.85, 0.97, 0.99, 0.55); } //Compute psi functions function getPsis(joinedimg){ // WTR in NCEP data is in kg/m^2,Appendix 2# Data import ndvi1984_full <-raster("ndvi_full1984.tif") # NDVI from entire Landsat scene temp1984_full <-raster("temp_full1984.tif") # LST from entire Landsat scene ndvi1984 <-raster("ndvi1984.tif") # NDVI from area of interest temp1984 <-raster("temp1984.tif") # LST from area of interest# Preprocessing joint.1984, values(temp1984_full)) names(joint.1984) <-c("NDVI", "Temperature") breaks <-seq(0.
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01 for all images. var wv = joinedimg.select('SRWVAP18') //CAREFUL: TIME OF DAY HARDCODED. / , multiply(0.01) //scale .add(277.65) //offset .multiply(ee.Image(0.1)// + scale =0.01 for all images. var wv = joinedimg.select('SRWVAP18') //CAREFUL: TIME OF DAY HARDCODED .multiply(0.01) //scale .add(277.65) //offset .multiply(ee.Image(0.1));
Image(0.14714).multiply(wv.pow(ee.Image(2))) .add(ee.Image(-0.15583).multiply(wv)) .add(ee. /cm2 var psi1 = ee. Image(1.1234)//conversion to g/cm2 var psi1 = ee.Image(0.14714).multiply(wv.pow(ee.Image(2))) .add(ee.Image(-0.15583).multiply(wv)) .add(ee.Image(1.1234));
Image(-1.1836).multiply(wv.pow(ee.Image(2))) .add(ee.Image(-0.37607).multiply(wv)) .add(ee.Image. Var Psi2 = Ee, var psi2 = ee.Image(-1.1836).multiply(wv.pow(ee.Image(2))) .add(ee.Image(-0.37607).multiply(wv)) .add(ee.Image(-0.52894));
Image(-0.04554).multiply(wv.pow(ee.Image(2))) .add(ee.Image(1.8719).multiply(wv)) .add(ee.Image. Var Psi3 = Ee, var psi3 = ee.Image(-0.04554).multiply(wv.pow(ee.Image(2))) .add(ee.Image(1.8719).multiply(wv)) .add(ee.Image(-0.39071));
Compute surface temperature (output in degrees Kelvin) function getSurfaceTemp(joinedimg){ var brightemp = joinedimg.select('B6_BRT'). } //, } //Compute surface temperature (output in degrees Kelvin) function getSurfaceTemp(joinedimg){ var brightemp = joinedimg.select('B6_BRT');
var radtemp = joinedimg.select('B6_RAD'). var radtemp = joinedimg.select('B6_RAD');
// W um^4 m^-2 var c2 = ee. Image. 7// W um^4 m^-2 var c2 = ee.Image(14387.7);
. // Um K Var Lambda = Ee, Image. 45711// um K var lambda = ee.Image(11.457);
//um (effective wavelength of TM B6) var beta = ee. Image. //um (effective wavelength of TM B6) var beta = ee.Image(1256);
multiply(c2).divide(brightemp.pow(2)) .multiply(radtemp.multiply(lambda.pow(4)).divide(c1) .add(lambda. //K Var Gamma = Radtemp, //K var gamma = radtemp.multiply(c2).divide(brightemp.pow(2)) .multiply(radtemp.multiply(lambda.pow(4)).divide(c1) .add(lambda.pow(-1)))
var delta = brightemp.subtract(radtemp.multiply(gamma)). var delta = brightemp.subtract(radtemp.multiply(gamma));
var toctemp = gamma.multiply(psis.select('psi1').multiply(radtemp) .add(psis.select('psi2')) .divide(e) .add(psis.select('psi3'))) (sigma).multiply(e) .multiply(toctemp.pow(ee.Image(4))) .divide(ee. Image(Math.PI). var toctemp = gamma.multiply(psis.select('psi1').multiply(radtemp) .add(psis.select('psi2')) .divide(e) .add(psis.select('psi3'))) (sigma).multiply(e) .multiply(toctemp.pow(ee.Image(4))) .divide(ee.Image(Math.PI));
' Toctemp, ' Toatemp, ' , ' Tocrad, set({ 'DATE_ACQUIRED':joinedimg.get('DATE_ACQUIRED'), 'LANDSAT_SCENE_ID':joinedimg.get('LANDSAT_SCENE_ID'), 'SUN_AZIMUTH':joinedimg.get("SUN_AZIMUTH"), 'SUN_ELEVATION':joinedimg.get. Image.cat(toctemp, brightemp, e, tocrad, radtemp) .select. SUN_ELEVATION"), 'system:time_start':joinedimg.get('system:time_start'), })return ee.Image.cat(toctemp, brightemp, e, tocrad, radtemp) .select([0,1,2,3,4], ['TOCtemp', 'TOAtemp', 'emiss', 'TOCrad', 'TOArad']) .set({ 'DATE_ACQUIRED':joinedimg.get('DATE_ACQUIRED'), 'LANDSAT_SCENE_ID':joinedimg.get('LANDSAT_SCENE_ID'), 'SUN_AZIMUTH':joinedimg.get("SUN_AZIMUTH"), 'SUN_ELEVATION':joinedimg.get("SUN_ELEVATION"), 'system:time_start':joinedimg.get('system:time_start'), });
24.771, -28.655Initialize base collections var refpoly = ee.Geometry.Polygon. //-//-Application-//---------24.771, -28.595. 24.87, -28.595], [24.87, -28.655//- //-Application- //-Initialize base collections var refpoly = ee.Geometry.Polygon( [[[24.771, -28.655], [24.771, -28.595], [24.87, -28.595], [24.87, -28.655]]]);
. var. var year=1984;
var end_date = ee.Date.fromYMD(year,6,30). var end_date = ee.Date.fromYMD(year,6,30);
// check that there is indeed only one scene //during this interval var jcoll = joinLandsatCollections(getLandsatTOA(start_date, end_date , refpoly), getLandsatSR(start_date, end_date, refpoly) .map(addAtmosBands)). // check that there is indeed only one scene //during this interval var jcoll = joinLandsatCollections(getLandsatTOA(start_date, end_date , refpoly), getLandsatSR(start_date, end_date, refpoly) .map(addAtmosBands));
jcoll = joinLandsatCollections(jcoll, getLandsatRAD(start_date, end_date , refpoly)). jcoll = joinLandsatCollections(jcoll, getLandsatRAD(start_date, end_date , refpoly));
var tcoll = jcoll.map(function(jimg){return getSurfaceTemp(jimg)}). var tcoll = jcoll.map(function(jimg){return getSurfaceTemp(jimg)});
Test single image var jimg = ee. //---Test single image var jimg = ee.Image(jcoll.first());
var timg_full = ee.Image(tcoll.first()).select('TOCtemp'). var timg_full = ee.Image(tcoll.first()).select('TOCtemp');
Image(tcoll.first()).select('TOCtemp').clip(refpoly). var timg = ee.Image(tcoll.first()).select('TOCtemp').clip(refpoly);
. //Print, jimg//print(jimg);
var ndvi_full = jimg.select('NDVI'). var ndvi_full = jimg.select('NDVI');
var ndvi= jimg.select('NDVI').clip(refpoly). var ndvi= jimg.select('NDVI').clip(refpoly);
. //Print, timg//print(timg);
Visualization Map.centerObject(refpoly). //---Visualization Map.centerObject(refpoly);
. = Var Thpalette, "000066", "00FFFF","FFFF00", "FF0000"var thpalette = ["000066", "00FFFF","FFFF00", "FF0000"];
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| sample_1155 | 0.5199 | arxiv | |
Title: The global freshwater system: Patterns and predictability of green-blue water flux partitioning
Daniel Althoff daniel.althoff@natgeo.su.se**correspondence:georgia.destouni@natgeo.su.se
Department of Physical Geography
Bolin Centre for Climate Research
Stockholm University
StockholmSweden
Georgia Destouni
Department of Physical Geography
Bolin Centre for Climate Research
Stockholm University
StockholmSweden
Title: The global freshwater system: Patterns and predictability of green-blue water flux partitioning
Authors: *Correspondence:(up to 10): water flux partitioningevapotranspirationrunoffclimate changeland- use changemachine learninginterpretable machine learningmodel applicability area
SCIENCE FOR SOCIETY]As the main input of freshwater on land, precipitation infiltrates the soil where some of it is stored as soil water or groundwater, while some is used by vegetation for transpiration as "green water", or contributes to the flows of groundwater, rivers and streams as "blue water". The green-blue water partitioning is key for sustaining life on land and below water, and for societal water and food security. We collected data from around the world to investigate and decipher global patterns in this water partitioning and explain how it is affected by climate and human land and water use conditions. Our analyses show large-scale emergence of vegetation priority in taking or getting (by irrigation) the green water part it needs and only what remains after that use goes to feed blue water flows. This makes blue water security for other uses vulnerable to future changes in precipitation and in vegetated land, such as for irrigated crops and forestry. In this study, we also develop and train a Machine Learning model as a tool for predictive assessment of how green-blue water partitioning may change around the world under different future climate scenarios.Summary:The partitioning of precipitation (P) water input on land between green (evapotranspiration, ET) and blue (runoff, R) water fluxes distributes the annually renewable freshwater resource among sectors and ecosystems. We decipher the worldwide pattern and key determinants of this water flux partitioning (WFP) and investigate its predictability based on a machine learning (ML) model trained and tested on data for 3,614 hydrological catchments around the world. The results show considerably higher WFP to the green (ET/P) than the blue (R/P) flux in most of the world. Landuse changes toward expanded agriculture and forestry will increase this WFP asymmetry, jeopardizing blue-water availability and making it more vulnerable to future P changes for other sectors and ecosystems. The predictive ML-model of WFP developed in this study can be used with climate model projections of P to assess future blue and green water security for various regions, sectors, and ecosystems around the world.Keywords (up to 10): water flux partitioning; evapotranspiration; runoff; climate change; landuse change; machine learning; interpretable machine learning; model applicability area.Title:Supplemental Information to: "The global freshwater system: Patterns and predictability of greenblue flux partitioning"
Introduction
Precipitation (P) is the main input source of freshwater on land, where the water is further partitioned to blue (runoff, R) and green (evapotranspiration, ET) water fluxes 1 . This water flux partitioning (WFP) has major implications for aquatic and terrestrial ecosystems 2,3 , water and food security 4,5 , and different societal sectors 6,7 . The WFP is regulated by land-atmosphere interactions 1,8 and is, therefore, vulnerable to disturbances and shifts in these. Around the world, regional and continental studies have found shifts in WFP due to climate change, direct human changes in land and water use, or both [9][10][11][12][13] . Yet, a conclusive understanding of how WFP inherently relates to various combinations of such changes at large scale still remains to be reached. Predictive capability for WFP also needs to be improved and further developed 14,15 as climate projections suggest more warming and shifted rainfall patterns with possible more intense heatwave, rainfall, drought and flood events in the coming decades 16 .
Understanding how WFP depends on changing climate and land use conditions around the globe is essential, for example, for adaptation to climate change and generally for freshwater security 17 .
However, high uncertainty has been attributed to Earth System Models' ability to represent historical hydroclimatic covariation patterns and trends in both regional and global assessments 11,14,15,18,19 . It is, therefore, important to also explore additional, complementary modelling frameworks for determining WFP 20,21 . The complex non-linear interactions between land and atmosphere and the increasing amount of accessible data make machine learning (ML) a possible important tool for meeting climate-related predictability challenges 20 , although its blackbox-like characteristics and possible limited applicability outside a model's initial training domain are reasons for concerns 22,23 .
Here, we develop and explore a global ML model and its pattern recognition and predictability capabilities for average WFP in hydrological catchments of various scales and locations with different climate, land-use and other geographically dependent conditions around the world. To train and test the model, we compiled data for 3,614 hydrological catchments (coloured fields in Figure 1A) with continuous temporal data coverage for daily runoff (limiting data component required for catchment-wise water balance closure) over at least 25 years within the period 1980-2020 (see further Supporting Information (SI) on runoff databases in Table S1). Global data are available in this period for land-use from 1992 (SI Table S2) and for climate (temperature and precipitation) over the whole period and longer (SI Table S3). To characterize the catchments and further explore the physical-hydrological reasonableness and implications of the global ML model, we also independently quantified and related ML model results to some additional hydrological catchment characteristics. These include catchment-average aridity index (see Experimental procedures (EP) and SI Figure S1), the minimum averaging time required to obtain temporally stable average WFP in each catchment (referred to as the water flux equilibration time, Teq; see EP and SI Figure S2), and an assumed (and tested) Teq-related indicator of average groundwater contribution to surface water runoff under zero monthly precipitation conditions (Rgw0; see EP and SI Figure S3). The hydrological variable quantifications considered the full period of data availability for each catchment (SI Table S1), while data for the period 1992-2020 were used for ML model training and testing, given the data availability conditions for the different model variables (SI Table S3). scatterplot of predicted versus observed R/P that also shows the location of 80% and 90% of the data points based on a two-dimensional kernel density estimation; and (D) a map of mean absolute error (MAE) obtained for each catchment.
To address general interpretability and applicability concerns with ML modelling, we adopted model interpretability techniques to decipher the key determinants of catchment-average WFP around the world and gain insight into the model decision-making. The ML model applicability to new unseen data was further investigated in relation to model variable values and independently estimated hydrological characteristics of catchments within and outside of the model area of applicability. The observational data and ML model results show that most of the world outside the polar regions has a much higher WFP to the green water flux (global area-weighted average ET/P = 0.62) than the blue water flux (global area-weighted average R/P = 0.38). For the future, the model implies that further warming, as well as land-use changes towards expansion of agricultural and forest areas, should be expected to enhance pressure on blue water availability and security, and make the blue water flux more vulnerable to future precipitation changes. The developed ML model can be combined with climate model projections to better assess these implications for different societal sectors and ecosystems around the world. Our findings also clarify and emphasize the need for additional data and ML model training, in particular for the northern subtropical and low-latitude temperate regions and the polar regions of the world.
Results and discussion
The final database used for the present investigations includes data for the 3,614 study catchments around the world ( Figure 1A) with varying temporal data coverage for the different synthesized types of data (SI Tables S1-S3). The Global Runoff Database Centre 24 (GRDC) provides required runoff data for many catchments, but a large part of these are located in Europe and North America.
To further extend the total catchment number and world coverage, we also used additional runoff datasets that are openly available for catchments in some countries (United States 25 , Brazil 26 , Chile 27 , Great Britain 28 , and Australia 29 ). Overall, the total set of study catchments covers a wide range of hydrological conditions, e.g., with aridity index PET/P ranging from 0.5 to 14.4 (mean:
1.2, SI Figure S1A-B) and covering the relevant ET/P versus PET/P Budyko space 30 (SI Figure S1C), where PET is potential evapotranspiration.
The independent quantification of water flux equilibration time (Teq, SI Figure S2) yields Teq values of less than 2 years in ~99.5% of the study catchments ( Figures 1A-B). This ensures stable average R/P and ET/P values over the selected 5-year temporal averaging window for these and the related explanatory variables in the ML model. The independent quantification of Rgw0/Ravg (SI Figures S3-S4) and its emergent considerable positive correlation with Teq (SI Figure S5) also support consideration of Rgw0/Ravg as a likely relevant groundwater indicator, since it is hydrologically realistic for Teq to be longer for larger relative contribution of relatively slowflowing groundwater to total runoff (with average value Ravg) through a catchment.
For WFP pattern recognition, we trained a ML model to predict the ratio between average runoff and average precipitation for each catchment (R/P, blue WFP). From this and catchment-wise average water balance P ≈ ET + R (assuming small long-term average water storage change in comparison with the main water fluxes P, ET and R) 9,11,12,31,32 , the corresponding average green WFP can in turn be estimated as ET/P ≈ 1 -R/P. The ML model uses as input catchment topography and hydro-climatic indices, and land use fractions summarized over 5-year periods (see EP for details on these explanatory variables). We used 80% of the catchments to train the model and evaluated its performance on the remaining 20% (test set). For the unseen data in the test set ( Figure 1C), the developed ML model was able to predict R/P with a mean absolute error ML model deciphering shows that, as physically expected, a greater average catchment slope implies greater average R/P and thereby lower associated ET/P in a catchment ( Figure 2A). Higher average annual temperature also relates to WFP as physically expected, with higher ET/P and thereby lower R/P ( Figure 2B). Changed mean annual P, however, does not imply any clear a priori expected WFP effect, as higher P could in principle lead to either maintained relative R/P and ET/P values, or increase in any of them at the expense of the other. As a main result of the ML model deciphering, we then see that the change direction (increase/decrease) of P tends to lead to a similar change direction in (increase/decrease) in R/P and thereby to an opposite change direction (decrease/increase) in ET/P ( Figure 2B). This is consistent with other recent multi-catchment results for drought conditions over Europe, showing strong and fast runoff reductions in response to precipitation deficits, but relatively small/negligible decreases or even increases in some places for corresponding evapotranspiration 9 . shapley values indicate that explanatory variables contribute to increase in R/P [ET/P]. Panels A-C show results for the most contributing explanatory variables of (A) topography, (B) climate (precipitation, temperature), and (C) land-use area fractions (of agriculture, forest, grassland, shrubland, relative to total catchment area). Figure S6 shows resulting shapley values for all explanatory variables in the ML model.
From ML model deciphering with regard to different types of land cover/use ( Figure 2C), larger relative vegetated area (and greater vegetation density, i.e., more for forests than grasslands) tends to imply higher ET/P and thereby lower R/P. This effect is most pronounced for managed vegetation, like agriculture and forests, for which R/P exhibits near-linear and super-linear negative correlation, respectively. That is, vegetation and particularly managed crops and forests tend to take their cut of water even under low P conditions. This is consistent with results in other recent studies, showing vegetation greening associated with increased ET, and reduced soil moisture and runoff 3,34,35 .
The remaining explanatory variables of the ML model show only minor marginal contributions to R/P (ET/P) prediction (SI Figure S6). Among the land cover/use types, water-covered area fractions of wetlands and surface waters also exhibit negative correlation to R/P (positive to ET/P, as should be expected since the rate of evaporation from open water surfaces is generally higher than ET rate from dry land areas), while R/P correlation is negligible for settlement and bare areas.
Permanent snow and ice exhibit a slight positive correlation with R/P over the small relative area range that these cover in most catchments, which may be related to the relatively high albedo of these land covers regulating energy availability 36 . Overall, the results for these remaining land cover/use variables, however, have lower confidence because most data points extend only over small relative area ranges, close to zero. Furthermore, it is not straightforward to draw general trade-off conclusions for land cover/use exchanges, since the shapley values are not free of interaction, i.e., trade-offs may be context-dependent. ET/P is on average much higher than R/P in the tropical and temperate zones of the northern hemisphere (1ºN to 56ºN) and tropical and subtropical zones of the southern hemisphere (3ºS to 40ºS), where most land area and its vegetation are located around the world, and where hydrological conditions tend to be more water than energy limited (SI Figure S7). Around the equator, in the tropical zone, ET/P and R/P tend to be similar, on average at around 0.50 each, while ET/P is relatively small and R/P is relatively large in the higher and lower latitude parts of the temperate zones in each hemisphere (above 56ºN and below 40ºS) and decrease/increase even more, respectively, in the polar zones. These are also the regions with the most energy-limited water conditions (low aridity index, PET/P) around the world (SI Figure S7), and the polar regions, where there is little vegetation, are the only places where R/P is on average higher than ET/P. climate variables, the ML model tends to lose predictability for unseen data in catchments with a greater time lag between peak temperature and peak precipitation ( Figure 3D). For land-use variables, predictability tends to be lost for catchments with lower relative forest and agriculture areas ( Figure 3E). Looking at the model-independent hydrological catchment characteristics, predictability tends to be lost for catchments with relatively high (>> 1) or relatively low (<< 1) aridity index (implying major water or major energy limitation, respectively), and greater Teq and associated greater Rgw0/Ravg ( Figure 3F). Figure 4A shows how the R/P (and associated ET/P) model error grows with increasing DI for the study catchments. Depending on the selection of DI threshold value (DIlim), the ML model AoA around the world changes ( Figure 4B). Selection of, for example, DIlim = 0.27 implies that 5% of the unseen data in the test set fall outside the AoA. The resulting MAE for R/P becomes then 0.13 for the catchments outside AoA ( Figure 4A), which can, e.g., be compared with the mean absolute R/P error of 0.06 for 95% of the test set data inside AoA ( Figure 4A). Selecting DIlim in the range 0.27-0.50 does not change the error much ( Figure 4A) but raises AoA from 35% to 60% of the total world land area (minus Antarctica) for increased DIlim from DIlim1 = 0.27 to DIlim2 = 0.50 ( Figure 4B). Figure 4C maps the resulting DI for ML model application around the world and Figure 4D shows the relative world area per latitude falling within AoA for DIlim1 = 0.27 and DIlim2 = 0.5 (for spatial coverage of DIlim1 and DIlim2, see SI Figure S9). Overall, and regardless of specific DIlim choice within the range 0.27-0.50, the relative land area falling within the ML model AoA is relatively small in the northern subtropical to the low-latitude temperate region and the polar regions of the world (AoA < 50% for DIlim2 above 66ºN, from 15ºN to 36ºN, and below 44ºS).
Conclusions
Available observational data, as well as ML model application around the world, show ET/P to be overall higher than or at lowest similar to R/P around most of the world outside the polar regions.
The ML model deciphering shows that this is because vegetation, and particularly managed agricultural crops and forests predominantly take their needed water share. This is most strongly evident in the tropical and temperate zones of the northern hemisphere and the tropical and subtropical zones of the southern hemisphere, and can make blue-water availability (related to R/P) highly vulnerable to climate-driven precipitation changes and/or directly human-driven crop, forest and other vegetation changes in these regions. These world parts are also where most people live and hydrological conditions tend to be more water than energy limited, with associated relatively high water security, drought, and flood risks.
In the global ML model application for WFP prediction, around 60% [35%] of the global land area falls within the model AoA for selected DIlim = 0.50 [0.27]. This AoA assessment shows that additional ML model training is needed for a more accurate prediction of green-blue WFP in the northern subtropical to the low-latitude temperate region (northern Africa and most of Asia) and the polar regions of the world (north-eastern North America, Greenland, Iceland, and Russian-Arctic). In general, WFP predictability of ML trained models can be tested, deciphered and assessed for and across different hydro-climatic and land-use conditions around the world, following the model-agnostic methodology used in this study.
For the future, the ML model developed in this study implies that WFP to green fluxes (ET/P) will tend to increase to an even higher level at the expense of blue water fluxes (R/P), which will tend to get even lower, in areas where climate change drives more water limitation, and human land
Experimental procedures
Resource availability
Lead contact
Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Daniel Althoff (daniel.althoff@natgeo.su.se).
Materials availability
This study did not generate new unique materials.
Data and code availability
All input data used for the study are openly available, as stated in the article. All data generated in the study have been deposited at Zenodo and are publicly available at: https://zenodo.org/record/6519659. The code used for the machine learning model and remaining analyses has also been deposited at https://zenodo.org/record/6519659. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.
Methods overview
The methodology combines (i) an independent quantification of hydrological characteristics, and (ii) a ML modelling framework for the possible prediction of WFP worldwide. The independently quantified hydrological characteristics are the aridity index, the water flux equilibration time (Teq), and the relative groundwater contribution to surface water runoff under zero monthly precipitation (Rgw0/Ravg). Besides characterizing the catchments, the quantification of Teq is important to ensure that the ML modelling regards temporally stable average WFP conditions for and across the study catchments with widely different hydrological conditions around the world. These hydrological characteristics are also important to explore the physical-hydrological reasonableness of the ML model applicability outside its initial domain. Below, we detail the data sources for the study, data curation, and the investigation procedures.
Data sources
We compiled a database for a total of 3,614 hydrological catchments around the world with available data for daily runoff (limiting data component required for catchment-wise water balance closure) over at least 25 years from 1980 to 2020. The hydrological catchments boundaries and runoff series were obtained from the Global Runoff Database Centre 24 and multiple CAMELS datasets [25][26][27][28][29] (for details concerning catchment selection, see SI Note S1, Table S1, and Figure S10). For these catchments, we derived daily precipitation time series from the Multi-Source For the ML modelling framework, the target variable is the blue WFP, represented by the ratio between average runoff and average precipitation (R/P) (and the complementary, water-balanced determined green WFP -ET/P). As input, the model takes 17 explanatory variables that were calculated for each catchment concerning hydro-climatic, land use and topography indices.
However, before synthesizing all of these for the catchments, we first determined a minimum time interval that ensures water flux equilibration for all catchments (see water flux equilibration Teq in the following section). This means that a long time series could be summarised in several data instances for a catchment. We selected a 5-year period as reference as it ensures stable flux partitioning for all catchments ( Figure 1A-B). For a hypothetical observational period from 1995 to 2012, the data instances would be summarised for the sub-periods 1995-1999, 1996-2000, …,
2008-2012.
Independently estimated hydrological characteristics
Aridity index
The aridity index (AI) was calculated as the ratio between potential evapotranspiration (PET) and
Water flux equilibration time
To determine water flux equilibration time Teq, we assessed the average R/P (avg(R/P)) calculated for different aggregation time scales (DT). For any DT, R/P instances are obtained from the P and R time series using a moving time-window of size DT (SI Figure S2A). These instances obtained over the whole data time series are then averaged to obtain avg(R/P)DT. As DT increases, avg(R/P) stabilizes to a more or less constant value (SI Figure S2B). The flux equilibration time Teq is assumed here as the minimum DT value (Teq = DTmin), for and beyond which avg(R/P) values obtained for any DT > DTmin differ less than 1% from each other.
Groundwater contribution to streams under zero monthly precipitation
To estimate the relative groundwater contribution to surface water runoff under zero monthly precipitation Rgw0/Ravg, we regress monthly R, normalized with average monthly R over the whole runoff series (Ravg), versus monthly P for each study catchment (SI Figure S3). The groundwater indicator variable is quantified as equal to the regression line intercept (IntR) for 0 ≤ IntR ≤ 1. A negative intercept (IntR < 0) implies no surface water runoff, i.e., dry streams with still-standing water, for zero monthly P. On the other hand, a positive intercept above 1 (IntR > 1) implies that the average runoff under zero monthly precipitation is larger than the total average runoff Ravg over the whole P and R time series, which may occur for snow-dominated catchments. In both cases (IntR < 0 and IntR > 1), the groundwater flow cannot be simply estimated from the R vs P regression line. Thus, a total of 1,274 (35% of all) and 105 (3% of all) study catchments with IntR < 0 and IntR > 1, respectively, were excluded from the Rgw0/Ravg analysis.
Modelling data curation
The modelling data are data instances corresponding to the blue WFP R/P (target) and 17 explanatory variables (input) that were summarised for every 5 years of a catchment time series.
The explanatory variables refer to 5 hydroclimatic indices, 10 land use fractions, and 2 topography indices. The hydroclimatic indices were derived from the precipitation and temperature time series.
These series were first approximated to sine curves to extract their corresponding annual averages, seasonal amplitude over the year, and a seasonality timing index representing the phase lag difference between peak precipitation and peak temperature over the year (for details, see SI Note S2 We chose the cubist regression for ML modelling the blue WFP R/P. The cubist regression is based on decision trees but presents linear models in the final nodes (leaves) of a decision tree instead of discrete values 45,46 . It also uses a boosting-like scheme to improve its prediction by building
Model area of applicability
To investigate the model applicability to new unseen data, we used the area of applicability (AoA) method 23 . This method consists of calculating the dissimilarity between new data and the model's known domain (training set). The dissimilarity index (DI) is based on the Euclidean distance between the standardized explanatory variables weighed by their importance for the ML model 23 .
The method uses the model training cross-validation to investigate DI for unseen data and suggests a threshold to classify new data as inside or outside the model AoA. We also further investigate the relationship between average expected error and DI for the test set.
Global extrapolation
The ML model was used to estimate the green-blue WFP over the world (excluding Antarctica).
The 17 explanatory variables were summarised for grid cells with a resolution of 0.25º x 0.25º and considering the recent period from 2000 to 2019. As the model was developed primarily to estimate R/P, we also derived the corresponding average green WFP as ET/P ≈ 1 -R/P. The predicted green-blue WFP were constrained to the range 0-1, as predictions outside the training domain (high DI) could fall outside this range. The associated global DI was also investigated.
Supplemental information
Document S1. Figures S1-S10, Tables S1-S3, and Notes S1-S4. Table S1. Summary of data sources for hydrological catchments and daily runoff data. Figure S1. The study catchments' (a) aridity index PET/P; and the PET/P (b) statistical distribution and (c) Budyko space distribution (versus ET/P) across all catchments, where PET is average potential evapotranspiration, ET is average actual evapotranspiration, and P is average precipitation for each catchment over the study period . The groundwater indicator variable Rgw0/Ravg is quantified as equal to the regression line intercept (IntR) for 0 ≤ IntR ≤ 1. Negative intercept, IntR < 0, implies no surface water runoff (essentially dry streams and/or stream networks with stillstanding water) for zero monthly P. This is not an unrealistic condition, but one for which groundwater flow cannot be simply estimated from the R vs P regression line; 1,274 (35% of all) study catchments with IntR < 0 were therefore excluded from the Rgw0/Ravg analysis. Moreover, IntR>1 implies unrealistically large average runoff under zero monthly precipitation, as this would be even larger than the total average runoff Ravg over the whole precipitation and runoff time series; 105 (3% of all) study catchments with IntR > 1 were therefore also excluded from the Rgw0/Ravg analysis. Figure S4. (a) Map of estimated average groundwater contribution to surface water runoff under zero monthly precipitation conditions (Rgw0) relative to total average surface water runoff (Ravg) for the investigated hydrological catchments, and (b) the statistical distribution of Rgw0/Ravg among the catchments. See Figure S3 for explanation of how Rgw0/Ravg is estimated. Catchments boundaries and daily runoff data.
Contents
Abbrev. Catchments Period** Mean obs. period (years) Mean obs. avail. (%)
Note S1
The hydrological catchments (boundaries and runoff data) used in this study were compiled from the Global Runoff Database Centre (GRDC) 1 were summarised for every 5-year period of the time series (see Section S3), the catchments runoff series were also screened for at least one 5-year period with "complete" data, i.e., no more than 3 missing days in any given month of a year (42 catchments discarded). The runoff data was also screened to discard catchments with (iii) odd behaviours in time series, such as unreasonable shifts in average runoff or interference likely caused by human-operated infrastructures, e.g., dams (67 catchments), and (iv) series with the average annual runoff above the average annual precipitation (196 catchments discarded). Finally, because data availability of other explanatory variables were also considered, 22 more catchments were discarded. The final database has a total of 3614 hydrological catchments (Table S1, Figure S10). Spatial and tabular data wrangling was performed in R 12 using mostly the rgdal 13 , terra 14 , dplyr 15 , tidyr 16 , doParallel 17 , and foreach 18 packages. For all visualizations, we used the ggplot2 19 package.
Hydro-climatic, land-cover/use, and topographical indices
Note S2
Catchments daily precipitation (P) time series were derived from the Multi-Source Weighted Ensemble Precipitation (MSWEP) 7 version 2.8. Catchments daily average temperature (T) time series were obtained by averaging the daily minimum and maximum temperature series derived from the Climate Prediction Center (CPC) Global Temperature data 8 . To obtain the catchment P and T annual averages, seasonal amplitudes, and phase lag between peak P and peak T over the year under a specific period, their respective time series were approximated to sine curves (Equations S1 and S2):
= ̅ [1 + sin(2 ( − )/ )] (S1) = ̅ + sin(2 ( − )/ )
where P and T are the daily precipitation and temperature time series (mm, ºC), respectively, P ̅ and T ̅ are the time-averaged precipitation and temperature (mm, ºC), respectively, and are the precipitation and temperature seasonal amplitude (dimensionless, ºC), respectively, sP and sT are the P and T phase shifts (days), respectively, t is the time (day-of-year), and is the duration of the seasonal cycle (365 days). When approximating the sine curves, the variable time-averaged, seasonal amplitude, and phase shift are calibrated and must be positive. For the ML modelling, P ̅ and was scaled from daily to annual averages while the temperature seasonal amplitude, , was normalized by the time-averaged temperature ( * = /( ̅ + 273.15)).
The phase lag between peak P and peak T (P-T timing) over the year can then be obtained from Eq. S3:
= cos(2 ( − )/365)
where TI is the phase lag between peak P and peak T over the year, or timing index. TI ranges from -1 and 1, where 1 indicate that P and T both peak in the same moment, i.e., precipitation peaks during summer, 0 indicates a phase lag of 3 months, and -1 indicates the maximum phase lag of 6 months.
Note S3
The land-cover/use classes were derived from land cover maps of the Climate Research Data
Package (CRDP). The CRDP was generated within the European Space Agency (ESA) Climate
Change Initiative -Land Cover (CCI-LC) project 9,10 and covers the period from 1992 to present.
The land cover classification system describes 22 main classes (level 1) and a total of 38 subclasses (level 2). For simplicity, the classes were grouped into 10 broad categories ( agriculture, forest, grassland, shrubland, sparse vegetation, wetland, bare area, settlement, water, and permanent snow and ice.
The catchment mean elevation (m) and mean slope (m/m) were derived from the Multi-Error-Removed Improved-Terrain Digital Elevation Model (MERIT DEM) 11 .
Machine learning model training
Note S4
The machine learning model was developed using the cubist regression [20][21][22] . The cubist regression hyperparameters "committees" and "neighbours" refer to the number of trees created in sequence, similar to boosting, and the number of nearest-neighbours points from the training set that can be used to adjust the final prediction, respectively.
Hyperparameter tuning was performed during training using a grid search (committees [0-30], neighbours [0-9]) and spatial cross-validation with 10 folds, i.e., data points from the same catchment were all allocated in the same fold.
We used the cubist 23 and caret 24 packages in R 12 for training the model and hyperparameter-tuning, and the CAST 25 package for the spatial partitioning of the training set for spatial cross-validation.
Figure 1 .
1(A) Map of the 3,614 investigated hydrological catchments (colored fields) that also shows their water flux equilibration time (Teq), along with (B) the box plot statistics of Teq across the catchments (with the + symbol showing the mean value). (C-D) Performance of the ML model for the blue water flux (R/P) partitioning in the test set of 757 catchments, in terms of: (C) a
(
MAE) of 0.07. This should be compared to the test set average R/P value of 0.35 (and corresponding average ET/P of 0.65). The average MAE calculated for individual catchments (Figure 1D) was similar to that of the entire test set (average MAE = 0.07, median MAE = 0.04). The ML model also scored a percentage bias of 1.20% and Kling-Gupta efficiency 33 (KGE) of 0.87 for the test set.
Figure 2 .
2Marginal contributions (shapley values) of the main explanatory ML model variables to WFP predictions for the entire dataset. Shapley values are relative to the average dataset prediction (R/P = 0.37, ET/P = 0.63). Positive [negative]
For example, replacing forests or shrublands for agriculture may have different effects in mountainous or flat terrains and in arid or humid climates. For each region, however, simulations can show the implications of such exchanges. For the remaining climate variables, higher seasonal amplitude in precipitation [temperature] may imply a slightly higher R/P [ET/P]. The time lag between peak P and peak T also shows a small marginal contribution, with somewhat higher ET/P [lower R/P] if P peaks in the warm season, and lower ET/P [higher R/P] if it peaks in the cold season. Applying the developed ML model to WFP prediction around the world (see EP for details on global extrapolation) yields an overall smaller average share of the total precipitation water input going to runoff (blue water flux; Figures 3A-B) than to evapotranspiration (green water flux; Figures 3B-C). The area-weighted spatial average values of local WFP in each pixel are R/P = 0.38 and ET/P = 0.62, while the flow volume-averaged WFP of total global P into global R and global ET yields R/P = 0.46 and ET/P = 0.54. Looking at latitudinal WFP distribution (Figure 3B),
Figure 3 .
3(A-C) Water flux partitioning and its average latitudinal distribution over land for (A, B-blue) R/P and (B-green, C) ET/P. (D-F) Box plot variable statistics that differ most between world parts within (training set, and part of test set) and those outside of (remaining test set part) the ML model area of applicability (AoA; considering here a dissimilarity index threshold of DIlim=0.27, see Figures 4A-B), for the variables: (D) P-T peak timing (climatic); (E) relative agriculture and forest areas (land-use); and (F) aridity index, flux equilibration time Teq, and indicator of groundwater runoff contribution Rgw0/Ravg (model-independent hydrological characteristics). The aridity index (F) is cropped to values below 3 (2% of data not showing). SI Figure S8 shows corresponding statistics (more similar within and outside of AoA) for other explanatory variables of the ML model. Resulting ML model error versus dissimilarity index (DI) for the study catchments suggests a relevant DI threshold in the range 0.27 ≤ DIlim ≤ 0.50 for classifying new unseen data as either inside or outside the model area of applicability (AoA) (Figures 3D-F and 4A-B). With regard to
Figure 4 .
4(A) Model error for the test set versus dissimilarity index (DI) for the study catchments, (B) global area of ML model applicability (AoA) for different selected DI threshold value (DIlim) for AoA, (C) map of DI around the world, and (D) latitudinal distribution of relative land area inside AoA.
uses expand to more managed (and more irrigated) agriculture and/or reforestation replacing open, sparsely, or non-vegetated land. The ML model results for WFP can be combined with Earth System Model projections of future temperature and precipitation scenarios to assess corresponding blue and green water availability, security, drought and flood risks for various regions, societal sectors, and ecosystems. To enhance ML model applicability under such changes, additional data and ML model training are needed in particular for the northern subtropical and low-latitude temperate region and the polar regions of the world.
Weighted-Ensemble Precipitation (MSWEP)37 version 2.8, and daily mean temperature time series from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) global temperature data 38 . Annual time series of land use/cover fractions were derived from land cover maps of the Climate Research Data Package (CRDP) that is generated within the European Space Agency (ESA) Climate Change Initiative -Land Cover (CCI-LC) project. For topography, we used the Multi-Error-Removed Improved-Terrain Digital Elevation Model (MERIT DEM) 39 .
P (AI = PET/P). PET was calculated with the Priestley and Taylor 40 equation (Equation 1). The net radiation (Rn) was calculated following the FAO-56 41 . We used temperature data from the CPC/NOAA dataset, while relative humidity and incoming solar radiation were obtained from the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) Prediction Of Worldwide Energy Resources (POWER) Project 42 funded through the NASA Earth Science/Applied Science Program. is an empirical constant accounting for vapor pressure deficit and resistance values, assumed as 1.26 for open bodies of water, and γ is the psychrometric constant.
successive trees. For hyperparameters optimization, we used spatial cross-validation with 10 folds and grid search (more details in SI Note S4). The final model can be accessed at the online repository of this study along with sample codes of its use44 . The model performance on the test set was assessed using the Kling-Gupta efficiency index 33 (KGE), coefficient of determination (r 2 ), mean absolute error (MAE), and percentage bias (PBIAS). Model interpretation The model interpretability gap was addressed using the Shapley values technique 47,48 . Shapley values is a model-agnostic technique based on game theory to fairly distribute the effect of the explanatory variables on the prediction 22 . For a single prediction, it returns the average expected marginal contribution of each explanatory variable in relation to the average prediction of the reference dataset. Here, we used the entire dataset as a reference and 1000 coalitions to obtain more accurate/stable shapley values. The shapley values were computed and aggregated for the entire dataset in order to obtain a fair understanding of the model mechanics.
4 Figure 5 Figure 6 Figure 7 Figure 7 Figure 8 Figure 8 Figure 9 Figure 9 Figure 10 Figure
45677889910S3. . S1. . S2. . S3. . S4. . S5. . S6. . S7. . S8. . S9. . S10.. . 12 Note S1. 11 Note S2. 13 Note S3. 14 Note S4. 14
Figure S2 .
S2Schematic illustration of how water flux equilibration time (Teq) is estimated for an arbitrary hydrological catchment. Panel (a) illustrates a moving time-window (DT) averaging of daily R/P (runoff/precipitation) for the example of DT = 6 months. Panel (b) illustrates average R/P (avg(R/P), green line) among the DT windows moving over the whole data time series, and the stabilization of avg(R/P) to a more or less constant value for increasing DT, along with the temporal standard deviation (std(R/P), green shade) around avg(R/P) for the moving DT windows. The flux equilibration time Teq is quantified as equal to the minimum DT value (Teq = DTmin), for and beyond which avg(R/P) values obtained for any DT ≥ DTmin differ less than 1% from each other.
Figure S3 .
S3Schematic illustration of the approach to estimate average groundwater contribution to surface water runoff under zero monthly precipitation conditions (Rgw0) from the regression line (blue) fitted to the data points (black dots) of monthly runoff (R), normalized with average runoff over the whole runoff time series (Ravg), versus monthly precipitation (P) for each study catchment.
Figure S5 .
S5Correlation between flux equilibration time Teq (Figure S2, main Figure 1A-B) and monthly values (according to the definition for zero monthly precipitation) of groundwater indicator Rgw0/Ravg (Figures S3-S4) among the study catchments.
Figure S6 .
S6Marginal contributions (shapley values) for all explanatory variables of the ML model to dataset predictions of blue water flux partitioning (R/P). Shapley values relate to the average dataset prediction (R/P = 0.37, ET/P = 0.63). Positive [negative] shapley values indicate that explanatory variables are contributing towards increase in R/P [ET/P].
Figure S7 .
S7Pixel-wise aridity index around the world.
Figure S8 .
S8Statistical distribution of machine learning model explanatory variables for instances categorized as inside and outside the area of applicability (AoA). Here, we used the dissimilarity index limit of 0.27 to classify instances as inside or outside AoA.
Figure S9 .
S9Global land areas inside the machine learning model area of applicability for different dissimilarity index limits.
Figure S10 .
S10(a) Centroids and (b) spatial coverage of the hydrological catchments used in this study. Catchments polygons have a 75% transparency to help display regions with nested/overlapping catchments.
). The ESA CCI-LC classification system describes the land uses in 38 sub-classes which were grouped into 10 broad categories that better correspond to the IPCC land categories 43 (see SI Note S3 andTable S2): agriculture, forest, grassland, shrubland, sparse vegetation, wetland, bare area, settlement, water, and permanent snow and ice. For the two topography indices, we used the MERIT DEM to derive the catchments' mean elevation and mean slope. The final database has been deposited in the study online repository44 . own runoff series. To better reflect the model prediction to new unseen areas, we used a spatial partitioning of the database, i.e., 80% of the catchments were assigned to a training set and the remaining 20% to the test set.Machine learning modelling
Model training and testing
For ML model training and testing, we use different parts of the total database compiled for the
3,614 hydrological catchments and the period from 1992-2020. This period was chosen based on
data availability conditions for all explanatory variables (see SI Table S1 and S3) and the number
of instances per catchment (average = 19.4, median = 21.0) was limited only by the length of their
Table S1 .
S1. 2 Table S2. . 3
Table
Table S2 .
S2Landcover classification system (LCCS) and classification adopted in this study, based
on the land cover maps of the Climate Research Data Package (CRDP) generated within the
European Space Agency (ESA) Climate Change Initiative -Land Cover (CCI-LC) project,
covering the time period from 1992 to present.
Value LCCS
Reclass.
0
No data
No data
10
Cropland, rainfed
Agriculture
11
Herbaceous cover
Agriculture
12
Tree or shrub cover
Agriculture
20
Cropland, irrigated or post-flooding
Agriculture
30
Mosaic cropland (>50%) / natural vegetation (tree, shrub, herbaceous cover) (<50%) Agriculture
40
Mosaic natural vegetation (tree, shrub, herbaceous cover) (>50%) / cropland (<50%) Agriculture
50
Tree cover, broadleaved, evergreen, closed to open (>15%)
Forest
60
Tree cover, broadleaved, deciduous, closed to open (>15%)
Forest
61
Tree cover, broadleaved, deciduous, closed (>40%)
Forest
62
Tree cover, broadleaved, deciduous, open (15-40%)
Forest
70
Tree cover, needleleaved, evergreen, closed to open (>15%)
Forest
71
Tree cover, needleleaved, evergreen, closed (>40%)
Forest
72
Tree cover, needleleaved, evergreen, open (15-40%)
Forest
80
Tree cover, needleleaved, deciduous, closed to open (>15%)
Forest
81
Tree cover, needleleaved, deciduous, closed (>40%)
Forest
82
Tree cover, needleleaved, deciduous, open (15-40%)
Forest
90
Tree cover, mixed leaf type (broadleaved and needleleaved)
Forest
100
Mosaic tree and shrub (>50%) / herbaceous cover (<50%)
Forest
110
Mosaic herbaceous cover (>50%) / tree and shrub (<50%)
Grassland
120
Shrubland
Shrubland
121
Shrubland evergreen
Shrubland
Shrubland deciduous
Shrubland
130
Grassland
Grassland
140
Lichens and mosses
Sparse vegetation
150
Sparse vegetation (tree, shrub, herbaceous cover) (<15%)
Sparse vegetation
151
Sparse tree (<15%)
Sparse vegetation
152
Sparse shrub (<15%)
Sparse vegetation
153
Sparse herbaceous cover (<15%)
Sparse vegetation
160
Tree cover, flooded, fresh or brackish water
Forest
170
Tree cover, flooded, saline water
Forest
180
Shrub or herbaceous cover, flooded, fresh/saline/brakish water
Wetland
190
Urban areas
Settlement
200
Bare areas
Bare area
201
Consolidated bare areas
Bare area
202
Unconsolidated bare areas
Bare area
210
Water bodies
Water
220
Permanent snow and ice
Snow and ice
Table S3 .
S3Summary of data sources for predictor variables.Abbrev.
Spatial
res.
Temporal
res.
Period
Description
MSWEP 7
0.10º
Daily
1979 -present Daily precipitation
(global)
CPC/NOAA 8
0.25º
Daily
1979 -present Daily min. and max. surface temperature
(global)
ESA CCI-LC 9,10
300 m
Annual
1992 -2020
Land cover classification maps
(global)
MERIT-DEM 11
90 m
-
-
Digital elevation model
(90N-60S)
and multiples Catchment Attributes andMeteorology for Large-sample Studies (CAMELS) datasets, i.e., for the contiguous United States 2 , Australia 3 , Brazil 4 , Chile 5 , and Great Britain 6 .We discarded 14 catchments from the CAMELS-AUS dataset because they had notes concerning the accuracy of their boundaries delimitation. To avoid using catchments accounted for both the GRDC and CAMELS datasets, we also discarded catchments from the GRDC dataset when the distance between a catchment gauge station to the nearest CAMELS gauge station was shorter than the minimum distance between gauge stations in that CAMELS dataset. A total of 350 catchments were discarded. 5775 hydrological catchments had daily runoff records available between 1980 and 2019. We further discarded hydrological catchments with (i) less than 25 years of daily runoff data available since 1980 (1527 catchments) and (ii) less than 80% of data in all months (316 catchments), i.e., catchments which data consistently missing in the same period of the year. Because data points
Table S2 )
S2that better correspond to the Intergovernmental Panel on Climate Change (IPCC) land categories 9 :
AcknowledgmentsThe authors would like to acknowledge the Bolin Centre for Climate Research at Stockholm University for the funding provided for this research (related to RA7 project SUB-ECOCLIM).Authors contributionsD.A. and G.D. contributed equally to study conceptualization, analysis of results, illustration, and writing of the paper. D.A. was the main responsible for compiling the data, modelling, and providing open access to the code and study data.Declarations of interestsThe authors declare no competing interests
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| sample_1160 | 0.9481 | arxiv | |
Goal oriented indicators for food systems based on FAIR data Goal oriented indicators for food systems based on FAIR data
Ronit Purian purianro@tauex.tau.ac.il
Tel Aviv University
Goal oriented indicators for food systems based on FAIR data Goal oriented indicators for food systems based on FAIR data
1indicatorsagricultureurban farmsfood supply chainlivestock emissionsmethane reductionFAIR data
Throughout the food supply chain, between production, transportation, packaging, and green employment, a plethora of indicators cover the environmental footprint and resource use. By defining and tracking the more inefficient practices of the food supply chain and their effects, we can better understand how to improve agricultural performance, track nutrition values, and focus on the reduction of a major risk to the environment while contributing to food security. Our aim is to propose a framework for a food supply chain, devoted to the vision of zero waste and zero emissions, and at the same time, fulfilling the broad commitment on inclusive green economy within the climate action. To set the groundwork for a smart city solution which achieves this vision, main indicators and evaluation frameworks are introduced, followed by the drill down into most crucial problems, both globally and locally, in a case study in north Italy. Methane is on the rise in the climate agenda, and specifically in Italy emission mitigation is difficult to achieve in the farming sector. Accordingly, going from the generic frameworks towards a federation deployment, we provide the reasoning for a cost-effective use case in the domain of food, to create a valuable digital twin. A Bayesian approach to assess use cases and select preferred scenarios is proposed, realizing the potential of the digital twin flexibility with FAIR data, while understanding and acting to achieve environmental and social goals, i.e., coping uncertainties, and combining green employment and food security. The proposed framework can be adjusted to organizational, financial, and political considerations in different locations worldwide, rethinking the value of information in the context of FAIR data in digital twins.
Introduction
There is currently a dire need in the improvement of both the quality and the quantity of food. Thus, a change in our food supply systems -and specifically agriculture -is clearly required. Agricultural research is a vital part of this transformation, and its development is key in understanding and dealing with the many problems in the current state of agriculture, as well as the environmental implications of food systems, and the interrelations with food security and the social practices of food production and consumption. Big earth data, socioeconomic surveys, demographic data, and many other sources for timely data should therefore be coordinated and integrated. This is a complicated endeavor where, in addition to the multidisciplinary nature of such research areas, efforts to encourage open science across academic research, industry research, and governmental studies for better operation and policymaking, increase the complexity.
Recently, the concept "digital twin" and its implementation in smart cities has been of great interest in various sectors. Digital twins are often envisioned as a means of collecting mass data for general-purpose use. However, creating specific goal-oriented indicators will provide much cleaner data, and provide a dimension through which to organize data, information, and knowledge for the relevant issues.
For many urban questions, new data sources with greater spatial and temporal resolution are required (OECD, 2019;OECD.Stat, n.d). When applying the food-supply use-case in an actual context, our focus is on the value of information that a digital twin may contribute to the environment, to people's health and to life quality in the city and in the region. In its first stage, this project introduced a highly advanced solution, based on hyperlocal data, to select a cost-effective location for urban farms. Detailed indicators were under development, considering existing data for reliable comparisons. Moreover, practices along the food supply chain, in several value cycles locally and globally -and with relation to quality standards, regulation, and new legislation -set a clear list of goal-oriented indicators.
This top-down approach is complementary to a bottom-up examination of data. Heat waves and water scarcity, green gas emissions, and food insecurity, are tremendesly disruptive to environmental, social, and economic systems. These of course include food systems, from production (e.g., an economic threat to the agricultural sector) to consumption (e.g., food scarcity). Such risks and uncertainties change the way we choose to conceptualize the digital representation. Developing the case study in Italy emphasized the role of local conditions and considerations in the design of valuable information systems.
To lay the foundation for a feasible and effective data system, first we wish to outline some possible indicators, rather the providing an extensive list of measures. To support decisions towards high-priority actions, we describe the vulnerability in a region and provide the reasoning for a cost-effective use case in the domain of food. This is a delicate process requiring attention to needs, identification of market anomalies, and other considerations. Overall, to create a valuable digital twin, we wish to outline the rationale towards significant adaptations -not necessarily a major change -by flexibly adjusting to a more viable way of function and structure in the city and in a region.
The project
The potential benefit of urban and peri-urban agriculture (UPA) to the environment is a main topic in sustainability research, followed by economic and social pillars. When comparing the thematic outcomes in the literature on sustainable and healthy cities, subjective wellbeing and food and nutritional security are leading themes. However, knowledge gaps still exist and create barriers in cultivating sustainability and wellbeing through urban policy and planning (Nitya et al., 2022). We wish to focus on the design of urban use-cases for digital twins, and help close these gaps.
First, we will illustrate a comprehensive enabling framework for monitoring and evaluating resource productivity and waste, agriculture's environmental performance, and the economic and social interrelations.
A coordinated effort is needed to ensure the development of valid evaluation criteria. Since our intention is to also proceed, in the near future, into a broad exploration and consolidation of ecosystem goods and services, the indicators were divided into three sections of objectives, as follows:
(1) Environmental section, emphasizing footprint indicators, with the objective to transform use of materials and waste generation throughout the food production-to-consumption processes.
(2) Socioeconomic section, devoted to inclusive green economy, with the objective to increase ecoentrepreneurship, food security and social resilience.
(3) Data strategy section, enabling knowledge sharing, with the objective to introduce a comprehensive framework for smart, green, and fair urban ecosystems.
Through the very basic production and consumption practices of food, we provide a solid framework for resource efficiency, circular economy, and the transition towards green recovery and growth and community building. This work is summarized in Table 1. To transform use and waste generation along the food production-to-consumption processes, e.g., to improve air quality in city neighborhoods.
To increase food security, public health, and social resilience, e.g., to provide fresh healthy food grown within the city.
To introduce a comprehensive framework for smart, green, and fair urban ecosystems, e.g., to increase resilience to climate change and to social risks.
Topic and expected outcomes
Emissions from road transport for food delivery: to reduce emissions of greenhouse gases and fossil fuels.
Agriculture's environmental performance: to reduce soil loss in agriculture; to reduce energy demand in buildings through green roofs.
Waste generation: to reduce the consumption of packaging, plastic materials, and water.
Local economy, food security, and health: to encourage public participation and education for all; to provide the infrastructure for a new ecosystem of local food markets; to promote collaborations and new business models.
Green employment: to support nutrition and environmental training; preparing for aging population and green job creation.
Stakeholder engagement: to share knowledge and propose principles for FAIR data governance; to propose local and global collaborations and partnership models.
Enabling framework: to demonstrate the value of urban agriculture and local consumption as a holistic enabling framework towards green transition.
How fine is the resolution we need? We will proceed from the wide range of data coverage to the most costeffective data specification.
Environmental indicators -footprint and technologies
Our solution comprises the many stages that food products go through, from production to consumption, and by that we take stock of current consumption of plastic materials, use and waste generation, emissions from road transport for food delivery -compared to zero-packaging and freight trucks, and minimizing water consumption (domestic, tourism, etc.) in a local agriculture market with direct producer-to-consumer coordination.
Waste disposal by hotels and restaurants (tonnes/year). Example: "Total waste in Mauritius amounts to 416,000 tonnes of solid waste in 2009 (2011)". Energy and water consumption in hotels and restaurants (ktoe and m3 /year). Example: "Water consumption from domestic, industrial and tourism accounts for 205 m3 /year or 27% of total water used (2012)".
Indicators were collected and curated for a pilot project in Genoa, a port city in the Italian region of Liguria, and the sixth-largest city in Italy. In Genoa, there is a unique link between tradition and innovation . The data collectively generated in this project holds promise to begin to integrate computational models associated with multiple urban sectors and data sources, including a potential for fulfilling the promise of crowdsourced data.
At this stage, footprint indicators and inclusive green economy are reviewed to map existing evaluation frameworks for different goals, ecosystems, and stakeholders, including companies, central and local governments, and cities. This stage provides the Generic Frameworks. Based on the current knowledge about footprint indicators and inclusive green economy, we will establish the environmental and socioeconomic pillars -on which to prepare a Federation Deployment. This prospective stage will be facing reality, i.e., the local factors (including conditions of demand and supply, and even political forces) that determine the feasibility of any model and technological solution.
Barriers are unavoidable, however, the local constraints are not necessarily an obstacle. In the process proposed here -moving from the holistic view of generic systems to local needs -local barriers turned out to be main features for the design and implementation of a digital twin solution, and intrinsic success factors.
Goals and measures -as mentioned above -aim at representing ecosystems. The evaluation frameworks, presented in Tables 2-3, address the need in a holistic view; each outlines an evaluation perspective and the reasoning that account for certain domains and stakeholders. From environment and green growth (2017) to environment and post-Covid green recovery (2022) policies and measures
For governments to reduce emissions of greenhouse gases and the share of energy demand met with fossil fuels, and increase energy security; to align the spread of investment across policies and key sectors such as agriculture, waste management and forestry; to invest more in skills and innovation. SPHERE (WBCSD, 2022) Sustainability-waste-packages
For companies to monitor and minimize their packaging's contribution to climate change and nature loss.
Principles include packaging efficiency circularity, impact on climate change and biodiversity loss, absence of harmful substances and waste mismanagement.
Cities Assessment Framework 2.0 (ClimateSmart, 2021)
Climate readiness and development
For cities while planning and undertaking development projects, towards a resilient urban habitat.
Principles include urban planning, green cover and biodiversity; energy and green buildings; mobility and air quality; water management; and waste management.
WorldFAIR (Codata, 2022) Global cooperation on FAIR data policy and practice
For reseachers and policymakers to adapt FAIR Implementation Profiles to each (cross-)discipline area.
Principles include Cross-Domain Interoperability Framework with 11 case studies from the physical, agricultural and environmental sciences (including chemistry, nanomaterials, geochemistry, ocean data, disaster risk reduction), the social sciences (social surveys data; population health surveys with clinical and genomics data for COVID-19 research in eastern and southern Africa), urban health, biodiversity (digital extended specimen), and the cultural heritage sector (digital representation of heritage artefacts). The indicators imply the problems a system aims to address.
At this stage after obtaining more information about the available data, the main attempt was to incorporate environmental goals into indicators e.g., to reduce emissions of greenhouse gases and fossil fuels.
Hyperlocal resolution data to support decisions such as the location of urban farms, creating a new urban habitat; or implementing renewable energy sources, lighting infrastructure, and more -were linked to goals such as, to reduce energy demand; to increase energy security. Mobile sensors were examined to collect high-resolution spatiotemporal data and carefully create, with unique algorithms, valuable climate information.
To propose a valid agenda to the digital twin industry, however, and to support its viability, the local factors must be considered with high attention to essential details. Rather than a detailed review of current indicators, a holistic yet selective view is proposed to select factors of high impact and to inspect their specific influences and possible interactions.
Encapsulating methane data should be a major goal in the construction of fine-grained data systems. Methane is a layer on which we present the building of the system (Why methane), further reviewing the state of agricultural methane emissions (Why food); and farming sector weaknesses and threats, strengths and opportunities (Why Italy).
In the conflicted playground of the climate agenda, methane plays the role of a tiebreaker. If we want to lead change, the sandbox of climate technologies must identify methane as a game changer.
Why methane
Methane is on the rise in the climate agenda and when considering the benefits and costs of methane mitigation, it is evident that policies and tools to achieve this goal should be of priority in the multifaceted domain of food systems (e.g., Crippa et al., 2021;IEA, 2022;Qu et al., 2021;Shepon et al., 2018;Tepper et al., 2021).
Methane reduction is expected to have "greater climate benefits", and its increase is expected to have "greater adverse climate impacts", according to the recent IPCC report on "Emissions trends and drivers" (IPCC, 2022; chapter 2, p. 17). From the mitigation perspective, the adverse results -as well as the opportunity for improvement -make methane a key element in the construction of a valuable set of indicators.
The reduction of methane is essential and, to cope with the global warming, a rapid and sustained reduction is also achievable (IEA, 2022). This leads to the question of how much can be mitigated, and by whom -which sectors can have a meaningful impact?
Why food
Agriculture is responsible for most methane emitted into the atmosphere, more than the energy sector which accounts for about "40% of total methane emissions attributable to human activity", according to Global Methane Tracker (IEA, 2022) -even when considering the increase in energy-related methane emissions as of post-pandemic higher demand and production of fossil fuel. Still, data is difficult to achieve. Global efforts to track methane emissions must rely on estimations, measurement initiatives, and scientific research, in addition to data reported by official public bodies to the UN Framework Convention on Climate Change (UNFCCC), which are "not yet accurate enough" (IEA, 2022), as can be seen in Figure 1.
Why Italy
A global look at methane emissions reveals that, despite an overall rise worldwide, emissions in the agricultural sectors are being reduced. The effort to reduce methane emissions has been successful in Italy, on a national level. However, the reduction occurred despite an increase in the agricultural sectors in Italy. Figure 2 shows the worldwide increase in methane emissions (a) and decrease in recent years in the agricultural sector (b). Conversely, Italy performed well in general emission reduction (c), but an increase is shown in agricultural methane emissions (d). To realize the salient inversion, we also show the % of change (e-f). National strategies for reducing on-farm methane emissions, however, often raise doubts and uncertainties. Representative organizations of the farmers resist their inclusion in the Emissions Trading Scheme (ETS) as governmental incentives are often conditioned with performance measures and possible taxes (e.g., FAO's Livestock, Climate and Environment community-of-action with the IPCC; He Waka Eke Noa in New Zealand, and more).
The societal aspects along the food supply chain cover a broad scope of life domains (O'Neill at el., 2017). Before presenting the broad view of societal issues, and in consistence with the process of eliminating the environmental indicators, a focus is proposed on a sector in crisis, the farming sector in Italy.
Climate events and agriculture in Italy Drought, heat waves, and poor technical infrastructure put the agricultural sector in Italy at risk. A third of the national agricultural production originates from the farms in the area of the Po River, and the prolonged drought has dried up the river. The government has declared a state of emergency, with the forecast for enhanced decrease in available water resources, expecting a decrease of up to 40% (AP, 2022).
The drought and the lack of effective water infrastructure, in the Northern regions in particular, has put at risk half of the livestock national production, according to a special brief by EURACTIV Network (2022) The vulnerability of food production systems to climate change, and specifically the combination of poor water infrastructure together with drought, make the adoption of green technologies and skills an urgent need. However, new skills and green innovation that combines new technologies for agriculture are not easy to achieve, rather, insufficient assessment of training and innovation in green technologies represents a possible inadequacy in the measurement of both the green transition and its employment effects of economic recovery (OECD, 2022; Table 4).
Green employment in Italy
Green jobs require skills transformation. As stated in recent reports on this timely topic, "Measuring the resulting employment effects of the green transition is challenging because it requires simultaneously evaluating all policies introduced and their direct and indirect economic and labour market impacts and interactions" (Cedefop, 2021;p. 16. Emphasis added). Moreover, the painful transition from green growth to post-Covid green recovery struggles in the area where it is most needed -in response to the economic breakdown, and sectoral unemployment, in different regions and territories.
When assessing the environmental impact of measures in the OECD Green Recovery Database (OECD, 2022, April 21; Table 1), green recovery fails to provide positive indicators (It provides a few positive ones, and no negative ones) in green skills transformation: "Relatively few recovery measures focus on skills training and on innovation in green technologies. This also represents a missed opportunity, as more attention to measures that can drive green job creation, notably to compensate for job losses in other industries, can help to ensure a 'just transition'" (OECD, 2022, April 19; 21. Emphasis added). Table 4 shows the absence of "Skills training" in the OECD Green Recovery Database (which leads to the next section). To conclude, the objective of green job creation through green initiatives, according to recent reports, is difficult to achieve.
When considering risk evaluation and characterization for adaptation and mitigation strategies, the agriculture crisis is both a threat (risk of losing third of Italy's agricultural production) and an opportunity -to helping the farming sector implementing new technologies; utilizing the market structure towards lean adaptation of small farms to a new mode of agile agriculture, and reducing anthropogenic greenhouse gas (GHG) emissions that contribute to climate change.
The purpose of indicators is, therefore, not only to provide a detailed account of what has been achieved. Choosing indicators is a process of narrating a story .
Socioeconomic status of agricultural workers, specifically during times of low yield, is a promising axis on which to propose evaluation indicators. Thus, we propose to focus on the response needed in the farming sector when carrying out the objective of green job creation through green initiatives.
At the same time, this objective deserves a broader attention, beyond a state aid scheme for farmer, and towards rethinking urban nature and the many influences of green areas on human health and wellbeing.
A new and inclusive framework (especially for socioeconomic indicators) must consider, along the environmental aspects, the factors that affect and change our behaviors and urban lifestyle. What are the societal influences of technological acceleration, the service economy, and globalization on our life in cities? How does the sharing economy, in its current form, shape our service markets -and the habitat?
Socioeconomic indicators -inclusive green economy
The socioeconomic impact of food supply systems goes much beyond food security for all, in quality and quantity.
Socioeconomic implications include, among other things, preparing for aging population, e.g., through vocational training towards green jobs, health education to encourage nutrition-related behaviors, and other measures of health and wellbeing. Thus, the same questions presented in the Environmental section -how to choose footprint indicators and how fine is the resolution we need -are presented in the Socioeconomic section -how to proceed from the broad challenges of inclusive green economy towards effective intervention and evaluation. Who are the groups in focus, what are the goals (accounting for reciprocity, coping with uncertainties, green employment for green recovery -dedicated to vulnerable sectors, or specific social groups?), and how to measure (indicators that are part of the expected evaluation).
Chronic urban problems such as inequality, air pollution, traffic congestion and food insecurity affect us all. However, some groups are more vulnerable than others. Heat waves, flooding, droughts, and other effects of the climate crisis may leave them defenseless. Socioeconomic indicators and cultural values (surveys, public participation, etc.) support decisions in public projects. New climate risks to health and wellbeing, for different demographics, can be detected and recognized. However, while welfare is often associated with socioeconomic conditions, our intentions are to integrate the environmental aspects into a new framework of welfare, health, and wellbeing, to propose a valid agenda for digital twins as an emerging industry sector, and support its viability.
Size of cities, determined by population density, is often related to new life routines. The fast pace of life, globalization, and technological acceleration have caused new social and environmental problems (Purian, 2021;Ronen & Purian, 2021). In order to lead the movement forward towards fair and green smart cities, pragmatic principles and evaluation indicators are being applied, addressing climate threats. In line with the shared socioeconomic pathways proposed by O'Neill at el. (2017) and Riahi et al. (2017) for possible futures in the 21st century, current issues force us to focus on interrelations among various factors.
In this project we aim to draw attention to themes such as natural assets that organically coexists with the local history and other resources to preserve and cherish, in every city and region, in a unique urban lifestyle. To do that, we propose to combine indicators that are detailed along shared life domains.
Market structure: In different domains (e.g., MaaS, in Purian et al., 2019), attempts are made to achieve responsible models of a community-based sharing economy, and for technology design and adoption that considers coordination and fair access to services.
Appreciation of nature: Protecting urban biodiversity and the benefits of biodiversity for human well-being are related to food systems through appreciation of nature in urban agriculture, mainly edible trees, shrubs and bushes that are nutritious wild food.
Urban cognition: The current era of technological acceleration in today's global cities raises problems of stress, cognitive load, uncertainty, and a growing need for belonging. Urban cognition and sociological influences of the unprecedented scope of data we generate can be relieved in the presence of green areas. Even small green spots in the city may contribute for better physical and mental health.
Social inclusion: Key issues include social polarization, new types of digital divide and the crucial need in digital literacy (e.g., inoculation to fight misinformation), and other effects of size in many life systems. The implementation of new technologies, that generate enormous amounts of data, further accelerates these patterns and dynamics of social exclusion. While many cities cope with population boom, aging population, labor migration, and lack of working hands, we wish to capture an inclusive evaluation framework, considering the severity of disparities.
Technological innovation for good: Community gardens and urban farms that are equipped with facilities for nutrient management, integrated farming and precision agriculture systems are an antidote to the feeling of powerlessness, not only due to poverty, but also due to lack of influence and perceived control in the smart city.
Community building is related to the food domain in several ways, from community gardens to delivery, cooking and consumption, and surplus foods and waste management. As urban areas expand and more people live in cities, a growing environmental awareness is being developed. Resilience, the ability to affect main affectors, and to believe in their benevolence when facing large institutions, depends on improving environmental quality and natural hazard protection, as well as food security for all, in quantity and in quality.
Eco-entrepreneurship that combines the local economy, and encourages green employment and trade, has the advantages of circular economy while also contributing to social resilience.
From a viewpoint of the consumers
Food security is an accurate manifestation of social and economic gaps, which do not necessarily coincide. The nutritional quality of food, health security, is almost a hidden aspect compared to the available supply in quantity. The ambiguous scope of food insecurity is core to challenges we face today. To what extent is food insecurity the result of "a lack of available financial resources for food at the household level" (proposed by Hunger + Health, 2022)? Rather than a household-level economic condition, a focus on community practices is proposed; extending merely financial disparities to indicate a broader view, namely, the social determinants of a poor diet that cause obesity, heart disease and many other medical conditions (e.g., FRAC, 2017).
From a viewpoint of the producers
Uncertainties are often mentioned in the context of farming reforms to reduce agricultural emissions. Such uncertainties, however, create the organizing themes around which to establish the partnerships. The Partnership Platform (UN, 2022), for example, is a way to tackle uncertainties and to create the required knowledge networks. Rather than straitened reforms, national strategies for reducing on-farm methane emissions should be coordinating actions across sectors and facilitating the creation of ecosystems and collaborations that build trust.
From a viewpoint of the digital twins
Threats and uncertainties are core to the design rationale of effective information systems, and digital twins are information systems that take issues of system goals and design to the extreme. The extremes are both in the need to integrate data from multiple sources, and in the need to address acute problems. Flexible design to address acute needs is possible when operating an infrastructure that requires openness, as a way of thinking. Openness is inherent to the system, from a holistic vision to data formats, throughout the data life cycle: in the format of FAIR data, which is necessary for machine readability as well as human understanding; and in the strategic vision that defines clear sets of goal-oriented indicators, organized along the main environmental, social, and economic dimensions of agriculture, nature, and food.
Openness is also consistent with the thrust of open science, and big earth data. After the problem statement, attaining a focused view of acute and complicated issues, next we develop the approach to address them with FAIR data that allow data partnerships and knowledge sharing, locally and globally.
Data strategy -innovation in the physical twin, based on FAIR implementation in the digital twin Knowledge sharing receives a new meaning with the conceptualization of FAIR data and the actual implementation of data systems that are machine readable and human understandable. Considering the connection between methane and food systems, what should a digital twin solution introduce to our urban-data toolbox? Previous works proposed conceptual frameworks for designing and implementing digital twins. In this work we would like to take a step further towards implementation, into a structure of open and FAIR data (Schultes et al., 2022). This is one contribution of our work. The second contribution is with the harnessing of technology towards a resolution of crucial systemic problems. To do that, we should be narrating a meaningful story, the story of the food.
WHAT: Use cases in food systems (the physical twin)
In the context of agricultural information systems, smart farming is an emerging domain (e.g., Verdouw et al., 2021). Beyond the agricultural aspects in knowledge-intensive farming, in this case study we demonstrate the need, and the ability, to integrate big and prominent issues, such as the methane question, into the design and actual operation of the physical farms and their digital twins. The new knowledge-rich agriculture is expected to be a source of data, shared among stakeholders (e.g., public participation in climate data -in local and global levels. Moreover, the intention when setting the focus on the food life cycle is to lay the foundation for new food systemsand ecosystems -that develop more sustainable work practices. To illustrate, possible use cases are presented, linked to main goals and questions along the design process:
Smart farms to reduce food scarcity and environmental costs of meat consumption We choose to apply a food systems perspective to climate change, mainly to reduce methane emissions from cattle. Reducing meat consumption may not include dairy cows, but many other ruminant livestock produce significant amounts of methane (e.g., sheep). To reduce meat consumption, vegetarian alternatives should be supplied. Mushrooms are nutritionally valuable as a substitute, and mushroom cultivation is common in knowledge-intensive agriculture and urban communities (e.g., the Fungi Academy https://fungiacademy.com). In addition, a systematic review and meta-analysis showed the advantage of local farms (Dorr et al., 2021a). Therefore, we propose to focus on urban mushroom farming (e.g., Dorr et al., 2021b).
This is a rather specific conclusion, reached based on the broad literature that already exists in this interdisciplinary topic. The current rich body of knowledge, in different domains, leads further on to more advanced decision points that require specific reference data for clear and measurable indicators.
Key decision points are primarily the use cases that design the digital twins, setting data requirements, as follows.
Nutritious produce and food safety
Nutritional values of beef replacement plant-based diets, and specifically the nutritional value of mushrooms, are main targets to achieve when designing food systems that are environmentally optimal (i.e., not one at the expense of the other, but improving both, the quality of nutrition and of environmental performance). Based on the system inputs and outputs, tools for assessing sustainable healthy diets already exist, including the efficient use of energy, land, and sunlight (Eshel et al., 2016;FAO, 2022;Jackson at el., 2021;Leger et al., 2021;Smith et al., 2021;Tepper et al., 2021).
This leads to several use cases of nutritional value, e.g., branding products as highly nutritional; and coping with complicated challenges of food safety and restricted products (e.g., UPU, 2017).
Dietary requirements for environmentally optimal supply
Moreover, dietary requirements can be a perspective through which to plan and better utilize the capacity of local agriculture, either on a national, regional or an urban level, according to household demand and environmental conditions, either current or predicted (Nixon & Ramaswami, 2022). Furthermore, to encourage change and facilitate the reduction of meat consumption, a recommended food basket should be developed, with adaptation to climate and economic conditions. The idea is to propose an innovative approach to public participation: setting the ultimate dietary recommendations -as a means of advancing nutritional perceptions, improving current themes about nutritional security from a health point of view. To satisfy this resolution, a digital twin depends on access to multiple data sources, and a capacity to integrate the interlinkages among the systems and ecosystems of climate, food, land, water and oceans, and people through direct and indirect links to the socio-economic system and human well-being, as presented by IPCC (2019) and FAO (2022).
Standards to satisfy consumers, producers, and regulators
Local data should be globally available to improve national and international standards and regulations. Today, to comply with international standards on food quality (e.g., ISO), harvest may be delayed -to meet measures of size, weight, or other criteria. However, for some agricultural products, harvest may better be carried out earlier -to provide fresh crop more often and satisfy the consumer. Variables to consider span from consumer behavior and preferences on the one hand to operation management on the other; mainly available cultivation area vs. delivery costs, packaging, and emission.
Who are the farmers Green recovery and the promise of inclusive green economy account for green jobs in the general public, e.g., for workers who can no longer perform physically demanding roles such as construction workers, commercial drivers, building cleaning, personal care, food service workers (Ross & Bateman, 2019). New skills are of great relevance to the low-wage workforce after certain age. Other case studies on urban farms and agriculture focus on education programs in schools, working with youth, or preservation of traditional knowledge. Indeed, various socioeconomic indicators populate the Generic Framework (Table 1), considering existing evaluation frameworks (Tables 2-3) in the first stage. In the next stage, a case study in Italy is developed towards a Federation Deployment. The agricultural market structure of small local farms near the city makes it essential to support the farming sector. As presented earlier, this sector is vulnerable to the climate crisis, facing not only droughts but also insufficient water infrastructure. While an agricultural partnership must include the farmers, and help them acquire technical skills to apply technological innovation in agriculture -they are not the exceptional mitigators but a strong link in a system that learns how to priorities problems and solutions in a cost-effective workplan that utilizes resources.
In addition to the "Environmental indicators -footprint and technologies", and in terms of "Socioeconomic indicators -inclusive green economy", the purpose of this section is to make the adjustments to the economic and the political conditions; making it feasible, in each and every ecosystem, to adopt financial means and to flourish, and for different stakeholders to join and engage. Training new urban farmers while generations of farmers, who were born on farms, are struggling is ineffective, negligent, and politically impossible. At the same time, their representative organizations should not act on their exclusive behalf.
To improve food systems, there is an urgent need for selecting and fine-tuning the very specific factors along the narrative of food, e.g., choosing farm location based on land use, energy use, and other trade-offs. A clear focus exists, reducing greenhouse gas emissions as the main game-changer, among the many other resulting indicators and their implications. Accordingly, Ministries of Agriculture may increase the share of agriculture in GDP and eventually act for the benefit of farmers -and the entire public.
To coordinate the production and consumption of nutritious, affordable, and environmentally optimal food yield, across sectors and stakeholders, in different countries, the integration of data from multiple food systems is an important demand that digital twins may fulfill, if designed openly according to the FAIR principles.
HOW: Software architecture (the digital twin)
Open science is a concept of inclusive shared knowledge, and FAIR principles are at the heart of open science.
A distinction should be made between the value of information (Purian, 2011), i.e., to assess the contribution of an information system to operation management, and the value of data (Mons et al., 2011), i.e., to enable the implementation of FAIR data practices in new ways that are essential to create strategic value.
The operational value of information Environmental footprint and resource use of urban agriculture are studied in recent years and provide a rather consistent view of trade-offs, suggesting decision points along the life cycle of circular urban farms, e.g., regarding location (even in proximity to end-users). As a reference for operation management: Niles et al. (2017) provide a "Food System Intervention Worksheet" with "Logical Approach to Support Prioritization of Interventions" in high, medium, and low-income countries, for various aspects along the food supply chain (Appendix 2 in Niles et al., 2017;pp. 70-72), next to a thorough review of Potential Interventions (pp. 32-69).
The strategic value of FAIR data While the direct target -to mitigate near-term climate change and improve food security -is well established in the literature (e.g., Shindell et al., 2012), the connection of these crucial issues to the FAIR data approach and infrastructure (Mons, 2020) is new.
A way to illustrate the value of data is through a connection of utility functions: either individually; in their original classes; or in new data clusters. The options are presented in Figure 3 in the form of networks among individual data points, classes of data points, and clusters of data points from different classes. In the paper on the "Value of Information in the Network" (Purian, 2011), collective action is analyzed when environmental and social criteria emerge, in addition to pragmatic criteria of existing systems and routines. An analytical model is developed (Table 5), a weighted graph representing "how information gains its value in the network, from different perspectives" (p. 9). As opposed to network models that represent size, i.e., the volume communication, the "agenda that organizations would adopt depends on the information that flows in the network, between individuals, organizations, governments, and other institutions in the society" (p. 13). Building on the UN's (2020; p. 12) SDG scheme for multistakeholder partnerships, we present the idea of a common axis or narrative, on which to organize the activity. The directed network in Figure 3 c implies a directed acyclic graph (DAG) for Bayesian inference (Purian et al., 2022).
Utility functions, connected in networks across data sources, provide the value described in Table 5. Group-forming network (GFN) N + aN 2 + bZ 2 -
The value V of a network equals to the sum of value of node i and the additional value from communication with node j and the additional value from communication with a group of nodes s as shown in the following equation: xi -the value of the i th node (data source).
P s s E j i ij N i j z y x V
How do we evaluate xi? What influences it?
yij -the additional value from communication between the i th node and the j th node.
How to measure yij? Is it none-negative?
zs -the value added by a group of nodes.
How to measure zs? Is it none-negative? Source: Purian (2011) While UN (2020) generally refer to "little collaboration" vs. "systematic collaboration" across sectors to create partnerships, our emphasis is on the integration of data (and indicators) across data sources.
One of the main questions, in the context of data management, is regarding the modularity level of data, and the resolution depends on the FAIR data life cycle along the proposed food supply chain. For this reason, implementing FAIR data operation is a strategic move. Life cycle assessments of novel agricultural technologies span across the many domains and externalities of food production and consumption. This requires detailed encapsulation of data.
Once the network is established, it matters whether the integration of data is creating a new axis of knowledge, or maintains existing routines. The meaning of data integration is to create new axes of action; a direction in Figure 3c.
To facilitate the coordination among stakeholders and sectors, and the creation of ecosystems and partnerships, FAIR data and open science for data-intensive research should be achieved with digital twins (Schultes et al., 2022).
Scenarios, data, and tools Scenarios: To outline the implementation of open and FAIR data (Mons, 2020;Wilkinson et al., 2016) in digital twins, we need to set goal-oriented indicators. Choosing footprint indicators and inclusive green economy as pillars to the framework was the first stage (Generic Framework; to achieve this goal, we introduce some of the main indicators and evaluation frameworks that may be beneficial for the solution). Transition towards implementation, in the following stage (Federation Deployment; setting the groundwork through use cases from which to assemble the data needed), revealed the success factors that play a key role in each pillar. In the environmental pillar: When considering the influences of agriculture on the environment and vice versa, reduction of greenhouse gas emissions is key. In the socioeconomic pillar: When considering the need in skills and technological innovation for green recovery, it becomes evident that our emphasis is on a solution for agriculture and farmers. Accordingly, scenarios were proposed to innovate with the capabilities of digital twins.
Data: Our goal is to define an axis or a narrative through which to choose the appropriate indicators, thus making sure the indicators are goal-oriented, sharable, and machine-readable. The proposed narrative is the main axis on which to develop the ontology, and to make it possible to share the new knowledge among stakeholders: public participation in climate data, and a nourishing food basket that meets dietary requirements; evaluation frameworks and standards; and more, locally and globally. References are provided, throughout the paper, to resources for specific domain data.
Tools: Throughout the food supply chain, between production, transportation, packaging etc., a plethora of indicators cover the environmental footprint and resource use. However, tools and methods to organize the data and manage it are just starting to gain attention. Ontology-based access policies are among the excitatory approaches to utilize FAIR data, based on concepts and relations from a domain ontology, and providing licensing for both humans and machines (Brewster et al., 2020). Bayesian inference is applied in new ways, as an approach to detect bias in a dataset (Purian et al., 2022), and to provide an explicit characterization of data. Global emissions from livestock, for example, were examined with Bayesian inference to quantify methane emissions and attribute the largest anthropogenic source on the global scale (Qu et al., 2021).
Bayesian networks and ontologies are main data tools for the digital twin toolbox (Purian et al., 2022).
Discussion
Creating goal-oriented indicators that enable coherent actions across environmental, social, and economic fields is challenging. To achieve this, we must provide a dimension -or a story -through which to organize data, information, and knowledge for the issues of wellbeing in cities, social resilience, and climate change, that are inherently linked. In the first stage of this study, we introduce some of the main indicators and evaluation frameworks, e.g., UNEP Indicators for Green Economy, that include many footprint indicators, from production to consumption (Tables 1-3). Improved consistency of geo-referenced high-resolution spatial data are among the major tools of the smart city. Accordingly, we examined a solution that combines urban farming and hyperlocal climate sensor data, towards food security and green growth. Circularity, a broader goal, also requires detailed information from multiple sources that may be beneficial for evaluation.
In this case study that examines the ability to incorporate a crucial, perhaps acute issue, into a long-term infrastructure of data techniques and methods. By doing that the contribution in twofold: choosing an urgent goal as an axis on which to organize a system; and going beyond a conceptual framework towards implementation.
Defining the question, setting the goal, is critical to the success of digital twins that aggregate enormous amounts of data. This prerequisite is shared by scientific disciplines and the common knowledge, from the very first map makers, to the golden age of information systems. Choosing just one example out of many, the coastline paradox (Mandelbrot, 1967) illustrates the need to set a scale that is relevant to the purpose of measurement; the length of the coast of England depends on the ruler's length. Since then, the field of information systems research insisted on the inner design of a data-information-knowledge continuum in systems (Simon, 1956). Setting the indicators means creating a representation of the city, therefore the importance of "narrating" the digital twin, re-establishing urban identity through technical decisions that may change the way the city acts and performs. This is the new science of management decision in the smart city.
Figure 1 .
1Global methane emissions by sector as of February 22, 2022: Estimates (light blue) higher than official reports (blue) IEA (light blue): International Energy Agency (IEA) based on data measured in scientific studies, measurement initiatives and estimations UNFCCC (blue): UN Framework Convention on Climate Change (UNFCCC) based on data reported by official public bodiesStudies persistently show the strong connection between methane and food systems(Porter, 2022). Recent studies, backed by new global databases, meta-analysis and systematic reviews, help understanding the numbers and options for abatement(Almeida et al., 2021; Crippa et el., 2021;Dorr et al., 2021a;2021b). Crippa et el. (2021) developed a food emissions database (EDGAR-FOOD), based on the Emissions Database of Global AtmosphericResearch (EDGAR), and the FAOSTAT database for land use and related emissions data. Land use change is a major factor in the estimations of food emissions when accounting for the alternative option of green land use. Altogether, agriculture and land use activities are responsible for 71% of global anthropogenic GHG emissions, with the remaining resulting from the various activities along the supply chain of food, including transport and fuel production, packaging and retail, consumption and waste management.
Figure 2 .Figure a .
2aMethane Source: https://data.worldbank.org/indicator/EN.ATM.METH.KT.CE Figure b. Source: https://data.worldbank.org/indicator/EN.ATM.METH.AG.KT.//data.worldbank.org/indicator/EN.ATM.METH.KT.CE?locations=IT Figure d. Source: https://data.worldbank.org/indicator/EN.ATM.METH.AG.KT.CE?location s=IT Data: World Bank; Climate Watch DATA, GHG Emissions. World Resources Institute, Washington, DC. https://climatewatchdata.org/ghg-emissions Methane emissions (% change from 1990) Agricultural methane emissions (% of total) Figure e. Source: https://data.worldbank.org/indicator/EN.ATM.METH.ZG?locations=IT Figure f. Source: https://data.worldbank.org/indicator/EN.ATM.METH.AG.ZS?locations=I T Data: World Bank; European Commission, Joint Research Centre (JRC)/ Netherlands Environmental Assessment Agency (PBL); Emission Database for Global Atmospheric Research (EDGAR) https://edgar.jrc.ec.europa.eu
that tracks the effects of climate change on the farming sector, and "how famers are coping with living life on the edge". A coverage by the Washington Post (2022) on the drought in Italy provided a map of the Evaporative Stress Index (ESI) to illustrate the average amount of water evaporating from land surface and vegetation between June and July. Comparing with normal values, they concluded, "Basically, there is no water left".
Figure 3 .
3Individual
identifies one node in the network j = identifies one node in the network s = identifies a group of nodes xi = the v of node i yij = the additional v from communication between node i and node j. zs = the additional v from communication between a group of nodes s. The questions the model describes, for each entity, are:
Table 1 .
1Green transition and food security through urban farming and hyperlocal climate sensor dataDomain
Environmental section
Socioeconomic section
Data strategy section
Focus
Footprint indicators > Methane
emissions, water
Inclusive green economy > Job
security and skills > in the
Agricultural sector
FAIR implementation > Human
& machine readability
Goal
Table 2 .
2Evaluation frameworks for governments, companies, and citiesGreen growth (OECD, 2017)
Table 3 .
3The role of climate indicators and sustainable development goals (SDGs) in evaluation frameworksSustainable development goal 13: Climate Action (right) and Climate Indicators
Curation (left), World Meteorological Organization (WMO) are among the
examples provided by the WEF (n.d.) for a holistic approach.
Table 4 .
4"Skills training" in the OECD Green Recovery Database, and (below) spread of investments across sectors in Italy
Table 5 .
5The value of information in the network vs. Reed's law, which describes the network size, as a referenceA network with:
Reed's law
(size)
New model
(value)
One node value
1
xi ≥ 0
i Є N
Connection
A
y(xi,xj)
i,j Є E
Group
B
z(xi)
s Є P
Network of size N
αN + aN 2
αxN + yN 2
Additional InformationCompeting Interests statement: There are no competing interests; financial and non-financial.Author Contribution statement: R.P. wrote the manuscript text.
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| sample_1197 | 0.9373 | arxiv | |
An Interpretable Model of Climate Change Using Correlative Learning
Charles Anderson anderson@colostate.edu
Computer Science
Colorado State University
Jason Stock stock@colostate.edu
Computer Science
Colorado State University
An Interpretable Model of Climate Change Using Correlative Learning
Determining changes in global temperature and precipitation that may indicate climate change is complicated by annual variations. One approach for finding potential climate change indicators is to train a model that predicts the year from annual means of global temperatures and precipitations. Such data is available from the CMIP6 ensemble of simulations. Here a two-hidden-layer neural network trained on this data successfully predicts the year. Differences among temperature and precipitation patterns for which the model predicts specific years reveal changes through time. To find these optimal patterns, a new way of interpreting what the neural network has learned is explored. Alopex, a stochastic correlative learning algorithm, is used to find optimal temperature and precipitation maps that best predict a given year. These maps are compared over multiple years to show how temperature and precipitations patterns indicative of each year change over time.
Introduction
Deep networks have been used successfully to model many complex relationships in data from a wide variety of domains. Both practice and theory suggest that large, deep networks may generalize better to untrained data samples. This leads to important questions regarding the interpretability of such large networks to understand the limitations and trustworthiness of these models. In many studies involving measurements of the natural world, domain experts are most familiar with simple statistical analysis, such as linear regression. Therefore, to simplify the interpretability and trust of models, models that are simple extensions of linear models should be the first step.
Here we follow this suggestion in an attempt to find indicators of climate change using a simple two-hidden layer neural network trained on global temperatures and precipitations from the sixth phase of the Coupled Model Intercomparison Project [1] (CMIP6). The potential of discovering indicators of climate change from the previous CMIP5 data was demonstrated by Barnes, et al., [2,3] who found that linear models map global temperature data to year quite well and a simplified interpretation of the models was performed by analyzing the resulting linear model weights. In follow-on work, they recast the regression problem as a classification task in order to use Layerwise Relevance Propagation (LRP) to identify spatial patterns significant to classifying specific decades [4].
Here we return to the regression approach and extend it by including temperature and precipitation CMIP6 data and modeling it with a neural network having two hidden layers. A correlative learning algorithm is then applied to interpret what our neural network has learned about how temperatures and precipitations change over the years.
In Section 2, a brief summary of local and global methods for interpreting what a neural network has learned are reviewed. Alopex is described as a global method. This is followed by a demonstration of the Alopex method by using it to interpret what a neural network has learned when trained on the MNIST data. This same approach is then applied in Section 3 to a neural network trained to predict the year from global temperature and precipitation data, revealing intriguing changes in this data over time.
Interpretation of Neural Network Models
Interpretability methods aim to convey information about a network's learning process and decision making. These methods largely fall in two categories, namely local and global. Local explanations provide insight on individual predictions. For example, saliency maps show certain pixels for a given sample with a positive saliency that increase accuracy in the prediction [5]. Further, methods such as LRP [6], DeepLift [7], and Gradient*Input [8] aim to provide pixel-wise relevance. In many cases these methods are mathematically equivalent (i.e., network's with ReLU activations or zero valued baselines) [9] and are cumbersome to reason about over a large set of data.
Global methods describe the general behavior of a network where explanations are made on a class of predictions or network components. Most common for neural networks are methods to understand high-level concepts (e.g., color or texture sensitivity) [10], visualizing maximal neuron or layer activations [11], or optimizing an input to maximize the probability of an output [5]. In this work, we focus on finding an optimal input that generalizes to individual outputs.
Both local and global methods that are gradient-free do exist (e.g., computing surrogate models as done with LIME [12] or Shapley value-based feature importance [13]). However, the majority of these methods rely on backpropagating gradients through the network (including [11,5]). Here we introduce Alopex as a global interpretaton method that does not rely on gradients. Specifically, we leverage local correlations between changes in input features and changes in the global error function to produce a global view on a class of predictions.
Algorithm 1 Alopex 1: f (x) is neural network model 2: T ← 1.0 3: K ← 100, 000 4: δ ← 0.0002 5: m 0 ← 0 6: t ← digit or year 7: x 0 ← vector of constant midrange values 8: for k ∈ {1, ..., K} do 9: y k ← f (x k ) 10: e k ← loss(y k , t) 11: c k ← (e k − e k−1 )(x k − x k−1 ) 12: p k ← 1/(1 + e −c k /T ) 13: d k ← δ, w.p. p k −δ, w.p. 1 − p k 14: x k+1 ← x k + d k + λm k 15: m k+1 ← d k + λm k 16: T k+1 ← 0.9998T k 17: end for 18: return x k+1
The Alopex [14] algorithm was developed by E. Harth to investigate the receptive field of neurons in the frog optic tectum. The intensities of individual pixels in an image presented to the frog were randomly initialized and updated during a number of steps. In each step the correlation between changes in a pixel's intensity and changes in the neuron's firing rate determined which way to adjust each intensity, which was increased if the correlation was positive and decreased if it was negative. This simple correlative learning process was adapted by K.P. Unnikrishnan, et al., [15] to train feedforward and recurrent neural networks. In a very similar manner to Harth's original work, we use Alopex to incrementally adjust the input values to our neural network using the correlations between input changes and changes in the loss of our model. This process converges on images that maximally predict a certain class in a classification problem, or a certain output value in a regression problem. The Alopex algorithm is summarized in Algorithm 1, where x is the input to our neural network model, f (x) is the output of the model and loss(y k , t) is the loss for predicted value y k and correct target value t.
Results on Climate Change Modeling
The CMIP6 [1] data was produced by 35 models of earth's atmosphere from which simulated global temperature and precipitation maps can be obtained for years 1850 to 2100. This data has a spatial resolution of 120 latitude and 240 longitude values. Not surprisingly, there are numerous correlations among temperatures and precipitations at multiple spatial locations, which was dealt with in prior work by performing ridge regression to limit the magnitude of weights in the first layer of the neural network models [2]. Here we use an alternative approach, Principal Components Analysis (PCA), to represent the data with independent factors and to decrease the data dimensionality by projecting the 2 × 120 × 240 or 57, 600 dimensional annual samples to the first 250 singular vectors, i.e., the ones capturing most of the variance in the data. The choice of 250 singular vectors was made by comparing the RMSE in predicted year for the validation data set when using the different quantities of top singular vectors from 1 to 1000.
A two-layer fully-connected neural network was trained on the CMIP6 data as follows. Each hidden layer contained 20 tanh units. PCA was applied separately to the temperature and precipitation data and the resulting 250-dimensional vector was input to the first hidden layer. The output layer of the neural network was a single linear unit trained to predict the year. Figure 2a shows the model structure and Figure 2b shows the results of training the network using the Scaled Conjugate Gradient algorithm [16] to minimize the mean square error in the predicted year. This plot suggests that years after about 2000 are easier to predict, possibly due to human-caused forcing functions included in the CMIP6 models.
Similar to the above demonstration of Alopex on the MNIST data, we applied Alopex to the CMIP6 model by searching for input temperature and precipitation maps that best predicted particular years. Alopex was initialized with PCA projected values near their median values with uniformly-distributed noise added. This was repeated 20 times. For each result the PCA projection was inverted to produce temperature and precipitation maps and the means of the resulting maps were calculated. The resulting maps for year 1850 were subtracted from the maps for following years to highlight changes
Conclusion
Results shown here suggest that the correlative learning algorithm, Alopex, may be helpful in interpreting neural network models by finding global, approximately optimal, input patterns corresponding to particular network output values. It can be similarly used to find global input patterns that cause any unit in the neural network to respond maximally. The fact that it is a correlative learning algorithm means that gradients are not required. However, it would be interesting to compare the results obtained here with other interpretation methods, especially gradient-based global approaches.
The temperature and precipitation maps resulting from the Alopex method reveal interesting changes over the years. Currently, specialists in climate and atmosphere modeling are being consulted to assist in determining relationships between these patterns and changes that are expected from current knowledge of effects on climate due to human activities.
This appendix includes additional figures illustrating the convergence of the Alopex algorithm for the MNIST digits ( Figure 4) and for two years of the CMIP6 data ( Figure 5). It also includes temperature and precipitation maps that most confidently predict years 1875, 1900, 1925, . . ., 2100 as differences from the maps of 1850 ( Figure 6).
Figure 1 :
1Input images generated by Alopex that maximize the likelihood of each digit. The images are averages of the final images from 20 repetitions of the Alopex algorithm.
Figure 2 :
2a. Model structure with 40 tanh units in each of two hidden layers and a linear output unit. b. Predicted versus actual year for all samples, which were partitioned into train, validation, and test subsets by years.Alopex is demonstrated by applying it to a simple network trained on the MNIST digits. The network contains two layers of 20 convolutional units each with kernel size 5 x 5 and stride of 1 x 1. The network is trained using Møller's Scaled Conjugate Gradient Algorithm[16] with cross-entropy loss. For each digit, Alopex is applied 20 times starting with different initial pixel values. The mean of the 20 resulting images are shown inFigure 1. All 20 images for each digit were classified correctly. Since Alopex starts with randomly-initialized pixel values, it is not dependent on particular image samples. Thus, this global method converges on images that are most confidently predicted as coming from the correct class. White, or high intensity, pixels strongly correlate with the digit class, while black pixels negatively correlate with the digit class. Pixels near the edges are medium intensity showing their values have little correlation with the digit class. Many questions arise when studying these images and they are being investigated in on-going work. Here we use MNIST just as a demonstration.
Figure 3 :
3Patterns in global temperature and precipitation that optimally relate to particular years. Colors correspond to differences from the temperature and precipitation maps found for year 1850. The left column of maps show areas of higher temperatures than those for 1850 in red and lower temperatures in blue. The right column of maps show areas of higher precipitation levels than those in year 1850 in blue and lower values in brown. from 1850. Figure 3 illustrates this result for target years 1900, 2000, and 2100. Results for other years are shown in Figure 6. Several interesting patterns can be discerned in these images. Year 2000 shows considerable warming in the Antarctic region and western United states. Year 2100 shows warmer temperatures in many areas. The precipitation maps on the right side show drier regions along the Pacific equator in Years 1900 and 2000. In Year 2100 wetter areas north and south of the equator in the Pacific Ocean are apparent. Similar questions arise when considering maps for other years as shown in Supplementary Figure 6.
Figure 4 :
4Input images generated by Alopex that maximize the likelihood of each digit. Above each image are graphs of the loss versus iterations of the Alopex algorithm. The images are averages from 20 repetitions of the Alopex algorithm. The loss of each iteration is plotted above each image, with different colors for different repetitions.
Figure 5 :
5Examples of Alopex applied to the CMIP6 neural network to generate temperature and precipitation maps that most confidently predict Year 1850 (top row) and 2100 (bottom row). On the left are plots of the mean square error in predicted year verus steps of the Alopex algorithm. Different colors are for 20 different initializations of Alopex.
Figure 6 :
6Patterns in global temperature and precipitation that optimally relate to a sequence of years. Colors correspond to differences from the mean temperatures and precipitations. The left column of maps show areas of higher temperatures than the mean in red and lower temperatures in blue. The right column of maps show areas of higher precipitation than the mean in blue and lower values in brown.
Tackling Climate Change with Machine Learning: workshop at NeurIPS 2022.
Acknowledgments and Disclosure of FundingAppendix
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| sample_1199 | 0.7712 | arxiv | |
TECHNO-ECONOMIC ASSESSMENT OF LONG-DISTANCE SUPPLY CHAINS OF ENERGY CARRIERS: COMPARING HYDROGEN AND IRON FOR CARBON-FREE ELECTRICITY GENERATION
8 Mar 2023
Jannik Neumann
Department of Mechanical Engineering
Institute for Technical Thermodynamics
Technical University of Darmstadt
Alarich-Weiss-Straße 1064287DarmstadtGermany
Rodolfo Cavaliere
D A Rocha
Department of Mechanical Engineering
Technical University of Darmstadt
Simulation of reactive Thermo-Fluid Systems
Otto-Berndt-Str. 264287DarmstadtGermany
Paulo Debiagi
Department of Mechanical Engineering
Technical University of Darmstadt
Simulation of reactive Thermo-Fluid Systems
Otto-Berndt-Str. 264287DarmstadtGermany
Arne Scholtissek scholtissek@stfs.tu-darmstadt.de.
Department of Mechanical Engineering
Technical University of Darmstadt
Simulation of reactive Thermo-Fluid Systems
Otto-Berndt-Str. 264287DarmstadtGermany
Frank Dammel
Department of Mechanical Engineering
Institute for Technical Thermodynamics
Technical University of Darmstadt
Alarich-Weiss-Straße 1064287DarmstadtGermany
Peter Stephan
Department of Mechanical Engineering
Institute for Technical Thermodynamics
Technical University of Darmstadt
Alarich-Weiss-Straße 1064287DarmstadtGermany
Christian Hasse
Department of Mechanical Engineering
Technical University of Darmstadt
Simulation of reactive Thermo-Fluid Systems
Otto-Berndt-Str. 264287DarmstadtGermany
TECHNO-ECONOMIC ASSESSMENT OF LONG-DISTANCE SUPPLY CHAINS OF ENERGY CARRIERS: COMPARING HYDROGEN AND IRON FOR CARBON-FREE ELECTRICITY GENERATION
8 Mar 20231Energy StorageEnergy CarriersHydrogenEnergy TransportCarbon-freeMetal fuel
The effective usage of renewable energy sources requires ways of storage and delivery to balance energy demand and availability divergences. Carbon-free chemical energy carriers are proposed solutions, converting clean electricity into stable media for storage and long-distance energy trade. Among them, hydrogen (H 2 ) is noteworthy, being the subject of significant investment and research. Metal fuels, such as iron (Fe), represent another promising solution for a clean energy supply, but establishing an interconnected ecosystem still requires considerable research and development. This work proposes a model to assess the supply chain characteristics of hydrogen and iron as clean, carbon-free energy carriers and then examines case studies of possible trade routes between the potential energy exporters Morocco, Saudi Arabia, and Australia and the energy importers Germany and Japan. The work comprehends the assessment of economic (levelized cost of electricity -LCOE), energetic (thermodynamic efficiency) and environmental (CO 2 emissions) aspects, which are quantified by the comprehensive model accounting for the most critical processes in the supply chain. The assessment is complemented by sensitivity and uncertainty analyses to identify the main drivers for energy costs. Iron is shown to be lower-cost and more efficient to transport in longer routes and for long-term storage, but potentially more expensive and less efficient than H 2 to produce and convert. Uncertainties related to the supply chain specifications and the sensitivity to the used variables indicate that the path to viable energy carriers fundamentally depends on efficient synthesis, conversion, storage, and transport. A break-even analysis demonstrated that clean energy carriers could be competitive with conventional energy carriers at low renewable energy prices, while carbon taxes might be needed to level the playing field. Thereby, green iron shows potential to become an important energy carrier for long-distance trade in a globalized clean energy market.Fossil fuels were still the source of over 80 % of the global energy supply in 2021 [1, 2], bringing annual CO 2 emissions to the historical peak of 36.3 Gt. The most recent assessment by the Intergovernmental Panel on Climate Change (IPCC) predicts that, without a more intense effort in decarbonization, drastic climate changes with catastrophic consequences for the environment and human society are inevitable[3]. During the 2021 United Nations Climate Change Conference (COP26) [4], an agreement on phasing down unabated coal power was reached, accelerating the decommissioning of coal power plants even before sustainable replacements are available.Besides the climate crisis, the globalized world is facing a surge in energy demand, which adds to several complications in the transport of commodities worldwide. Moreover, the recent war against Ukraine raises additional uncertainties on the future availability, prices, and security of supply routes for fossil fuels, including coal, oil and natural gas (NG), which are directly influenced by sanctions and retaliatory movements enacted by governments[5,6].The European Union as a whole, and Germany in particular, heavily rely on energy imports. Therefore, the need for diversification of the European energy mix is increasingly urgent. This process shall involve phasing down fossil fuel consumption and accelerating the transition to locally available (i.e. domestic) renewable energy. Nevertheless, this change comes with several challenges. Renewable sources such as wind and solar radiation are, in general, converted directly to electricity, which cannot replace traditional fuels in several applications. Further, as the share of renewables increases in the energy mix, maintaining grid stability also becomes an issue, currently handled by backup thermal power plants running on coal, NG or petroleum products. Finally, several countries exhibit limited renewable energy potential, preventing their complete energetic self-sufficiency in a decarbonized future and therefore rely on energy imports for years to come[7]. Efficiently converting renewable electricity into green energy carriers (ECs) is a proposed solution. In this stable form, their energy content can be transported, traded, stored and utilized when and where power is required, being considered by some [8] as the key to unlocking a sustainable, cost-effective and safeguarded energy supply.Electrical energy can be stored by electric, (electro-)chemical, mechanical and thermal means. Due to their high volumetric energy density, stability and versatility, chemical ECs are suggested to enable long-distance energy trade and clean remote power generation and also to serve as alternative fuel sources for heavy-duty machinery and vehicles[8]. Among several proposed candidates, carbon-free ECs such as hydrogen [9], ammonia[10,11], and metals[12]are considered some of the most promising, and have been the focus of intense research and investment recently. The first two are well-known for their potential and applications, while the possibilities of metals such as iron or aluminium as ECs are still to be explored, demanding more research and development[13][14][15][16].Due to its versatility as EC and chemical precursor, hydrogen is gaining unprecedented momentum. In the context of the hydrogen economy, converting electricity into H 2 is touted as a way of storing energy from renewable sources[9]. However, due to its very high reactivity, diffusion characteristics, and low volumetric energy density, it is challenging to transport H 2 over long distances or to store it for long periods[17,18]. In this context, metal-based cycles can offer advantages by providing low-cost, safe and energy-efficient storage and transport of the EC. Iron, for instance, can be produced with clean hydrogen-therefore generating no direct CO 2 emission-and can either be used in its synthesis or directly applied in burners, such as those of existing coal power plants for electricity generation, through retrofitting[8,9,19,20]. By applying this concept, time and money can be spared in developing new systems and infrastructure construction, becoming an interesting technology for countries that still rely on coal due to the absence of ready-to-use alternatives[15].A complete feasibility study of an EC must consider the aspects of each process involved in the supply chain, which is schematically shown inFig. 1. While numerous studies on hydrogen and hydrogen-based ECs exist [18, 21-27], similar studies for iron as EC are still very scarce. Kuhn et al. [28] calculate a cycle efficiency of 27 % for iron as EC not considering transport. Debiagi et al. [15] estimate a round-trip efficiency of 26 %-31 % including transport by ship from Casablanca to Rotterdam. Dirven et al. [29] estimates a cycle efficiency of 15 %-30 %, including power generation, transport and regeneration of metal fuels. The first and only available techno-economic evaluations
for iron as EC are published by Metalot, a dutch non-profit network organisation [30,31]. Their analyses relate to high-temperature heat supply, and they conclude that the cost of iron is in the range of hydrogen and superior to ammonia as EC for high-temperature heat supply.
This work presents an assessment and comparison of carbon-neutral hydrogen (green H 2 ) and iron (green Fe) as chemical ECs for long-distance energy trade, considering aspects of the combined supply chain, including synthesis, transport, storage and utilization in electricity production (c.f. Fig. 1), and the impact of each step in the total costs, CO 2 emissions and energy efficiency. To the best of the authors' knowledge, this work presents the first comprehensive techno-economic analysis and comparison between iron and other ECs for electricity generation. As potential clean EC importers, Germany and Japan are taken as case studies, considering aspects of their energy mix, port infrastructure and retrofitting possibilities. As potential EC exporters, Morocco, Saudi Arabia and Australia are taken considering their energy mix, industry, and pledged future policies. The proposed comprehensive formulation are employed for estimations of costs, emissions, and energy efficiencies. Finally, a sensitivity analysis to evaluate the effect of critical variables, an uncertainty analysis to determine the extent of variation between available data, and a breakeven analysis to determine the point of competitiveness between green and conventional ECs are presented.
Properties, production and power generation methods of selected energy carriers
Long-distance energy trade and efficient energy storage are essential to safeguard the supply chain and grid stability when decarbonizing the energy mix. In order to select the most suitable carriers, it is necessary to assess aspects of their production and utilization, costs and associated CO 2 emissions, and their physical-chemical characteristics. Thus, this section brings relevant information for conventional fuels, hydrogen and iron.
2.1. Relevant properties of selected chemical energy carriers. The energy density is an essential feature of ECs. Substances that present high volumetric and/or gravimetric energy densities, commonly achieved when in liquid or solid phases, are desirable, requiring smaller storage and cargo units for a certain amount of internal energy, and therefore fewer trips, saving in fuel, equipment and other costs. The energy densities of selected substances are shown in Fig. 2.
Significant properties of selected chemical ECs are reported in Table 1. Iron is a very dense material, has lower gravimetric energy density when compared to coal, but its volumetric energy density is significantly higher, reducing the required transport and storage unit volumes. NG and hydrogen reach volumetric energy densities in the same order of magnitude as liquid and solid ECs only when compressed or liquefied for transport.
2.2.
Conventional fuels: oil, gas and coal. Coal, petroleum and NG are the primary global sources of energy for transport, power generation and heating applications, and are also the main contributors to CO 2 emissions and global warming [3,34]. In 2019, oil, NG and coal combined Representative hydrocarbon fuels are characterized by a balance between the two properties. H 2 has a high gravimetric energy density but a low volumetric density, even when compressed or liquefied. In contrast, metals have a very high volumetric energy density with a low to medium gravimetric energy density.
Tab. 1. Properties of selected chemical ECs [32,33]. [34]. In the power sector alone, the share of coal reached 36.6 % in 2021 (10 PWh), while the share of NG has risen to 22.1 % (6.1 PWh), and that of oil and other fossil fuels, to 3 % (0.81 PWh). 11.8 Gt of CO 2 were emitted by the electricity sector alone, of which 8.23 Gt came from coal, 2.97 Gt from NG, and 0.57 Gt from oil and other fossils [35]. A clear pattern of fluctuation in trade prices for conventional fuels is evident from the recent data shown in Table 2, which varies based on time and the specific trading location. Additionally, increasingly strict policies on CO 2 emissions, including carbon taxes [36][37][38], is intended to discourage fossil-fuel use. Current EU carbon prices (end of 2022) are in the order of 90 EUR·t −1 CO 2 [39], but the IEA predicts them to rise to 130 USD·t by 2050 across all advanced economies [40]. Coupled with the drastic reduction of renewable energy costs [9] and the fact that only a few countries control fossil fuel markets, renewables are soon expected to become more economically attractive [9,41], overcoming a fundamental challenge of the energy transition.
2.3. Hydrogen. Hydrogen (H 2 ) is touted as an ideal EC due to its optimal physical-chemical properties, low toxicity, versatility and simplicity of production. As a zero-carbon fuel, its combustion does not produce any CO 2 . It can be employed in numerous power production systems, to provide heat to industries that still rely on fossil fuels, and also as a reducing agent in chemical processes. For its potential, hydrogen has become the focus of extensive research [9] and investments [7,46]. The Net Zero Emissions Scenario from the IEA [47] predicts a hydrogen demand of 530 Mt by 2050 driven by the transport, industry and electricity sectors. Within the power sector, the use of hydrogen is expected to increase significantly (102 Mt in 2050 [47]), as it can Tab. 2. Recent and historic prices of conventional fossil fuels. The prices shown represent the one-month futures of the Dutch TTF Natural Gas [42] and Henry Hub [43] for NG as well as the API2 Rotterdam Coal Futures [44] and Newcastle Coal Futures [45] for coal. Coal properties are taken from the average of the values presented in Table 1. help balance the increasing generation from intermittent solar and wind power by storing seasonal energy for future use. Presently, 90 Mt of pure hydrogen are produced annually, primarily used in oil refining (44 %) and for chemicals production (45 %, of which 3 4 for ammonia and 1 4 for methanol) [48]. Another 5 Mt of non-pure hydrogen are used in steelmaking, and marginal amounts for heat and power [48]. Hydrogen can be converted in fuel cells [49] and gas turbines [50] for power production. Hydrogenenriched NG combustors are already commercially available [50,51], while pure hydrogen-burning commercial turbines are under development [51,52].
Green-H 2 production is becoming highly efficient. However, it still lacks scale, being only 0.7 % of the total pure hydrogen produced worldwide [9,48]. Governments and industry are pushing the increase in electrolyzer capacity, with existing plans in Germany [7], the European Union [46], Australia [53] and Japan [54,55]. Based on current and future initiatives, green H 2 production could reach 8 Mt by 2030, which is 4 Mt less than the required hydrogen production capacity in the IEA's Announced Pledges Scenario and 72 Mt less compared to the Net Zero Emissions Scenario by 2030 [40]. The main issues of green-H 2 are still the high cost of infrastructure and the dependency on electricity prices [9,46].
2.4.
Iron. The idea of using iron (Fe) as a green EC has been proposed recently [8,12,13], despite having been idealized as a fuel for more than a century [29]. Iron is chemically stable, has low toxicity, abundance, and a very high volumetric energy density, and is relatively low-cost to produce in processes currently evolving towards a zero-carbon footprint [56][57][58]. These characteristics are ideal for an EC. Furthermore, iron has burning characteristics similar to those of coal [12,15], reaching very high temperatures when burned in clouds of microparticles, generating zero CO 2 emissions, potentially enabling its use in retrofitted coal power plants [8,15] which allows the reuse of soon-to-be redundant infrastructure and short implementation times. The stable products of its combustion are solid iron oxides, which are non-toxic and can be collected and recycled back into metallic iron form. The recycling (reduction) can be carried out cleanly and efficiently, directly using renewable electricity or green-H 2 . In that case, it can become the core of a clean redox cycle, showing high potential for long-term storage and transport of renewable energy, see Fig. 3.
The iron production processes in the steel industry involve the reduction of Fe x O y oxides present in iron ore, being the blast-furnace-basic oxygen furnace (BF-BOF) the most common [19], in which the oxides are reduced using coke (i.e. heated coal in the absence of oxygen), with the resulting material being later reacted with limestone to release excess carbon in the form of CO 2 . This process is highly endothermic and traditionally uses fossil fuels to generate heat in both steps. However, an emerging technology is the direct reduction of iron (DRI) using methane, syngas or hydrogen to reduce the oxides in iron ore pellets, followed by melting and alloying in an electric arc furnace (EAF) [19].
Green iron production requires decarbonizing both direct and indirect CO 2 emissions. One solution is to perform DRI with H 2 and heat provided by renewable sources [19,[60][61][62], an alternative being pursued by important industrial players [56][57][58]. The overall energy efficiency of the Fig. 3. Schematic of an iron reduction-oxidation cycle for energy storage, transport and use [59]. Iron and iron oxides are used in a reduction-oxidation cycle as carbon-free carriers of renewable energy. Left: renewable energy is used to reduce iron oxides via electrochemical (i.e. electrolysis) or thermochemical processes (i.e. reacting oxides with green hydrogen), storing the energy. Right: iron is used as a fuel in a combustor to release heat, e.g. in a power plant, to generate electricity, similarly to the traditional combustion of solid fuels. Solid iron oxides (Fe x O y ) can be collected and transported to the reduction facilities, closing the cycle. process can achieve 60% or more, depending strongly on the electrolyzer efficiency that generates the hydrogen [62,63].
Transport and storage of energy carriers
From production to utilization of the ECs, a long supply chain includes preparation, loading, unloading, and delivery to the final application, which is schematically shown in Fig. 1. Between these steps, intermediate storage is important, balancing supply and demand. For gaseous ECs, liquefaction is necessary for effective storage and transport. All those steps increase costs, add to the energy demand, and contribute to CO 2 emissions. This section presents conventional and alternative modes of long-distance transport and storage, along with the perspectives in terms of technology and infrastructure.
3.1. Preparation: liquefaction of gaseous fuels. The liquefaction of NG is operated today on a global scale with an existing liquefaction capacity of 1.26 million metric tons per day in 2021 [64]. Refrigeration cycles are used to liquefy NG, in which the NG or a refrigerant cools down through compression, heat dissipation and expansion [65].
The total global capacity of hydrogen liquefiers is 350 metric tons per day, with the largest liquefier having a capacity of 32 metric tons per day [66]. Existing hydrogen liquefiers require 30-60 % of the chemical bound energy for the liquefaction [66][67][68][69]. It is predicted that the specific energy demand can be further reduced to as low as 13 % [66,69] with new concepts and larger plants (lower specific insulation losses). Furthermore, due to learning curves and economies of scale, the specific capital costs (CC) might be reduced significantly. However, these improvements refer to concepts with low technology readiness levels, and it remains to be shown if these numbers can be obtained with commercially available H 2 -liquefiers in a few years. Table 5 shows the ranges of critical liquefaction-related values, while a compilation of literature values is reported in Table S 3. 3.2. Long-distance maritime transport: vessel types, capacities and fuel consumption. Currently, long-distance maritime trade for solid ECs is feasible using bulk cargo ships, i.e. vessels that store their cargo freely in internal deposits. Conversely, gaseous fuels are transported as liquefied cargo via liquid bulk ships, requiring refrigeration to maintain temperatures below their condensation point throughout the trip. Coal and iron, for instance, can be transported in solid form at room temperature and atmospheric pressure, simplifying the loading and maintenance processes. A significant drawback, however, is that due to the reactivity of iron dust, powder iron cargo must be stored either in inert gas or sealed in appropriate containers, such as super bags. In terms of propulsion, most ships use heavy fuel oil (HFO) in their engines, while some LNG carriers use NG released from the boil-off to generate power.
No ship built to this day can transport hydrogen in volumes comparable to the cargo units of large LNG ships, the state-of-the-art in terms of liquid bulk vessels. The only currently available vessel is the Suiso Frontier, a diesel-propelled liquid hydrogen (LH 2 ) pilot ship, with a deadweight tonnage (DWT) of 8000 t and a cargo volume of 1250 m 3 [70]. There, H 2 is kept liquid at -253°C [71] through thermal insulation. An LNG ship with a similar DWT could carry considerably larger cargo, supposedly due to the space used for LH 2 insulation. There are ongoing projects for future H 2 vessels, capable of carrying 160000 m 3 of LH 2 [72]-roughly 128 times the capacity of the Suiso Frontier. Another example is the C-Job Naval Architects plan of a new, 37500 m 3 fuel-cellpowered vessel, expected to be commissioned by 2027 [73]. Provaris Energy is at conceptual stage of development of a compressed (250 bar) H 2 carrier [74]. In terms of propulsion, there are already plans for hydrogen-fuelled internal combustion engines, which could directly use the stored cargo as fuel, making use of the boil-off effect [75].
3.3. Storage of energy carriers. The viability of ECs also depends on intermediate and longterm storage. The requirements for the different ECs vary significantly, in some cases having a substantial effect on costs and overall efficiency. Coal is usually transported via trains or trucks from a coal mine to a harbour, where it is unloaded and piled [76]. Due to its low reactivity at ambient conditions and solid state, no special processing is required [76]. On the other hand, iron shows reactivity with air at ambient conditions, which would result in oxidation, consequently depleting the energy content and posing risks of ignition. Therefore, fine iron powders should be isolated from the ambient air, such as in sealed containers. Conversely, iron oxides produced from combustion processes are generally inert, requiring no special material handling. To be kept liquid, LNG and LH 2 demand the maintenance of cryogenic temperatures, i.e, -162°C and -253°C, respectively, which lead to additional energy expenditures.
Global LNG storage capacity was nearly 71 million m 3 as of April 2022 [64]. Despite great insulation efforts, some heat absorption from the environment cannot be circumvented due to the significant temperature difference between the tank content and the surroundings. The absorbed heat is balanced by the evaporation of some of the liquid (latent heat of vaporization), leading to boil-off gas (BOG). Additional energy is required (0.5-1.27 kWh · kg −1 BOG [77][78][79]) to re-liquefy the inevitable BOG.
The global LH 2 storage capacities are orders of magnitudes smaller, with the largest active LH 2 tank having 3200 m 3 , used as a rocket fuel storage operated by NASA, with a boil-off rate (BOR) of 0.064 wt.% per day [80].
To suit the projected large-scale LH 2 vessels (e.g. 160000 m 3 ), the required tank scales for intermediate storage to enable international transport of LH 2 by ships are two orders of magnitude larger and have yet to be demonstrated. Similarly to LNG storage tanks, BOG cannot be entirely prevented, needing to be re-liquefied or flared off if no demand application can be coupled. Moreover, a recently built storage tank by NASA [80] features an integrated refrigeration system, leading to net zero boil-off [80][81][82], with a trade-off of additional capital expenditures of 3.1 million USD (0.06 USD · kg −1 of BOG per year) and an energy demand of 6.33 kWh el · kg −1 BOG . Other estimates in the literature assume capital costs (CCs) of 6.85-7.42 USD · kg −1 of BOG per year and energy demand of 3.3-11.0 kWh el · kg −1 BOG [83,84] for re-liquefaction.
Metrics for energy supply chain assessment: general formulation
In order to analyse and compare the ECs from production to utilisation, three assessments with corresponding metrics are utilised:
(1) Energetic assessment: thermodynamic system efficiency, (2) Environmental assessment: combined CO 2 intensity, (3) Economic assessment: LCOE (levelized cost of electricity).
According to the schematic shown in Fig. 1, the combined formulation to evaluate these metrics considers the following steps of the supply chain: production, liquefaction (if applicable), shortterm storage at the export terminal (intermediate storage), long-distance shipping, long-term storage at the import terminal, and the utilization in a power plant. Short-distance transport is out of the scope of the present work since it requires a detailed assessment of many locations and routes, both between producers and export ports, and import ports and power plants.
All calculations were carried out considering the material transported by a single cargo ship, with its cargo capacity fully occupied by the selected EC. Boil-off of LNG and LH 2 , as well as other energy losses, affect the content of the cargo during the trip and the storage. Only CO 2 emissions associated directly with each step of the process are considered, with indirect emissions associated with the electricity generation taken from estimates available in the literature.
4.1.
Energy balance and efficiency. The relative share of energy losses for each step in the supply chain can be calculated by the ratio of the energy required or dissipated in each step and the total energy input of the system. The total energy input of the supply chain can be calculated according to:
W total = W prod + W liq + W store 1 + W trans + W store 2 [kWh] ,(1)
using equations A5, A7, A9, and A12 of the Appendix. Therefore, the share of the total required energy in each step is given by:
i = 100 · W i W total [%] .(2)
The thermodynamic system efficiency is given by the ratio of electrical energy output to the total energy input:
η = 100 · W elec W total [%] .(3)
4.2. Carbon dioxide emissions. The CO 2 emissions can be considered as the sum of the contribution of each stage, as calculated using equations A6, A8, A10, A14, and A23 of the Appendix. For processes where methane (CH 4 ) is emitted, the equivalent in CO 2 intensity, calculated by the relation between the global warming impact of methane and that of CO 2 , is also accounted for. If given on the basis of electric energy output, the combined equivalent CO 2 emitted can be calculated as:
E CO 2total = E CO 2prod + E CO 2liq + E CO 2store 1 + E CO 2trans + E CO 2store 2 + E CO 2elec W elec [kg CO 2 · kWh −1 ] .(4)
4.3. Levelized costs of electricity. Relating costs to the electric energy output, the LCOE can be calculated as the sum of the cost contributions of each stage:
C total = C prod + C liq + C store 1 + C trans + C store 2 + C elec W elec [USD · kWh −1 ] .(5)
In the analysis presented, a carbon tax T CO 2 is taken into account by adding it to the total costs, multiplied by the amount of CO 2 emitted in the relevant stage. It is assumed that the carbon tax only applies to direct emissions from the power plant (utilization step) and does not extend to CO 2 emissions resulting from other steps along the process chain, such as transport, mining, or drilling for the conventional ECs.
C total,CT = C total + E CO 2elec · T CO 2 W elec [USD · kWh −1 ] .(6)
Even if an EC's energy efficiency and emission profile is suitable, it must achieve a competitive cost of electricity for its successful adoption. Therefore, the equations for the costs are shown in more detail. For a reasonable estimation of the LCOE, the main aspects involved in every stage of the process must be considered, which include capital expenditures (CAPEX) and operating expenses (OPEX). 4.3.1. CAPEX and OPEX. The annuity method is a well-established approach for evaluating projects from an economic perspective due to its ease of use and transparency. It calculates equal annual payments based on the present value of the initial investment costs. The calculation involves utilizing a capital recovery factor (CRF) and a constant discount rate i over the project's economic lifetime n
CRF = i(1 + i) n (1 + i) n − 1 .(7)
The CAPEX corresponds to the yearly annuity based on the specific capital costs (CC in USD · kg −1 EC ) of acquired equipment facilities, technology and other assets. In this sense, the capital costs are multiplied by the CRF to determine equal annual payments:
CAP EX = CRF · CC EC [USD · (kg EC · year) −1 ] .(8)
The fixed OPEX includes the yearly rent, wages and maintenance costs, among others (note that fuel, electricity, and Suez Canal costs for ships are calculated separately). It is usually given as the fraction γ of the (specific) CC:
OP EX = γ · CC EC [USD · (kg EC · year) −1 ] .(9)
4.3.2. Cost of production. Conventional production plants can operate almost all year round, whereas production plants utilizing renewable energy are subject to variable renewable electricity full load hours due to volatility. Consequently, the installed capacity of plants utilizing renewables must be larger than the nominal capacity of downstream plants (such as the liquefier in the case of H 2 ). This fact is usually considered with a capacity factor (CF), defined as the mean plant operation times divided by the maximum operating hours. The corresponding CAPEX and fixed OPEX have to be adjusted with the CF. The cost of the process can be calculated considering the CAPEX, the OPEX incorporating the corresponding CF and the cost of the feedstock:
C prod = m EC · (CC EC · CRF + γ prod CF prod + C feedstock ) [USD · year −1 ] .(10)
In this study, the production capacity factor is assumed to only apply to the electrolyzer and not to subsequent steps in the process chain for green ECs (i.e. hydrogen liquefier, shaft furnace). To allow the continuous operation of these subsequent process steps, intermediate hydrogen storage and renewable energy could be required (not explicitly considered here). Furthermore, the CAPEX, OPEX and conventional fuel feedstock are considered the same in all the production countries for each EC.
For the cases in which the feedstock is only electricity, it can be calculated as a function of the electricity cost:
C f eedstock = W prod m EC · C elec [USD · kg −1 ] .(11)
4.3.3. Cost of liquefaction. The costs associated with liquefaction can be given by the CAPEX, OPEX and the associated electricity input and costs:
C liq = m EC · (CC liq · (CRF + γ liq ) + C elec · w liq ) [USD · year −1 ] .(12)
4.3.4. Cost of storage. The storage costs involve the electricity input for maintaining the EC in transportable form (i.e. re-liquefaction of the BOG for NG and H 2 .) Furthermore, the CAPEX and OPEX are only considered proportionally to the operation time t store . Therefore, the total cost of the storage can be computed from:
C store = m EC · ( CC store · t store t year · (CRF + γ store ) + C elec · w store [USD · year −1 ] .(13)
4.3.5. Cost of long-range transport. Long-range transport costs are calculated based on the fuel consumed by the ship, minus the amount of which that comes from the boil-off of the EC when used as fuel during the one-way trip, along with the CAPEX and OPEX, on a USD per day basis, and the costs of passage through the Suez, if they are used during the trip. Analogously to the storage, the total operation days per year (t trans ) are considered:
C trans = t trans t year · (CAP EX trans + OP EX trans )+ 2 · C canal + C f uel · W trans − (m cargo − m ECtrans ) · LHV EC LHV f uel [USD · year −1 ] . (14)
For a more detailed calculation of the variables involved in (C trans ), readers are referred to the Appendix. 4.3.6. Cost of electricity generation. The total costs of the power plant operation are given by the sum of the CAPEX and the OPEX, considering its operating hours through a capacity factor. No additional fuel costs are accounted for since the cost for the synthesis, transport and storage are allocated to the preceding processes:
C elec = W elec · (CC elec · CRF + γ elec CF elec · 8760h ) [USD · year −1 ] .(15)
4.4. Sensitivity analysis. Evaluating the influence of a certain parameter upon the overall LCOE, a sensitivity analysis is performed according to:
S f,x = x i f (x i ) · ∂f ∂x x i ,(16)
where S f,x refers to the sensitivity of the target quantity f with respect to the input quantity x. The sensitivity is determined in a discrete way, using a defined perturbation of an input variable to evaluate its influence on the result:
S f,x = x i f (x i ) · f (x i + ∆x) − f (x i ) ∆x .(17)
If the variation is defined as a fraction of the base input variable, Eq. (17) can be reformulated as:
S f,x = f (x i · (1 + R sens )) − f (x i ) R sens · f (x i ) .(18)
4.5. Uncertainty analysis. As expected, since many estimates refer to novel technologies, the values of the variables used in the present work vary substantially depending on the data source. Along these lines, the calculations would benefit from uncertainty analysis. This study aggregates input quantities and parameters from literature research and online databases. Due to the sample's inherent bias, the input quantity's standard deviation, σ, is calculated using only the highest and lowest values encountered. Nevertheless, the approach shall provide trends and insights into the relative uncertainty σ f,x i of the metric f , which originates from the uncertainty of the input quantity x i . The relative uncertainty is computed as:
σ f,x i = ∂f (x i ) ∂x i · σ x i ,(19)
where the first term on the right-hand side represents the partial derivative of f with respect to x i and σ x i represents the standard deviation of the input quantity x i . In order to approximate limits for the metric f , best-and worst-case scenarios are evaluated using the most favorable and adverse reported estimates of the input quantities x i , respectively.
Case study
This section presents a case study, considering the potential EC trade between selected clean energy exporters and importers. Routes from Morocco, Saudi Arabia and Australia to Germany are considered, as well as a route between Australia and Japan, using the formulation presented in this work. 5.1. Importers of ECs: Germany and Japan. Germany and Japan are two of the largest energy importers in the world [34]. Both countries are global economic powers ranking as the fourth and third biggest economies worldwide, respectively [85]. At the same time, they lack sufficient natural resources to supply their energy demands. After the Fukushima incident, Germany committed to phase-out nuclear power plants [86] and increased the electricity generation from fossil fuels to compensate for the reduced energy supply [35]. Despite increasing solar and wind power generation in recent years, both Japan and Germany still strongly rely on fossil fuels, with shares of 67.9 % (Japan) and 48.2 % (Germany) of the total electricity generation [35], see Fig. 4. Aiming to reduce CO 2 emissions, both countries have stated policies to increase the share of renewable energy sources and consider importing green ECs in the long term [7,54,87]. Political stability and good commercial relations with countries in Asia, the Middle East, and Northern Africa allow the establishment of trade partnerships with net energy exporters.
Similarly to other European countries, Germany reduced its supply of NG due to the recent Ukrainian crisis and resorted to the reactivation of several coal power plants to stabilize its energy supply while taking into account a temporal relapse in terms of CO 2 emissions. The country seeks clean and secure energy solutions for its economy in the long term. The recent adjustments in the energy supply underline that its geographical location allows various ECs to be imported via land and sea. On the contrary, Japan's energy imports must arrive primarily via sea routes, often over long distances, requiring stable and efficient ECs suitable for such trips. and Australia have been chosen as potential energy exporters due to their abundant sun and wind, which entails a potential for producing considerably more electricity than what is demanded nationally. These countries are reportedly pursuing projects on renewable electricity production and have increased their share of renewables in the energy mix in recent years [35]. Exporting the surplus energy to distant countries requires the electricity to be converted and stored employing suitable ECs. In order to avoid CO 2 emissions in the supply chain downstream, zero-carbon ECs are pursued As of today, Morocco is still a net energy importer [1] and strongly relies on coal for its electricity supply (58.8 % of its annual electricity mix [35]). However, the country has pledged to significantly increase its renewable electricity capacity by 2030, with 2.2 GW for wind power and 4.0 GW of solar. Risks for such initiatives stem from the country's low investment capacity, which makes it dependent on international partners to achieve its goals [88]. Morocco has intense trade relations with the EU, its leading commercial partner, and it is already linked to the European NG grid through the Maghreb-Europe Gas Pipeline [89]. Due to its political stability, partnering the country's energy potential with the EU's investment capacity could lead to a rapid scale-up of renewable energy supply, storage, and export, mutually increasing energy security.
Saudi Arabia is one of the world's largest fossil fuel exporters. As of 2021, its electricity mix is based on NG by 61 %, on oil-derived fuels by 38.6 %, with solar power only accounting for 0.5 % and other sources less than 0.1 % [35]. However, due to its extensive arid territory and unique geographical position, it exhibits immense potential for solar-based electricity generation year-round. In 2020, photo-voltaic solar power (PV) reached a record low of USD 0.0104 /kWh in the country which hints at the high potential for an economically viable production of ECs [41]. Overall, the country's economy is considered as high-income [90] with an established infrastructure for trading bulk goods. In the future, solar-fueled production of zero-carbon ECs will allow Saudi Arabia to diversify its portfolio as an international green energy exporter.
Australia is an important energy exporter, with net annual values of 2923 TWh of coal and 1149 TWh of NG exported [1]. Of the 244.6 TWh of electricity produced in the country in 2021, 51.3 % was harnessed from coal, 17.9 % from NG and 10.9 % from solar power [35]. Solar and wind electricity are the fastest-growing sectors in their energy mix. Australia also has an enormous potential to generate clean energy from these sources year-long due to the vast arid regions. Apart from that, the country has the world's largest iron ore reserve (51 Gt). In 2020, it was the biggest producer of iron ore, with a yearly production of 0.92 Gt, roughly 37 % of the total global supply [91]. The Pilbara region, in the West of the country, presently accommodates both the largest iron ore mining facilities in the country [92] and the location of the Asian Renewable Energy Hub [93]. The latter is an ambitious project for PV and wind electricity generation with 26 GW combined capacity, of which up to 23 GW will be dedicated to producing green hydrogen and ammonia for export. This geographical location would also be ideal for a reduction site in a circular iron economy, enabling the production and recycling of green iron at scale, with the iron ore infrastructure of Port Hedland available for long-distance trade. 5.3. Trade routes. Trade routes are chosen between important seaports of the energy exporters and importers, see Fig. 5. For the green energy importing countries, Germany and Japan, the clusters of seaports of Hamburg and Chiba are selected, respectively. These ports are assumed to provide sufficient capacity for processing and redistributing large amounts of ECs.
As a potential green energy exporter, Morocco can supply ECs to Europe without using the Suez Canal, which is a cost-advantage compared to other routes. The route to Germany by sea is the shortest among all Northern African countries, with a distance of 3098 km between the ports of Casablanca and Hamburg. To the West, Saudi Arabia has access to the Red Sea, using the Suez Canal to transport goods to the Mediterranean region and Europe. Its route to Germany covers a distance of 7686 km between the ports of Yanbu and Hamburg, which can be considered a medium-range distance in this comparison.
The Pilbara region in the Northwest of Australia can be connected to Europe via the Suez Canal, with a distance of 18172 km from Port Hedland to Hamburg. To Japan, the route between Port Hedland and Chiba results in a travel distance of 6704 km. All trade routes are evaluated for fossil and renewable energy carriers. Thus, even though not being typical coal exporters, the hypothetical shipping of coal from Morocco and Saudi Arabia is included for mathematical comparison. 5.4. Variables and assumptions: costs, CO 2 emissions, energy efficiencies. In order to calculate the costs, emissions and efficiency of each step of the supply chain, careful quantification of the variables must be carried out. Given the wide range of the variables incorporated in this model, the calculated results refer to the average between best-and worst-case scenarios based on the values that yield the lowest/highest costs, efficiency, and CO 2 emissions, respectively. The best-and worst-case results are indicated using error bars. Here, values are collected from the literature and combined with assumptions per the state-of-the-art technologies.
Global variables: Several global variables, which are used in the analysis, are defined in Table 3 (assumptions marked by footnotes). All equipment is considered to have an economic lifetime of 20 years. Assuming a interest rate of 5 %, the fixed CRF can be calculate with Eq. 7 to 8 %. Fuel prices are set conservatively to the range indicated in Table 2 for the Rotterdam trade hub and the Henry Hub for coal (8.0-43.7 USD · MWh −1 ) and NG (8.8-18.5 USD · MWh −1 ), respectively. Coal properties are taken from the averaged values presented in Table 1.
While market prices for electricity can vary broadly according to time and location, they are chosen according to present-day values and expectations referring to the range given by IRENA [94].
Tab. 3. Global variables used in the case study. CO 2 taxation: To account for future CO 2 taxation in Germany and Japan, 86 USD/t CO 2 (90 EUR/t CO 2 ) are assumed as a baseline for the utilization of ECs, which is based on the market value of the EU carbon credits. Later, a parametric variation of the carbon tax is carried out in a break-even analysis to demonstrate the impact of carbon taxation on EC supply chains due to evolving policies. The CO 2 -intensity of the global electricity mix estimated by the IEA [1] is assigned to conventional electricity.
EC production: Variables related to the production of ECs (costs, CO 2 emissions and efficiencies) are given in Table 4. All values, except for the total costs for green ECs, have been obtained from literature and pertain to existing, planned, or conceptualized production facilities. Notably, the assumption is made that green iron is produced from recycled iron oxides, eliminating the need for feedstock costs. However, the required iron ore costs, especially if constantly recycled, are insignificant (as discussed in Sec. S 2). The calculations for the production of green iron efficiency are based on those presented by Vogl et al. in reference [62]. The total specific costs for green ECs are determined by the specified variables.
Tab. 4. Ranges of crucial production-related characteristics.The CC given for H 2 and Fe correspond to the electrolyzer and the shaft furnace with corresponding EAF, respectively. More detailed information are available within Liquefaction of NG and hydrogen: Reference quantities for the liquefaction are given in Table 5. NG and H 2 -existing liquefaction specifications are based on the present technology, while for H 2 -concepts, the assessment is based on projections from the literature. The latter is used for the evaluation.
Tab. 5. Ranges of crucial liquefaction-related characteristics. H 2 -existing corresponds to state-of-the-art/existing liquefiers, and H 2 -concepts correspond to potential future liquefiers. The latter is used within the case study. A compilation of literature values can be found in Table S Long-distance transport: For the present analysis, ships using conventional fuels for fossil ECs are compared to zero-carbon alternative ships for clean fuels. Further, all ships are chosen according to the maximum cargo capacity with the constraint that the overall ship dimensions allow a passage of the Suez Canal. The vessels identified for all ECs and their specifications are listed in Table 6. While the fossil ECs NG and coal are already traded internationally via sea routes, this is not the case for H 2 and iron 1 . Therefore, assumptions about future cargo ships transporting these ECs must be made here.
As stated in Sec. 3.2, sea ships that can transport liquefied hydrogen at scale are unavailable as of 2023. Nevertheless, it can be expected that such ships will be commercially available in the Tab. 6. Specifications of conventional and alternative vessels for EC transport. Iron and coal cargo are measured in metric tonnes (90 % of DWT capacity), while the other ECs are measured in m 3 (manufacturer's CBM). The LHV of HFO is considered that of Diesel (42.7 MJ/kg) [107]. Fuel costs for HFO refer to the global average on 2022-05-17 for very low sulphur fuel oil from Ship & Bunker [108]. LNG and LH 2 vessels use the boil-off gases (natural or forced) as the main fuel. CAPEX for the considered vessels are calculated using the correlations of Mulligan [109]. upcoming decade, as verified by published roadmaps of cargo ship manufacturers [72,74] and one already existing pilot ship [70]. Thus, a future LH 2 carrier is assumed to have 160000 m 3 of cargo, in line with the assumptions of Johnston et al. [18], the IEA [9], and the next-generation Kawasaki LH 2 ship [72]. Considering the necessary structural adaptations to maintain the temperature below -253°C during the trip, thermal insulation would have to be considerably more efficient than that of LNG ships, leading to a reduced cargo capacity and increased costs when compared to a similarly sized ship. Therefore, the ship is assumed to have the external dimensions of the reference LNG ship, 1.35 times lower volumetric capacity and 20 % more expensive. In Sec. S 1 of the supplementary material, the effect of these assumptions on a potential H 2 supply chain is studied by varying the hydrogen ship cargo capacity and costs.
Similar as for coal, a solid bulk carrier with comparable DWT capacity is chosen for iron transport. Even though iron transport demands certain safety measures, i.e. sealed big bags or cargo containers, which require additional storage space, the limiting factor for storage will be the mass of the material 2 While other zero-carbon fuels are conceivable for maritime transport, in the green scenarios for H 2 and Fe, it is assumed that the ships are fueled by H 2 . Moreover, it is unlikely that a company operating a retrofitted power plant would also own the ships transporting iron and iron oxides. Considering the globalized transport of fossil fuels today, it can be assumed that a trading network of specialized companies would be established along the energy supply chain, likely increasing overall costs. The cost assessment utilizing the ship's CC and the CRF to annualize shipping costs should therefore be considered as an initial assessment to provide guidance. Similar approaches have been reported in the literature [18,23].
The ship's speed eventually leads to different transport times for the previously defined routes, as shown in Table 7.
Storage facilities: Storage specifications are shown in Table 8. Intermediate storage is assumed to last for the round-trip duration (see Table 7) with six additional days for loading and unloading the cargo. Long-term storage is fixed to 90 days in order to account for seasonally varying demands for the ECs, which has to be paired with the trends in the availability of renewable energy supply (i.e. EC demand can be expected to increase during winter times). Table 8 shows the ranges of critical storage-related values, while a compilation of literature values can be found in Table S 4
.
Tab. 7. Transport times Round-trip times with respect to the defined trade routes and the transport speeds given in Table 6 for the different ECs in days. Power generation: Using hydrogen and iron for power generation, the efficiencies are estimated to be close to those of NG (gas turbine) and coal power plants, respectively. For NG, the efficiency is estimated as that of a combined cycle gas turbine (CCGT) facility [96], while being assumed as lower, at 50%, for H 2
3
. The capacity factor for the power plants is set to 0.06-0.34, in line with assumptions for future intermittence backup (medium to peak load power plants) [96]. The variables related to power generation are summarized in Table 9.
Tab. 9. Overview of assumptions and references with respect to power generation from different ECs. Values are based on [20,40,96,110]. More detailed information can be found in Table S 5.5. Results and discussion.
Metrics for maritime transport of different ECs.
For quantifying the impact of various ship characteristics (e.g. size, fuel requirements, speed) on the supply chains of different ECs, reference data has been collected for different vessels. In particular, the relative energy demand and the specific capital costs are evaluated and analyzed. In order to facilitate comparison, both quantities are related to the transported energy that is chemically bound by the EC (measured in kWh EC ). For simplicity, the nominal speed of the ships is used, and unless otherwise specified, an engine efficiency of 50 % is assumed. In the following charts, vessel sizes are normalized with the maximum vessel size (in terms of net cargo) whose external dimensions still allow passage of the Suez Canal. The basis for normalization corresponds to the ships given in Table 6. Fig. 6 shows the relative energy demand which stems from moving a ship (kWh Fuel ) in relation to the energy content of the cargo, per 1000 km travelled. While the data for LNG and coal vessels correspond to real operating ships, it is assumed that the coal carriers can be repurposed to transport iron. As discussed in Sec. 5.4, for LH 2 , it is assumed that a hypothetical hydrogen carrier shows similarities to existing LNG vessels but with reduced net cargo capacity due to higher insulation requirements. As expected, the figure illustrates that the relative energy demand for all ship types decreases significantly with increasing ship size. While the vessels for the conventional ECs, coal and LNG, show relative energy demands of 0.1 % to 0.2 % per 1000 km, respectively, the transport of iron requires more energy ( 0.4 %-0.5 % per 1000 km for medium and large vessels), which is directly linked to its lower gravimetric energy density compared to coal (see Table 1). In contrast to these operating (or repurposed) vessels, the largest operating LH 2 vessel, which is a pilot ship, shows a relative energy demand of more than 10 %, which is prohibitive for long-distance transport. However, even if the technology could be scaled to reasonable H 2 carriers sizes in the future, the relative energy requirement remains higher (0.5 % to 0.6 % per 1000 km for medium and large ships) than for iron. As highlighted in Fig. 6, this agrees with reference values for proposed designs documented in the literature. The assessment is only contrasted by the numbers reported by the IEA [9] that assumes a more favorable transport efficiency for H 2 , which is comparable to coal transport. Fig. 6. Relative energy demand for selected vessels regarding their normalized size based on the Suez Canal limit (e.g. 1 corresponds to the maximal sizes suited for the Suez Canal). The lists of vessels are given in Table S 5, S 6 and S 7. It is assumed that 90 % of the DWT of the solid bulk carriers is available for cargo. The net cargo volume for hydrogen ship is assumed to be 0.75 % of current LNG ships. Highlighted points correspond to (proposed) designs from the literature (Kawasaki [71], Hank [23], IEA [9], Johnston [18], Abe [116], Alkhaledi [117]). Fig. 7 shows the specific capital costs for different ship types in terms of the energy content of the cargo. The results are based on the empirical correlations for LNG vessels and solid bulk carriers developed by Mulligan [109] depicted in Sec. A5.1 of the Appendix. While the prices for iron carriers are based directly on the estimates for solid bulk carriers, it is assumed that vessels capable of transporting LH 2 are 20 % more expensive compared to LNG vessels, as previously discussed. Medium to large vessels for the conventional ECs coal and LNG show specific CCs of 0.15-0.3 USD ·kWh −1 EC and 0.05-0.15 USD ·kWh −1 EC , respectively. Interestingly, the specific cost for very large bulk solid carriers increases again beyond a certain size, indicating limits for the economics of scale. Analogously to the relative energy demand of iron ships, the specific CCs of iron-carrying vessels are notably higher (0.25-0.5 USD ·kWh −1 EC ) compared to coal transporting vessels due to the gravimetric energy density differences. The cost assessments for future hydrogen vessels, as well as cost estimates reported in the literature (diamond symbols in Fig. 7), indicate even significantly higher costs for H 2 -transport. It is emphasized that the estimates for H 2 -vessels are subject to significant uncertainty, which is also indicated by the deviations among the literature values of over 100 %. [109]. The diamonds correspond to literature values (Hank [23], IEA [9], Johnston [18], Guidehouse [118], Abrahamse [119], Hyunyong [84], Fikri [120]).
Long-distance maritime transport of conventional ECs is both energy-and cost-efficient, as evidenced by its decades of successful application worldwide. Even though the cost and relative energy requirements for transporting iron are higher compared to transporting conventional ECs, the present analysis shows that long-distance transport of iron via medium and large cargo ships is possible and will not exceed single-digit energy expenditures (in terms of the percentage of chemically-bound energy) even for very long distances such as Australia-Germany.
5.5.2.
Holistic energy supply chain analysis. The combined results for the energetic assessment (thermodynamic system efficiency), the environmental assessment (CO 2 -emissions), and the economic assessment (LCOE) of the EC supply chains are shown in Fig. 8. It is worth to notice that the cost assessment for hydrogen supply chains is shaded, indicating the significant uncertainty associated with its maritime transport, storage, and liquefaction. The cost estimate should therefore be understood as a hypothetical value. A more extensive exploratory cost assessment, which includes a variation of important transport parameters for the H 2 supply chain, is provided in Sec. S 1 of the supplementary material for interested readers. Fig. 8 (top) shows the energy losses for the individual processes along the energy supply chains of the ECs studied here. Notably, the energy share by process varies broadly between the ECs. Overall, coal and NG are the most energy-efficient ECs. However, given the differences in the process chains for conventional (primary energy without required production) and renewable ECs (secondary energy with required production), it is crucial to approach this comparison between conventional and renewable ECs with caution. Most energy losses for NG originate from its utilization process (i.e. electricity generation) and liquefaction, with only minor losses due to storage and transport. As expected, the latter takes a higher toll on the efficiency when the ECs are transported over longer distances (due to maritime fuel consumption and longer intermediate storage times). On the other hand, coal does not need to be transformed to be transported and stored; it is also safe to be piled up in warehouses or yards. Therefore, the handling and processing of this EC require minor relative energy input. The main energy losses in the supply chain stem from the utilization, which is less efficient than that of NG. The impact of transport distance is also low for coal due to the high energy content that can be shipped per trip. The zero-carbon ECs, on the other hand, are very energy-intensive to produce, requiring an energy input that ranges from around 30 % to 50 % of the total energy expenditure of the considered supply chain. Green hydrogen further exhibits high energy losses due to liquefaction, transport, and storage since achieving and maintaining its liquid state at cryogenic temperatures significantly increases the energy demand for handling the EC. Even in its liquid form, LH 2 transport is less efficient due to the small volumetric energy density of LH 2 , but also due to the expected limitation in cargo capacity, which stems from the application of considerable thermal insulation. Consequently, the impact of the transport distance on the overall energy efficiency is comparatively high. Further losses are related to the boil-off (despite BOG being assumed to be used as fuel), which also has to be addressed for intermediate storage times. Iron is the most energy-intensive fuel to be produced. For the production and transport of conventional iron, fossil fuels are utilized, accounting for up to 50 % of the energy supply chain. Despite being less energy-intensive, green iron production relies on hydrogen for the reduction reactions, thus inheriting the production efficiency of the gas. Contrary to H 2 , green iron storage and transport is very efficient. Due to the very high volumetric energy density of iron, high amounts of chemical energy can be shipped per trip, while its chemical stability facilitates efficient storage similar to coal. Nevertheless, material handling (packing, loading, unloading and storage) requires additional effort and sealable containers, such as super-bags, to avoid oxidation and ensure security. Overall, the impact of the distance on the energy expenditures for transport is lower than for H 2 but higher than for fossil fuels due to the energy content delivered for each trip.
The overall supply chain energy efficiency is shown separately in Fig. 9 together with error bars corresponding to best-case and worst-case scenarios. As stated before, after extraction, transport, storage and utilization, NG and coal, are the most efficient ECs with 46 % -52 % usable energy. For the zero-carbon ECs, H 2 and iron, the holistic energy supply chain analysis yields efficiencies of 23 % -26 % with either one being more efficient depending on the transport distance.
Assuming that all processes are optimized along the supply chains (upper bound of error bars in Fig. 9), the maximum potential efficiencies are 32 % and 29 % for green H 2 and iron (assuming the route CAS-HAM), respectively. Note that short-range transport has not been considered here, which can influence the efficiencies of all ECs.
Comparing the CO 2 emissions in Fig. 8 (middle row), the largest emissions per kWh el are produced from coal in the utilisation step, while other CO 2 emissions along its supply chain are negligible small in comparison 4 . In contrast, the utilisation of NG leads to lower CO 2 emissions, but other emitting processes are the liquefaction 5 and the extraction process (CH 4 emissions). In this case study, green hydrogen and iron, by definition, do not produce any CO 2 , using fully decarbonised processes to produce, prepare, transport, store, and utilise the EC. In real scenarios, it is supposedly very challenging to avoid indirect emissions along the whole energy supply chain due to the production of machinery, infrastructure construction, and other auxiliary processes. It has to be stated, though, that the CO 2 emissions from transport, independent of the route, have a minimal relative impact on the overall emissions compared to the very high CO 2 intensity of conventional fossil fuels.
Analyzing the levelized costs for electricity (LCOE) in Fig. 8 (bottom), it is found that contributions from different steps along the energy supply chain vary widely for different ECs. NG has the lowest share of fuel costs (production), which can be associated with the comparably low fuel prices for NG at the Henry Hub (see Table 2). However, capital costs and electricity expenses for the liquefaction and storage processes heavily affect the final price. NG utilization is also low-cost due to comparably low infrastructure and operation expenses. Coal has higher fuel costs but the least expensive storage, primarily due to easy handling and storage. When comparing the pre-utilization costs of coal and NG, coal shows overall lower costs. However, the use of coal results in high expenses for the power plant construction and operation, which make up the bulk of its supply chain costs. Especially due to the low capacity factors for the power plant (CF = 0.06 − 0.34, medium to peak power plant), the high investment costs for the coal-fired power plant are dominant. Transport of both fossil fuels is also inexpensive due to the efficiency of their transport. On the other hand, H 2 appears as the most expensive of all ECs, which can be attributed to the particularities of its supply chain, especially the high energy demand of the production process, the liquefaction and storage costs, which require advanced infrastructure and elevated electricity expenses. Due to the characteristics of H 2 , the effect of transport distance on transport and storage is also significant. Firstly, the ship fuel consumption is affected, but, more importantly, the transport distance affects the follow-up costs from increased intermediate storage times and cargo losses from the usage on board (boil-off). Among the ECs evaluated, iron has the highest production costs. However, its advantageous transport and storage characteristics in comparison to hydrogen and the possibility of retrofitting existing coal-fired power plants give it a potential competitive advantage over hydrogen. As expected, CO 2 taxation (red bar for NG and coal in Fig. 8, bottom) negatively affects fossil fuel overall costs. However, the assumed value of 86 USD/t CO 2 in the utilization step only is not high enough to make green ECs economically competitive unless improvements on the green chains reach close to the best-case scenarios. The influence of the factors above is further investigated through a sensitivity analysis in the next section. 5.5.3. Sensitivity analysis. In this section, the relative impact of changes in the supply chain on the LCOE is investigated for the fossil fuels, NG and coal, and the potential zero-carbon alternatives, H 2 and iron for the trade route between Germany and Australia (Hed-Ham). A positive perturbation of 1 % is imposed on selected variables, and the sensitivity of the LCOE is evaluated according to Eq. (16). Thus, a sensitivity factor of -0.5 indicates that a 1 % increase in the respective variable leads to a 0.5 % reduction in the LCOE. The analysis reveals where improvements in the supply chain would more significantly affect the costs, representing important information for decision-makers and indicating where further development might be most beneficial. Fig. 10 shows the ten highest sensitivities calculated for the considered energy supply chains. For all ECs, the most influential variable for the LCOE is the utilization efficiency, which, when improved, leads to the most significant cost reduction. Furthermore, the capital costs of the infrastructure and the CRF show high sensitivity, which underlines the high investments associated with the required infrastructure. Particularly for coal, the power plant capacity factor (operation hours per year) significantly affects the LCOE due to the high capital costs of coal-fired power plants. Notably, the feedstock costs for coal are highly sensitive, while those for NG are not among the top ten sensitivities. This is due to the low reference feedstock cost of NG compared to coal. The LCOE of NG, on the other hand, is negatively influenced (hence, lowering the LCOE) by an increase in the liquefaction efficiency. Considering the liquefaction and storage demands for NG, an increase in storage time, which leads to energy losses as well as operational costs in the supply chain, considerably increases the price of the electricity derived from this fuel. Transport efficiency, measured by the ship size, capacity, and speed, has a moderate impact on both fossil fuels. Considering the moderate sensitivity to the carbon tax for coal, and the low sensitivity to NG, it can be concluded that its application would have only a moderate impact unless the taxation was drastically increased. The effect of the carbon tax on the competitiveness of green ECs is analyzed in more detail in Sec. 5.5.5.
Opposite to fossil fuels, which have to be extracted, the zero-carbon ECs, H 2 and iron, have to be produced from electricity, whose price is clearly indicated as the second and third in the sensitivity of Fig. 10. It shows the reliance on access to cheap renewable energy, i.e. as found in sunny arid regions (photovoltaic potential) or windy coastal areas (wind energy potential), which can justify long distance transport of the ECs. The efficiency of the production process is notably also highly influential. Unsurprisingly, sensitivities associated with plant equipment and infrastructure, such as CC and CRF, show a significant overall impact on the LCOE. It is interesting to notice, though, that the efficiencies of the production processes of green H 2 and green Fe only show approximately half the impact on the cost compared to the utilization efficiency. This is due to the high losses in efficiency associated with the utilization step and indicates that investing in research and development for efficient technologies for the thermochemical conversion of H 2 (such as gas turbines) and iron (such as retrofit coal-fired power plants) is key for the economic competitiveness of the respective EC. It should be noted that the LCOE for the H 2 supply chain shows the highest sensitivity to the ship's speed and size, which is in line with the discussion in Sec. 3.2. Together with the scaling ratio V H 2 /V LN G , which compares the cargo volume of H 2 ships to LNG ships of the same outer dimensions, the ship size directly influences how much EC can be transported per trip, while the speed determines the supply chain time. On the other hand, the green iron supply chain shows a lower sensitivity to transport parameters, indicating that its transport, even with minimal modifications-i.e. the type of fuel-, will unlikely become a barrier for the technology.
Uncertainty analysis.
Besides the sensitivity, the uncertainties associated with the variables used for the overall supply chain assessments can influence the results. Therefore, an attempt is being made to quantify the influence of assumptions, particularly for potential future energy supply chains, namely the supply chains for green H 2 and Fe. Predictions about future technological developments are challenging in an interconnected and globalised world. However, this uncertainty analysis can still yield insights into decisive aspects to be analysed and monitored when implementing such clean energy supply chains. Relative uncertainties of the LCOE are evaluated as described in Sec. 4.5 and the results for the supply chains for green H 2 and green Fe are shown in Fig. 11. Note that, according to Eq. (19), variables which exhibit a significant impact on the supply chain (high sensitivity in Fig. 10) but only show a small uncertainty induce only a small relative uncertainty on the LCOE and thereby affect the ranking of the parameters.
Inspecting Fig. 11, the largest uncertainty for the LCOE of green H 2 and iron is, by far, caused by the clean electricity costs. Both supply chains are sensitive to this parameter and show high uncertainty. While the global economy relies on fossil fuels and no relevant large-scale production Fig. 11. Uncertainty analysis of LCOE for green H 2 and green iron.
facilities exist for zero-carbon ECs, mostly demonstration plants and theoretical assessments exist for clean electricity costs for potential clean energy exporters. Part of the high uncertainty shown in Fig. 11 also includes variability in clean energy production potential, which stems from geographic location, climate, and local infrastructure, which is also reflected in the relatively high uncertainty of the capacity factor for the electrolyzer. These high relative uncertainties underline the importance of suitable locations for the production of zero-carbon ECs, and it can also be understood as a great opportunity if producers succeed in implementing very efficient H 2 production.
The second largest uncertainty for green H 2 relates to the capital costs of the storage. Interestingly, this uncertainty also affects the iron supply chain since it is assumed that the iron transporting vessels would use green hydrogen as fuel, which depends on the production and storage steps in the hydrogen supply chain. Additionally, the efficiency of the electrolyzer for hydrogen production, which is part of both EC's supply chains, induces significant uncertainty. While the electrolyzer technology is currently scaled to large dimensions and will conceivably improve in the coming years, this uncertainty will soon become smaller. Relevant differences between the uncertainty assessments for the LCOE of the supply chains of green H 2 and iron are H 2 -(re)liquefaction and capital costs. H 2 -liquefaction does not play a role for green iron, but this process is important for the green H 2 supply chain. Efficient and cost-effective liquefaction still has to be implemented at scale and, if improved, could yield significant benefits for the LCOE of H 2 in general. On the other hand, the capital costs for the hydrogen supply chain lead to further uncertainties since most of the infrastructure and equipment (production facilities, gas turbines, ships) still have to be developed and later constructed. Given that coal power plants can be retrofitted for iron and that suitable ships already exist, CCs lead to notably less uncertainty for this EC in the present model.
5.5.5.
Break-even analysis. The previous analyses indicate that the cost of producing renewable energy significantly impacts the economic performance of carbon-free ECs. On the other hand, the LCOE for conventional EC supply chains is moderately (i. e. NG) to strongly (i. e. coal) influenced by the cost of their raw materials and the carbon taxation policy aimed at reducing CO 2 emissions. To identify the cost combinations at which green EC have lower LCOE than conventional EC supply chains, a break-even analysis is performed for both the best and average scenarios, as illustrated in Fig. 12.
Both the figures show that coal is more affected by carbon pricing than NG due to its higher carbon intensity and that the hydrogen supply chain is more sensitive to the price of renewable energy than iron due to its higher share of energy costs in the LCOE. In the best case scenarios (Fig. 12 a)) iron and hydrogen can already be competitive with LCOE of approximately 0.14 USD · kWh el −1 at very low prices for renewable electricity (e.g. 0.01 USD · kWh el −1 ) and low carbon pricing of 90 USD · t −1 assumptions (c.f. 5.4). For NG, the intersection is roughly at 220 USD · t −1 CO 2
. At NG prices of 50 USD · MWh −1 (which is in the order of recent prices of the Dutch TTF Natural Gas Future, see Table 2) and a carbon tax of 220 USD · t −1 CO 2 the supply chains for iron and hydrogen become competitive with NG at a price around 0.03 USD · kWh el −1 for renewable energy. In comparison to the best-case assumptions, which include the lowest capital and operational expenses, highest efficiencies, and high capacity factors for the corresponding power plants, the averaged results between the best-and worst-case scenarios (Fig. 12 b) show a significant higher offset (for all ECs) and impact of the costs for renewable energy, especially for hydrogen. The higher uncertainty with hydrogen-related parameters results in a significantly higher LCOE for hydrogen compared to iron. In this scenario, hydrogen can only be competitive with NG at extraordinary carbon taxes and at very high carbon taxes (e.g. 400 USD · t −1 CO 2 with coal. On the other hand, the supply chain of iron can get competitive at carbon taxation around (250 USD · t −1 CO 2 with coal and NG.
The break-even analysis illustrates that carbon-neutral ECs such as green hydrogen and iron can become competitive with conventional ECs at low costs of renewable energy. However, it is unlikely that these green ECs will reach this level of competitiveness without implementing a carbon taxation system to account for some of the environmental impact by conventional ECs. The European Union Emission Trading System serves as an example of a carbon pricing system (EU carbon prices (end 2022) are in the order of 90 EUR · t −1 CO 2 [39]), with recent announcements of tighter CO 2 allowances [122] leading to higher carbon prices and consequently increased competitiveness for alternative green ECs.
Conclusions
In the present work, a techno-economic assessment for the long-distance energy supply chains for carbon-free electricity generation of the two promising zero-carbon energy carriers (ECs), H 2 and iron, is presented. In particular, the thermodynamic efficiency (energetic assessment), CO 2 emissions (environmental assessment), and the levelized cost of electricity (LCOE, economic assessment) are analyzed. For comparison, analogous assessments are being carried out for the supply chains of the well-established fossil fuels, coal and natural gas, for which international long-distance trade has been established for decades. With respect to the zero-carbon energy carriers, the following conclusions can be drawn:
(1) Energetic efficiencies: Green iron exhibits energy efficiencies that are comparable to those of green hydrogen. Optimizing all processes along the energy supply chains and depending on transport distances, the potential for the power-to-power energy efficiency is 19%-29% for iron and 16%-32% for hydrogen.
(2) Influence of transport and storage: For short-distance transport and immediate usage, hydrogen might exhibit a competitive advantage since iron requires additional processing steps to be regenerated from its oxides. For long-distance transport and/or long storage times, however, these advantages become overcompensated by the more favorable transport and storage characteristics of iron compared to hydrogen. (3) Economic assessment: Our analysis indicates the advantages of iron compared to hydrogen, mainly due to the retrofitting potential of existing infrastructure and more favorable transport and storage characteristics. This comparison is, however, subject to many uncertainties, which largely stem from the costs associated with the required large-scale infrastructure for iron (iron oxide regeneration plants) and for hydrogen (liquefiers, storage, transport) that does not exist today. (4) Cost comparison to fossil fuels: Realizing the techno-economic potentials along the considered zero-carbon energy supply chains, it is conceivable that iron and hydrogen can become cost-competitive with fossil fuels. However, this largely depends on low renewable energy prices and the introduction of carbon taxation. The analysis further shows that access to cheap renewable energy can overcompensate the costs associated with long-distance transport.
The current study considers overarching characteristics of energy supply chains and does not account for specifics on the system scale of individual plants, localized infrastructure for shortrange transport, or climate/weather effects, some of which are valuable aspects for follow-up work. As the technologies of zero-carbon energy carriers evolve, future research could further be carried out along the following directions:
• Regeneration of iron: The reduction of iron is one of the challenges for realising the metal energy cycle and is subject to research and development. It can be assumed that synergies with efforts to decarbonise steel production will soon lead to technological progress for this process. Incorporating operating data for clean reduction plants will reduce uncertainties in the assessment of iron as an energy carrier. • Implementation times: Hydrogen supply chains include processes which have yet to be realised at large scales (i.e. liquefaction, transport, and storage), which raises questions about the implementation times for the required infrastructure. On the other hand, iron could largely profit from retrofitting infrastructure formerly used for coal. Opportunities and challenges for green H 2 and green iron are linked to sub-processes with very different technology readiness levels (TRL) along their respective supply chains, influencing the implementation times. It remains to be investigated how this might affect the adoption of these zero-carbon energy carriers, given that decarbonisation goals for many industries require effective measures sooner than later. • In-depth economic modeling of intermittent renewable energy supply: The economics of variable renewable energy (VRE) plants, such as the recycling facilities for iron oxides, are more complex than the current analysis might suggest. For instance, it might be beneficial in specific scenarios to sell energy from renewable sources directly into the electricity market at the plant's location rather than storing it in a chemical energy carrier and then shipping it to other countries. An investigation of such energy markets' drivers requires sophisticated economic modeling considering, for instance, spot market pricing or long-term contracts. Such investigations could help refine and improve LCOE estimates for emerging zero-carbon energy carriers such as hydrogen and iron.
Considering the substantial funding programs for green hydrogen technologies from governments worldwide, it is safe to assume that a H 2 -infrastructure will be implemented in many countries. The present study further suggests that also green iron shows the potential to become an important energy carrier for long-distance trade in a globalized clean energy market and should therefore be discussed as a technological option.
Acknowledgments
This work was funded by the Hessian Ministry of Higher Education, Research, Science and the Arts -Clean Circles cluster project. The authors thank Prof. Andreas Dreizler for his advice and valuable feedback. The authors further acknowledge Sunil Chapagain, Evrim Cicek, Lukas Schleidt, Bipal Shrestha, Kieu-Ly Tran and Ying Lin for support with the data collection and literature review.
Appendix: Detailed formulation
For a certain vessel with its cargo measured in volume or mass, the energy carrier (EC) mass is given by:
m EC = m cargo = ρ EC · V cargo [kg](A1)
If boil off gas (BOG) occurs at any phase of the transport, i.e. during the long-range transport and the intermediate storage, the mass of the EC at a certain phase can be given as a function of the initial cargo mass, multiplied by the boil off rate (BOR) of every stage between that phase and the ship loading. For the mass before and after the ship loading, equations A2 and A3 can be used, respectively:
m EC = m cargo · Π(1 + BOR i ) t i [kg] (A2) m EC = m cargo · Π(1 − BOR i ) t i [kg](A3)
The primary energy content for a given mass of the EC is:
P E EC = m EC · LHV EC [kWh](A4)
A2. Production
To produce a synthetic EC, a certain amount of energy input is required, consisting of the internal energy of the feedstock and the energy needed to synthesize it. This energy input can be calculated by determining the overall energetic efficiency of the production process.
W prod = P E EC η prod [kWh](A5)
Such syntheses process can have a CO 2 intensity, the ratio between the mass of the emission and the mass of EC generated. In the present work, such value is taken as a constant, based on the report from the IEA [9]. Therefore, the CO 2 emitted per ship cargo can be measured as:
E CO 2prod = I CO 2prod · m EC [kg CO 2 ](A6)
A3. Liquefaction
Liquefaction processes can be assumed as demanding a constant energy per unit of mass:
W liq = m EC · w liq [kWh](A7)
This energy is considered to be provided solely by electricity. In this sense, the process will have associated CO 2 emissions solely related to the emission intensity of the electricity generation:
E CO 2liq = I CO 2elec · W liq [kg CO 2 ](A8)
A4. Storage
To temporarily store ECs in ports, before their export by ship or their distribution locally, a certain amount of energy is necessary to maintain the substances in transportable form (i.e. reliquefaction of the BOG for NG and H 2 .). In the present work, the required time of loading and unloading, from the pipelines or trucks to the export terminal facilities and later to the ship, and from the ship to the import terminal facilities and later to the pipelines or trucks for the delivery, is estimated to be 6 days. Considering the combined energy to be provided solely by electricity, depending on the mass and the time, the necessary energy for the storage can be given by:
W store = m EC ·ẇ store · t store [kWh](A9)
If the only energy source is electricity, the CO 2 emissions are given by the emission's intensity of the power generation:
E CO 2store = I CO 2elec · W store [kg CO 2 ](A10)
The costs for storage are the sum of the CAPEX, the fixed OPEX, and the electricity costs. The CAPEX is given by the annualized specific costs considering the operational days per year.
In contrast to the CF for the production, as the number of days of operation increases (t store ), so do the associated costs.
CAP EX store = CRF · CC tank · t store t year [USD · (kg EC year −1 )] (A11)
A5. Long-range transport
The long-range transport in ships, from the export terminal to the import terminal, is required for moving the EC between the locations. Excluded from the analysis are costs and energy for loading and unloading. Furthermore, ships that transport liquid fuels are considered to use thermal isolation in order to keep the conditions, being more energy-efficient but subject to boil-off, either losing cargo or using it to fuel their engines. The energy demand of such ships is given by the ship's engine power capacity, its efficiency or heat rate, and the travel time:
W trans =Ẇ engine η engine · 24 h day · t trans [kWh](A12)
If the travel time is taken, considering a certain constant speed, and that the total travel distance is twice the distance between the ports, therefore considering the round-trip, it can be calculated by the equation below:
t trans = 2 · d trans 24 · v ship [days](A13)
The CO 2 emissions of each trip depend on the emission intensity of the fuel consumed. The total CO 2 can be given by:
E CO 2trans = W trans · I CO 2f uel [kg CO 2 ](A14)
In the case of liquefied ECs, the net mass of EC after the trip, is given by:
m ECtrans = m cargo · (1 − BOG trans ) ttrans/2 [kg](A15)
In the case of ships transporting and consuming the EC (i.e. H 2 or NG), the boil-off value is the greater value between the natural boil-off and the forced boil-off due to the engine consumption: Therefore, the forced boil-off can be given by:
BOG f orced = 100 · 1 − 1 − W trans m cargo · LHV EC 2/ttrans [%](A18)
If the natural boil-off in energy content is equal or greater than the energy consumed, or if the only fuel is the EC of the cargo, the shipping costs are given by: C trans = CAP EX trans + OP EX trans + 2 · C canal [USD] (A19) A5.1. Capital costs of ships. To define the capital costs of the ships used in the present work, the formulation from the work of Mulligan [109] was used. In this formulation, taken from the fitting of a pool of vessel sizes and costs, uses an offset for each ship, the producer price index (PPI) for ship building and the deadweight tonnage of the vessel (DWT) in 10 6 kg.
CC ship = of f set ship + 2.6 · P P I + 1.8055 · DW T − 0.01009 · DW T 2 + + 0.0000189 · DW T 3 [10 6 USD] (A20)
For the LH 2 ship, considering that such ships are still not available in commercial scale, it is possible to calculate the capital cost as a function of the cost of a similarly-sized LNG ship, assuming a multiplier:
CC LH 2 = M LH 2 /LN G · CC LN G [10 6 USD] (A21) The offset for each ship can be given by
A6. Electricity generation
When utilized for electricity generation in a power plant, the net output depends on the net efficiency of the corresponding power plant.
W elec = η elec · m EC · LHV EC [kWh el ](A22)
The direct CO 2 emissions of this operation depend on the emission intensity of the EC:
E CO 2elec = I CO 2EC · ·m EC [kg CO 2 ](A23)
Fig. 1 .
1Schematic for the supply chain of an EC from production to utilization. Dashed boxes mark the processes considered in the current work.
Fig. 2 .
2Volumetric and gravimetric energy densities of selected chemical ECs.
Fig. 5 .
5Maritime trade routes from Morocco, Saudi Arabia and Australia to Germany and Japan.
Fig. 7 .
7Specific capital costs for selected vessel regarding their normalized size based on the Suez Canal limit (e.g. 1 corresponds to the maximal sizes suited to the Suez Canal). The lists of vessels are given in the supplementary material, Tables S 5, S 6 and S 7 for which the capital costs are based on the correlations developed by Mulligan
Fig. 8 .
8Overview of the performance of the different ECs in terms of energy share by process (top), CO 2 emissions (middle) and LCOE (bottom) for the specified routes. The corresponding process steps shown inFig. 1are color-coded.
Fig. 9 .
9Overall thermodynamic system efficiency of the energy supply chain for the selected ECs and routes.
Fig. 10 .
10Sensitivity analysis with respect to the LCOE of the selected ECs. A negative sensitivity factor (e.g. −0.5 %) indicates that a 1 % increase in the variable results in a beneficial decrease in the LCOE (e.g. 0.5 %).
Fig. 12 .
12CO 2with coal at a fuel price of 10 USD · MWh −1 and the corresponding Break-even analysis assuming a transport distance of roughly 8000km (YAN-HAM). LCOE of coal and NG supply chains are shown as function of the carbon tax for different fuel prices. The LCOE of iron and hydrogen are shown as variations of renewable energy costs (horizontal lines). a) best-cases for all ECs, b) averaged-cases for all ECs.
BOG trans = max(BOG ship , BOG f orced ) [wt.% · day −1 ](A16)In those cases, the energy of the extracted cargo is considered equal to the energy demand of the ship:W trans = (m cargo − m ECtrans ) · LHV EC = = (m cargo − m cargo · (1 − BOG f orced 100 ) ttrans/2 ) · LHV EC [kWh] (A17)
STP, 2 liquid, 3 350 bar, 4 700 bar supplied 1.36 EWh of energy and generated 33 Gt of CO 2Density
Boiling point Grav. energy density
Vol. energy density
[kg · m −3 ]
[°C]
[kWh · kg −1 ]
[kWh l −1 ]
Coal
1200-1600
n.a.
7-10
8.3-15.8
Iron (Fe)
7870
n.a.
2.1
16.1
Nat. Gas (CH 4 )
0.66 1 /410 2
-161.6
13.9
0.009 1 / 5.7 2
Hydrogen (H 2 )
0.08 1 /30 3 /57 4 /73.5 5
-259.9
33.3
0.0025 1 / 1 3 / 1.89 4 / 2.61 2
1
Fig. 4. Electricity mix in Japan and Germany[35].5.2. Exporters of ECs: Morocco, Saudi Arabia and Australia. Morocco, Saudi Arabia,9.75%
Hydro
9.74%
Nuclear
6.67%
Bio
4.48%
Wind
1.08%
Other Renew.
0.34%
Other Fossil
5.05%
Coal
30.6%
Gas
32.3%
1031 TWh
Clean
32.1%
Fossil
67.9%
585 TWh
Clean
51.8%
Fossil
48.2%
Wind
19.9%
Coal
29%
Gas
15.7%
Other Fossil
3.48%
Hydro
2.91%
Nuclear
11.8%
Solar
8.55%
Bio
8.51%
Table S 2.
Sincludes CAPEX, OPEX and costs for renewable energy 2 related to the extraction (mining, drilling) of the ECsUnit
NG
Coal
Green H 2
Green Fe
References
Efficiency
[%]
NA
NA
50-74
46-60
[9, 41, 62, 63]
CF electrolyzer
[−]
NA
NA
0.19-0.74
0.19-0.74
[9, 96, 97]
Specific CC
[USD · kW −1
el /t −1
EC ]
NA
NA
450-1400
225-430
[9, 41, 98-100]
Total cost
[USD · kg −1
EC ]
0.13-0.26 0.07-0.37 0.74-11.96 1 0.11-0.84 1
CO 2 emissions
[kg CO 2
· kg −1
EC ]
0.66 2
0.06 2
0
0
[1, 9, 19, 101]
1
3. Unit
NG
H 2
References
Existing Concepts
Specific energy demand [kWh el · kg −1
EC ] 0.24-3.75
10-20
4-13
[66, 69, 69, 102-104]
Specific CC
[USD · kg −1
EC ]
0.19-2.21 8.6-14.3 3.21-17.1
[102-105]
OPEX as share of CC
[%]
2-4
2.5-4
[9, 102, 103]
Costs of H 2 calculated per route, combining the specific costs of production and storage of the fuel.Unit
NG
Coal
Green H 2
Green Fe
Vessel type
N/A
LNG carrier bulk carrier LH 2 carrier
bulk carrier
Net Capacity
[t or m 3 ]
216000
160000
160000
160000
Boil-off rate
[% · day −1 ]
0.08-0.3
N/A
0.1-0.4
N/A
[77, 79]
[103]
Engine Power
[kW]
39240
19620
39240
19620
Speed
[km ·h −1 ]
36
26
36
26
Fuel type
N/A
NG
HFO
H 2
H 2
Fuel cost
[USD · kg −1
fuel ]
1.0
1.0
0
*
Ship capital cost
[10 6 USD/ ship]
236.0
78.3
283.2
78.3
OPEX
[% of CC]
4
4
4
4
Suez trip cost
[USD]
300000
300000
300000
300000
CO 2 -emissions [110] [kg CO 2
· kWh −1
fuel ]
0.201
0.293
0
0
Reference ship
N/A
Kharaitiyat Genco Titus Kharaitiyat
Genco Titus
[107, 111]
[112, 113]
[107, 111]
[112, 113]
*
Tab.8. Ranges of crucial storage-related characteristics. A compilation of literature values can be found inTable S 4.LNG Coal LH 2
Fe
CAS-HAM
7.2
9.9
7.2
9.9
YAN-HAM 17.8
24.6 17.8 24.6
HED-HAM 42.1
58.2 42.1 58.2
HED-CHI
15.5
21.5 15.5 21.5
Unit
LNG
Coal
LH 2
Iron
References
Boil-off rate
[wt.%· day −1 ] 0.0-0.15
NA
0.04-0.40
NA
[18, 77, 80, 103, 114]
Specific CC
[USD · kg −1 ]
0.65-40 3.45 · 10 −4 11.95-148.80 3.45 · 10 −4
[18, 23, 105, 115]
OPEX as share of CC
[%]
4
4
2-4
4
[18, 103]
10. Unit
NG
Coal
H 2
Iron
Specific CC
[USD·kW −1
el ]
842-1158 1579-2316
CC NG
(0.1-0.5 CC) Coal
Capacity Factor
[-]
0.06-0.34
OPEX
[USD·kWh −1
el ]
21.05
23.16
OPEX NG
OPEX Coal
Net efficiency
[%]
60
46-50
50
46-50
Direct CO 2 -emissions [kg CO2 · kWh −1
EC ]
0.20
0.35
0
0
Table A1 .
A1Tab. A1. Offset for equation A20, by ship type[109] EC
Unit
Natural Gas
Coal
Iron
Ship type
[-]
LNG ship
dry bulk carrier dry bulk carrier
Offset
[10 6 USD]
-253.012
-418.202
-418.202
Although, it should be noted that direct reduced iron (DRI) is already being shipped internationally as briquettes or fines in the volume of 21.1 Mt (2020) with regulations in place by the International Maritime Organization Code of Safe Practice for Solid Bulk Cargoes[106].
Note the density difference of a 4-5 factor between coal and iron.
Extensive research is being carried out for H 2 -fueled gas turbines. However, substantial technological development is still required to reach similar efficiencies as NG-CCGT.
It is worth noticing, however, that the coal source considered in this comparison is the open pit mining, which generates far fewer methane emissions than deep mining[121] which could change this assessment.5 It is considered here that the electricity required for liquefaction is at least partially based on fossil fuels.
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| sample_1202 | 0.6069 | arxiv | |
Monitoring biodiversity loss in rapidly changing Afrotropical ecosystems: An emerging imperative for governance and research
Achieng A O
Arhonditsis G B
Febria C
Opaa B
T J Coffey
Department of Fisheries and Aquatic Science
University of Eldoret
EldoretKenya
School of Veterinary Medicine and Science
University of Nottingham
NottinghamUnited Kingdom
Obiero K
Z Ajode
Department of Fisheries and Aquatic Science
University of Eldoret
EldoretKenya
Kenya Marine and Fisheries Research Institute
SangoroKenya
Irvine K
Barasa J E
Kaunda-Arara B
Monitoring biodiversity loss in rapidly changing Afrotropical ecosystems: An emerging imperative for governance and research
Ecosystem ChangeEnvironmental DegradationBiodiversity ConservationGovernancePolicy Implementation
Africa is experiencing extensive biodiversity loss due to rapid changes in the environment, where natural resources constitute the main instrument for socioeconomic development and a mainstay source of livelihoods for an increasing population. Lack of data and information deficiency on biodiversity, but also budget constraints and insufficient financial and technical capacity, impede sound policy design and effective implementation of conservation and management measures. The problem is further exacerbated by the lack of harmonized indicators and databases to assess conservation needs and monitor biodiversity losses. We review challenges with biodiversity data (availability, quality, usability, and database access) as a key limiting factor that impact funding and governance. We also evaluate the drivers of both ecosystems change and biodiversity loss as a central piece of knowledge to develop and implement effective policies. While the continent focuses more on the latter, we argue that the two are complementary in shaping restoration and management solutions. We thus underscore the importance of establishing monitoring programs focusing on biodiversity-ecosystem linkages in order to inform evidence-based decisions in ecosystem conservation and restoration in Africa.
Introduction
Biodiversity loss is the reduction or disappearance of any aspect of community dynamics, or variety of organisms in an ecosystem through elimination of genes, species or biological traits (1). Unprecedented biodiversity loss has been experienced across ecosystems globally in the past century (2), yet the drivers of change show no evidence of decline, and even more so, appear to increase in intensity, undermining ecosystem stability and resilience to environmental perturbations (3). Biodiversity loss poses significant risk to the global economy as it translates into escalating losses of a wide variety of ecosystem services and catastrophic effects from habitat conversion (4). It has been rated as one of the top five risks to the global economy, as an estimate of more than half of the global GDP is dependent upon the natural capacity, and can therefore be vulnerable to biodiversity loss (5,6). Consequently, the Convention on Biological Diversity at the 15 th Conference of Parties (COP15), December 2022 in Montreal Canada, adopted a global biodiversity framework with four overarching goals to protect nature, including (i) halting human-induced extinction of threatened species and reducing by tenfold the rate of extinction of all species by 2050, (ii) sustainable use and management of biodiversity, (iii) fair sharing of the benefits from the utilization of genetic resource, and (iv) securing resources for the implementation of the framework so it can be accessible to all parties (7).
The inextricable link between ecosystem degradation and biodiversity loss (8) as a result of the human footprint (9)(10)(11)(12) and environmental perturbation is invariably signified in scientific studies (11,12), expert judgements (10,(13)(14), and global reports (15,16). These anthropogenic disturbances on ecosystem processes (water cycle, energy flow, nutrient cycling, and community dynamics) modify the synergies between biotic and abiotic ecosystem components, and consequently disrupt their collective functioning (17). Biodiversity, being the living web of an ecosystem that forms the basis for life on Earth, plays a fundamental role in regulating the physical and chemical ecosystem components (18), including their provisioning and supportive role (19). Thus, biodiversity loss often alters the pools and fluxes of materials and energy, thereby impacting a multitude of ecosystem functions (20,21).
Recent advances in research from developed countries (especially in temperate ecosystems) on biodiversity and ecosystems function focus on a range of topics, broadly summarized as: (i) simulations of the influence of biodiversity on multiple ecosystem processes (22); (ii) mechanisms that catalyze the biodiversity-ecosystem relationships (23); (iii) links between multitrophic biodiversity and ecosystem functioning (24); (iv) incorporation of genetic, functional and structural diversity, in addition to species richness (25); (v) functional linkages among ecosystems in the form of matter, energy and organismal exchange (20); and (vi) linkages between biodiversity loss and policy (26). These studies have established relationships between biodiversity and ecological processes, including the implications of changes in environmental conditions for diversity components and exchange of matter/energy at different temporal and spatial scales (reviewed in 26). Furthermore, emerging knowledge has facilitated our understanding of the spatial and temporal patterns of human pressure on ecosystems. As such, they can provide the basis for policy design and implementation, development of strategies for conservation and management, with emphasis on governance, sustainable use and protection of ecosystems, including mitigation of environmental damage and biodiversity loss. Existing biodiversity models could be adopted and customized in representing biodiversity loss mechanisms in Afrotropical ecosystems to improve our understanding on biodiversity-ecosystem relationships and strengthen policy implementation in the region, if input parameters from biodiversity data become available.
In order to develop and implement effective policies for mitigating biodiversity loss, it is important to address the drivers, along with their associated causes, of ecosystem degradation. Some of the common drivers include: population growth, resource-use demand, socioeconomic development (27) and heavy reliance on natural resources for livelihood, especially in developing countries, including the continuing heavy international/ foreign resource extraction. Conservationists broadly summarize them as direct (habitat change, climate change, invasive species, overexploitation and pollution) and indirect (demographic and sociocultural, economic and technological, institutional and governance, conflicts and epidemics) drivers of ecosystem change (28,29). These direct and indirect drivers have a chronic impact in African ecosystems, while an additional uncertainty factor is the data deficiency on the status of biodiversity, owing to: (i) political instability in some countries that leads to inconsistent (or lack of) policies, resource over-exploitation, and habitat destruction; (ii) absence of effective intergovernmental agencies responsible for prioritizing continental policy-driven biodiversity actions; (iii) little support from governments on environmental management and biodiversity monitoring programs; and (iv) lack of standardization of biodiversity datasets and monitoring programs over time and space (30)(31)(32).
In this regard, Africa lags behind in many aspects of biodiversity studies due to data deficiency, including the ubiquitous knowledge gaps about all the major facets of taxonomic, ecological and physiographical diversity, in addition to the lack of established thresholds of environmental change that lead to biodiversity loss (13). Furthermore, insufficient financial and technical capacity when studying biodiversity loss impedes sound policy formulation and effective implementation of conservation and management practices. Very few studies and reviews focus on the interplay between biodiversity and ecosystem change in the continent, except for reports from international organizations, which tend to be generic, often with gaps in scientific evidence. Since natural resources are one of the pillars for socioeconomic development and a primary source of livelihood in the continent (33), the aim of this paper is to ignite the conversation on monitoring biodiversity loss in rapidly changing ecosystems in Africa. Our goal is to emphasize the need for data-driven biodiversity policy interventions and management implementation. Our thesis is that challenges in funding and lack of highly qualified personnel present fundamental hindrances to data acquisition and design for execution of quality scientific studies in the region, whereby we can evaluate the drivers of ecosystem change and biodiversity loss, effectively inform the policy-making process, and design appropriate restoration solutions.
Conceptual Framework
Drivers of ecosystem change and biodiversity loss are intricately connected with funding, research and governance ( Figure 1). Major direct and indirect drivers of ecosystem degradation have an impact on biodiversity (gene, species, functional groups, and community dynamics) and ecosystems (processes, structure, and function). Biodiversity and its components (which are profoundly understudied in Africa) are interlinked with ecosystem processes, structure and functions through mechanisms that facilitate and complement those processes. Consequently, ecosystem degradation leads to biodiversity loss, and biodiversity loss iteratively leads to ecosystem change ( Figure 1). From our perspective, the limited understanding of the mechanisms that shape the relationships between biodiversity and ecosystems are the primary concern in Africa. This knowledge gap is further exacerbated by the lack of institutional, infrastructural and human capacity, which in turn leads to poorly informed management interventions. The lack of political will and underfunding to monitor ecosystem change and biodiversity loss are critical for effective conservation and management, including the implementation of mitigation measures of ecosystem impairment and restoration of biodiversity in the region.
Direct impact
Indirect impact link one-way link both-way Africa harbors an enormous wealth of biodiversity, distributed across numerous environmental gradients. The continent straddles the equator, extending 37 0 N and 35 0 S; it has a great latitudinal range and enormous variety of climate types that shape its uniquely rich ecosystem diversity (34). The diverse range of terrestrial, aquatic inland and coastal ecosystems are also largely transboundary resources. From the north, the continent borders the Mediterranean Sea and extends to the expansive Sahara Desert before transitioning to tropical ecosystems with dense forests, intermixed by shrubland, woodland, grassland, montane and Afroalpine, bushland and thickets, arid and semi-arid land, followed by the Kalahari and Namib desert to the south, and finally, the Cape region with Mediterranean climate (Supplementary Table 1; 32). Major land use and land cover classifications with granular satellite images of 10 m resolution are conspicuously dominated by forested areas, shrubland and grassland within the Sub-Saharan Africa, deserts at the north and south, while agriculture dominates human activities throughout the continent (Figure 2a).
Ecosystems in Africa
Its Great Rift Valley, with extraordinary geographical features of numerous deep and spectacular gorges cutting into the margins of a plateau, is a source of many rivers and streams (35), flowing either into the inland lentic ecosystems or into the sea. The region also harbors the African Great Lakes that hold over 25% of the world's unfrozen freshwater (36,37) and >90% of Africa's total freshwater (38). Terrestrial and aquatic ecosystems in Africa also support numerous habitats with exclusive reservoirs of world's biodiversity, including eight of the world's 36 recognized biodiversity hot spots (39), host approximately one-quarter of the world's mammals and birds (40), have the second largest tropical rainforest with unmatched endemic species globally (41), in addition to aquatic inland and marine amphibians, reptiles and fish (42). Moreover, Key Biodiversity Areas are continuously being identified and mapped in the region for monitoring and conservation (43,44). The continent is rich in taxonomic and physiographic diversity, and displays greater connectivity from terrestrial to aquatic ecosystems that contributes to high functional diversity (45). Plant endemism peaks within Mediterranean habitats at the north and south of the continent (46) while vertebrate endemism peaks within the tropics, especially in the aquatic ecosystems within the African Great Lakes (47). Furthermore, it has numerous phytochorions within watersheds or wetlands (Supplementary Table 1; Figure 2b) with terrestrial and aquatic food web links from the highly diverse and rich biotic communities. Evidence of connectivity in ecosystems and biodiversity is clear in protected areas (48,49), but human activities leading to ecosystem degradation impair this connectivity. All the maps were generated with QGIS 3.26.3 software. The first map (a) was modified from Ersi Land cover-Living Atlas (https://livingatlas.arcgis.com/landcover/) by downloading satelite images from Sentinel-2 land use and land cover classification, and classifying the major land use/land cover. While the second map (b) by combining shapefiles and raster downloads for HydroRIVERS (https://www.hydrosheds.org/products/hydrorivers) for the major river basins in Africa, global protected areas (https://www.protectedplanet.net/en/search-areas?geo_type=site) and cliped protected areas in Africa, raster images from the Global Lakes and Wetland Database (https://www.worldwildlife.org/pages/global-lakes-and-wetlands-database) and finally, terrestrial ecoregions shapefiles (https://www.gislounge.com/terrestrial-ecoregions-gis-data/) used for demacating vegetation cover.
Biodiversity studies in Africa
Despite the numerous ecosystems in Africa, studies have shown that there is a paucity of quantitative information on biodiversity in many countries, include species, populations, distributions, offtake and threat status (Table 1; 31). In some countries, these datasets are unevenly available (50). For instance, a review of response from 44 African countries on the status of Ramsar sites during the 12 th Meeting of the Conference of Parties (COP12) in Uruguay in 2015, and COP13 in Dubai in 2018, revealed key challenges with biodiversity data that includes availability, accessibility, and usability, in addition to technical and financial capacity for data collection and management (31). A similar observation was made in other ecosystems in Africa, in addition to the widespread absence of credible science-policy interface to shape environmental management decisions (32,51). Some of the available data could not be accessed due to lack of agreeable data-sharing policies and lack of consensus on what to monitor, with different organizations and projects adopting diverse measurements (32), while data presentation and use are often influenced by donor conditions on sharing (31). Africa has therefore been ranked as last in terms of long-term ecological research amongst other continents that own regional and continental-scale monitoring networks (52). To make matters worse, many African countries are lacking even the rudimentary elements of conservation science, reflecting the fact that biodiversity conservation is still perceived a trivial theme in the national research agendas (53).
Case study of African Great Lakes Region.
Our studies confirmed the aforementioned assertions within the African Great Lakes region, where there is a dearth of basic information on diversity, distribution and population characteristics of riverine fish species in the Lake Victoria basin (54)(55). The inconsistent data collection, storage and use impedes quality research on biodiversity and hampers effective management of environmental changes, including evaluation of the riverine environment as refuge for the declining fish species populations within the Lake Victoria basin. In these studies, we collected data with field surveys and corroborated the detected trends with historical information from peerreviewed and grey literature; a process that took several years during compilation and cleaning to acquire reliable data. We have used data for preliminary studies on the ecological concept of size-spectrum with fish species among the rivers to monitor potential effects of the changing environment on communities and ecosystem functions (56). We have also assessed the ecological health of these rivers using fish assemblages and the concept of niche breadth from the compiled data (57). These studies are amongst the first published work using the ecological concept of size-spectrum and niche breadth for riverine fish species in Africa.
Our additional review on data availability from eleven countries within the African Great Lakes region revealed the need for harmonized long-term multi-lake monitoring of the seven African Great Lakes and their catchments. We observed some regular, but also irregular or rare monitoring in some catchments, mainly when sporadic funds or short-term projects became available (37). Our second review on training aquatic and environmental scientists in ten countries in this region observed only a handful of academic institutions with postgraduate programs in the disciplines, in addition to limited specialized human resources grappling with a multitude of socioeconomic challenges (36). These case studies reinforce the problem with biodiversity data deficiency, the need for long-term monitoring, and generally the dearth of reliable studies to inform decision making, as well as the need for empowerment of the institutional capacity to train experts able to conduct reliable research on biodiversity-ecosystem linkages and make recommendations to guide the implementation of biodiversity-conservation policies.
Challenges with Funding and Research
Monitoring biodiversity-ecosystem relationships within the diverse Afrotropical ecosystems is challenged by fundamental shortfalls in funding, which is the major impediment for the development of effective biodiversity conservation policies globally (58). A global ranking of 124 countries according to funding for biodiversity conservation, recorded 45 of the 54 African countries as underfunded (58). The limitations of funding and research in many African countries are further exacerbated by the low number of institutions and professionals in the continent. This hinders dissemination of relevant knowledge (59-61) on its diverse ecosystems, including the processes and mechanisms that maintain the biotic-abiotic interactions, sustain ecosystem functions and regulate degradation. The limited capacity of professionals from Africa to participate in designing research and submitting proposals that can win highly competitive funding as principal investigators, except through collaboration with researchers from developed countries (as co-investigators), impacts the flow of funding in biodiversity research and the capacity of that research to closely target the regional needs (62). Thus, funding agencies must commit to long-term investment in African scientists to break this cycle. Funding and research play central roles in knowledge co-creation (63)(64). Hiring skilled human resources, building technological and infrastructural capacity, conducting well-designed experiments using state-of-the-art methodologies, acquiring reliable data and producing quality publications, are requisite credentials for researchers to establish their reputation and obtain competitive funds (65). This creates a vexing cycle that hinders access to highly soughtafter grants and biases the understanding of biodiversity loss and conservation priorities in Africa. Studies have shown that decades of severe underfunding have prevented institutions from achieving their potential on biodiversity studies and conservation (66,67).
In-depth studies on ecosystem processes are therefore scarce. This includes empirical knowledge and simulations of nutrient biogeochemical cycles (68,69) to solidify our understanding on how additional nutrient loads would impact these ecosystems and species diversity. Topics of particular interest are the high endemism, energy flows within and among trophic levels, trophic transfer efficiency and tracing food pathways (using stable isotopes) to understand feeding habits and how ecosystem degradation impacts the exchange of matter and energy among organisms. We lack many fundamental pieces of knowledge to effectively parameterize simulation models of hydrological and biogeochemical processes that shape the exchanges of mass from watersheds to inland waters and/or marine ecosystems. Considering the connectivity among African ecosystems, the latter uncertainty constitutes an emerging imperative in biodiversity research, as the degradation and broader impact on community dynamics stretches far and wide (29).
However, there are successfully funded projects through collaborations with academic and research institutions from abroad to strengthen the local research capacity. Our recent review on environmental science programs in ten African countries reinforces the importance of these collaborations (36) which, in addition, create a global network of experts to provide mentorship in biodiversity studies. Nonetheless, collaborators from abroad merely play supportive role (36,59), and the research is often driven by donor objectives rather than the real priorities identified in scientific fora. Furthermore, international research and funding agencies are not within the governance of the host countries. Their agenda and priorities are sometimes set at international levels, therefore being disconnected from national scientific systems (59) and insufficient for detailed long-term monitoring ecosystem degradation and biodiversity loss. Funding for in-depth studies and long-term monitoring of ecosystem degradation and biodiversity loss remains a challenge, which cripples the capacity of academic and research institutions. As a result, mentoring professional scientists to formulate and conduct studies that link the heterogeneous ecosystems and biodiversity loss in Africa, including the processes, mechanisms and linkages of biodiversity and ecosystem function, is still an arduous task. This has led to incoherent research activities and inconsistent biodiversity databases, while the existing biodiversity monitoring initiatives are often based on short-term, poorly designed surveys, largely dependent on volunteer researchers or international partners, biased towards large animal species, and published in difficult-to-access outlets (30).
Drivers of Ecosystem Change and Biodiversity Loss
As a consequence of the aforementioned issues, there is a worrisome increase in the level of ecosystem degradation due to the surging need for natural resources triggered by global and regional demands for commodities and human population growth (70,71), which is currently more than 1 billion, with a growth rate of 2.3% per annum (72). The demand for forest products, through logging, fuelwood, clearance for settlement (73), land use and cover changes stemming from agricultural intensification (74) and urban development, overexploitation of biodiversity for consumption and illegal poaching of wildlife (75), pollution especially from nutrients, heavy metals and other toxic elements, of rivers, wetlands, lakes and marine ecosystems leading to eutrophication and toxicity have resulted in rapid ecosystem impairment and biodiversity loss. These demands on resource use have formed the basis for research into the drivers of ecosystem change and biodiversity loss in Africa, including climate change (76)(77)(78), land use and habitat change (79,80), invasive species (81,82), overexploitation of resources (83,84) and pollution (85,86). Further proposed mineral extractions can potentially pose serious threats for some of the most biodiverse areas in Africa (87). Given the time-lag between ecological degradation and its impact on biodiversity and human systems, there are increasing concerns over the lack of awareness of the negative implications of these accelerating trends, and the high likelihood for a late response when the ecosystem degradation will have reached an irreversible state.
We therefore emphasize the need for data-driven studies that are designed to link biodiversity with ecosystem degradation in Africa, and complement studies that focus either on drivers of ecosystem change or on biodiversity loss patterns. From our perspective, this is a critical research direction if we strive to effectively support the science-policy interface in the context of ecosystem restoration and conservation. The exploitation of these ecosystems has led to significant increases in provisioning services for socioeconomic development and livelihood, but at the expense of a range of other supporting (e.g., nutrient cycling), regulating (e.g., clean air and water) and cultural services (8,19), and further loss in biodiversity components, such as genetic diversity, functional diversity, and abundance and activity of organisms (88).
Efforts to establish Biodiversity database and access
There is an appreciable effort in some countries and also globally, to solve the problem of biodiversity data deficiency in Africa, including creating databases and making the data available and accessible (31). Some of these database and data sources are: 1) Albertine Rift Conservation Society Biodiversity Management Information System (ARBIMS: http://arbims.arcosnetwork.org/out.biodiversitydata.php) with biodiversity data on African Mountains, Great Lakes and Albertine Rift, with occurrence (presence-absence) data on species being compiled by individuals; 2) FishBase for Africa (http://www.fishbase.us/tools/region/FB4Africa/ FB4Africa.html) with some of the fish species found in Africa and their ecological and biological interactions; 3) Global Biodiversity Information Facility (http://www.gbif.org/) also with species occurrence data for some countries in Africa; 4) IUCN Red List on Threatened Species (http://www.iucnredlist.org/) and 5); WWF/ZSL Living Plant Index (https://www.livingplanetindex.org/). Some countries have also established national biodiversity data compilation centres, such as (i) South African National Biodiversity Institute (SANBI: https://www.sanbi.org/); (ii) Uganda's National Biodiversity Data Bank (NDBD: http://www.nbdb.mak.ac.ug/) hosted by Makerere University website; and (iii) Egyptian Environmental Affair Agency National Biodiversity Unit (https://www.cbd.int/doc/world/eg/eg-nr-01-en.pdf; but we could not trace the link to this website). These are great initiatives that recognize the challenges with biodiversity data in the region and make strides in championing solutions to the problem in Africa.
Conclusions
While there are many subjects of interest in biodiversity and an array of possibilities in the science-policy interface, the existing scientific knowledge is not adequate to inform the development of robust policies or even to articulate targets of biodiversity research in many African countries. The limited data reliability, accessibility, and (ultimately) usability represent an impediment to draw inference that informs decisions on ecosystem conservation and management. Mitigating biodiversity loss also requires understanding on how the drivers of ecosystem change impact community dynamics and demography, and thus fundamental knowledge of the community-ecosystem linkages. The problem of biodiversity loss is further exacerbated by a multitude of other factors including the surging demand for natural resources, population growth, and associated conflicts between resource use and conservation. Since many countries in Africa (about three quarters of the continent) are classified as least developed, research funding automatically emerges as a major imperative. Given that the international community has committed funding for biodiversity conservation in developing countries, we argue that it is critical to design scientifically sound and logistically sustainable monitoring programs to establish biodiversity benchmarks in Africa. In the same vein, our study underscores the importance of factoring in the biodiversity-ecosystem linkages, if we strive to improve our predictive capacity of future conditions in an everchanging world.
Figure 1 :
1Conceptual framework linking the drivers of ecosystem change and biodiversity loss with the need for funding and targeted quality research in Africa.
Figure 2 :
2Major land-use and land-cover classifications (a) and terrestrial and aquatic ecosystems connectivity in Africa (b).
Table 1 :
1Challenges with biodiversity studies in Africa Key challenges that includes data availability, accessibility, usability, quality, and financial and technical capacity for data collection, management and use.In some cases, data presentation and use are influenced by donors placing conditions on sharing.BIODIVERSITY RESEARCH NEEDS
AFRICAN COUNTRIES
DATA SOURCE
REFERENCE
Continentwide
Review on status of
Ramsar sites from 44
African countries
during COP12 and
COP13 in the years
2015 and 2018
respectively
Stephenson et al., 2020
Stephenson et al., 2021
Uneven availability of biodiversity data.
South-Sudan, Ethiopia, Kenya,
Uganda, Tanzania, Rwanda,
Burundi, Democratic Republic of
Congo, Malawi, Zambia,
Mozambique
Survey to local
conservation experts
in eleven (11)
countries working in
high conservation
values on monitoring
and capacity needs
Han et al., 2014
Data gaps include species, populations, distributions,
offtake, trade and threat status; habitat cover or
distribution; protected area coverage and management
effectiveness.
Lack of agreeable data-sharing policies.
Widespread absence of credible science-policy
interfaces.
Angola, Botswana,
Burkina Faso, Cameroon, Djibouti,
The Gambia, Ghana, Guinea
Bissau, Kenya, Malawi, Mali,
Mauritania, Morocco, Niger,
Senegal, South Africa, Tanzania,
Chad, Uganda, Zimbabwe, Somalia
and Egypt.
COP12 with more
than 40 stakeholders
from government,
Civil society
organization, United
Nation agencies and
delegates form 20
African states
Stephenson et al., 2017
Africa ranked last in-term of long-term ecological
research amongst other continents that own regional
and continental-scale monitoring networks.
Continentwide
Review of 1442
scientific publications
on ecosystem
monitoring and related
research from 1987 to
2014 mostly published
in English.
Yevide et al, 2016
Several countries lack research attention in
conservation science, reflecting the fact that research
is poorly aligned with biodiversity distribution and
conservation priorities.
Angola, Malawi, Rwanda, Burundi,
Eswatini, Somali, Djibouti, Eritrea,
Sudan, South Sudan, Central
African Republic, Chad, Niger,
Benin, Libya, Tunisia, Algeria,
Mauritania, Senegal, Guinea and
Western Sahara
Analyzed 2,553
articles published
between 2011-2015
Di Macros et al., 2017
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Supplementary Table 1: Biotic zones of Africa and their vegetation types (modified from Happold and Lock. Supplementary Table 1: Biotic zones of Africa and their vegetation types (modified from Happold and Lock, 2013)
Sub-Mediterranean semi-desert grassland and shrubland, to succulent semi-desert shrubland. Mediterranean Coastal Mediterranean sclerophyllous forestMediterranean Coastal Mediterranean sclerophyllous forest, Sub-Mediterranean semi-desert grassland and shrubland, to succulent semi-desert shrubland.
Sahara Arid Regs, hamadas, wadis, desert dunes with and without perennial vegetation, absolute desert, saharomontane vegetation and oases. Sahara Arid Regs, hamadas, wadis, desert dunes with and without perennial vegetation, absolute desert, saharomontane vegetation and oases.
Sahel Savanna Sahel semi-desert grassland and shrubland, acacia wooded grassland and deciduous bushland, edaphic grassland and herbaceous swamp and aquatic vegetation. Sahel Savanna Sahel semi-desert grassland and shrubland, acacia wooded grassland and deciduous bushland, edaphic grassland and herbaceous swamp and aquatic vegetation.
Sudan Savanna Sudanian undifferentiated woodland, islands of Isoberlinia, edaphic grassland, Acacia wooded grassland and edaphic grassland mosaic with broad-leaved trees. Sudan Savanna Sudanian undifferentiated woodland, islands of Isoberlinia, edaphic grassland, Acacia wooded grassland and edaphic grassland mosaic with broad-leaved trees.
Guinea Savanna Woodland, abundant Isoberlinia and edaphic grassland in Upper Nile with semi-aquatic vegetation. Guinea Savanna Woodland, abundant Isoberlinia and edaphic grassland in Upper Nile with semi-aquatic vegetation.
Northern Rainforest-Savanna Guinea-Congolia/Sudanian mosaic of lowland rainforest and secondary grassland. Eastern Rainforest-Savanna Lake Victoria mosaic of lowland rainforest and secondary grassland. Rainforest Guinea-Congolian lowland rainforest, lowland rainforest and swamp forest. Rainforest Guinea-Congolian lowland rainforest, lowland rainforest and swamp forest. Northern Rainforest-Savanna Guinea-Congolia/Sudanian mosaic of lowland rainforest and secondary grassland. Eastern Rainforest-Savanna Lake Victoria mosaic of lowland rainforest and secondary grassland.
Southern Rainforest-Savanna Guinea-Congolia/Zambezia mosaic of lowland rainforest and secondary grassland, Zambezian dry evergreen forest and secondary grassland, edaphic and secondary grassland on Kalahari sand and wetter Zambezian woodland and secondary grassland. Southern Rainforest-Savanna Guinea-Congolia/Zambezia mosaic of lowland rainforest and secondary grassland, Zambezian dry evergreen forest and secondary grassland, edaphic and secondary grassland on Kalahari sand and wetter Zambezian woodland and secondary grassland.
Afromontane undifferentiated montane vegetation, evergreen and semi-evergreen bushland and thicket (Ethiopian Highlands only) and Mediterranean montane forest and altimontane shrubland. Afromontane-Afroalpine, Afromontane-Afroalpine Afromontane undifferentiated montane vegetation, evergreen and semi-evergreen bushland and thicket (Ethiopian Highlands only) and Mediterranean montane forest and altimontane shrubland
semi-desert grassland, shrubland, Acacia-Commiphora deciduous bushland and thicket. Somalia-Masai Bushland Somalia-MasaiSomalia-Masai Bushland Somalia-Masai semi-desert grassland, shrubland, Acacia-Commiphora deciduous bushland and thicket.
Zambezian miombo woodland dominated by Brachystegia,Julbernardia and Isoberlinia, Colophospermum mopane woodland and scrub woodland, drier Zambezian miombo woodland dominated by Brachystegia and Julbernardia, North and South Zambezian undifferentiated woodland, dry deciduous forest and secondary grassland and edaphic and secondary grassland on Kalahari Sand. Zambezian Woodland, Wetter, Zambezian Woodland Wetter Zambezian miombo woodland dominated by Brachystegia,Julbernardia and Isoberlinia, Colophospermum mopane woodland and scrub woodland, drier Zambezian miombo woodland dominated by Brachystegia and Julbernardia, North and South Zambezian undifferentiated woodland, dry deciduous forest and secondary grassland and edaphic and secondary grassland on Kalahari Sand.
Arid Zambezian transition from undifferentiated woodland to Acacia deciduous bushland and wooded grassland, Kalahari Acacia wooded grassland and deciduous bushland, Bushy Karoo-Namib shrubland, Namib Desert, dwarf, succulent and Montane Karoo shrubland. South-West, South-West Arid Zambezian transition from undifferentiated woodland to Acacia deciduous bushland and wooded grassland, Kalahari Acacia wooded grassland and deciduous bushland, Bushy Karoo-Namib shrubland, Namib Desert, dwarf, succulent and Montane Karoo shrubland.
. Highveld Highveld, Highveld Highveld grassland.
Cape Cape shrubland (Fynbos) and bushy Karoo-Namib shrubland. South-West, South-West Cape Cape shrubland (Fynbos) and bushy Karoo-Namib shrubland
| sample_1208 | 0.5262 | arxiv | |
Avoiding methane emission rate underestimates when using the divergence method
Clayton Id
Roberts
Institute of Astronomy
University of Cambridge
Madingley RoadCB3 0HACambridgeUnited Kingdom
Rutger Ijzermans
Shell Global Solutions International B.V
Grasweg 311031 HWAmsterdamThe Netherlands
IDDavid Randell
Shell Global Solutions International B.V
Grasweg 311031 HWAmsterdamThe Netherlands
Matthew Jones
Shell Global Solutions International B.V
Grasweg 311031 HWAmsterdamThe Netherlands
IDPhilip Jonathan
Department of Mathematics and Statistics
Lancaster University
LA1 4YWLancasterUnited Kingdom
Shell Research Ltd
SE1 7NALondonUnited Kingdom
I D Kaisey Mandel
Institute of Astronomy
University of Cambridge
Madingley RoadCB3 0HACambridgeUnited Kingdom
Department of Pure Mathematics and Mathematical Statistics
Statistical Laboratory
University of Cambridge
Wilberforce RoadCB3 0WBCambridgeUnited Kingdom
The Alan Turing Institute
Euston RoadNW1 2DBLondonUnited Kingdom
IDBill Hirst
Atmospheric Monitoring Sciences
AmsterdamThe Netherlands
Id Oliver Shorttle
Institute of Astronomy
University of Cambridge
Madingley RoadCB3 0HACambridgeUnited Kingdom
Department of Earth Sciences
University of Cambridge
Downing StreetCB2 3EQCambridgeUnited Kingdom
Avoiding methane emission rate underestimates when using the divergence method
Methane is a powerful greenhouse gas, and a primary target for mitigating climate change in the short-term future due to its relatively short atmospheric lifetime and greater ability to trap heat in Earth's atmosphere compared to carbon dioxide. Top-down observations of atmospheric methane are possible via drone and aircraft surveys as well as satellites such as the TROPOspheric Monitoring Instrument (TROPOMI). Recent work has begun to apply the divergence method to produce regional methane emission rate estimates. Here we show that spatially incomplete observations of methane can produce negatively biased time-averaged regional emission rate estimates via the divergence method, but that this effect can be counteracted by adopting a procedure in which daily advective fluxes of methane are time-averaged before the divergence method is applied. Using such a procedure with TROPOMI methane observations, we calculate yearly Permian emission rates of 3.1, 2.4 and 2.7 million tonnes per year for the years 2019 through 2021. We also show that highly-resolved plumes of methane can have negatively biased estimated emission rates by the divergence method due to the presence of turbulent diffusion in the plume, but this is unlikely to affect regional methane emission budgets constructed from TROPOMI observations of methane. The results from this work are expected to provide useful guidance for future implementations of the divergence method for emission rate estimation from satellite data -be it for methane or other gaseous species in the atmosphere.
Introduction
Methane is a powerful greenhouse gas, with a far greater warming potential (84 times greater on a 20-year timescale) and shorter atmospheric lifetime (9 years instead of centuries) than carbon dioxide 1, 2 . These attributes make methane an attractive target for mitigating the short-term effects of climate change, and have been the focus of recent climate summits and global commitments towards emission reductions 3 . Nevertheless, in recent years, the rate of increase of atmospheric methane has itself increased. 4,5 . Roughly 30% of anthropogenic methane emissions are attributed to the fossil fuel industry 6,7 , making increased monitoring and accounting of emissions from this sector an important factor in meeting national commitments towards methane emission reductions.
Satellite observations are a powerful tool for monitoring atmospheric methane abundances 8 , with remote sensing of methane from space providing opportunities for repeated and unscheduled monitoring of emissions. The era of greenhouse gas observing satellites began with the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) 9 in 2003, and subsequent generations of satellites have given rise to instruments with ever increasing capabilities. The TROPOSpheric Monitoring Instrument (TROPOMI) provides daily global coverage of methane observations with an updated 5.5x7 km 2 pixel resolution 10 , whilst other instruments such as GHGSat provide intermittent, targeted methane observations down to 50x50 m 2 resolution 11 . Many greenhouse gas-observing satellites lack the spatial resolution calculate asset-level emissions, and so aircraft and drone surveys are used to bridge this gap. These instruments can image and estimate facility-level methane emission rates 12,13 , and such facility-level measurements can be used for reporting under the Oil & Gas Methane Partnership 2.0 (OGMP 2.0) framework. This is a multi-stakeholder initiative launched by UNEP and the Climate and Clean Air Coalition, aimed at improving the accuracy and transparency of methane emissions reporting in the oil and gas sector 14 . Recently, "top-down" methane emission estimates calculated from aircraft observations have been found to be in disagreement to "bottom-up" emission estimates reported from industrial activity 15,16 , and more work is required to reconcile these standards of reporting methane emissions.
There are a variety of methods for constructing top-down emission estimates from satellite observations of methane. Some analysis uses forward models of Gaussian plumes and Bayesian methods to estimate regional methane emission rates 17 . Bayesian methods require specifications of priors on spatial distributions of emission rates, which are sometimes constructed from bottom-up emission estimates. However, another method to estimate emissions using top-down observations is via the divergence method 18 . The divergence method for estimating the spatial distribution of methane emissions is attractive because it is entirely data-driven and does not rely on prior estimates of spatial emission distributions as extensively as Bayesian methods do. In the divergence method, the total sources and sinks of emission E are calculated via the emission equation
E = ∇ · F adv [kg m −2 s −1 ],(1)
where F adv is the advective flux of a quantity of interest (e.g., methane or other pollutants). Originally presented as a method for estimating the location and emission rates of sources of nitrogen dioxide, this methodology is now being used to estimate regional-level methane emission rates 19,20 .
It is important to make explicit some important simplifying assumptions that are currently intrinsic to this methodology. Firstly, plumes of any gas (including methane) propagate through the atmosphere not only by advection, but also molecular and turbulent diffusion [21][22][23] ; in atmospheric transport, turbulent diffusion is usually the dominant effect over molecular diffusion in practice. The emission equation E = ∇ · F adv that is central to many regional-level methane budget estimates does not take the effect of turbulent diffusion into account. Correcting for turbulent diffusion requires the usage of a modified emission equation
E = ∇ · F adv − F dif [kg m −2 s −1 ],(2)
where F dif is the turbulent diffusive flux of a quantity of interest. Secondly, regional methane emission rate estimates are often time-averaged. The linear property of the divergence operator means that time-averaged estimated emission rates could be calculated either by time-averaging daily estimated emission rates, or by taking the divergence of time-averaged daily fluxes.
To the best of our knowledge, no work has yet been done to examine the consequence of this choice of order of operations when the divergence method is applied to methane observations.
In this work, we derive analytical expressions for F dif , and generate synthetic simulated satellite observations of Gaussian plumes to examine under what physical scenarios it becomes important to include F dif in the emission equation. We find that when a plume of methane is relatively diffusive, methane emission estimates via the divergence method can become inaccurate if F dif is excluded from the divergence calculation (under certain conditions). In this case, the estimated emission rate of the source is underestimated, and the spatial distribution of emissions is incorrectly distributed. We also demonstrate that time-averaged emission estimates calculated from spatially incomplete observations may be inaccurate if care is not taken to use time-averaged fluxes in the emission equation (as opposed to taking the time-average of daily emission estimates via the divergence method). We compare the results of our synthetic study to a case study of the Permian basin, using TROPOMI observations of methane 24 . We find that it is unlikely that a regional methane emission budget calculation of the Permian via the divergence method would be negatively biased due to the effects of any turbulent diffusion. We do find though that the sparse nature of the TROPOMI methane data product results in negatively biased time-averaged methane emission rate estimates, in the case where the divergence method is used to calculate daily emission rate estimates which are then time-averaged to produce the time-averaged emission rate estimate. When using the divergence method in conjunction with spatially sparse observations, it is important to take the divergence of time-averaged daily fluxes to obtain a time-averaged emission estimate.
Results
Synthetic case study
We generate simulated satellite observations of ideal steady-state Gaussian plumes 21 resulting from isolated point sources with known emission rates, and use them in an investigative synthetic case study. These plumes are characterised by a known 2/17 emission rate Q true [kg s −1 ], wind speed w [m s −1 ], wind angle θ relative to the x-axis of the observation grid, and constant of turbulent diffusion K [m 2 s −1 ]. Simulated plume observations are generated via Eq. 3, which is derived in S1. Note that when we calculate grid cell values, we numerically spatially integrate Eq. 3 over the area of the grid cell, and so the results of our synthetic study are independent of grid cell resolution. This is important to bear in mind as real observational instruments will have pixel resolutions spanning from meter to kilometer scales. Fig. 1 shows some examples of how these parameters affect plume morphology. For our simulated observations, we use the divergence method to estimate the spatial emission field both with and without including the diffusive flux term in the emission equation. We find in our synthetic study that there are a variety of scenarios where the use of the divergence method results in negatively biased estimated emission rates, i.e., when turbulent diffusion is neglected in some cases, or when time-averaged estimated emission rates are calculated without time-averaging daily flux fields when daily observations are spatially incomplete. Fig. 2 demonstrates the application of the divergence method to a simulated satellite observation of a plume. We find that when estimating the emission field without including the turbulent diffusion term in the emission equation, emissions are incorrectly spatially distributed in the estimated emission field. Rather than estimating a single point of positive emission, we instead find that "arrowhead" shapes of positive emission are estimated, in conjunction with negative emissions (or sinks) downwind within the plume shadow. To obtain a total estimated emission rate Q est , we spatially integrate the estimated emission field within a circle of fixed radius centered on the source location. We find that the total estimated emission rate of the emission field is underestimated. When increasing the opening angle of a plume (which scales as a function of K/w), the total estimated emission rate decreases for a fixed radius of spatial integration over the estimated emission field. This demonstrates that the emission rates of "diffuse" plumes are poorly estimated when using the divergence method, relying solely on advective fluxes. To first order, the underestimation is proportional to K/w. It is important to note in our synthetic study that we measure estimated emission rates as percentages of the true emission rate, and so results are independent of the mass emission rate of the point source. For a real instrument, higher emission rates mean a higher measured signal-to-noise ratio.
Underestimating emission rates due to turbulent diffusion in the plume
The total area for spatial integration of the estimated emission field also influences Q est . In Fig. 3 we alter the radius r of the cirular area of integration for a single simulated observation, and find that increasing the radius of integration increases Q est , i.e., the total estimated emission rate is less negatively biased. Although emissions are incorrectly distributed in the estimated emission field, they are distributed such that that integrating the estimated emission field over a larger area improves the total estimated emission rate. Thus, we determine that in our procedure for estimating the emission rate of a plume, r and K/w are two independent parameters which determine the extent to which Q est is underestimated. In Fig. 4 we vary r and K/w over physically realistic values and examine how greatly Q est is underestimated for an ideal Gaussian plume resulting from a point source of emission. We find that in the most extreme cases, Q est can be underestimated by more than 40%.
In practice, different plume measurement methodologies will correspond to different parameter locations on Fig. 4, and have characteristic biases associated with them. We indicate three examples on the right hand edge of Fig. 4 of regions where certain instruments tend to lie. Global coverage satellites such as TROPOMI tend to have very large fields of view as well as lower pixel resolutions 9, 10, 25 . Regional emission budgets performed on the scale of tens of kilometers are unlikely to experience a high level of negatively biased emission estimates due to the lack of a diffusive term in the divergence method (e.g., see Sec. 2.2). More targeted satellites have higher pixel resolutions and are capable of imaging plumes on the scale of tens of meters 11 . Although such satellites have fields of view that can still exceed ten kilometers or more, it would still be possible (given the high pixel resolution) to spatially integrate estimated emission fields over small enough areas to experience the outlined negative bias of the uncorrected divergence method, an issue that could arise if attempting to spatially isolate one plume from another adjacent source. Lastly, plume imaging surveys based from aircraft or drones 12, 13 would likely have the smallest field of view and would consequently be most likely to experience negative biases in emission estimates if they were to use the divergence method for emission rate estimation.
The significance of diffusion on the accuracy of the divergence method can be seen most directly when a diffusive term is included in the emission equation, i.e., Eq. 6. Making this addition to the method, we show in Fig. 5 that when the expression for diffusive flux (as calculated by Eq. 7) is included in the emission equation, then the estimated emission field is correctly constrained to a point source (allowing some slight deviation due to numerical derivative effects). Q est is found precisely to equal Q true .
A caveat to the efficacy of including diffusive flux in the divergence method to restore accurate emission estimates is that it is in practice difficult to estimate the constant of turbulent diffusion K. In our synthetic study, it is possible to know and 3/17 choose the precisely correct value of K to calculate F dif , but for real data this is much harder to calculate. Based on a number of real methane plumes measured by GHGSat 26 , a typical value of K was determined to be highly variable and in the the range between 10 and 400 m 2 s −1 (see Sec. 4.4). Beirle et. al. (2019) 18 was the first study to showcase the divergence method for estimating emission rates, and used TROPOMI observations of nitrogen dioxide to estimate emission rates from cities and power plants. They pointed out that, due to the linear properties of the divergence operator, it was sensible to time-average daily fluxes of nitrogen dioxide first and then take the divergence of the time-averaged flux to obtain a time-averaged estimate of nitrogen dioxide emissions. Beirle et. al. (2019) outlined that this was a sensible procedure as the time-averaged nitrogen dioxide advective flux would have a smooth spatial distribution and thus allow for a more accurate calculation of spatial derivatives.
Miscalculating emission rates due to missing data
TROPOMI observations of methane differ significantly from that of nitrogen dioxide, in that the spatial coverage of the methane data product is much less complete than the nitrogen dioxide data product 27,28 . Fig. 6 demonstrates the problem this poses as we look to apply the divergence method to TROPOMI observations of methane; when we randomly mask 10% of the observational data of a single simulated plume, the corresponding emission field estimated via the divergence method is missing a significantly larger amount of spatial coverage, and dramatically underestimates the total emission rate. This is because the numerical methods for calculating spatial derivatives 29,30 (see Eqs. 9 and 10) require eight valid neighboring data points, and so any missing observational data is magnified into even more missing spatial coverage of the estimated emission field. Time-averaging observations prior to numerically calculating spatial derivatives, and choosing to describe average emission rates over time domains rather than at specific time points, hopefully allows a chance at circumnavigating the problem of truncated spatial observations. We next investigate two different methodologies for calculating time-averaged emission estimates using the divergence method: in the first (which we denote by E 1 ), we calculate daily estimates of emission fluxes and then temporally average them 19,20 , and in the second (which we denote by E 2 ), we temporally average daily advective fluxes of column density C and then take the divergence of the temporally averaged flux to obtain a timeaveraged estimated emission field 18 . In this section we do not correct the estimated emission fields of our simulated plumes for the effects of turbulent diffusion as we did in Sec. 2.1.1, and focus only on the differences between the E 1 and E 2 methodologies.
In Fig. 7 we simulate a time-averaged study of 30 steady-state Gaussian plumes. Plume parameters are left unvaried, and each of the 30 repeated simulated observations has a random 30% of its pixels masked. We then display the resulting estimated emission fields obtained via E 1 and E 2 , and find that the emission field of E 2 is spatially complete, whereas E 1 is still missing some spatial coverage. The total integrated emission rate of E 1 is also severely underestimated, but the total integrated emission rate of E 2 retrieves the correct time-averaged emission rate (apart from the slight negative bias due to the presence of diffusion in the plume, which was discussed in the previous section). Figures showing the difference in resulting estimated emission fields under non-static conditions are shown in the supplement.
We investigate how the difference in performance of the two methods varies as a function of amount of daily missing data, and when plume parameters are allowed to vary in time. These results are shown in Fig. 8. We find that as the amount of missing observational data increases, both methodologies underestimate the true average emission rate, but that method E 2 (i.e., averaging daily fluxes of C and taking the divergence once) allows for estimates that are far more robust against missing data. This holds true for both static and time-varying simulated plume observations, although the time-averaged estimated emission rates for the time-varying plumes have more variance than the static plumes. This simulation differs from realistic physical scenarios in that data is randomly masked in a physically uncorrelated manner (which would not be the case with cloud cover), but it nonetheless demonstrates that the way in which time-averaged emission estimates are calculated using the divergence method is not trivial. Additionally, Fig. 8 demonstrates that it is also possible to over-estimate the source emission rate, though this typically only occurs at a critical "turn over" point where the fraction of daily missing data begins to dominate over the number of repeated observations. Past this point, we find that estimated emission rates will only be underestimated as a consequence of spatially incomplete data, but the exact location of this critical value is highly dependant on the number of repeated observations and the spatial distribution of missing data.
Permian basin case study
The Permian basin is the largest oil and gas producing region in the United States, producing nearly 6,000 barrels of oil a day as of January 2023 33 . Due to its prominence and size the Permian is frequently a target of ground-based, airborne, and space-based campaigns monitoring methane emissions 34,35 . We grid three years of daily TROPOMI methane observations of the Permian basin (2019-2021) onto a 0.2 x 0.2 latitude-longitude grid using an area-weighted oversampling 36 and calculate yearly emission estimates. We use the TROPOMI Level 2 methane data product 24 , and reduce the TROPOMI-observed column average mixing In the first column we show yearly methane emission rate estimates for the Permian via E 2 , when we average over advective fluxes for the year and take the divergence to yield a time-averaged emission estimate. In the next column we show the same yearly emission rate estimate calculated via E 1 , where we calculate daily methane emission estimates and time-average them. In the penultimate column we show the difference of the total estimated emission rate between the two methodologies, when the estimated emission fields are only spatially integrated over the intersection of the two estimated emission fields. This is to examine whether the difference in the estimated emission rate is driven by differences in spatial coverage or not. Supplementary figures 4, 5, and 6 plot these estimated emission fields. Also shown in the last column is the average daily spatial coverage of the Permian basin by our regridded TROPOMI methane observations.
Year Table 3. Yearly estimates of methane emission from the Permian basin [Tg/year]. We present yearly estimates (calculated using both the E 1 and E 2 time-averaging methodologies), and compare results between when using the fourth-order central finite difference and the second-order central finite difference to calculate numerical derivatives. The second-order central finite-difference requires fewer valid neighbors to calculate derivatives, and so could potentially lessen the discrepancy between the results of the E 1 and E 2 methodologies. We find that for the year 2019 (which had the poorest average spatial coverage over the Permian by the TROPOMI methane data product), the difference between the yearly methane emission budgets estimated via E 1 and E 2 is slightly decreased, but the gap between the two is not bridged within error. Also shown in this table is the percentage area coverage of the Permian basin by the estimated emission field produced by the E 1 methodology. As expected, the percentage area coverage is improved by the usage of the second order central finite difference in calculating derivatives, and the greatest improvement is seen in the year 2019. However, this increase in spatial coverage of the estimated emission field is not sufficient alone in bridging the discrepancy of results produced by the E 1 and E 2 methodologies.
E 2 = ∇ · F adv t E 1 = ∇ · F adv t ∩ E 2 − E 1 Avg.
Year 4th order CFD 2nd order CFD ratios of methane to above-background column densities 20 . The 2019-2021 average methane enhancement over the Permian basin is shown in Fig. 9. Using ERA5 wind data from the European Centre for Medium-Range Weather Forecasts 37 , we calculate daily advective fluxes of methane, and then calculate yearly time-averaged methane emission maps of the Permian basin using both the E 1 and E 2 methodology. We state here again as a reminder: in the E 1 methodology, we use the divergence method to estimate daily emission fields, which are then time-averaged, and in the E 2 methodology, we first time-average daily advective fluxes methane, and use the divergence method to estimate the emission field from the time-averaged fluxes. The yearly estimated emission fields produced via the two methodologies are shown in the supplement, and the estimated emission fields produced via the two methodologies for the entire time period 2019-2021 is shown in Fig. 10. Our yearly total estimated methane emission rates for the Permian are shown in Tables 1 and 2. We find good agreement between our time averaging methodology E 2 and other Permian emission estimates from previous work, but find that the E 1 methodology (in which daily emission estimates for the Permian are time-averaged) significantly underestimates the time-averaged emission rates when compared to previous estimates in the literature. The difference in results between the two methodologies is likely due to the sparse daily spatial coverage of the TROPOMI methane data product over the Permian basin. For the years 2019-2021, the average daily coverage of our regridded TROPOMI observations of the Permian basin never exceeds 50% (Table 2). In Table 3, we examine whether the choice of order of central finite difference influences the results obtained when calculating time-averaged emission rate estimates for the Permian. Although the spatial coverage of the estimated emission field produced via E 1 improved by using the second order central finite difference to calculate derivatives instead of the fourth order central finite difference, we did not find any significant change in the total estimated emission rates.
E 1 E 1 % coverage * E 2 E 1 E 1 % coverage *E
We also investigate whether the difference in results between the E 1 and E 2 methodologies can be attributed purely to the difference in spatial coverage of their respective time-averaged estimated emission fields. In Table 2 we show the difference in total estimated emission rate between E 1 and E 2 for when we only spatially integrate over the intersection of their spatial coverages. In this scenario, any difference in total estimated emission rate is due to the change in order of operations between the two different methodologies, rather than the difference in spatial coverage obtained. We find that for the year 2019, the difference in average total estimated emission rate between E 1 and E 2 can potentially be explained entirely by the difference in spatial coverage of the estimated emission fields. This is shown in Fig. S4. However, for the years 2020 and 2021, the spatial coverages of the estimated emission field obtained via E 1 and E 2 are complete, and thus the difference in total estimated emission rates cannot be explained by a difference in spatial coverage. Increasing the spatial coverage of the region of interest by the methane data 31, 38 may close the gap in the results obtained between the two methods. We additionally calculate the percent change of our yearly estimated methane rates for the Permian when including the diffusive flux calculation of Eq. 8, and find in all cases that the total estimated emission rate is increased by less than a millionth of a percent when K = 400 m 2 s −1 , the maximum value for the constant of turbulent diffusion that we consider in this work. This is not unexpected given the results shown in Fig. 4, which suggests that integrating over large areas sufficiently corrects for any negative bias introduced by 6/17 neglecting turbulent diffusion in the divergence method.
Discussion
In this work, we examine the conditions under which the divergence method for estimating emission rates may prove to produce negatively biased results. Using a simulation study with synthetic satellite observations of ideal Gaussian plumes, we showed that highly-resolved, diffuse plumes may have negatively biased emission rates when their estimated emission fields are spatially integrated over narrow fields of view. Our simulation study suggests that this affect would only be of concern for observations obtained by high-resolution, narrow field of view methodologies, e.g., drones, or where high-resolution satellite data has clipped the area into which a plume extends. In contrast, our case study of the Permian basin with TROPOMI methane observations does not find that yearly estimated methane emission budgets are impacted by including even a high estimate of turbulent diffusion. In the future, as satellites become more capable of resolving individual plumes, it will become important to correct for turbulent diffusion when estimating the spatial distribution of emissions via the divergence method. Conditions where diffusion may be dominating over advection may also be identified by screening for very low wind speeds 20 .
We also examine two possible methodologies for calculating time-averaged emission estimates using the divergence method. Using simulated spatially incomplete plume observations, we find that time-averaging daily emission rate estimates produced via the divergence method will consistently underestimate the true average emission rate. We compare these results to an alternative methodology previously described for nitrogen dioxide observations 2 . By this method, daily advective fluxes are time-averaged, and the divergence is taken thereof in order to obtain a time-averaged emission estimate. We find in our synthetic study that this latter methodology yields robust emission estimates even in the face of spatially incomplete observations. We compare these two methodologies by constructing yearly methane emission budget estimates for the Permian basin for the years 2019-2021, using the TROPOMI Level 2 methane data product 24 . We find that these two methodologies do not produce congruent emission rate estimates, and that the latter methodology produces estimates in agreement with previous top-down estimates for methane emission in the Permian basin 17,20 . Methods and datasets exist that can augment the spatial coverage of the TROPOMI methane data product 31,38 , which in turn would augment the spatial coverage of the advective flux field of methane prior to the application of the divergence method. Spatial smoothing and interpolation could also be used to try and make the spatial coverage of the advective methane flux field more complete. In this work, we do not explore these avenues further, preferring to examine the differences between the E 1 and E 2 methodologies.
When using the divergence method for methane emission rate estimation in the Permian, we find areas bordering the Delaware and Midland basins that are estimated to have negative emission rates. We do not expect this to truly be the case. Even in the "perfect" case in our synthetic study when the point source of emission is correctly estimated (see Fig. 5, panel c), we still estimate some grid cells to have negative emission rates. In this case, this is an effect of the discretisation of the emission equations and the manner in which numerical derivatives are calculated over our grids. Therefore, in some areas, especially in the vicinity of large methane sources, the divergence method will return negative emissions. These are local artefacts; the area-integrated emissions remain positive both in our synthetic study and our case study of the Permian basin (and in this latter case, our results are in good agreement with previously estimated methane emission rates). Whilst the TROPOMI methane observations over the Permian can not be considered to be ideal plumes, it may be the case that the regions of negative estimated emission are analogous to those in the synthetic study, as we know that that they are bordering known regions of strong positive emission. Other work also demonstrates that some regions of negative emission estimated via the divergence method in the Permian can be related to changes in orogoraphy or surface albedo 20 . One could develop a model that prohibits the estimation of negative methane emissions in a Bayesian framework, though at this stage this would no longer purely be the "divergence method", which is driven entirely by the data and the principle of the conservation of mass.
We conclude that the divergence method for estimating methane emissions (as described in this work) would be best applied to regional analyses where the affects of turbulent diffusion are unlikely to dominate over the scale of advective methane fluxes. Whenever possible, spatially completely methane data products should be used. When using spatially incomplete datasets, it may be the case that taking the divergence of time-averaged advective fluxes of methane will produce more accurate methane emission rate estimates.
7/17 4 Methods and Data
Generating simulated satellite observations of plumes
For our synthetic studies we generate simulated top-down observations of ideal Gaussian plumes 21 via the equation
C (x, y, θ ) = Q 2 π w K (x cosθ + y sinθ ) exp − (y cosθ − x sinθ ) 2 w 4 K (x cosθ + y sinθ ) kg m −2 ,(3)
where Q is the point source emission rate [kg s], w is the wind speed [m s −1 ], K is the constant of turbulent diffusion [m 2 s −1 ], and θ is the wind angle relative to the x-axis (in the anti-clockwise direction). Eq. 3 is derived in S1 . There are a variety of assumptions that are fundamental to the ideal Guassian plume equation 21 , but most important of note here is that diffusion is assumed to be dominated by advection, and thus diffusion only takes place perpendicular to the wind vector characterised by w and θ .
Calculating emissions and flux terms
We calculate spatially varying estimated emission fields E using both simulated plume observations and the TROPOMI L2 methane data product. We calculate E via two different emission equations.
The first emission equation (commonly found in literature 18,20 ) is
E = ∇ · F adv kg m −2 s −1 ,(4)
where F adv [kg m −1 s −2 ] is the advective flux of some column density C. In the case of our synthetic plume observations, C is generated via Eq. 3. For TROPOMI observations of methane, we convert column-averaged mixing ratios to above-background column density enhancements 20 . F adv is then given by
F adv = C w [kg m −1 s −1 ],(5)
where w is a spatially varying wind vector with magnitude w and angle θ relative to the x-axis of our grid. For our synthetic studies we specify w and θ ourselves. For our work with TROPOMI observations of the Permian basin, we take w to be the ERA5 wind data on multiple pressure levels, temporally averaged daily over a wind history at 1700, 1800 and 1900 hours, and then averaged vertically to an altitude of 500m to account for changes in wind vector through the boundary layer 20 .
To examine the extent to which turbulent diffusion influences estimated emission rates via the divergence method, we also calculate E via a second emission equation
E = ∇ · F adv − F dif kg m −2 s −1 .(6)
F dif is the turbulent diffusive flux of some column density C, and for an ideal Guassian plume is given by
F dif = K ∂ C ∂ x sin 2 θ − ∂ C ∂ y cosθ sinθ e x + K ∂ C ∂ y cos 2 θ − ∂ C ∂ x sinθ cosθ e y [kg m −1 s −1 ],(7)
where θ is the wind angle relative to the x-axis of our grid. C is again either generated via Eq. 3 or calculated from TROPOMI satellite observations of methane. Eq. 7 is derived under the assumption that diffusion only takes perpendicular to the wind vector w. If, however, we choose to ignore this assumption (but still assume that K is constant in space), that we can work directly in the (x, y) grid and state that
F dif = K ∂ C ∂ x e x + K ∂ C ∂ y e y(8)
Eqs. 4, 5, 6, 7, and 8 are derived in S2.
8/17
We need to calculate spatial derivatives over a cartesian grid to fully obtain E in Eqs. 4 and 6. For first derivatives, we use the fourth-order central finite difference 29
∂ V ∂ p | p=i = V | p=i−2 − 8V | p=i−1 + 8V | p=i+1 −V | p=i+2 12 d (9)
where V is a spatially varying quantity and d is the grid spacing in coordinate p. This numerical recipe is commonly used for emission estimates via the divergence method 18,20 . For second derivatives, we use the fourth order discretization 30
∂ 2 V ∂ p 2 | p=i = − 1 12 V | p=i−2 + 4 3 V | p=i−1 − 5 2 V | p=i + 4 3 V | p=i+1 − 1 12 V | p=i+2 d 2 .(10)
Calculating time-averaged emission rates
We calculate time-averaged estimated emission fields using two methodologies. In the first (denoted by E 1 ), we calculate daily estimated emission fields and time average them to obtain E 1 . In the second methodology (denoted by E 2 ), we time-average daily fluxes of C, and take the divergence of the time-averaged flux to obtain E 2 . With spatially complete observations of C over an entire time period, the two methods yield identical results, but for TROPOMI observations of methane, data is often spatially masked due to cloud cover and albedo effects. Detailed equations describing these two methodologies is given is S4.
Estimating the constant of turbulent diffusion K
It is in practice difficult to estimate constants of turbulent diffusion. If K is assumed to be constant in space and time, then the standard deviation "width" of a Gaussian plume can be described via
σ 2 = 2 K x u [m 2 ],(11)
where σ is the width of the plume [m], x is the downwind distance in the plume [m], u is the wind speed [m s −1 ] and K is the constant of turbulent diffusion [m 2 s −1 ] 21, 39 . We take multiple GHGSat scenes of isolated methane plumes 26 and measure values of σ at multiple downwind locations within each plume. We then fit a linear function to σ 2 against x for each plume using the method of least squares. The slope of the fitted function yields 2 K/u, and thus K can be determined as u is known for each scene. We determine using these plumes that K can vary between 10 and 400 m 2 s −1 . The estimated emission field of the plume using the divergence method and emission equation E = ∇ · F adv . As the plume in a was constructed using a point source of positive emission located at the origin, we can see in b that the estimated emission field has an incorrect spatial distribution. "Positive" emissions are incorrectly distributed in a horseshoe-shaped pattern around the origin, and "negative" emissions (or sinks) downwind in the shadow of the plume. When the estimated emission field is integrated over a circular region of radius r = 500 m centered on the origin, the total emission rate is slightly underestimated. For a fixed r and true point source emission rate Q true , the total estimated emission rate Q est will be underestimated to a greater extent if K/w is increased. When K/w increases for the plume, the plume becomes more "diffuse", and the emission equation E = ∇ · F adv becomes less able to explain the resulting column density as arising from a point source of emission. The estimated emission field using the divergence method, integrating over a circular area of radius r = 250 m to obtain the total estimated emission rate Q est . c The same estimated emission field as in b, this time integrated over a circular region with r = 500 m to obtain Q est . As r increases, Q est is underestimated to a lesser extent.
Figure 4.
A contour plot demonstrating the extent to which a plume's emission rate will be underestimated as a function of radius of integration r and K/w, the ratio of the constant of turbulent diffusion to the wind speed. Shown on the right had side of the plot are general regions where certain observing methodologies would lie on this spatial scale. The range of values of K/w (i.e., the x-axis) are chosen to represent a range of physically realistic values, estimated from high-resolution GHGSat scenes containing methane plumes. Global coverage satellites like TROPOMI tend to have larger pixel sizes and large fields of view, and hence are less likely to be affected by the negative bias. Targeted satellites can have narrower fields of view on the order of km scales, but due to their higher pixel resolutions can still image plumes on the scales of hundreds of meters. Consequently, these instruments may be affected by the negative bias of estimated emission rates, depending on how they are used. Surveys conducted via drone or plane may be especially susceptible to this bias if the divergence method is used to estimate emissions.
Figure 5.
A simulated column-integrated Gaussian plume, and resulting estimated emission fields via the divergence method. a A simulated observation of a plume. b The emission field of the plume estimated via the divergence method, using the emission equation E = ∇ · F adv . c The emission field of the plume estimated via the divergence method, using the emission equation E = ∇ · F adv − F dif . The term F dif is calculated according to Eq. 7. The emission field in c is now correctly estimated as a point source, with some small perturbations due to the numerical derivative. The correct total estimated emission rate Q est is now obtained. The point source of emission is located at the origin with actual emission rate Q true = 10 kg s −1 . 10% of the pixels in a are randomly masked to simulate the effect of poor data or otherwise unavailable observations, as is often the case for satellite observations of methane column density. b The resulting estimated emission field for the plume observation in a, obtained using the divergence method and emission equation E = ∇ · F adv . Our algorithm uses the fourth-order central finite difference to calculate numerical gradients 29 , which means that every unavailable pixel in a results in a 4x4 cross of pixels in b where we are unable to calculate E. Consequently, any amount of missing data in a quickly becomes a large amount of missing coverage in b. Integrating over the available pixels in b yields a severely underestimated estimated emission rate Q est . Scaling up Q est by the fraction of missing coverage yields a scaled total emission estimate of 16.2 kg s −1 , and does not correct the underestimation. In Fig. S7 in the supplement we demonstrate that this scaling procedure is not sufficient to correct for the problem of missing data, and can actually significantly overestimate the total emission rate (as is the case in this particular example), depending on the fraction of daily missing data and number of repeated observations that go into the time-averaged calculation. In all other estimates of total emission rate in this study, we quote "unscaled" results, i.e., the answer obtained by spatially integrating the estimated emission field over available grid cell values. It is also important to note that individual or time-averaged emission fields estimated via the divergence method in our synthetic study will vary depending on the spatial distribution of missing data, which is a random process. We do not cherry pick particular realisations of spatial distribution for missing data, and examine the variance that is inherent to this random process in Fig. 8. b Estimated emission field when daily advective fluxes are averaged, with the divergence taken thereof to obtain the estimated emission field. Although the extended three-year time period means that complete spatial coverage is achieved for all the basins, the intermittent missing data on a daily basis means that the methodology of E 1 estimates a significantly lower emission rate than the methodology of E 2 . We find the three-year estimated emission fields E 1 and E 2 to be correlated with r = 0.87 .
Figure 1 .
1Simulated column-integrated ideal Gaussian plumes. All the plumes shown have the same emission rate of Q true = 10 kg s −1 and wind angle θ = 45 degrees. a Simulated plume observation with w = 8 m s −1 and K = 40 m 2 s −1 . b Same simulated observation as in a, this time with doubled K. c As in a, this time with doubled K and doubled w. Note that panels a and b are plotted with the same colorscale with the colorbar shown on the left hand side, and that panel c is plotted with the colorbar on the right hand side. The simulated plume in b has a wider opening angle than in a due to the increased ratio of K to w. The plume in c has the same opening angle as the plume in a because K/w = 5 m for both plumes. However, the column density of the plume in c is half that of the column density in a, because according to Eq. 3, column density scales as ∼ (K w) −1/2 .
Figure 2 .
2a A simulated column-integrated Gaussian plume, with wind angle θ = 45 degrees and other parameters as indicated on the plot. b
Figure 3 .
3a A simulated column-integrated Gaussian plume. b
Figure 6 .
6a A simulated observation of a plume with wind angle θ = 45 degrees, wind speed w = 5 m s −1 , and K = 60 m 2 s −1 .
Figure 7 .
7a A time-averaged observation of 30 static plumes with constant plume parameters. Each individual plume has a random 30% of its pixels masked (similarly to panel a inFig. 6). b The resultant average estimated emission field, constructed by time-averaging the estimated emission fields of each of the 30 individual plumes. c The average estimated emission field obtained by first time-averaging all the advective fluxes of the 30 individual plumes, and then taking the divergence of the time-averaged fluxes. The estimated emission field in c is much more resilient to the missing data, and provides a much more accurate estimate of the average emission rate than in b.
Figure 8 .
8Underestimation of time-averaged estimated emission rate, plotted as a function of the percentage of observational data present for each individual plume that goes into into the time-averaged estimation. In a, each time-averaged calculation uses 30 individual plumes, each one static with constant wind speed, angle, point source location and emission rate, etc. Each of the 30 simulated observations differs only in the spatial distribution of the masked pixels. In b, each time-averaged calculated uses 30 individual plumes, but the wind speed, wind angle, and source location are randomised. Each of the 30 simulated observations then have the same percentage of pixels randomly masked. This scenario represents a higher degree of complexity, where time-invariant assumptions about sources of emission no longer hold. We find that for both scenarios, it is better to time-average advective fluxes and take the divergence once, as opposed to time-averaging individually estimated emission fields (from the perspective of accurate emission flux estimation).
Figure 9 .
9Average methane enhancement over the Permian basin for the years 2019, 2020, and 2021 as observed by TROPOMI. a The Delaware basin. b The Central basin. c The Midland basin. d The Ozana Arch basin. e The Val Verda basin. Basin boundaries taken from the Energy Information Administration.
Figure 10 .
10Estimated emission fields for the five Permian subbasins for three years of observations, 2019-2021. a Estimated emission field obtained when daily estimated emission fields are averaged.
Table 1 .
1Estimates of Permian methane emission rates [Tg/year]. We compare our yearly estimates via the E 2 methodology (where daily methane fluxes are averaged) to those in other literature and find good agreement. Uncertainties on our time-averaged emission estimates are calculated via the algebraic propagation of the daily variance of advective flux of methane at each grid cell. This methodology is described in supplementary section S4. Year This work Veefkind et. al. 2023 * Schneising et. al. 2020 || Liu et. al. 2021 Zhang et. al. 2020 + Calculated using TROPOMI methane mixing ratios from the Weighting Function Modified Differential Optical Absorption Spectroscopy (WFM-DOAS) algorithm version 1.5 31 . 1σ uncertainty of 25%. + Date range for this paper was March 2018 -March 2019. || Value taken from Veefkind et. al. 2023 20 , i.e., calculated using the methods of Schneising et. al. 2020 32 , but using the same data as Veefkind 2023 20 .2019 3.1 ± 0.7 3.0
2.9 ± 1.6
3.1 (2.8, 3.8)
2.7 ± 0.5
2020 2.4 ± 0.6 2.8
2.3 ± 1.7
-
-
2021 2.7 ± 0.5 -
-
-
-
*
Table 2 .
2Comparison of yearly methane emission rate estimates [Tg/year] for the Permian when using the two different time-averaging methodologies.
This is average percentage coverage of the Permian basin by the TROPOMI Level 2 methane data product for each day within the given year. This is not the percentage coverage of the Permian basin by the time-averaged estimated emission field for the year.Daily Coverage *
2019 3.06 ± 0.66
1.45 ± 0.31
0.31 ± 0.57 29.37 %
2020 2.39 ± 0.55
1.25 ± 0.30
1.16 ± 0.62 37.68 %
2021 2.67 ± 0.54
1.75 ± 0.26
0.92 ± 0.60 41.15 %
*
This is the percentage coverage of the Permian basin of the time-averaged estimated emission field for this year, and not the average daily coverage of the Permian basin for the year by the methane data product.2
2019
1.45 ± 0.31
73.29%
3.06 ± 0.66
1.84 ± 0.26
89.53%
3.10 ± 0.49
2020
1.25 ± 0.30
98.19%
2.39 ± 0.55
1.20 ± 0.22
100%
2.37 ± 0.41
2021
1.75 ± 0.26
98.92%
2.67 ± 0.54
1.63 ± 0.20
99.64%
2.61 ± 0.41
*
AcknowledgementsC R acknowledges financial support from Shell Research Ltd through the Cambridge Centre for Doctoral Training in Data Intensive Science grant number ST/P006787/1. For the purpose of open access, C R has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. C R thanks Dr. J P Veefkind at TU Delft for insightful discussion and advice.Author contributionsC R retrieved all data, wrote all code and conducted the analysis of this work. O S and D R supervised the project. R I guided the analysis. M J, P J, K M, and B H contributed discussions of the data, satellites and meteorological context. All authors reviewed the manuscript.Conflict of interestWe report no competing interests.
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| sample_1229 | 0.6344 | arxiv | |
A Universal Hurricane Frequency Function
December 28, 2009
Robert Ehrlich rehrlich@gmu.edu
Physics & Astronomy Department
George Mason University
FairfaxVA
George Mason University
22030FairfaxVA
A Universal Hurricane Frequency Function
December 28, 2009_ Corresponding author address:
Evidence is provided that the global distribution of tropical hurricanes is principally determined by a universal function H of a single variable z that in turn is expressible in terms of the local sea surface temperature and latitude. The data-driven model presented here carries stark implications for the large increased numbers of hurricanes which it 2 predicts for a warmer world. Moreover, the rise in recent decades in the numbers of hurricanes in the Atlantic, but not the Pacific basin, is shown to have a simple explanation in terms of the specific form of H(z), which yields larger percentage increases when a fixed increase in sea surface temperature occurs at higher latitudes and lower temperatures.
3
Introduction
There are numerous factors that either promote or inhibit the formation of hurricanes or tropical storms, and it is well-known that two of them have special significance: the sea surface temperature SST (or simply T) and the latitude at the time and place of storm formation. The importance of latitude is that it governs the strength of the Coriolis Effect, a principal factor in creating some initial vorticity, while the SST is the source of an updraft of air that can create a tropical low. Here, we assert more specifically that the probability density of a hurricane or tropical storm forming can be expressed in terms of a simple mathematical function of those two variables, ) , ( T H . Alternatively, we can even write H in terms of a single combined variable | | sin ) (
2 / 1 0 T T z
, where T is the SST, T 0 is a threshold value of 25.5 0 C, and is the latitude. The functional form of H(z) most consistent with the data is found to be a simple power law, H(z) = Cz n , where C = 0.00073, and n = 3.5+0.5, for most regions of the globe. This result appears to be independent of time, and location, with the exception of those regional departures.
The study reported here rests on four key assumptions.
a. Existence
There exists a probability function H which describes whether a hurricane (also referred to as a cyclone or typhoon) forms. Furthermore, we assume that H depends on numerous variables, of which only the SST and the latitude play a universal role, with the other ``secondary" variables, being restricted in time or space.
b. Secondary variables
The secondary variables influencing H do so in a way that simply multiplies it by a constant factor that is regionally and temporally limited, and can be explained in terms of previously studied regional or oscillatory phenomena that enhance the value of H by a specific factor over that spatial or temporal region.
c. Data-driven
The function H can be found using the data on recorded hurricanes, without requiring a fundamental understanding of the basic physics describing exactly how a hurricane forms. This latter subject is one of current research interest, and the clue offered by the specific functional form of H presented here may advance that search for understanding.
Since the function H is justified by appealing to data rather than fundamental theory, the result is a model rather than a theory.
d. Validation
Given a specific form of H derived from the data, we can test the model by crosschecking it for consistency using the data, and more importantly, by seeing whether future hurricane data agrees with the model. 5
Methods
This work has relied on the data sets maintained by NOAA for the Atlantic and Eastern Tropical storms can be thought of as heat engines which derive their energy from the warm surface temperature of the ocean --or more precisely the temperature difference between the warm ocean and the much lower temperature at high altitude in the 6 atmosphere, which can represent a differential of around 100 0 C. It has been observed that tropical storms do not arise unless the SST, T, exceeds some threshold value T 0 cited in various sources as being 26 or 27 0 C. The other key variable in storm formation besides SST is the latitude, which is important because the horizontal component of the Coriolis force varies as its sine. The Coriolis force produces some initial vorticity that helps the storm self-organize. Thus, tropical storms do not form very close to the equator, and they have opposite senses of rotation in the two hemispheres.
In searching for a function H, we make use of the above well-known aspects of tropical storm formation, and hence assume that the relevant variables entering the distribution H involve the quantities 0 T T and sin . Since it is much easier searching an unknown function of a single variable than one involving two variables, we divide the search process into two steps: first, finding a single combined variable z expressed in terms of 0 T T and sin and second finding an appropriate functional form of z that best fits the data. One plausible combination of the variables when because we want the resulting H(z) generated using the data themselves to satisfy these six requirements:
0 0 T T is | | sin ) ( 0 b a T T z ,
a. Threshold H (z) must have the correct threshold behavior. This requirement is guaranteed by our choice of z for all a and b, as long as H(z) vanishes when z approaches zero.
b. Symmetry
H (z) must be a symmetrical function between the hemispheres even though the actual numbers of storms is not symmetric.
c. Monotonicity
H (z) must be a monotonic function of z since we expect H to increase continually as either 0 T T or increasealthough we cannot rule out a priori the possibility that it levels off at some saturation value for large z.
d. Uniformity
H (z) must have the same functional form in each basin across the globe.
e. Normalization
H(z) ideally should also have the same normalization in each basin, or if not, the variations should be explainable in terms of known regional phenomena.
f. Zeroes
H(z) must not predict storms occurring in any regions of the globe where none are observed, e.g., in the South Atlantic.
8
Let us now explain exactly how H(z) is deduced from the data themselves. The point of origin of each recorded storm in the data base places it in a specific latitude-longitude cell (taken here to be 4 x 4 degrees), and since the time of occurrence of that storm is known, we can use the SST-record to find the T in that cell when the storm formed. Given a particular trial definition relating z to T and , we can then compute the z-value associated with each storm. The z-values are binned, and we simply count the number of storms N j in the jth bin between z j and z j+1 . We then use the SST-record to obtain T for a given month for each latitude-longitude cell to find the number of months during the 47year record from 1960-2007 that a given cell had a temperature T. Finally combining that T with the values of each cell, we find the number of months M j that cells in a given geographic basin (such as the Atlantic) had a specific binned z-value, z j . The computed value of H for that z j simply equals N j /M j , which represents the observed number of storms per month in 4x4 degree latitude-longitude cells for a given z. Since these numbers are always less than one, it is more appropriate to think of them as the probability of having a storm per month. Once we have deduced from the data a set of H-values with associated uncertainties (discussed later), we can proceed to find the functional form of H based on a best fit to the data-derived values. Given the fairly stringent requirements on the form of H(z) discussed earlier, the search for an H(z) that fits the data is fairly easy, given any trial choice of a and b used to define the variable z.
9
For example, we have found that the simplest choice:
| | sin ) ( 0 T T z
is found to give poor results, while the choice:
| | sin ) ( 2 / 1 0 T T z
, gives good ones as we shall see in the next section. Based on chi square for the Asian Pacific basin the best fitting exponent
b in | | sin ) ( 0 b a T T z
is actually b=0.49 +0.01.) One interesting property of our
choice of | | sin ) ( 0 b a T T z
is that it yields a common temperature threshold T 0 for all latitudes, which may seem surprising. Other possible choices such as
| | sin ) ( 0 b a c T T z
would not have this feature, but they would introduce one more free parameter, and would imply that H(z) is no longer separable into functions of T and . Were our choice not found to yield a good fit to the data, one would need to explore such more complex definitions of z.
Results
In order to test how well the data from various regions of the world agree with a power law in z, i.e., | | sin
) ( ) ( 2 / 0 n n n T T Cz z H
, we have relied heavily on the data for the Asian Pacific basin. These data constrain H(z) far more than Atlantic data, since (a)
the Asian Pacific basin includes over five times as many storms as the Atlantic basin, (b) it includes storms over a larger range of latitudes (31 bins in z versus only 17 for Atlantic data), and (c) the Asian Pacific includes appreciable numbers of storms in both hemispheres, whereas fewer than 1% of Atlantic storms are in the Southern Hemisphere.
We show in fig. 1 Before discussing the quality of fit for data in the other hurricane basins, we digress to consider the size of the error bars used in fig.1, which directly affects the quality of the fits.
a. Size of Uncertainties
Although one often only displays error bars on the dependent variable only, here the independent variable z also has a significant uncertainty that must be taken into account.
T T z
, we see that because the data is binned in 4 by 4 degree bins and also in increments of 0.25 0 C in T, we need to use an uncertainty (due to binning) of
0 2 and C T 0 125 . 0
. When these errors are propagated and added in quadrature to find the uncertainty in z using representative values of T and for storms, we find that 15 . 0 z .
11
Finally, since the quantity H(z)/z n should be a constant if H(z) satisfies a z n power law, we may use standard error propagation methods to find the variance in H(z)/z n by combining the separate uncertainties in z and H according to:
2 2 1 2 n n z H z z nH
Note that it is this resultant uncertainty that is used to compute chi square under the requirement that H(z)/z n remains constant, and thus:
2 2 2 ) ( 1 C z z H n b.
The Other Hurricane Basins
Let us now consider how well the data from other basins fits H(z), starting with the Eastern Pacific, principally the region off the Southern coast of Mexico --a region of very frequent storms. This data (the filled triangles in fig. 2) appears to be at odds with what was seen in the Western (Asian) Pacific basin in two important respects. First, although most of the data again lies on a z 3.5 power law (upper) curve, its normalization is 3.6 times higher than for the Western Pacific data. Second, three data points with the largest z-values lie on the lower curve having the original normalization shown for fig. 1.
As it happens the Easter Pacific is one area significantly affected by the Madden-Julian
Oscillation (MJO). The MJO is a large-scale quasi-periodic modulation of tropical winds that travels eastward from Asia to America. It has been previously shown that hurricane activity in the Eastern Pacific is around four times more likely during the phase of the 12 oscillation associated with ascending rather than descending wind flowssee Maloney (2000). Furthermore, the MJO oscillation leads to a significant modulation of the SST by around 0.5 0 C during the cycle, with the phase of the increased hurricane activity being associated with a reduction in SSTsee i.e., no factor of 3.6 multiplier. Thus, the data from all portions of the globe having significant numbers of hurricanes are consistent with this same functional form, and even the same normalization, provided one includes a factor of 3.6 enhancement in those regions subject to constant or quasi periodic influences that have been found previously to increase hurricane formation. Furthermore, the function H(z) does not predict any storms should occur in regions of the globe where none are found.
c. Temporal Trends
The results presented until now all deal with the spatial distribution of hurricanes, and the function H(z) was deduced with no direct reference to temporal variations --except through the correlation between local SST and time. The model can, however, be used to predict temporal variations based on the SST of each latitude-longitude bin at any given time. The procedure is to sum the fitted H(z) over all cells with a given z for that particular time. Therefore, the model (if correct) should agree with the observed temporal variations in numbers of storms over some extended time period. In what follows, we make these comparisons with the data three different ways. One comparison (figs. 3, and 4), shows the numbers of hurricanes predicted to occur each month of the year (averaged over the period 1960-2007) by the model with those actually observed in three particular basins: the North Asian Pacific, the Southern Hemisphere, and the combined Atlantic and Eastern Pacific basins. In most cases the agreement is fairly good, with the Southern Hemisphere probably being the worst. It should be noted that the horizontal error bars extend 50% beyond the half-month associated with the bin width.
The reason for increasing these error bars is that it has been found that the process of hurricane genesis from some initial disturbance has a tendency to cluster in time sometimes over a period of several weeks. Gray (1979). Since we want to associate SST with the very start of the process, not the observed first point on a hurricane track, we therefore add an extra + 1 week uncertainty to the horizontal error bars. observed percentage increases were identical, the data points should lie on a line through the origin with unit slope. Despite the large error bars, it is reassuring that the best fit straight line passing through the origin has a slope 1.25 + 0.15 that is only slightly farther from 1.0 than one standard deviation. In fact the chi square for a line with unit slope (shown dotted) is 15.5, giving an acceptable probability of 26%.
What constitutes a test of the model?
As previously noted, all three types of time trend comparisons discussed above did not factor into the original selection of H(z) which relied on fitting data that was averaged over time, temperature and latitude for any given z-value, and hence there was no a priori guarantee that good fits to the temporal trends could be assured, or even that the data would be describable using a single variable z. Nevertheless, the good temporal trend fits cannot really be said to validate the model, because for any given \phi, the time and temperature are strongly correlated variables. On the other hand, even if the model is viewed as merely a data-fitting exercise, the finding of a function of a single variable that fits the data reasonably well could have great utility, should the model continue to describe the distribution and numbers of hurricanes in the coming years, as global temperatures continue to rise. The true test of the model therefore will come if the numbers of hurricanes in various basins increase in the manner predicted by the model.
In particular, one should be able to see the upturn in the Asian Pacific region seen in the model but not yet in the data. Failure to see any such increase in perhaps three to five years of further rising SST's would be fatal for the model. It has been shown by others that the trend in Atlantic hurricanes correlates well with mean SST's going as far back as 1850 --see Mann (2007), but the new element here is that of a universal function of local SST (at the time of hurricane formation) that fits the data world-wide, with regional adjustments in normalization. For example, our model offers a simple explanation why with warmer SST temperatures in recent decades, we have witnessed a significant rise in the number of Atlantic hurricanes, but very little if any rise in Pacific hurricanes --an inconsistency which has led some researchers to a (probably false) conclusion that SST is not that important in determining how often hurricanes form. The model explains the apparent inconsistency, because in comparison to the Western Pacific, much of the region showing the highest percentage increases in storms in the Atlantic basin occurs in cells at higher latitudes, where SST's are cooler.
For a given increment in temperature T , the function H(z)=Cz 3.5 produces a much larger percentage increase for lower temperatures (above T 0 than for higher ones that are further from the 25.5 0 C threshold.
Implications
This is not a paper about global warming, but the implications for a warmer world are stark. While it has previously been shown that destructive potential of hurricanes is likely to increase in a warmer worldsee: Emanuel (2005), earlier model predictions on the numbers of hurricanes have been highly inconsistent, with many models even suggesting their numbers might decrease, even as they become more destructivesee:. Oouchi (2006) and . If our results stand the test of time, they imply not only that the numbers of hurricanes will increase as SST rises, but they will do so in proportion to the 3.5 power of the temperature excess above 25.5 0 C for any given location. Thus, consider for example a location where the temperature in a given month is 27.5 0 C, or two degrees above the 25.5 0 C threshold. An average 2 0 C rise in the temperature from global warming during that month would increase the numbers of
imagine other possible choices. The second part of the search for the form of the function can be done visually by trial and error (for any given trial values of a and b)
Maloney (2001} These preceding findings can help explain the otherwise anomalous results of fig.2. Given that most storms in the Eastern Pacific occur in a fairly narrow range of latitudes off the Southern coast of Mexico, larger z values are equivalent to higher temperatures. We thus see that the three filled triangle data points for the highest z-values are consistent with a H(z) = Cz 3.5 , with the original normalization observed for the Pacific data, while the data corresponding to lower z-values are consistent with H(z) = 3.6Cz 3.5 , given the effect of the MJO in increasing hurricane formation approximately four-fold during the phase associated with lower SST.A similar regional effect must be invoked to explain the data in the Atlantic basin, for which a narrow band of increased hurricane genesis can be observed between South America and Africa at a latitude range of between 10 and 15 degrees North latitude. As can be seen (open squares infig. 2), the data in this band again lie on a n=3.5 power law curve with the same factor of 3.6 enhancement that was found for the Eastern Pacific data. As it happens, this narrow band of the Atlantic is during the summer a major portion of the Intertropical Convergence Zone (ITCZ), where winds from the two hemispheres converge, and it creates an area of low atmospheric pressure and the rapid upward convection of moist air --conditions which are conducive to the formation of 13 hurricanes. The remainder of the Atlantic basin away from this band is also consistent with H(z) = Cz 3.5 (chi square = 17.1 for 17 d.o.f), with the original normalization --
A second temporal variation we may check is the year-to-year variation in numbers of hurricanes in different basins. The poorest of the comparisons is that for the Asian Pacific basin where the model shows a rise towards the end of the 47-year interval 1960-2007, while the data (fig. 5) shows almost no rise. The extent of the discrepancy can be judged by a comparison of a quadratic fit to the model (dotted curve) that is superimposed on the data. This discrepancy is bothersome, but it has not yet reached a statistically significant level --at least if one includes N statistical uncertainties in both the data and the model. The chi square for the fit is a perfectly acceptable 38.0 for 47 d.o.f.) It must also be noted that the Asian basin data is much less reliable than the Atlantic data in terms of time trends, especially for data prior to 1985, according Charles Sampson who has made corrections to this data.--Sampson (2008}. 15 In contrast to the Pacific time trend, that for the Atlantic basin agrees very well with the model. Even though the Atlantic data pre-1960 may have missed some storms, some researchers have argued that the number missed is not very significantsee: Mann (2007) Therefore we show the time trends in the data and model all the way back to the beginning of the Atlantic record in 1854. The agreement between data and model over this extended period is fairly good. For example, if one just uses the statistical errors in the data themselves, the chi square is 222 (153 d.o.f.) with a probability of only 0.02%, but when one also includes statistical errors in the model it drops to 105, which is ``too good.'' (i.e., P = 99.9 %) Furthermore, separate quadratic fits to the data and model for the period 1960-2007 are nearly indistinguishable --see dotted curve in fig. 6 for the fit to the model. A final method of comparing data and model time trends is to divide the time interval 1960-2007 into two halves, and ask what the model predicts for the increase from the first half of the interval to the second in each 4x4 degree latitude-longitude cell. One then can look at the observed increase in hurricane activity in each cell over that same time period, and group together all those cells corresponding to given levels of predicted increases (in increments of 10 %), and then see what their average observed increase is. A direct comparison can then be made between the observed and predicted increases --figure 7. The horizontal error bars correspond to half the bin width in fig 7, and the vertical error bars correspond to statistical variations in the numbers of hurricanes in each case --which are quite large for very large predicted increases which are present only for a very small number of cells, where very few storms are predicted or observed. If the predicted and
22 FIG. 4 FIG. 1 .FIG. 2 .FIG. 3 FIG. 4 FIG. 5 FIG. 6 FIG. 7
2241234567hurricanes there eleven-fold for an n=3.5 power law.Hurricanes, are among the worst natural disasters in terms of both lives lost and property damaged, as a result of coastal flooding due to storm surges. An eleven-fold increase in hurricanes at a particular location would just be one part of the story, which would include (1) a potentially larger increase in the total number of hurricanes given the increase in the size of the basin as temperatures rise, (2) an increase in the destructive potential of each hurricane, and (3) an increase in the height of the storm surge due to rising sea levels that would invariably occur in a warmer world.List of FiguresFIG. 1. Probability density of hurricanes H(z) (times 1000) computed from storm data in the Asian Pacific basin for the period 1960 -2007 shown as a function of the variable z defined in terms of the sea surface temperature T and the latitude having negative z-values. H(z) represents the probability of having a storm per month for a given z-interval. The size of the horizontal and vertical error bars is discussed in the text. The data is consistent with the n=3.5 power law curve. FIG. 2. Probability density of hurricanes H(z) (times 1000) versus z computed from storm data in the Eastern Pacific basin (filled triangles) and for a latitude band of the Atlantic basin described in the text (open squares) for the period 1960 -2007 Apart from three high-z points in the Eastern Pacific basin, the data is consistent with the n=3.5 power law curve, but with 3.6 times the normalization used in fig. 1 ---solid curve. For clarity, error bars have been omitted for the Atlantic data points. FIG. 3 Number of storms predicted per month of the year during the period 1960 --2007 versus numbers actually observed for the combined Atlantic and Eastern Pacific basins. The model predictions (continuous curve) have been normalized to the data to match the total area. Number of storms predicted per month of the year during the period 1960 --2007 versus numbers actually observed for the North Asia basin (filled circles) and the Asian Southern Hemisphere (open triangles). The model predictions (continuous curve) have been normalized to the data to match the total area. FIG. 5 Number of storms predicted per year during the period 1960 --2007 versus numbers actually observed for the North Asia basin (open triangles), and the nearly flat trend line fit to the data. The model predictions (continuous curve) have been normalized to the data to match the total area. FIG. 6 Number of storms predicted per year during the period 1854 --2007 versus numbers actually observed for the Atlantic (filled diamonds). The model predictions (grey curve) have been normalized to the data. A quadratic fit to the model is shown for the period 1960 --2007. FIG. 7 Observed percentage increase in numbers of storms versus the predicted percentage increase during the two halves of the 48 year interval 1960 --2007. Each data point groups together all cells across the globe having a predicted increase falling in decadal intervals 0 to 10%, 10 to 20%, ... The data should be consistent with a line through the origin having unit slope shown dotted, whereas the best fit line has Probability density of hurricanes H(z) (times 1000) computed from storm data in the Asian Pacific basin for the period 1960 -2007 shown as a function of the variable z defined in terms of the sea surface temperature T and the latitude according to and with Southern Hemisphere data artificially displayed as having negative z-values. H(z) represents the probability of having a storm per month for a given z-interval. The size of the horizontal and vertical error bars is discussed in the text. The data is consistent with the n=3.5 power law curve. Probability density of hurricanes H(z) (times 1000) versus z computed from storm data in the Eastern Pacific basin (filled triangles) and for a latitude band of the Atlantic basin described in the text (open squares) for the period 1960 -2007 Apart from three high-z points in the Eastern Pacific basin, the data is consistent with the n=3.5 power law curve, but with 3.6 times the normalization used in fig. 1 ---solid curve. For clarity, error bars have been omitted for the Atlantic data points. Number of storms predicted per month of the year during the period 1960 --2007 versus numbers actually observed for the combined Atlantic and Eastern Pacific basins. The model predictions (continuous curve) have been smoothed, and have been normalized to the data.Number of storms predicted per month of the year during the period 1960 --2006 versus numbers actually observed for the North Asia basin (filled circles) and the Asian Southern Hemisphere (open triangles). The model predictions (continuous curve) have been smoothed, and have been normalized to the data.Number of storms predicted per year during the period 1960 --2006 versus numbers actually observed for the North Asia basin (open triangles), and the nearly flat trend line fit to the data. The model predictions (dashed continuous curve) have been smoothed, and have been normalized to the dataNumber of storms predicted per year during the period 1854 --2006 versus numbers actually observed for the Atlantic (filled diamonds). The model predictions (grey curve) have been normalized to the data. A quadratic fit to the model is shown for the period 1960 -Observed percentage increase in numbers of storms versus the predicted percentage increase during the two halves of the 47 year interval 1960 --2006. Each data point groups together all cells across the globe having a predicted increase falling in decadal intervals 0 to 10%, 10 to 20%, ... The data should be consistent with a line through the origin having unit slope shown dotted, whereas the best fit line has a slightly larger slope.
Pacific regions, and by the Joint Typhoon Warning Center (JTWC) Task Force of the U.S. Navy and Air Force for the World's other oceans. These data sets show both the to the present, and the tracks of tropical storms and hurricanes occurring over the period 1945 to the present for storms in the Western (Asian) Pacific and Indian Oceans, including the Southern Hemisphere, as well as those of Atlantic and Eastern Pacific. For the present study we focus only on the latitude-longitude location for the first point on the track of each storm (assumed to be its point of origin), and we have included both tropical storms as well as hurricanes, which we henceforth do not distinguish. The era of meteorological satellites began in the early 1960's, so it might be expected that geographic distributions of points of origin of tropical storms would be less biased for storms recorded since 1960 --a suggestion which is confirmed by the observed depopulation of storms in regions far from shipping lanes of Atlantic storms before 1960compared to later ones. Thus, in order to use a data set that is not clearly biased in terms of geographic distribution, we only use storms since 1960 in finding H(z).reconstructed SST by month in 2 0 x 2 0 latitude-longitude bins for each month from 1854
H(z) values derived from the data for the Asian Pacific basin, where we artificially display Southern Hemisphere data points as having negative z-values, so as to demonstrate the degree of symmetry for the data-derived function H(z). The data may be seen to agree well with a n=3.5 + 0.5 power law for H(z), with C= 0.00073+.00006, and T 0 = 25.5 0 C. The chi square for the fit is 29.2 for 30 d.o.f. (P = 51 %).
The former uncertainty arises because of the statistical errors inherent in the computation of H for each data point. Thus, to find H we assume that N j and M j are uncertain by the independent variable z is not merely + 0.05, as might be expected based on half the bin width in z, but instead the larger value + 0.15. The reason for this enlargement of thej
N , and
j
M respectively, yielding for
M
H
H
H
/
)
1
(
. The uncertainty in
z-errors is that from the definition of
|
|
sin
)
(
2
/
1
0
Detection of a 40-50 day Oscillation in the Zonal Wind in the Tropical Pacific. R A Madden, P R Julian, P R , J. Atmos. Sci. 28Madden, R.A., & P. R. Julian, P.R., 1971: Detection of a 40-50 day Oscillation in the Zonal Wind in the Tropical Pacific, J. Atmos. Sci., 28, 702-708.
Least Squares when both Variables Have Uncertainties. J Orear, Am. J. Phys. 50Orear, J., 1982: Least Squares when both Variables Have Uncertainties, Am. J. Phys., 50, 912-916
Modulation of Hurricane Activity in the Gulf of Mexico by the Madden-Julian Oscillation. E D Maloney, D Hartmann, Science. 287Maloney, E.D., & D. Hartmann, D., 2000: Modulation of Hurricane Activity in the Gulf of Mexico by the Madden-Julian Oscillation, Science, 287, 2002-2004
MJO-Related SST Variations over the Tropical Eastern Pacific During the Northern Hemisphere Summer. E D Maloney, J T Kiehl, J. of Clim. 15Maloney, E.D., & J. T. Kiehl, 2001: MJO-Related SST Variations over the Tropical Eastern Pacific During the Northern Hemisphere Summer, J. of Clim., 15, 675-689.
Hurricanes: Their formation, structure, and likely role in the tropical Circulation, Meteorology over the Tropical Oceans. W M Gray, B. ShawRoy. Meteor. SocGray, W. M., 1979: Hurricanes: Their formation, structure, and likely role in the tropical Circulation, Meteorology over the Tropical Oceans, D. B. Shaw, Ed., Roy. Meteor. Soc., 155-218.
Informal correspondence with Charles Sampson of the Joint Typhoon Warning Center. Sampson, Sampson, 2008: Informal correspondence with Charles Sampson of the Joint Typhoon Warning Center.
. M E Mann, K A Emanuel, G J Holland, P J Webster, Atlantic Tropical Cyclones Revisited. 88EosMann, M.E., Emanuel, K.A., Holland, G.J., & Webster, P.J., 2007: Atlantic Tropical Cyclones Revisited, Eos, 88, 349-350.
Increasing Destructiveness of Tropical Cyclones over the Past 30. K Emanuel, Emanuel, K., 2005: Increasing Destructiveness of Tropical Cyclones over the Past 30
. Nature. 436YearsYears, Nature, 436, 686-688
Tropical cyclone climatology in a global-warming climate as simulated in a 20km-mesh global atmospheric model: frequency and wind intensity analysis. K Oouchi, J Yoshimura, H Yoshimura, R Mizuta, S Kusunoki, A Noda, J. Meteorol. Soc. Japan. 84Oouchi, K., J.Yoshimura, H. Yoshimura, R. Mizuta, S. Kusunoki, and A. Noda, 2006: Tropical cyclone climatology in a global-warming climate as simulated in a 20km-mesh global atmospheric model: frequency and wind intensity analysis. J. Meteorol. Soc. Japan, 84, 259-276.
Influence of greenhouse warming on tropical cyclone frequency. J Yoshimura, M Sugi, A Noda, J. Meteor. Soc. Japan. 84Yoshimura, J., M. Sugi and A. Noda, 2006: Influence of greenhouse warming on tropical cyclone frequency. J. Meteor. Soc. Japan, 84, 405-428.
The Sun's Variable Radiation and its Relevance for Earth. J Lean, Ann. Rev. Astron. Astrophys. 35Lean, J., 1997: The Sun's Variable Radiation and its Relevance for Earth,'' Ann. Rev. Astron. Astrophys., 35: 33--67.
| sample_1248 | 0.5692 | arxiv | |
Environmentally-Extended Input-Output analyses efficiently sketch large-scale environmental transition plans: illustration by Canada's road industry
Anne De Bortoli1 anne.debortoli@polymtl.ca
CIRAIG
École Polytechnique de Montréal
P.O. Box 6079H3C 3A7MontréalQuébecCanada
Americas Technical Center
Eurovia Canada Inc
3705 Place Java #210J4Y 0E4BrossardQCCanada
Technical Direction
Eurovia Management, 2 rue Thierry Sabine33700MérignacFrance
LVMT
Université Gustave Eiffel
Ecole des Ponts ParisTech, 6-8 Avenue Blaise Pascal77420Champs-sur-MarneFrance
Maxime Agez1
CIRAIG
École Polytechnique de Montréal
P.O. Box 6079H3C 3A7MontréalQuébecCanada
Environmentally-Extended Input-Output analyses efficiently sketch large-scale environmental transition plans: illustration by Canada's road industry
10.1016/j.jclepro.2023.136039https://doi.org/10.1016/j.jclepro.2023.136039, accepted version, Journal of Cleaner Production 1industryenvironmental transition planEnvironmentally-Extended Input-Output analysisroad sectormulticriteria assessmentgreen purchase strategiesgreenhouse gas emissions
Industries struggle to build robust environmental transition plans as they lack the tools to quantify their ecological responsibility over their value chain. Companies mostly turn to sole greenhouse gas (GHG) emissions reporting or time-intensive Life Cycle Assessment (LCA), while Environmentally-Extended Input-Output (EEIO) analysis is more efficient on a wider scale. We illustrate EEIO analysis' usefulness to sketch transition plans on the example of Canada's road industry: estimation of national environmental contributions, most important environmental issues, main potential transition levers of the sector, and metrics prioritization for green purchase plans. To do so, openIO-Canada, a new Canadian EEIO database, coupled with IMPACT World+ v1.30-1.48 characterization method, provides a multicriteria environmental diagnosis of Canada's economy. The construction sector carries the second-highest environmental impacts of Canada (8-31% depending on the indicator) after the manufacturing industry (20-54%). The road industry generates a limited impact (0.5-1.8%), and emits 1.0% of Canadians' GHGs, mainly due to asphalt mix materials (28%), bridges and engineering structures materials (24%), and direct emissions (17%). The industry must reduce the environmental burden from material purchases -mainly concrete and asphalt products -through green purchase plans and eco-design and invest in new machinery powered with cleaner energies such as low-carbon electricity or bioenergies. EEIO analysis also captures impacts often neglected in process-based pavement LCAsamortization of capital goods, staff consumptions, and services -and shows some substantial impacts advocating for enlarging system boundaries in standard LCA. Yet, pavement construction and maintenance only https://doi.org/10.1016/j.jclepro.2023.136039, accepted version, Journal of Cleaner Production 2 explain 5% of the life cycle carbon footprint of Canada's road network, against 95% for the roads' usage (72% from vehicle tailpipes releases, 23% for manufacturing vehicles). Thereby, a carbon-neutral pathway for the road industry must first focus on reducing vehicle consumption and wear through better design and maintenance of roads. Finally, EEIO databases must be developed further as a powerful tool to fight planet degradation, and openIO-Canada must be specifically expanded and refined to allow for more robust and larger multicriteria assessments.
Introduction and background
The rise of environmental threats calls for a drastically hurried industrial environmental transition. Building an efficient action plan at the industry level requires a deep multicriteria understanding of environmental life-cycle impacts to determine the most effective levers. But the tools and data to reach sufficient knowledge seem unsatisfying for the industry.
First, the compilation of sectoral national greenhouse gas (GHG) inventories can be an interesting source of data to understand the carbon structure of an economy and its industry.
However, GHG emissions are only one environmental dimension. An improvement towards reducing these emissions could mask worse performance in other environmental categories, as a consequence or independently of the taken measures. Moreover, these inventories are not suitable for industries as they only consider the emissions of production taking place on the territory -an approach known as "production-based" or "territorial" (Caro et al., 2014).
Territorial approaches help decreasing impacts on a given territory but tend to push governments to shift the emissions outside the country by relocating polluting practices (Peters and Hertwich, 2008) and importing the most carbon-intensive products, which can lead to increases in the global emission levels of GHGs and degrade the national economy (Rieber and Tran, 2008). Therefore, these analyses must be complemented with supply-chain-wide analyses accounting for foreign impacts. Such analyses, called national "consumption-based" environmental assessments -i.e. accounting for the impact from cradle-to-consumer, disregarding the production location -remain limited (Harris et al., 2020), even though they seem particularly suitable to orientate sustainable purchases and productions accounting for the entire supply chain.
Given the methodological choices made for national accounting, industrial sectors and companies face three important challenges to determine their impact on the environment. First, because national inventories follow the territorial approach, companies do not have easy access to data on their indirect emissions -called "scope 3" assessment according to the GHG protocol (WBCSD and WRI, 2004) -as most of these indirect emissions occur beyond the borders of one single territory. Yet, the assessment of the so-called scope 3 is crucial to implementing comprehensive impact reduction procedures, such as green purchasing policies and environmental research and development (R&D) plans. For instance, in pavement construction, bitumen constitutes a major source of environmental impacts (de Bortoli, 2020) and falls within scope 3 according to the GHG Protocol definitions. Second, the governmental services responsible for national GHG inventories often perform aggregations of the emissions by broad categories before releasing environmental information (Government of Canada, 2021a). This further hinders the potential use of this data by companies. Indeed, data is too aggregated to allow specific industrial sectors to access a representative footprint of their activities. As an example, to our knowledge, the road construction sector is not considered as such in national inventories, and even less the more specific sectors of materials it produces or consumes (i.e., aggregates, cement, binders, etc.). Third, national inventories only provide a footprint, most of the time solely focusing on GHG emissions. It does not describe intersectoral links which would allow companies to identify the main sources of impact in their supply chain and lack a multicriteria comprehensiveness.
While national inventories are mostly focused on GHG emissions, as well as water and energy use, some countries also register other pollutant emissions by economic sector, such as the US EPA through its Chemical Data Reporting (US EPA, 2011), or the French CITEPA (CITEPA, 2021). However, these environmental matrices only report flows, i.e., masses of substances emitted which need further analyses before being usable by companies, to determine what the environmental impacts of these pollutants is. These flows thus need to be transformed from emissions to impacts, through characterization factors that model fate, exposure, and effect of these pollutants in the natural environment.
Two environmental quantification methods overcome the limitations previously raised: Life Cycle Assessment (LCA) and Environmentally Extended Input-Output (EEIO) analysis. Both carry out multi-criteria appraisals -e.g., focus on several environmental impact categoriesadapted to industry transition plans, that is, from cradle-to-gate, i.e., from the extraction of materials to the products leaving the factory. However, using LCA to analyze the environmental impacts of a sector at the national level requires an enormous amount of data, thus triggering the intensive time consumption of data collection, which is one of the main obstacles to the large-scale application of LCA. Moreover, the lack of digitization in certain sectors such as the construction sector can hinder access to the required data. On the other hand, EEIO analysis allows for such large-scale analyses, and databases to perform them constantly emerge Agez, 2021;Stadler et al., 2018;Yang et al., 2017;Andrew and Peters, 2013;Lenzen et al., 2013Lenzen et al., , 2022. These two methods fulfill different roles. EEIO enables large scale assessments thanks to its complete coverage of the economy, while LCA mainly focuses on supply chain assessments through its much more supply-chain specific data.
Hybrid LCA -completing LCA with EEIO analysis -is also an interesting tool to fill the gaps of what can be difficultly model through a simple process-based LCA due to a lack of data (LCIs or foreground data).
EEIO analysis is already used within academia to quantify the environmental contributors to national economic sectors with a consumption-based approach. However, EEIO applications either focus on the consumption of final demand sectors (e.g., households, government) (Castellani et al., 2019;Cellura et al., 2011), or the impact of a whole economy typically without going into intersectoral details (Dawkins et al., 2019;Lenzen, 2007;Moran et al., 2018;Xia et al., 2022). Regarding applications to specific industrial sectors, the literature has so far mainly focused on food (Reutter et al., 2017) or tourism (Sun et al., 2020). But to our knowledge, there is no application in the road industry, only one EEIO analysis focusing on the GHG emissions from the entire construction sector in Ireland (Acquaye and Duffy, 2010).
EEIO analysis is therefore a powerful decision support tool but is often overlooked outside of academia. It could be used more widely to allow industries to build environmental transition plans by identifying major environmental contributors, selecting relevant sets of environmental indicators to monitor, prioritizing R&D topics, building green purchasing policies, and identifying major improvement levers for production sites.
The overall objective of this article is to illustrate the possible uses of EEIO analysis to build environmental transition plans for companies and industries on a wide scale such as a nation. This illustration will be based on the example of the road industry in Canada. We will first present the EEIO analysis method, and the database used for the Canadian context (section 2), before detailing the calculations that will be carried out (section 3). Then, the results (section 4) include a cross-sectoral vision of Canada's multicriteria environmental impacts (12 midpoint indicators, 2 endpoint indicators) and the contribution of the construction sector, an intra-sector environmental picture of the road industry highlighting direct transition levers, and finally an overview of its impact by scope to give a perspective on these levers. In the last section, the results will be discussed to lead to some recommendations to decision-makers before detailing the benefits and limits of using EEIO analysis instead of LCA on large scale systems (section 5).
2 Method and material 2.1 The EEIO analysis method EEIO analysis, also shorten as "EEIO", is a method that links environmental consumptions or releases to monetary transactions (Miller and Blair, 2009). Data (both economic and environmental) are obtained and compiled by national statistics agencies, often through surveys sent to companies. Academics and government agencies then integrate this data to form tables that can be readily used to estimate emissions and impacts on the environment. This quantification accounts for emissions in a cradle-to-gate fashion. Hence, it includes scopes 1 and 2, as well as upstream scope 3. Although generally focused on the climate change issue, it can cover a large range of pollutants (i.e., 35 pollutants in the EXIOBASE EEIO database (Stadler et al., 2018)), mineral resources and land use and thus can be used to study other environmental issues, such as acidification or eutrophication.
Impacts on the environment linked to a given final demand (e.g., households) are determined using the following equation:
= • • ( − ) •(3)
Where vector presents the different potential impacts on the environment, is a matrix regrouping characterization factors translating emissions to potential impacts on the environment, matrix regroups the environmental extensions linking estimated consumptions and/or emissions for 1$ of each category of product, is the identity matrix, is the technology matrix describing the normalized monetary exchange between sectors of the economy, and vector being the final demand.
Sources of Canadian data
OpenIO-Canada is the EEIO database used in this article (Agez, 2021 Figure 1 gives an overview of the calculation process used to understand the sources of the environmental impacts of Canada and its road sector in 2017, based on the latest data made available by the Canadian Government. A consumption-based approach is adopted throughout this paper, i.e., impacts stemming from international exports are excluded while international imports, local production, and consumption are included.
Calculations
Overview
Characterization method and indicators
The life cycle impact assessment method IMPACT World+ (IW+) v1.30-1.48 was selected as it was deemed the most scientifically up-to-date and relevant method for Canada (Bulle et al., 2019 (also called Global Warming Potential (GWP)), freshwater acidification, eutrophication and ecotoxicity, marine eutrophication, ozone layer depletion, particulate matter (PM) formation, photochemical oxidant formation, terrestrial acidification, carcinogenic and non-carcinogenic human toxicity resp. "cancer" and "non-cancer"). As for the endpoint indicators, the damage to ecosystem quality and human health are considered. Both the long-and short-term effects of climate change on these damages are considered in IW+. Due to the lack of available national data, some IW+ indicators were not considered, such as ionizing radiations, resources (mineral and fossil), land transformation and occupation, as well as water scarcity. Nevertheless, an indicator of water use was calculated, using the data reported by Statistics Canada (n.d.). Water use only accounts for withdrawn water and not released water. It is therefore different from water consumption indicators, which consist of the difference between withdrawn and released water.
Aggregation of sectors by category
This study relied on the "Detailed level" of openIO-Canada which describes the Canadian economy in 492 sectors. An additional category for direct emissions from final demands (e.g., coming from the use of personal vehicles by households) was also included. However, a 492sectors classification being too much for a meaningful interpretation, contributions were aggregated. This aggregation was deemed necessary to make the results readable and usable for the orientation of road industry environmental transition plans, and it was made based on industrial road expertise and confirmations of some categories' meaning by the Statistical Information Service of Statistics Canada. The aggregation work was incremental, and the different aggregations tested are reported in the SM. The last two levels of aggregation are presented in Table 1 to explain better the results in Figure 4 and Figure 5. Disaggregated results (i.e., with the 492 sectors detail) are also available in SM. It shows that the manufacturing sector is by far the most important contributor to the environmental impact of Canadians' consumption on all midpoint impact categories. It goes from a minimum of 20% of the total water use to 54% of the impact on freshwater ecotoxicity, and accounts for a quarter of the impact of Canada on climate change. The construction sector is then globally the second most important contributor with contributions higher than 10% of the total (excluding on water use) and reaching up to 31% of the total on carcinogenic human toxicity. 12% of Canadians' impact on climate change is due to the construction sector, 41% of it being due to residential buildings. Services other than public administration and Non- consumption represent 3.81tCO2e/capita. As the direct emissions of Canadian households solely come from GHGs emissions and water consumption -as the NPRI data do not cover households -, it is within expectations that it only contributes to these two impact categories.
Utilities present limited contributions (<5%) excluding on freshwater acidification (13%), marine eutrophication (11%), PM formation (9%), terrestrial acidification (12%) and water use (9%). Finally, agriculture, education, health, resources, and transportation sectors have low contributions, generally from 0 to 5%. Let's note that "Agriculture" accounts for agriculture, forestry, fishing, and hunting activities, and "Resources" encompass oil, gas, and mining.
Transportation is a low contributor, including on GWP, because it only accounts for freight and public transportation directly bought by households. Indeed, household private transportation is encompassed within direct emissions. Besides, freight is not highly consumed by households and public transportation is rather low-emission. Finally, all other forms of transportation are included in the sector that buys them. For instance, impacts from freight services purchased by the construction sector are included in the environmental impact of this sector.
Most important environmental issues
Based on the IW+ methodology, climate change -cumulating long-and short-term effects -is by far the most important midpoint contributor to the two damages: it brings respectively 95 and 82% of the human health and ecosystem quality damage ( Figure 3). The rest of the human health damage is mainly brought by PM formation due to electricity consumption, while the ecosystem quality is otherwise mostly damaged by marine acidification, generated at 98% by CO2 solubilization. the cradle-to-gate impacts of the road industry, except for climate change where they represent 17% of the total impact. These low contributions might be due to a low number of road industry facilities reporting to NPRI.
National burden from the road industry
The results also highlight that the category "bridges & tunnels" -a category including purchases of concrete, cement, steel, and aluminum -weighs heavily (from 11 to 60%) with regards to the majority of the environmental impacts of the road industry. Asphalt mixture materials purchases -in which we included the purchases in asphalt products, asphalt binders, aggregates, and other minerals as well as chemicals -highly affect 2/3 of the impact categories, particularly climate change (25%), freshwater acidification (29%), marine eutrophication (24%), ozone layer depletion (34%), PM formation (40%), photochemical oxidant formation (28%), and terrestrial acidification (28%). Energy purchases -including electricity, natural gas, and other fuels -account for 2% to 11% of the impacts (resp. for freshwater eutrophication and smog). On climate change, fuel purchase accounts for 9% of the impact and direct emissions for 17%, meaning a upstream scope 3 accounting for 32% of the climate change impact from energies, a higher contribution than the 10 to 15% usually highlighted in European databases (e.g. ADEME, 2019), probably due to the major supply from Canadian oil sands, known for their higher extraction and transformation impact (Charpentier et al., 2011;Chen et al., 2019;Masnadi et al., 2018). Infrastructure and capital goods -covering the maintenance/repairs of machinery, buildings, and infrastructure, as well as other metals than steel, plastic, and rubber approach. For instance, three different contributors need to be aggregated to represent twothirds of the climate change impact (53%). These three contributors are the asphalt products (18%), the concrete (18%) and the direct emissions (17%). The other 20 sectors account for the rest of the impact (47%).
Asphalt (e.g. bitumen) and asphalt products as well as concrete are also major contributors to the impact of the road industry across multiple other impact categories: freshwater acidification (27 and 24%), carcinogenic human toxicity (8 and 21%), non-carcinogenic human toxicity (4 and 35%), marine eutrophication (17 and 39%), PM formation (19 and 20%), photochemical oxidant formation (21 and 29%), terrestrial acidification (23 and 28%) and water use (15 and 10%). While asphalt products account for binders and asphalt mixtures purchases (i.e. asphalt binder and aggregate production as well as asphalt mixing and products' transportation on the upstream life cycle of these products) related to pavement and sidewalks construction, concrete mainly connects to the construction of bridges, tunnels, and other structures (e.g. sidewalks and rare concrete pavements). We can conclude from Figures 4 and 5 that asphalt and asphalt products impacts must mainly be due to bitumen and asphalt mixing operations (e.g. burnt fuels).
Paper and paperboard purchases appear to be a negligeable contributor except on freshwater eutrophication (8%, Figure 5). While reducing paper consumption in companies is often promoted as an important environmental action, it appears insignificant for the road industry outside of freshwater eutrophication issues. Moreover, the crushing contribution of services on freshwater eutrophication (Figure 4) is brought by the purchase of external services, that accounts for 48% of the impact ( Figure 5). Within the different external services bought, "Architectural, engineering and related services" and "Management, scientific and technical consulting services" contribute the most.
Steel purchases, machinery maintenance/repairs and other goods purchases (mainly wires and lighting fixtures) all significantly impact freshwater ecotoxicity and both toxicities (cancer and non-cancer).
Energy purchases by the road industry in Canada account around 10% of the contributionssumming natural gas, waste oil and other fuels. We note a negligible contribution from natural gas, while waste oil and other fuels -specifically heavy fuel oil -globally account for similar impacts. Waste oil does not appear particularly problematic on indicators accounting for the release of toxic substances such as human toxicities or ecotoxicity, while we know they constitute a serious risk (Government of Canada, 2018). This is probably because mostly small companies produce it, and that these small companies do not have to report to the NPRI. The direct emissions triggered by the combustion of fuels from production tools, machinery and company fleets, contribute specifically to climate change (17%) as specified previously.
Aggregates are particularly impacting on PM emissions (21%), despite the use of specific techniques to reduce dust, such as water spraying in some quarries especially close to densely populated areas.
Finally, concrete is an overall much higher contributor to the impacts than cement. It indicates that the industry mainly purchases concrete mixtures instead of manufacturing its own, as cement is the most carbon-intensive component of concrete. The cement bought is partly used in own-made concrete, and partly used to stabilize soils in pavement foundations. 4%. This analysis informs on which areas to focus the R&D topics and green purchases efforts.
From a larger point of view, it also informs which LCIs to regionalize in priority in a road process-based LCA to enhance the quality of the results: the most important contributing processes must be regionalized first.
Metrics prioritization for green purchase plans
Endpoint indicators in environmental quantification methods exist for decades (Steen and Ryding, 1992), and the pros and cons of midpoint and endpoint indicators in LCA have been largely debated, showing that both approaches have different adequate usages (Bare et al., 2000). One major benefit of the use of damage indicators in LCA is to offer a concise but quality graph) have a particularly higher contribution to climate change than to the ecosystem quality endpoint indicator, while the opposite is true for aggregates and concrete (orange and brown dots above the regression line in the human health graph), indicating that these purchases have a bigger contribution to damages on human health than to climate change. Direct emissions impact is excluded from the analysis presented but its inclusion gives a higher R 2 (see SM). In the end, this analysis suggests that GWP is currently a good proxy to represent wider environmental impacts of Canada's road industry for each category of purchase and thus to support green purchase strategies for each category of suppliers. These conclusions must not be directly extrapolated to other sectors or locations, and they still depend on the openIO-Canada database and the IW+ characterization method. Finally, this example shows how to use EEIO analysis to assess the redundancy of indicators in an endpoint-oriented environmental strategy and reduce the number of metrics on which to support green purchases plans. This is a practical application concretely useful for industries and companies to actually implement green purchase plans, especially when sustainability teams do not have advanced LCA knowledge to conduct and interpret complex multicriteria assessments. Indeed, it reduces the complexity and the requests made to suppliers, while still allowing to select suppliers on a simple set of indicators. This would raise the greening strike force of consuming companies by a ripple effect on the entire upstream chain of suppliers. . This contribution is a bit higher than the 10 to 15% contribution from the fuel supply chain that can be found in databases such as the French ADEME's database (ADEME, 2019). This could be explained by the higher impact of the fuel on the Canadian market -partly coming from high carbon-intensive oil sandscompared to the impact of the European market's fuel (Charpentier et al., 2011;Masnadi et al., 2018).
To conclude, as the environmental carbon footprint of Canada's road network mainly comes from its use stage, the main lever of its decarbonization consists in a better management of the pavement-vehicle interactions (PVI) to reduce vehicle consumption and deterioration through optimally designed and maintained roads, rather than trying to reduce the impacts from the construction. This concretely means reducing the roughness of the road -for instance by controlling the popular International Roughness Index better -, as well as curves and slopes.
This recommendation corroborates previous results at the road scale (de Bortoli, 2014;de Bortoli et al., 2022), showing that higher environmental impacts from a more intensive maintenance scheme can be more than offset by their consequential benefits on the use stage (de Bortoli et al., 2022), some previous studies focusing on the fuel consumption benefits rather than on the whole vehicle life cycle (Wang et al., 2014(Wang et al., , 2012Araujo et al., 2014). As these results show, the manufacturing of vehicles is already an important contributor to transportation impacts. It thus emphasizes the risk of burden-shifting due to the well-expected fleet electrification. Indeed, the current manufacturing of electric vehicles is more impactful -on GHG emissions as well as critical metal consumption -than those of combustion engine cars (ADEME et al., 2013;Roy and Ménard, 2016). This raises awareness about the necessity of carefully estimating the prospective impacts of current electrification policies for each region, to be sure that excess impacts from manufacturing are counterbalanced by higher benefits in the use stage. Finally, reducing the traffic in terms of kilometers traveled is obviously the most straightforward way to reduce the environmental impacts (of transportation), as in general reducing any consumption is.
Discussion
The environmental transition of the Canadian road industry
Insights for the road industry actors
Our results highlight how EEIO analysis can help quickly sketch an environmental transition plan by first understanding the multicriteria environmental responsibility of an industry at the national scale, also accounting for embodied emissions in the supply chain -including imports, revealing the main contributors to these impacts, and reducing the environmental dimensions to consider in R&D and green purchase plans. This case study shows the major roles of purchases of concrete and asphalt products, as well as direct emissions on the climate change midpoint indicator for Canada's road industry (18, 18 and 17% of the impact). As regards direct emissions, and since the climate change midpoint indicator also brings a major contribution at the endpoint level, it calls for efforts on the energy consumed by production tools, machinery, and company fleets. As such, switching from heavy fuel to natural gas would for instance reduce these emissions by 31% per megajoule consumed due to lower carbon factors (Quebec Ministry for the Energetic transition, 2019). Biofuels also generally show lower impacts than fossil fuel but can generate burden-shifting (Jeswani et al., 2020), calling for studying carefully their local and global impacts from specific sourcing. Electrification of construction machinery, company fleets, and production processes is a much more promising avenue where electricity mixes are low-carbon such as in Quebec, yet subject to an increase in electric capacity respecting electricity decarbonization. Our results also emphasize the importance of engineering structures on the overall impact of infrastructure which corroborates railway process-based LCAs Chang and Kendall, 2011). This contribution would mainly be due to the GHG emissions of concrete (and more specifically of cement) and metals, building machines having a limited contribution to this impact .
Moreover, this limited impact of the construction process compared to the provision of materials has also been demonstrated in many road LCAs (e.g. the meta-analysis by de Bortoli, 2020). More generally, the contributions of the different types of purchases made by the road industry in Canada will enable this industry to prioritize the development of a green purchasing charter for categories with a strong environmental impact, which concerns -apart from engineering structures -asphalt mixture and materials to produce them. When looking further at the environmental impact from the "Asphalt (except natural) and asphalt products", EEIO results show that 43% of the carbon footprint comes from purchases in asphalt binder, 22% from fuel purchases, 10% from aggregates, 9% from crude oil purchases (aiming at producing asphalt binders and fuels), and 5% from freight. This embodied carbon structure is consistent with previous studies (de Bortoli, 2020) and confirms the prevalence of asphalt binders and fuels for asphalt mixing and asphalt binder production in the emissions from asphalt mixture production.
Finally, we used EEIO analysis at the national industrial scale, but it can also be a powerful tool at the company scale to hierarchize environmental actions. Indeed, EEIO analysis can also be statically used internally by companies to screen environmental levers based on their buying reports, or even dynamically to simulate the environmental impacts of a change in the purchases of the company, relating to a change in the buying choice, the materials or services sold, or the production process. This process must involve all the departments of a company:
R&D, material, buying, and production departments.
The trifling contribution of road construction compared to road usage
Quantifying the environmental contribution of each life-cycle stage of the road to its lifetime impact is a recurring question in the literature, especially to understand to which extent the pavement use stage is important, as it is often excluded from road LCAs scope (Santero et al., 2011). Several studies emphasized that the vehicle pipe emissions carry a crushing contribution to the road life-cycle impact (de Bortoli, 2018;Wang et al., 2014Wang et al., , 2012Chappat and Bilal, 2003). When included, the impact of vehicle manufacturing and maintenance has shown to be also important in the rare studies accounting for it, for instance representing 21% of the primary energy consumed by a road system over 30 years (de Bortoli, 2014) or around 15% of the carbon footprint of passenger car modes (de Bortoli and Christoforou, 2020;Chester and Horvath, 2009). However, these assessments were always carried out on a particular road or a particular mode (e.g. passenger car transportation), and a more global overview at the network level was missing. The environmental picture that we give for Canadian roads demonstrates that decarbonizing the road construction industry might not be a priority to tackle the impact of road transportation, contrary to building and maintaining roads to lower vehicle consumption and tear and wear, or directly reducing vehicle manufacturing and use's GHG emissions.
Results show that fleet replacement is far from being a secondary question in terms of road's climate transition, which may be explained by the fact that cars in Canada are the second heaviest in the world, weighing 1717 kg on average in 2017 (IEA, 2019). Fleet replacement is a particularly thorny question with the penetration of electromobility, as electric vehicles emit more at the manufacturing stage but less during the use stage than internal combustion engine (ICE) vehicles, which can lead to lowering GHG emissions on the entire life cycle as shown in
Quebec (Roy and Ménard, 2016).
Limitations and future work on the openIO-Canada model
Overview
OpenIO-Canada has been designed with a few inherent limitations and assumptions that are made clear in this section. First, the physical flow accounts of Statistics Canada (used to quantify GHG emissions and water use) are provided at a more aggregated level (240 sectors) than the economic data that is used by openIO-Canada (492 sectors). Hence, an economic allocation approach was adopted to distribute GHG emissions and water use. For instance, physical flow accounts only provide GHG emissions for the "Crop and animal production"
sector. OpenIO-Canada thus considers any more refined subsector that belongs to the broad "Crop and animal production" sector and uses the weighted average of their sales share to determine their emission level. In other words, if the "Wheat" sector represents 6% of the total sales of "Crop and animal production", the "Wheat" sector will be attributed 6% of the total GHG emissions of "Crop and animal production". This approach triggers inconsistencies as the emissions do not follow sales, for example, in the EXIOBASE database, the GHG emission factor for the wheat sector is 1.56kgCO2eq/€ while the one for cattle is 4.54kgCO2eq/€.
Second, openIO-Canada does not provide a version with capital goods endogenized. Capital endogenization is a method used in EEIO analysis to distribute the impacts of capital formation (e.g., the construction of a machine) to the different sectors of the economy requiring the formation of capital. Using an example to make it clearer, openIO-Canada records the construction of a building (and its associated emissions) but does not link the construction of the building to the economic sector that required the building. Therefore, contribution analyses on sectors provided by openIO-Canada do not include the formation of capitals, but rather only include recurring operations such as maintenance and repairs.
Third, international imports are considered produced as in the importing province, as usually done in EEIO databases. As an example, an American car imported in Quebec will thus be considered produced the same way as a car directly produced in Quebec, both for economic and environmental flows. This approach is called "DTA" for "Domestic Technology
Assumption", and is a issue specific to single region input-output approaches. Integrating the openIO-Canada table into a global multi-regional input-output (MRIO) system would allow for regionalizing import impacts. Fifth, EEIO analysis is a powerful tool to quickly assess large-scale systems but is rather limited in its ability to assess disruptions such as technical or material innovations or new national production sectors. A few studies manually simulated new productions, such as Leurent and Windisch (2015) did in an economic input-output analysis to assess the macroeconomic impacts of a potential French electric battery production sector, while other coupled EEIO databases to equilibrium models to simulate disruptions van Sluisveld et al. (2016). Lately, the industrial ecology community rather turned toward prospective LCA, a growing corpus of studies being dedicated to these assessments (Thonemann et al., 2020).
Focus on the underestimated non-GHG direct emissions
As What is usually considered outside the system boundaries of road process-based LCAsnamely staff consumptions, services, and sometimes infrastructure and capital goods amortization -accounts according to openIO-Canada for 15 to 73% of the impacts, resp. on marine eutrophication and freshwater eutrophication. In particular, external services are always excluded from these studies and bring between 4 and 48% of the impacts, resp. on human non carcinogenic toxicity and freshwater eutrophication. EEIO analysis is thus an interesting tool to rapidly screen the impact of time-consuming aspects to model in process-based LCAs and decide whether to include them in the system boundaries of an LCA in a more specific study.
Amortization of infrastructure, machinery, and buildings is more often included, especially in the ecoinvent database. Yet the models are often very generic and/or outdated, as illustrated by the quarries: a single model for each type of site (loose rocks or solid rocks) was created between the end of the 90s and the beginning of the 2000s, based on 4 Swiss quarries (Kellenberger et al., 2007). However, the impact of the depreciation of infrastructure is even more important as the carbon intensity of energies decreases. If the contribution of this depreciation is already significant, it will undoubtedly be more and more so, which calls for improving the classic LCA models. Note, all the same, that our EEIO database on this point has limits: we consider the impacts of the year 2017 to be representative, while there can be strong heterogeneities depending on the year of purchase. Capital goods should also be endogenized in openIO-Canada as it has been done in EXIOBASE and US-EEIO (Miller et al., 2019).
It may also be interesting to use the major contributors to the environmental impacts highlighted through EEIO analysis to prioritize the regionalization of life cycle inventories (LCIs) for a sector, particularly if the national market differs from the markets modeled in existing databases, or if national technologies do not coincide with existing models in the case of domestic production.
However, as EEIO analysis is in most cases entirely based on economic allocations (except for a few hybrid-unit versions), the importance of the contributors found with EEIO analysis could be distorted compared to LCA contributors, as LCA results are more disaggregated than EEIO results, and mainly uses non-economic allocation methods such as mass or other physical allocations to deal with multifunctional systems. Thus, comparing EEIO analysis and processbased LCA results, and using both types of methodologies to interpret and use results in decision-making support could bring more robustness on the environmental structure and levers of a system, or more insights on the uncertainties to deal with. EEIO analysis and LCA must then be used complementarily to strengthen environmental decision processes.
Uncertainty and data quality in EEIO analysis versus LCA
EEIO databases generally cover a more limited number of substances than LCI databases which typically consider more than a thousand substances. Nevertheless, there is great variability in the magnitude of the environmental consequences of substances. For instance, with only about 35 pollutants covered, EXIOBASE has been found to still reliably cover many impact categories apart from those related to toxicity (Muller, 2019).
Another potential drawback of EEIO analysis pertains to the reliability of national pollutant inventories, used by EEIO databases and compiled by government agencies, which rarely stem from actual measurements on industrial sites. In the case of Canada for example, certain specific emissions must be measured on an annual or multi-year basis, e.g., the emissions of certain pollutants for facilities burning used oil in Quebec. Most emissions on the other hand are simply reported based on calculation methodologies prescribed by the Government of Canada which may be incomplete or obsolete. As an illustration, a calculator is made available for asphalt plants to estimate their pollutant emissions (Government of Canada, 2020b).
Parameters -such as annual production, fuel consumption, type of production, or asphalt mixing temperature to name but a few -are fairly comprehensive and make it possible to take into account technologies and specific equipment. However, according to this "hot mix asphalt plant" calculator's documentation, its emission factors are based on US EPA data published between 1994 and 2005. Moreover, the calculator does not differentiate emissions from a boiler using waste oil and oil #6, while used oil facilities need to be tested regularly due to the risk related to specific metals and contaminants emissions. It, therefore, seems necessary to increase the consistency of emission reports, for example by providing updated calculators. The more so as a specific calculator also exists for waste oil combustion (Government of Canada, 2018), but the existence of this calculator is not pointed out in the section relating to the production of asphalt mixtures. Finally, efforts should be put on the quality of these databases, in terms of completeness, reliability, as well as technological, geographical, and temporal representativeness. Moreover, giving access to the information on the quality of the background data could allow analysts to assess the robustness of their assessments. This data quality problem also concerns LCA but is commonly addressed in LCA through data quality characterization and various uncertainty propagation methods (Baker and Lepech, 2009), while it is more rarely the case in EEIO analysis (see the example by Lenzen et al. in 2010).
Conclusions
EEIO analysis must be used as one tool to orientate the environmental transition plans of industries as proved by the example of the pavement industry in Canada. First, it estimates faster than LCA the multicriteria environmental contribution of an industry for cradle-to-gate on a large scale such as a country: in our illustration, the road industry accounts for around 1.0% of most of the country's damages on a consumption-based approach, i.e. 10% of the construction sector impacts. It thus unearths industrial key drivers on which organizing the environmental transition through green purchase and R&D prioritization strategies. The road industry in Canada must reduce (1) its direct emissions through the investment in new machinery using cleaner energies such as low-carbon electricity, biomass, and natural gas, and
(2) the impact of material purchases, especially concrete and asphalt products. Second, EEIO analysis spots the critical midpoint indicators explaining most of the damage to areas of protection such as ecosystems and human health, allowing for reducing the set of classical LCA indicators to monitor ecological transition plans, multicriteria assessments being less understandable for non-experts as the number of metrics rises. Climate change dominates the midpoint category contributions to damages in the pavement sector, followed by marine acidification, and PM formation due to aggregates. Third, EEIO analysis rapidly seizes often neglected sources of impacts in traditional LCA: capital goods amortization, staff consumption, and services. It must be used to set the system boundaries adapted to specific LCAs. Finally, it helps estimate the impacts of some types of goods at a large scale on a cradle-to-grave perimeter: its application to Canada's road network confirms that the use stage of the roads is capital to its environmental impact (95% of the GHG emissions), mainly due to vehicle tailpipe emissions (72% of the total impact) but also to vehicle amortization (23%). The construction and maintenance of the roads contribute little over the life cycle (5%), and the major lever for decarbonization is expected from better managing PVI to reduce the use stage impacts through better designed and maintained roads.
Figure 1
1Illustration of the calculation method framework and presented results
Figure 2
2shows the contribution of 12 aggregated sectors of the Canadian economy -mainly following the classification of the economy by Statistics Canada (Statistics Canada, n.d.) -and 11 impact categories of the IW+ LCIA method, as well as a "Water use" indicator, on a consumption-based approach, encompassing the entire supply chain.
Figure 2
2Contributions of industrial sectors to the different IW+ environmental impacts of Canada at the midpoint level, consumption-based approach
Figure 3
3Contributions of the different IW+ environmental impacts of Canada at the endpoint level, consumption-based approach 4.2 Environmental transition plan for the road industry in Canada In this section, we want to answer three main questions. First, what is the contribution of the road industry to the national environmental impacts of Canadians (section 4.2.1)? Second, what are the main potential levers to the environmental transition plan of the road industry (section 4.2.2)? And third, how to reduce the multicriteria dimension of green purchase strategies for decision-makers by prioritizing metrics (4.2.3)?
Figure 4
4offers a first overview of the drivers of the environmental burdens generated by the road industry. We created categories based on our road industry expertise to aggregate the 492 sectors of openIO-Canada. The results illustrate that direct emissions are a low contributor to
Figure 4 Figure 5
45Contribution of different activities to the different IW+ environmental impacts of the road industry at the midpoint level shows the contributions of direct emissions and purchases of the road industry to the different IW+ environmental impacts at the midpoint level. The figure illustrates the significant number of different factors to account for in the road industry when adopting a multicriteria
Figure 5 Figure 6
56Contributions of different activities to the different IW+ environmental impacts of the pavement industry at the midpoint level shows the contribution of direct emissions and purchases by category of Canada's road industry for endpoint indicators. The main contributors are almost identical between the
Figure 6
6Environmental drivers of Canada's road industry at the endpoint level
Figure 3
3already showed that, at the sector scale, GHG flows represent the most impact at the endpoint level. Figure 7 now focuses on this correlation for each category of purchase by the road industry in Canada. A linear regression shows a very good correlation between the contribution of each category of purchase to the GWP and the two endpoint indicators in the case of the road industry, with a coefficient of determination R 2 equal to 0.995 and 0.991 resp. for ecosystem quality and human health. The figure shows that other fuels purchases (blue dot under the regression line in the ecosystem
Figure 7
7Correlation between GWP (X-axis) and damages (Y-axis) per category of purchase from Canada's road industry 4.3 Canadian roads' carbon footprint by life-cycle stage Previously, the breakdown by contributors of Canada's road industry was presented. In this section, the impact of the production/maintenance/end-of-life of the road industry (shown previously) is compared to the roads' usage by vehicles (downstream scope 3 according to the GHG protocol (WBCSD and WRI, 2004)), including vehicle tailpipe and fuel supply chain GHG emissions. The relative contributions of this comparison are presented in Figure 8, and absolute values are in
Figure 8
8GHG emissions drivers on Canada's road network
specified in the limitations of openIO-Canada, the NPRI only covers a part of Canada's industrial sites. Indeed, according to the Canadian Environmental Protection Act, only the "owners or operators of facilities that meet published reporting requirements are required to report to the NPRI" (Government of Canada, 2020a). These requirements are a facility with more than 10 full-time employees -i.e. 20 000 hours of work per year -and carrying out specific activities, including quarry operations and operation of stationary combustion equipment (Government of Canada, 2021d). In Canada, around 8000 facilities report their pollutant releases in the 2017 NPRI, based on reporting requirements that mainly consider the type of activities, the total number of hours worked and substances manufactured (Government of Canada, 2011). But, in 2020 for instance, the manufacturing sector accounted for 90359 establishments, and the oil and gas extraction sector only 4125 (Government of Canada, 2021a
). It is the first opensource EEIO database developed for Canada. The database represents the whole Canadian economy while providing details at the provincial level, for years from 2014 to 2017. Hence, the model includes economic exchanges between the different provinces as well as specific consumptions and polluting emissions for each economic sector of each province. The economic data of openIO-Canada comes from the Supply and Use tables provided by Statistics Canada (StatCan) (Statistics Canada, n.d.), using a classification breaking down each province's economy in 492 commodities. The database is a single region input-output database and as such models international trade with local data, thus applying a domestictechnology assumption. It is therefore assumed that production abroad has the same intensity
as in Canada. GHG emissions and water use data are derived from the physical flow accounts
of StatCan, while the 323 other types of pollutants come from the National Pollutant Release
Inventory (NPRI) (Government of Canada, 2021b). Physical flow accounts are provided with
a lower level of detail than the economic accounts. (e.g. 240 vs 492 sectors for GHG
emissions and water flows). An economic allocation is thus performed to distribute the
environmental flows between the different products of the economic sectors. Moreover, we
attribute to imported products the same environmental flows as similar goods produced in the
importing region, as is typically done in many national EEIO tables (Eurostat : Statistisches
Amt der Europäischen Gemeinschaften, 2008).
Table 1
1Detail of the last two levels of agregation -levels 4 and 5
Aggregation level #5
Aggregation Level #4
Direct emissions
-
Bridges & tunnels
Concrete, cement, steel, aluminum, other metals
Asphalt mix materials
Asphalt products, crude oil, asphalt binders, aggregates, other minerals,
chemicals
Energies
Electricity, natural gas, other fuels
Freight
Air, rail, road, water, and other freight services and supports
Infrastructure and capital goods
Other metals, machinery, plastic and rubber, buildings and infrastructure
Services
Administrative services, other services, upstream sales
Staff consumptions
Other goods, paper and paperboard, staff transportation
4 Results and interpretation
4.1 Canada's environmental impacts
4.1.1 Environmental footprint contributions
Our analysis first focused on the diagnosis of the Canadian economy as a whole to get an
overview of the environmental impact contributors in Canada and the environmental footprint
of Canada and Canadians on a consumption-based approach. In 2017, Canada's consumption
was responsible for the release of 692 million tons of CO2eq (MtCO2eq). Considering a
population of 38.4 million inhabitants (Statistics Canada, 2021), the average Canadian emits
around 18.0 tCO2eq-GWP100 per year. This is consistent with the values published by
Table 2
2shows the contribution of the road sector to the total impact of Canada, as well as the contribution of the entire construction sector. It presents contributions within 0.54% to water use to 1.80% to particulate matter formation. In the climate change impact category, it accounts for 1.02%. It is also responsible respectively for 1.07 and 1.10% of the damage to ecosystems and human health. Overall, the contribution of the road sector to the national environmental impacts of Canada appears to be rather minor. Nevertheless, environmental preservation concerns now all sectors, whatever how important their impacts are, especially under the major risks generated by climate changes.0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Human health (DALY)
Ecosystem quality (PDF.m2.yr)
Climate change
(Eco)toxicity
Freshwater eutrophication
Marine acidification
Marine eutrophication
Freshwater acidification
Terrestrial acidification
Ozone layer depletion
Particulate matter formation
Photochemical oxidant formation
Table 2
2Contribution of the road and construction sectors to the total impact of Canada. The contribution of the road sector is included in the contribution of the entire construction sector.INDICATOR
CONTRIBUTIONS PER SECTOR
ROAD
SECTOR
ENTIRE CONSTRUCTION
SECTOR
ECOSYSTEM QUALITY
1.07%
12.13%
HUMAN HEALTH
1.10%
11.82%
CLIMATE CHANGE, SHORT TERM
1.02%
16.56%
FRESHWATER ACIDIFICATION
1.52%
11.67%
FRESHWATER EUTROPHICATION
0.68%
17.82%
MARINE EUTROPHICATION
1.64%
13.10%
FRESHWATER ECOTOXICITY
0.68%
30.88%
HUMAN TOXICITY, CANCER
1.28%
25.11%
HUMAN TOXICITY, NON-CANCER
1.67%
21.17%
OZONE LAYER DEPLETION
0.78%
20.82%
PARTICULATE MATTER FORMATION
1.80%
18.34%
PHOTOCHEMICAL OXIDANT FORMATION
1.43%
16.52%
TERRESTRIAL ACIDIFICATION
1.51%
12.13%
WATER USE
0.54%
7.52%
4.2.2 Main potential levers for the transition
1.
Midpoint contribution analysis
-mainly have a significant impact (>10%) on freshwater ecotoxicity, human cancer, and noncancer toxicities, ozone layer depletion and water use where they represent respectively 22, 15, 16, 18 and 15% of the contributions. Services -encompassing intragroup and external services as well as upstream sales -, have a prevalent role on the impact of freshwater eutrophication where they represent 56% of the impact. On other environmental indicators they contribute by 7 to 23%, thus being one the major contributors across all environmental indicators. Staff consumption -combining paper and paperboard purchases, other goods purchases, and staff transportation only has a significant impact (>10%) on freshwater eutrophication, freshwater ecotoxicity, human cancer and ozone layer depletion. Finally, freight services have negligible impacts except on climate change where they bring 5% of the emissions.
complete overview of the environmental issues for non-LCA expert decision-makers.Nevertheless, damage indicators are rarely used, and an overwhelming number of studies only focus on a midpoint climate change impact, i.e. GHG emissions. Depending on cases, solely focusing on the climate change impact might still represent a decent estimate for endpoint categories, provided results are correlated.0%
20%
40%
60%
80%
100%
Ecosystem quality
Human health
Direct emissions
Concrete
Cement
Steel
Other metals
Asphalt and asphalt products
Waste oil
Electricity
Natural gas
Other fuels
Aggregates
Other metals Other minerals
Chemicals
Freight
Staff transportation
Machinery
Other goods
Paper and paperboard
Plastic and rubber
Intragroup services
External services
Upstream sales
Buildings and infrastructures
Table 3 .
3It shows that the construction, maintenance, and end-of-life of the Canadian road network only represent 5% of its life cycle carbon footprint, i.e. 8 Mt CO2eq over the total 179 Mt CO2eq from the Canadian road transportation system. Most of the carbon and 20% from freight services (see SM). PVs include private freight trucks as well as sportutility vehicles (SUVs) and pickup trucks. Private freight trucks would account for one-third of the PVs emissions. SUVs and pickup trucks are very popular in Canada and account for services' life cycle emissions (see SM). Within the vehicles' amortization emissions, PVs account for 50%, freight services vehicles for 38%, and light commercial vehicles (LCV) for 12%. Finally, if vehicles' use stage emissions are further broken down, we see that providing vehicle fuel generates 15% of the road transportation system GHG emissions, while PVs'y = 0.932x -3E+06
R² = 0.9948
0.00E+00
1.00E+08
2.00E+08
3.00E+08
4.00E+08
5.00E+08
6.00E+08
0.0E+00
2.0E+08
4.0E+08
6.0E+08
Ecosystem quality damage (PDF.m2.yr)
GHG emissions (kgCO2eq)
y = 4E-06x + 2.6982
R² = 0.9912
0.00E+00
1.00E+03
2.00E+03
3.00E+03
4.00E+03
5.00E+03
6.00E+03
0.0E+00
1.0E+09
Human health damage (DALY)
GHG emissions (kgCO2eq)
Table 3
3GHG emissions from the Canadian road transportation systemScope
Source
GWP (kg CO2eq)
Infrastructure
Roads
8.23E+09
Tailpipe emissions
Buses
4.46E+07
LCVs
4.73E+08
Freight services
1.92E+10
Tourism
2.94E+07
School buses
1.58E+08
Taxis
2.19E+08
Private vehicles
8.24E+10
Fuel supply chain
Fuel
2.64E+10
Manufacturing
Buses
1.58E+08
Trailers
6.75E+08
LCVs
4.96E+09
Companies' trucks
1.52E+10
Tourism vans
5.09E+08
Other vehicles
4.13E+08
Private vehicles
1.93E+10
Maintenance
4.91E+08
TOTAL
TOTAL EMISSIONS
1.79E+11
Fourth, the NPRI has some limitations. This readily available Canadian national emission andconsumption database does not cover all the flows accounted for in LCA databases, such as
ecoinvent. While NPRI covers a fair amount of 323 types of substances, some flows are
nevertheless missing, such as land occupation/transformation, ionizing radiations, water
consumption, as well as mineral and fossil resource use. Moreover, the NPRI covers emissions
of the 8000 most important complying industrial sites across Canada. Pollutant emissions
(other than GHG emissions) are thus underestimated, as many smaller industrial sites are not
covered by the NPRI.
all substances except GHGs, the latter being assessed with physical accounts). As a result, the estimation of the climate change indicator reliably covers the whole Canadian economy while the estimation for other impact categories may not. This, to date, limits somehow the robustness Moreover, the overwhelming contribution of climate change to the damage to ecosystems and human health (section 4.1.2.) could result from the truncation of the NPRI data used in the current version of openIO-Canada. It could also explain the low contributions of direct emissions to midpoint indicators (section 4.2.2.). Assessing this bias will require improving the coverage of non-GHG emissions by openIO-Canada in the future, nonetheless, all the methodological aspects proposed to use EEIO analysis to sketch environmental transition plans are totally valid.5.3 Articulation between EEIO analysis and LCA for transition plans5.3.1 EEIO analysis as a screening tool to build upon for LCAEEIO analysis can be a screening tool for transition plan development, but it can also be used to orientate LCA methodological choices such as system boundaries or LCI regionalization, by looking at the contribution of specific products and services calculated with EEIO databases, as detailed below.). Thus, the completeness of the activities covered by the NPRI database is rather poor
in number of sites but may be good in the percentage of production covered as it includes major
producers. Nevertheless, we do not have access to this information yet, and this flaw in the
coverage leads to an unknown underestimation of the substances assessed with the NPRI (i.e.,
of some conclusions, for instance the correlation between climate change and endpoint
categories shown in section 4.2.3. Indeed, if only climate change is characterized
comprehensively, it creates a bias towards its contribution in both endpoint categories.
Acknowledgement: the authors want to thank Ivan Drouadaine, Amelie Griggio, and Marc Proteau for funding this project and supporting it technically. They also thank Jimmy Mikedis, Supervisor of the Data Service Centre of Statistics Canada, Anna Hatzihristidis, Consulting analyst at the Statistical Information Service of Statistics Canada, as well as their colleagues, for their help in navigating Canada's use and supply table classification codes. They are also grateful to Bitume Quebec, and especially Stéphane Trudeau, technical director, for exchanging on the market of bitumen and roads in Canada. Funding source and role: this study has been conducted under the research project HEATI (Harmonized Environmental Assessment of Transportation Infrastructure) funded by the technical department of Eurovia -VINCI group. The work has been hosted at the Americas Technical Center of Eurovia Canada. statement: OpenIO-Canada is accessible online: https://github.com/CIRAIG/OpenIO-Canada. The case study calculation algorithm is available on Zenodo (https://doi.org/10.5281/zenodo.6505413). Excel spreadsheets of category aggregation, as well as raw and worked results, are also made available in the supplementary material. Authors' contribution: Conceptualization: ADB; Methodology: ADB, MA; Data curation: ADB, MA; Formal analysis: ADB; Software: MA; Validation: ADB; Visualization: ADB, MA; Roles/Writing -original draft: ADB; Writing -review & editing: MA; Funding acquisition: ADB.Data
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| sample_1309 | 0.9913 | arxiv | |
Doppler wind measurements in Neptune's stratosphere with ALMA
May 12, 2023 May 12, 2023
Óscar Carrión-González
LESIA
Observatoire de Paris
Université PSL
CNRS
Sorbonne Université
Université Paris Cité
5 place Jules Janssen92195MeudonFrance
Raphael Moreno
LESIA
Observatoire de Paris
Université PSL
CNRS
Sorbonne Université
Université Paris Cité
5 place Jules Janssen92195MeudonFrance
Emmanuel Lellouch
LESIA
Observatoire de Paris
Université PSL
CNRS
Sorbonne Université
Université Paris Cité
5 place Jules Janssen92195MeudonFrance
Thibault Cavalié
LESIA
Observatoire de Paris
Université PSL
CNRS
Sorbonne Université
Université Paris Cité
5 place Jules Janssen92195MeudonFrance
Laboratoire d'Astrophysique de Bordeaux
Univ. Bordeaux
CNRS
Allée Geoffroy Saint-Hilaire
B18N, 33615PessacFrance
Sandrine Guerlet
LESIA
Observatoire de Paris
Université PSL
CNRS
Sorbonne Université
Université Paris Cité
5 place Jules Janssen92195MeudonFrance
Laboratoire de Météorologie Dynamique/Institut Pierre-Simon Laplace (LMD/IPSL)
Sorbonne Université
CNRS
École Poly-technique
Institut Polytechnique de Paris
École Normale Supérieure (ENS)
PSL Research University
ParisFrance
Gwenaël Milcareck
Laboratoire de Météorologie Dynamique/Institut Pierre-Simon Laplace (LMD/IPSL)
Sorbonne Université
CNRS
École Poly-technique
Institut Polytechnique de Paris
École Normale Supérieure (ENS)
PSL Research University
ParisFrance
Aymeric Spiga
Laboratoire de Météorologie Dynamique/Institut Pierre-Simon Laplace (LMD/IPSL)
Sorbonne Université
CNRS
École Poly-technique
Institut Polytechnique de Paris
École Normale Supérieure (ENS)
PSL Research University
ParisFrance
Noé Clément
Laboratoire d'Astrophysique de Bordeaux
Univ. Bordeaux
CNRS
Allée Geoffroy Saint-Hilaire
B18N, 33615PessacFrance
Jérémy Leconte
Laboratoire d'Astrophysique de Bordeaux
Univ. Bordeaux
CNRS
Allée Geoffroy Saint-Hilaire
B18N, 33615PessacFrance
Doppler wind measurements in Neptune's stratosphere with ALMA
May 12, 2023 May 12, 2023Astronomy & Astrophysics manuscript no. aanda Letter to the EditorPlanets and satellites: atmospheres -Planets and satellites: gaseous planets -Radiative transfer
Context. Neptune's tropospheric winds are among the most intense in the Solar System, but the dynamical mechanisms that produce them remain uncertain. Measuring wind speeds at different pressure levels may help understand the atmospheric dynamics of the planet.Aims. The goal of this work is to directly measure winds in Neptune's stratosphere with ALMA Doppler spectroscopy. Methods. We derived the Doppler lineshift maps of Neptune at the CO(3-2) and HCN(4-3) lines at 345.8 GHz (λ ∼ 0.87 mm) and 354.5 GHz (0.85 mm), respectively. For that, we used spectra obtained with ALMA in 2016 and recorded with a spatial resolution of ∼0.37" on Neptune's 2.24" disk. After subtracting the planet solid rotation, we inferred the contribution of zonal winds to the measured Doppler lineshifts at the CO and HCN lines. We developed an MCMC-based retrieval methodology to constrain the latitudinal distribution of wind speeds. Results. We find that CO(3-2) and HCN(4-3) lines probe the stratosphere of Neptune at pressures of 2 +12 −1.8 mbar and 0.4 +0.5 −0.3 mbar, respectively. The zonal winds at these altitudes are less intense than the tropospheric winds based on cloud tracking from Voyager observations. We find equatorial retrograde (westward) winds of −180 +70 −60 m/s for CO, and −190 +90 −70 m/s for HCN. Wind intensity decreases towards mid-latitudes, and wind speeds at 40 • S are −90 +50 −60 m/s for CO, and −40 +60 −80 m/s for HCN. Wind speeds become 0 m/s at about 50 • S, and we find that the circulation reverses to a prograde jet southwards of 60 • S. Overall, our direct stratospheric wind measurements match previous estimates from stellar occultation profiles and expectations based on thermal wind equilibrium. Conclusions. These are the first direct Doppler wind measurements performed on the Icy Giants, opening a new method to study and monitor their stratospheric dynamics.
Introduction
Voyager 2 measurements of Neptune's atmosphere revealed some of the most intense zonal winds ever measured in the Solar-System planets (Hammel et al. 1989;Smith et al. 1989). This was done by tracking cloud motions in images of Voyager's ISS instrument, and constrained Neptune winds to be −400 m/s (retrograde) at the equator, with a prograde jet of about + 250 m/s at latitude 70ºS (Limaye & Sromovsky 1991;Sromovsky et al. 1993). Subsequent cloud-tracking measurements with the Hubble Space Telescope (Sromovsky et al. 2001a,b) and ground-based observatories with adaptive optics (Fitzpatrick et al. 2014;Tollefson et al. 2018) confirmed this general wind pattern (Fletcher et al. 2020).
Cloud-tracking methods, however, generally lack an accurate constraint of the atmospheric altitudes probed by the observations. Although clouds are mostly expected to be located in the upper troposphere (∼100 mbar-1 bar), determining the exact cloud-top pressure levels requires multiple-scattering radiativetransfer computations. These are highly dependent on the assumed optical properties of the atmospheric aerosols, and on e-mail:
oscar.carrion@obspm.fr, oscar.carrion.gonzalez@gmail.com the assumed vertical distribution of gaseous species and aerosols (e.g. Luszcz-Cook et al. 2016). Furthermore, cloud pressure levels have been found to vary with latitude by about an order of magnitude (Irwin et al. 2011(Irwin et al. , 2016Hueso et al. 2017). Even clouds at similar latitudes have been found to be located at pressure levels as different as 30 and 300 mbar .
Above the cloud level, wind information has been derived primarily from the thermal wind equation that relates the latitudinal temperature gradient to the vertical wind shear. Temperature fields from Voyager/IRIS spectra were initially used for this (Conrath et al. 1989). Later, additional ground-based thermal observations became available . At tropospheric levels, these data consistently indicate a warm equator, cool mid-latitudes and a warmer south pole. Albeit it cannot be applied at the equator, the thermal wind equation implies decaying winds with altitude at low latitudes (-30°to 30°) and essentially altitude-independent winds at mid-to-high southern latitudes. Relatively small changes were found in the predicted circulation pattern from 1989 to 2003 (southern summer solstice), except near the south pole, found to be anomalously warm (by ∼5 K) in 2003 (Orton et al. 2007).
Additional wind measurements with other techniques were performed for a reduced number of latitudes. French et al. (1998) Article number, page 1 of 8 arXiv:2305.06787v1 [astro-ph.EP] 11 May 2023 measured stratospheric winds from three stellar occultations over 1985-1989, constraining the wind-distorted shape of the planet. They inferred that wind speeds at the 0.38 mbar level are 0.6±0.2 times those of Voyager cloud-tracking from Sromovsky et al. (1993). Also, they found tentative evidence of winds at 0.7 µbar further decaying to ∼0.17 times the tropospheric values. This was the first direct evidence for the decay of winds above the tropopause, with an estimated wind shear in agreement with that inferred from Voyager temperature fields at deeper levels.
In this work we aim to directly measure Neptune's stratospheric winds based on Doppler lineshift measurements of CO and HCN lines with the Atacama Large Millimeter/submillimeter Array (ALMA). Millimetric and submillimetric measurements have already been used to directly measure the winds in the atmospheres of Venus (e.g. Lellouch et al. 2008, and references therein), Mars (Lellouch et al. 1991;Cavalié et al. 2008;Moreno et al. 2009), Jupiter (Cavalié et al. 2021), Saturn (Benmahi et al. 2022), and Titan (Moreno et al. 2005;Lellouch et al. 2019;Cordiner et al. 2020). No such analysis was available for the Icy Giants to date. Besides probing the otherwise difficult-to-sound stratosphere, an advantage of the technique is that it is insensitive to aerosols, reducing considerably the uncertainties on the probed levels.
Observations
We observed Neptune on April 30, 2016, during 20 minutes onsource, with 41 antennas of the ALMA interferometer in the C36-2/3 hybrid configuration, yielding an angular resolution of about 0.37". The spectral setup included the CO(3-2) line at 345.7959899 GHz and the HCN(4-3) line at 354.5054773 GHz, as well as the CS(7-6) line at 342.883 GHz (whose detection was reported in Moreno et al. 2017), with a spectral resolution of 1 MHz.
The bandpass, amplitude and phase calibration procedure of the CS visibilities was described in Moreno et al. (2017), and we applied the same calibration procedure to the CO and HCN data using the ALMA/CASA data reduction software.
The resulting calibrated visibilities were then exported into the GILDAS package to i) apply a self-calibration technique using Neptune's continuum to improve image quality ii) perform the imaging and deconvolution using the Högbom algorithm (Högbom 1974). We obtained a synthetic elliptical beam (robust weighting 0.5) of 0.39"×0.34" (polar angle (PA) of -47 • ) for CO and 0.37"×0.35" (PA = -82 • ) for HCN. The planet's angular diameter was 2.24". This yields a spatial resolution of about 20 • at the equator. The resulting spectral maps are shown Fig. A.1 with signal-to-noise ratio (SNR) at line peak at the limbs of about 150 and 50, respectively for CO and HCN. The final clean images were built with a sampling of 0.05" over -1.4" and +1.4" (3136 points).
An example of the observed lines is shown in Fig. 1. The detailed analysis of the lineshapes in terms of spatial/vertical distribution of temperature, CO and HCN is left for future work. For the purpose of measuring winds from line central positions, we performed Gaussian fits: we used 3-Gaussian fits for CO (with initial FWHM of 4, 20, 80 km/s) and 2-Gaussian fits for HCN (with initial FWHM of 3, 16 km/s) as shown in Fig. 1. We retained the narrowest component to measure the Doppler lineshift. The high SNR in our maps allowed us to derive the Doppler lineshifts with an averaged velocity accuracy of 25 and 37 m/s, respectively for CO and HCN (Fig. 2, right column).
Model
Radiative transfer
We used the same Neptune radiative transfer model described in Moreno et al. (2017), as well as their thermal profile and their CO and HCN vertical distributions, to model the spectral lines of CO and HCN, and to compute the wind weighting function shown in Fig. 1. Wind weighting functions account for the spectrally-dependent wind information content of each channel within lines (see e.g. Lellouch et al. 2019), and were convolved by the beam. At the limb, which is where most of the wind information comes from, CO lines probe the 2 +12 −1.8 mbar level, and HCN probe the 0.4 +0.5 −0.3 mbar level.
Wind retrieval methodology
In order to interpret the measured Doppler lineshifts, we developed a retrieval framework for the wind profiles based on the Markov-Chain Monte Carlo emcee sampler (Foreman-Mackey et al. 2013). The observed lineshifts correspond to the sum of the line-of-sight Doppler displacement due to the planetary rotation and the winds. The planet rotation was modelled as solidbody rotation at the altitude of the 1 mbar level above the local planet radius. Although somewhat different rotation periods have been proposed (Helled et al. 2010;Karkoschka 2011), a period of 16.11 h (Warwick et al. 1989;Lecacheux et al. 1993) is adopted here to enable comparisons with the Voyager winds.
We parameterized the wind profiles (W), assumed purely zonal, as a polynomial function depending on the latitude (φ, given in degrees) in the form:
W = n (a n × φ n )(1)
and explored with emcee the parameter space described by the coefficients a n , given in m/s. The box priors which set the limits of the parameter space were [-500, 500] for the a 0 coefficient and [-1, 1] for the rest of coefficients. We tested polynomial orders from 0 to 5 for the wind parameterization, as discussed in Sect. 4. The MCMC sampler tests points of the n-dimensional parameter space of a n coefficients. For each test point, we computed the wind profile at latitudes φ ∈ [−90 • , 90 • ] and the resulting wind map, with a pixel stepsize of 0.05". To simulate the line-of-sight Doppler lineshifts at each point of the map, we projected the zonal winds onto the planet geometry, accounting for the sub-observer latitude of 26.2ºS. We then weighted the modelled lineshifts by the local intensity of the CO (resp. HCN) line and convolved by the ALMA beam, following a similar procedure to Lellouch et al. (2019). After adding the contribution of the solid body rotation, the test wind map (W test ) was compared with the one measured by ALMA (W ALMA ) for the molecule under study (Fig. 2, middle) by means of the χ 2 figure of merit: This convergence criterion ensures that the sampling of the parameter space has been completed and the sampled test points are effectively independent (Goodman & Weare 2010). For the analysis of each retrieval run, we discarded the samples of the first τ steps ("burn-in phase"). For each retrieval run, we defined the ensemble of good fits as those sampled wind profiles with a χ 2 value in the 68.3% (i.e. 1-σ) confidence level. That is, with χ 2 verifying:
χ 2 = N p i=1 W test − Wχ 2 − χ 2 min ≤ C × χ 2 min N × f oversampling(3)
Here, χ 2 min is the minimum χ 2 value among all the samples in the run, and χ 2 min /N is the reduced value of χ 2 min , with N equal to the degrees of freedom of the retrieval (N = N p − n). The factor f oversampling = Area beam /Area pixel accounts for the fact that with a spatial sampling step of 0.05" and a beam of 0.37", the measurements are considerably oversampled, and the number of independent measurements is N p / f oversampling . The coefficient C denotes the 1-σ confidence region in the n-dimensional parameter space, where n is the number of a n coefficients in the polynomial fit. For polynomial orders 0 to 5, C is 1.0, 2.3, 3.53, 4.72, 5.89, and 7.04, respectively (see Ch. 15.6 in Press et al. 2007).
Results
With the method above, we carried out wind retrievals for the CO and HCN measurements. We ran retrievals for wind parameterizations with polynomials of orders between 0 and 5. Previous cloud-tracking studies had generally assumed latitudinally symmetric wind profiles and thus omitted odd polynomial orders (Sromovsky et al. 1993;Fitzpatrick et al. 2014;Tollefson et al. 2018). However, the spatial resolution achieved in our data is potentially sensitive to latitudinal wind asymmetries. We therefore kept odd polynomial orders in our retrievals.
The retrieval results for CO and HCN with polynomial fits of orders 0 to 5 are shown in Fig. B.1. The 6th-order polynomial fit to Voyager's cloud-tracking measurements (Sromovsky et al. 1993) is shown for comparison. For each tested polynomial order, we include in Fig. B.1 the map of residuals between the observed Doppler lineshifts and the best-fitting model (solid rotation plus wind) to assess the variation of fit quality as a function of polynomial degree. For both CO and HCN, we find that the value of χ 2 /N is practically the same for retrievals or orders 3, 4 and 5. This implies that these polynomials are similarly able to fit the measurements at the latitudes we are sensitive to. Indeed, the three parameterizations retrieve similar values of the zonal winds at latitudes over 20 • N to 70 • S.
Given Neptune's sub-observer latitude of 26.2°S and projection effects, wind information is restricted to latitudes southward of 40°N. In addition, the beam size of 0.37" prevents detailed information at southern polar latitudes. Angular speed considerations indicate that the wind speed should theoretically be zero at the pole. We find that this constraint is met within error bars for 4th and 5th-order polynomial fits. Order n=4 thus represents a good compromise between the model's mathematical complexity and physical realism, and we adopt it as the reference wind parameterization. Figure 3 shows the retrieved wind profiles for the reference n=4 parameterization. Table 1 shows the polynomial coefficients for CO and HCN best-fit wind profile, as well as the coefficients that parameterize the envelope of good solutions -those verifying Eq. (3)-using a fourth-order polynomial fit. Fig. 3 also shows our retrieved wind measurements at 0 • , 20 • and 70 • S as a function of pressure. For reference, the plot includes previously reported zonal winds (see discussion in Sect. 5). −50 m/s for HCN. Additional measurements will be needed to confirm this behaviour, eventually when regions further North become observable.
Discussion
Our results provide a new method to probe Neptune's stratospheric winds and wind shear, also yielding latitudinal information. In Fig. 3, representative values of wind speeds at 0°, 20°, and 70°S from CO and HCN are plotted in the context of previous measurements. Within errors, our values agree with thermal winds calculated by Fletcher et al. (2014), both for their reanalysis of the Voyager/IRIS data and for their 2003 Keck data. Our retrieved winds also agree with the wind speed at 0.38 mbar derived by French et al. (1998) from stellar occultations. Comparison with the Voyager 2 cloud-tracking winds (Sromovsky et al. 1993) also confirms a decay of the wind intensity with latitude, and a smaller wind shear at high latitudes. Although the various observations pertain to different epochs, our results validate predictions of the thermal wind equation and argue for a preservation of the general circulation pattern over the 28 year interval (∼60 degrees in heliocentric longitude) spanned by the data around the 2005 southern summer solstice. and ∼1 bar respectively, this indicates a +70 +30 −20 m/s wind shear per pressure decade, (or ∂u/∂z = +30 ± 10m/s per scale height) where the positive sign is related to the retrograde wind direction. At 70ºS, our winds are about 70 +180 −170 m/s less intense than Voyager's. We find a much smaller wind shear at 70ºS, although the uncertainties are larger than for equatorial winds: −20 ± 60 m/s per pressure decade (or ∂u/∂z = −9 ± 25m/s per scale height). Our results compare well with the estimates from French et al. (1998, their Fig. 11b), who studied the wind-shear between Voyager's cloud-tracking winds (which they assumed at 100 mbar) and their occultation data at 0.38 mbar. French et al. (1998) determined a wind shear of about +30 m/s per scale height at the equator, and -15 m/s per scale height at 70ºS.
In contrast, cloud-tracking measurements from Tollefson et al. (2018) appear somewhat at odds with our estimated wind shear, as their H band measurements -assumed by the authors to probe deeper levels-indicate less intense winds than the K' band. Tollefson et al. (2018) assumed that the H-band (resp. K' winds) probe the 1-2 bar (resp. 10-100 mbar) level. This led them to an inverted wind shear, with equatorial winds becoming more intense with increasing altitude. They attempted to explain this behavior by invoking a thermal-compositional wind equation that accounts for density changes associated to latitudinal variations of the methane abundance. Such an approach is not warranted according to our results. Furthermore, the absolute sounded pressures are uncertain and highly model-dependent, and both bands might not be probing such different pressure levels (Tollefson et al. 2018, Fig. 16 therein). Similarly, Fitzpatrick et al. (2014) find differences between their cloud-tracking H and K'-band winds. The pressure levels of the observed clouds are also uncertain in this case, with both H and K'-band clouds spanning pressure levels between 0.1-0.6 bar (Fitzpatrick et al. 2014, Fig. 11 therein).
In itself, the consistency of our direct wind measurements with thermal wind calculations does not highlight a particular mechanism responsible for the wind decay with altitude: the thermal wind equation simply states a balance between vertical wind shears and temperature meridional gradients. The wind decay reported here indicates a drag source, which could be the propagation and breaking of gravity and/or planetary waves (common in planetary stratospheres), although this has to be tested in dynamical simulations. On Saturn and Jupiter, interactions between vertically-propagating waves and the mean zonal flow drive strong acceleration and deceleration of the stratospheric equatorial zonal flow (e.g. Cosentino et al. 2017;Bardet et al. 2022). Wave breaking as a source of friction was also hypothesized by Ingersoll et al. (2021) to maintain the stacked circulation cells in Jupiter's upper troposphere.
Our measurements open a new window in the study of Neptune's stratospheric dynamics. Also, our findings provide useful information for general-circulation modelling studies (Liu & Schneider 2010;Milcareck et al. 2021), which require observations to compare with the outputs of the numerical simulations. Our wind measurements remain nevertheless modest in precision, as a result of combined limited integration time and low spatial resolution. Future dedicated observations, possibly combined with long-term monitoring (given the duration of Neptune seasons), are expected to yield further insight into the topic.
Fig. 1 .
1Example of measured spectra (left column) of CO(3-2) and HCN(4-3) lines (black) at the position of the sky western equatorial limb, at an offset from Neptune centre (-1.1", 0.0"). Individual Gaussian fit components with FWHMs of about 4, 20, 80 km/s are shown in dashed blue, and their sum in red. Also shown, the beam-convolved solid body velocity (black dotted line) and the fit velocity (red dotted line). The difference of these two velocities allows us to derive the Doppler winds. Right: Normalized wind contribution functions (WCF) at the limb for each molecule. convergence criterion to stop the run at a number of steps larger than 50 times the autocorrelation time (τ, see Foreman-Mackey et al. 2013, for details).
Fig. 2 .
2ALMA Doppler measurements for the CO(3-2) line (top row) and the HCN(4-3) line (bottom row). Left: measured Doppler lineshift. Middle: line-of-sight winds, after subtracting the solid-body rotation. Right: root-mean square (rms) of the measured winds. The top-right ellipse in each subplot shows the synthetic beam. Latitudes are shown in 20 • steps, with the equator in a thicker line.
+2 8.76×10 −1 6.04×10 −2 -7.44×10 −4 -5.50×10 −6 CO upper error -1.29×10 +2 -3.25×10 −1 5.42×10 −2 1.41×10 −3 2.72×10 −5 CO lower error -2.28×10 +2 8.53×10 −1 1.42×10 −2 -2.89×10 −3 -3.06×10 −5 HCN best fit -1.87×10 +2 -8.11×10 −1 8.39×10 −2 4.53×10 −4 2.14×10 −6 HCN upper error -1.07×10 +2 -7.46×10 −1 6.61×10 −2 1.29×10 −3 2.11×10 −5 HCN lower error -2.40×10 +2 4.92×10 −1 7.47×10 −2 -1.79×10 −3 -2.92×10 −5At the equator, we retrieve retrograde (westward) zonal winds of −180 +70 −60 m/s from CO measurements, and −190 +90 −70 m/s from HCN. We find a decrease in the wind intensity towards mid-latitudes. At 20• S, wind speeds are −170 +50 −40 m/s for CO (−140 +60 −60 m/s for HCN), and at 40 • S they are −90 +50 −60 m/s for CO (−40 +60 −80 m/s for HCN). Winds continue this trend towards southern latitudes, becoming 0 m/s at about 50 • S. At 70 • S, winds are prograde (eastward) although uncertainties are larger (180 +130 −110 m/s for CO, and 180 +110 −140 m/s for HCN). Further South than 70 • S, winds remain unconstrained due to the limited spatial resolution. Wind speeds in the observable northern-hemisphere latitudes are compatible, within errors, with a symmetric wind profile. At 20 • N, zonal winds are −150 +30 −80 m/s for CO and −170 +80
Fig. 3 .
3Retrieval results. Left: Retrieved best-fitting wind profiles for CO (red line) and HCN (blue line) measurements, using a fourth-order polynomial. Red and blue shadowed regions contain the ensemble of good fits according to the χ 2 criterion from Eq. (3). The semi-transparent grey rectangle indicates the unobservable northern latitudes. The solid black line shows the sixth-order fit to Voyager's cloud-tracking winds(Sromovsky et al. 1993). Right: Wind variations with altitude at the equator, 20ºS and 70ºS, both for our measurements and for a set of references in the literature (see Sect. 5 for details). Cloud-tracking winds fromFitzpatrick et al. (2014) andTollefson et al. (2018) are not shown at 70 • S as they have uncertainties of about 1000 m/s. Winds fromFletcher et al. (2014) do not correspond to a direct measurement, but to the computed thermal wind equation applied to a reanalysis of the 1989 IRIS/Voyager data (dashed grey lines) and to 2003 Keck data (dashed cyan lines).
Table 1 .
1Polynomial coefficients of the best fits to the CO and HCN zonal wind measurements. Also given, the coefficients that approximate the envelope of good fits to a fourth-order polynomial.
(2) where rms ALMA is the 1-σ error of the ALMA measurement for the molecule under study(Fig. 2, rightmost column) and N p is the number of pixels in the wind map.We used 50 chains (or "walkers") to simultaneously explore the parameter space independently in order to avoid possible χ 2 local minima. The 50 walkers ran for up to 5×10 4 steps, with a Article number, page 2 of 8 Óscar Carrión-González et al.: Doppler wind measurements in Neptune's stratosphere with ALMA
Article number, page 4 of 8 Óscar Carrión-González et al.: Doppler wind measurements in Neptune's stratosphere with ALMA
A&A proofs: manuscript no. aanda ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-20-CE49-0009 (project SOUND). T. Cavalié acknowledges funding from CNES.Appendix A: Measured spectral mapsFig. 3, the top row shows the retrieved wind profiles for CO and HCN but using different polynomial orders for the wind parameterization. The value of χ 2 min /N is shown in the legend. We also show the residual maps of CO (middle row) and HCN (bottom row) after subtracting the best-fitting wind profile to the measurements.
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| sample_1321 | 0.651 | arxiv | |
Co-optimization of power line shutoff and restoration under high wildfire ignition risk
Noah Rhodes *nrhodes@wisc.edu
Department of Electrical and Computer Engineering
University of Wisconsin-Madison Madison
WI United States
Line A Roald
Department of Electrical and Computer Engineering
University of Wisconsin-Madison Madison
WI United States
Co-optimization of power line shutoff and restoration under high wildfire ignition risk
Index Terms-Wildfire risk mitigationpreemptive power shut- offsgrid restorationmixed-integer optimization
Electric power infrastructure has ignited several of the most destructive wildfires in recent history. Preemptive power shutoffs are an effective tool to mitigate the risk of ignitions from power lines, but at the same time can cause widespread power outages. This work proposes a mathematical optimization problem to help utilities decide where and when to implement these shutoffs, as well as how to most efficiently restore power once the wildfire risk is lower. Specifically, our model co-optimizes the power shutoff (considering both wildfire risk reduction and power outages) as well as the post-event restoration efforts given constraints related to inspection and energization of lines, and is implemented as a rolling horizon optimization problem that is resolved whenever new forecasts of load and wildfire risk become available. We demonstrate our method on the IEEE RTS-GMLC test case using real wildfire risk data and forecasts from US Geological Survey, and investigate the sensitivity of the results to the forecast quality, decision horizon and system restoration budget. The software implementation is available in the open source software package PowerModelsWildfire.jl.
I. INTRODUCTION
Wildfire ignitions caused by electrical equipment are an increasing concern for power grid operators. In Australia, electrical infrastructure accounts for 30% of bushfire ignitions during droughts and heat-waves [1]. The state firefighting organization in California reports that between 2015-2020, wildfires ignited by electrical equipment were responsible for more than 70% of damages ($17.5 billion) despite accounting for only 10% of ignitions [2]. Given these insights, focus on wildfire-grid interactions has expanded from almost exclusively considering how the grid is impacted by fires (discussed in e.g. [3]- [7]) to also consider how to reduce the risk of wildfire ignitions. Refs. [8]- [11] review approaches to reduce the risk of ignitions, many of which are already being implemented or planned by utilities. For example, Pacific Gas & Electric (PG&E) in California plans to underground 10,000 miles of distribution lines over the course of more than a decade at a cost of $20 billion [12], along with other measures such as more frequent vegetation clearing. Unfortunately, the significant cost and need for qualified crews and equipment means that these risk reduction approaches take time to implement. Meanwhile, power system operators rely on short-term measures to reduce risk, including changes to the protection This work was supported by the U.S. National Science Foundation AS-CENT program under award 2132904. system settings [3] or Public Safety Power Shutoffs (PSPS), which de-energize grid equipment during high wildfire risk events. While highly effective in reducing wildfire risk [13], PSPS also cause large scale power outages that may last for days [14] with significant economic and health impacts. To address the question of how to balance the benefits of wildfire risk reduction with the impacts of power outages, [15] proposed a framework to optimally balance wildfire risk reduction and power outage sizes when deciding which lines to shut off. Other approaches focus on accelerating the solution time to enable efficient planning of optimal PSPS on large networks in real time, including data-driven methods to plan PSPS by training machine learning models with optimization problems results [16]- [18], or using a dynamic programming approach to optimize a PSPS [19]. Studies on how to reduce the impact of and need for PSPS include [20], which proposes an optimal investment model for installation of batteries and under-grounding power lines, and [21], which studies how microgrids can improve resilience against unplanned outages due to events like wildfires, and [22], which expands on timevarying risk and operational factors such as energy storage for temporal load-shifting. Other related research considers extensions to distribution grids [23], consideration of fairness of repeated PSPS events [24], and improved forecasting of wildfire ignition risk [18], [25].
Although the above methods may help identify locations where de-energization is needed, they do not consider the postevent restoration process. Before a line can be re-energized, it must be inspected by utility crews to ensure that no damage that could cause ignitions has occurred. Thus, while de-energization of a line can happen instantaneously, the restoration process can take hours or days [26]. To balance power outages and ignition risk, we therefore need to consider the size and duration of power outages both during the initial shut-down and throughout the restoration process.
In this paper, we aim to address this gap. Our first and main contribution is to develop the multi-period optimal power shutoff and re-energization (MOPSAR) problem, a mixedinteger optimization model which co-optimizes power shutoffs and re-energization. The formulation leverages prior work on balancing wildfire risk and power outages for a single time period [15] and post-disaster restoration planning [27], but significantly extends these (and other) existing formulations in several ways. First, our model is the first to integrate both power shutoffs and re-energization in one model. Second, we solve the MOPSAR problem as a rolling horizon problem which is rerun daily with updated wildfire risk forecasts, which allows us to consider evolving wildfire risk over a prolonged time horizon and mitigate the impact of forecast errors. Third, we include a new penalty on shutoffs of low-risk lines, as such power shutoffs may increase the operational vulnerability of the network during a shutoff.
Our second contribution is to use our improved problem formulation to investigate important aspects of the problem. We assess how line inspection constraints impact both wildfire risk and power outage sizes, how using a longer forecast horizon impacts the solution quality and computational time, and how the choice of power shutoff penalty impacts the tradeoff between grid vulnerability and wildfire risk.
The remainder of the paper is organized as follows. Section II introduces the problem formulation. Section III presents the case study and problem setup, and analysis of the results. Section IV concludes the work.
II. MODELING AND PROBLEM FORMULATION
In this section, we formulate the Multi-period Optimal Power Shutoff And Restoration (MOPSAR) problem that provides an optimized schedule for both power line shutoffs and restoration. It is solved daily in a rolling horizon framework as new risk forecast data is made available each day.
A. Rolling Horizon Formulation
We consider a power grid with a set of buses B, lines L, generators G and loads D. This grid has elevated wildfire risk, and the operator is planning a public safety power shutoff to mitigate the wildfire threat. The operator must make decisions on the power lines they may shutdown, customers they may disconnect, and how to re-energize the grid. Their goal is to reduce wildfire risk while minimizing the size and duration of customer power outages and maintaining grid reliability.
Wildfire risk depends on ambient conditions such as vegetation cover, humidity and wind speed. The Wildland Fire Potential Index (WFPI) [28] provides wildfire risk data for the contiguous United States, is released daily and includes current data along with 7-day forecasts. Because it takes time to restore a power line after it has been shut off, we need to take the forecasted risk into account when deciding on an optimal schedule for power shutoffs and restoration. Furthermore, because the wildfire risk forecasts evolve and become more accurate with time, it makes sense to update the schedule daily as new information becomes available. We therefore formulate our problem as a rolling horizon problem.
For a given day T , a Multi-period Optimal Power Shutoff And Restoration (MOPSAR) problem, shown in Model 1, is solved. This problem considers the status of the power lines at the beginning of day T (i.e. whether a line is energized or not) as well as grid constraints, and current and forecasted wildfire risk for all timesteps t ∈ T where T = {T, ..., T +H} includes the current day and all days in the forecast horizon H. Once a solution is obtained, the power shutoff and restoration actions for the first day t = T are then implemented on the power grid. The next day, we repeat the optimization process with T ← T +1, incorporating the updated power line statuses based on the solution from the previous day and updated wildfire risk information. We next present the mathematical formulation of the MOPSAR problem.
B. Objective function
The system operator is pursuing three different objectives, namely maximizing load, minimizing wildfire risk and maintaining grid reliability. We describe each of these below.
1) Load served: The load D Served is calculated as
D Served = t∈T d∈D x dt w dt P D dt .(1)
Here, P D dt is a parameter expressing the total demand for electricity from load d at time period t and w dt is a weight used to express increased priority for certain loads (e.g. a hospital may have a higher weight). We assume that load can be continuously shed, with the continuous decision variable x dt representing the percentage of load that is served. The total demand served D Served is obtained by summing over all loads d ∈ D and all time periods t ∈ T .
2) Wildfire risk: We express the total risk of wildfire ignitions based on the wildfire risk associated with each transmission line in the network, i.e.
R F ire = t∈T ij∈L z ijt R ijt (2)
Here, R ijt represents the risk of a wildfire ignition from line ij at time t if the line is energized (we discuss how to obtain these risk values in the case study). The binary decision variable z ijt represents the status of the line, with z ijt = 1 indicating that it is on and z ijt = 0 indicating that it is off. This formulation assumes that by choosing to de-energize the line, i.e. z ijt = 0, we reduce the wildfire risk of line ij at time t to zero.
3) Grid Vulnerability: Because grid operational security benefits from redundant transmission paths, we would like to keep low risk lines in operation even if they do not contribute to serving more load. To incorporate the effect of power shutoff on grid operational security, we introduce a penalty on power shutoffs,
V system = t∈T ij∈L (1 − z ijt )V(3)
Here, V represents the increased vulnerability of the grid associated with turning off an individual line and V System represents the total vulnerability of the network. Next, we combine R F ire and V System in a single term,
R F ire − V System = |L||T |V + t∈T ij∈L z ijt (R ijt − V ) (4)
This expression highlights that V represents the minimum wildfire risk for which it is beneficial to disable a line, and we will hence refer to V as the risk threshold 1
. When R ijt > V ,
it is beneficial to turn of line (i, j) to reduce wildfire risk in the system. When R ijt < V , the wildfire risk of line (i, j) is not high enough to have a benefit of disabling the line. Given the above modeling considerations, we formulate the objective function (7a). The objective function uses the total load D T ot and the total wildfire risk before a power shutoff R T ot as normalization factors, with D T ot , R T ot defined as
D T ot = t∈T d∈D P D dt , R T ot = t∈T ij∈L R ijt(5)
With this normalization, the objective expresses the percentage of load and wildfire risk after implementation of the PSPS,
with 0 ≤ D Served /D T ot ≤ 1 and 0 ≤ R F ire /R T ot ≤ 1.
The trade-off parameter α ∈ [0, 1] allows us to express a preference for serving load or mitigating wildfire risk. The preference for mitigating wildfire risk vs limiting grid vulnerability is given by our choice of the risk threshold V .
C. Restoration Constraints
An important and novel aspect of our formulation is the consideration of a limited restoration budget, i.e. a limited capacity to inspect and restore power lines. The limits on how many miles of lines can be restored in each time period is described by constraints (7e)-(7g). Constraints (7e) set the indicator variable for restoration y L ijt to 1 if a line is off in the previous period z L ijt−1 = 0 and on in the current period z L ijt = 1. These logical constraints are implemented in the optimization problem by (6), where the three inequalites form the logical negation of z L ijt−1 as well as the and operation,
y L ijt ≤ (1 − z L ijt−1 ) (6a) y L ijt ≤ z L ijt (6b) y L ijt ≥ (1 − z L ijt−1 ) + z L ijt − 1 (6c)
Constraint (7f) implements the same constraint for the initial condition parameter z L ij0 of the line in the first period. Constraint (7g) limits the amount of restoration that can occur in a single period according to the restoration budget Y t . The effort required to restore a line scales with length ij , and the parameter Y t thus represents the total length of lines that the utility is able to inspect in time step t. Finally, (7h) enforces that z L ijt and y L ijt take on binary values.
D. Power Flow Constraints
To model how de-energization and restoration of lines impact the amount of electricity served to customers, we need to model the power flows in the system. Equations (7i)-(7n) represents the DC power flow in each time period, while accounting for load shedding and energization status of lines.
Nodal power balance is enforced by (7i) where total generation P G gt , transmission line power P L ijt , and load served x D dt P D dt must sum to zero at each bus. The sets G i , L i , D i represent the sets of generators, lines and load demands at bus i. Eq. (7j) ensures that the fraction of load served for each load x D dt is constrained to be within 0 and 1. Eq. (7k) ensures that the power P G gt from each generator g is non-negative and below the upper limit P G gt , which may vary with the time
P G gt ∀g ∈ G, P L ijt ∀(i, j) ∈ L, θ it ∀i ∈ B, x D dt ∀d ∈ D, z L ijt ∀(i, j) ∈ L, y L ijt ∀(i, j) ∈ L maximize: (1 − α) D Served D T ot −α R F ire −V System R T ot (7a)
subject to ∀t ∈ T :
D Served = t∈T d∈D x dt w dt P D dt (7b) R F ire = t∈T ij∈L z ijt R ijt (7c) V system = t∈T ij∈L (1 − z ijt )V (7d) y L ijt = (¬z L ijt−1 ) ∧ z L ijt ∀(i, j) ∈ L, for t = T (7e) y L ij1 = (¬z L ij0 ) ∧ z L ijt ∀(i, j) ∈ L, for t = T (7f) (ij)∈L y L ijt ij ≤ Y t (7g) z L ijt ∈ {0, 1}, y L ijt ∈ {0, 1} ∀(i, j) ∈ L (7h) g∈Gi P G gt + (i,j)∈Li P L t − d∈Di x D dt P D dt = 0 ∀i ∈ B (7i) 0 ≤ x D dt ≤ 1 ∀d ∈ D (7j) 0 ≤ P G gt ≤ P G gt ∀g ∈ G (7k) − P L ij z L ijt ≤ P L ijt ≤ P L ij z L ijt ∀(i, j) ∈ L (7l) P L ijt ≤ −b ij (θ it − θ jt ) + θ ∆ ij (1 − z L ijt ) ∀(i, j) ∈ L (7m) P L ijt ≥ −b ij (θ it − θ jt ) + θ ∆ ij (1 − z L ijt ) ∀(i, j) ∈ L (7n)
period t for renewable energy sources, based on the forecasted maximum output. While the problem formulation can support non-zero lower bounds on generation by including additional binary variables for generator on/off status, we remove the unit commitment aspect in this paper for simplicity. Constraint (7l) keeps the power flow P L ijt on the line from i to j between the power limits −P L ij z L ijt and P L ij z L ijt when the line is energized, i.e. z L ijt = 1. When a line is de-energized, z L ijt = 0, the power flow across the line is 0. Equations (7m), (7n) define the line power flow, while accounting for line energization status. When a line is energized, z L ijt = 1, these constraints reduce to the ordinary linearized DC power flow,
P L ijt = −b ij (θ it − θ jt ),(8)
where b ij is the line suseptance, and θ it and θ jt is the bus voltage angle for bus i at time t. When the line is de-energized, z ijt = 0, the power flow is decoupled from the voltage angle difference through the big-M values θ ∆ ij and θ ∆ ij , which can be calculated as in [29]. This allows the power flow to be set to 0 in (7l) without constraining the voltage angle differences.
III. CASE STUDY
We next demonstrate the efficacy of our proposed model and study the impact of the forecast horizon, restoration budget, and the risk threshold on solutions.
A. Case study setup
We first describe our implementation and the data used. 1) Implementation: The optimization model is available in the open source package PowerModelsWildfire.jl [15], implemented in the Julia language [30]. We use the Gurobi v9.1 optimization solver [31] with an optimality gap of 0.01%.
2) Test System: We base our case study on the RTS-GMLC [32] system. This synthetic test system has geographic coordinates located in southern California, a region which has been affected by Public Safety Power Shutoffs. The system has one year of hourly load and renewable energy profiles, and we use the data from the wildfire season in October and November. Because we use wildfire risk data with one daily value, we select the hour with highest level of system load, where the demand is the most difficult to serve, from each day to represent the power flows. The RTS-GMLC system has relatively high power limits on the transmission lines. To obtain a more interesting case with more realistic congestion, we increased the active power demand using the API method in [33], which finds the maximum amount all loads can be scaled to assuming generation is unconstrained. This method scaled each load in the network by a factor of 2.14, and we scaled the capacity of each generator by the same amount. We use a uniform load priority weight w dt = 1.
3) Wildfire risk data: Wildfire risk data was obtained from the United States Geological Survey's (USGS) Wildland Fire Potential Index (WFPI) [28]. The WFPI incorporates fuel models and forecasts for precipitation, dry bulb temperature and wind speeds to create a daily forecast of the WFPI for up to 7 days. For each line and each day, we calculate the wildfire risk as the highest WFPI value along the line [34]. Figure 1a shows a histogram of all the realized wildfire risk values (i.e. not including forecasted data) for all lines from Oct 20th to Nov 10th 2021. During the study period many lines have either zero risk or risk in the range between 70-120, while a small number of lines have extreme risk > 160. Figure 1b shows the total system risk before any power shutoffs (i.e., the sum of all wildfire risk values for all lines, assuming all lines are energized) based on the forecasted (in orange) and realized (in black) wildfire risk values. There are substantial forecast errors, demonstrating the importance of resolving the problem as new data becomes available.
4) Baseline Parameters:
We set α = 0.7 as we found this to provide a trade-off with significant risk reduction and minimal load shed under this specific loading and wildfire risk scenario, and allows us to analyse the impact of new parameters in MOPSAR problem. For analysis on the impact of changing α, refer to [15]. Unless otherwise specified, we set the restoration budget to Y t = 75 miles/day, the forecast horizon to 4 days and the risk threshold to V = 100 WFPI.
B. Baseline Solution
We first test our method on the RTS-GMLC system using the baseline parameter settings.
1) Total system risk and load shed:
We first analyze the impact on total system risk and total load served for the baseline case. Fig. 2 (top) shows the total system risk value without (orange) and with (blue) power shutoffs, while Fig. 2 (bottom) shows the total load without (orange) and with (blue) power shutoffs. In the first few days, the grid risk is moderate. A small number of lines are de-energized to reduce the risk, but no load shed occurs. On Oct 29th, a large spike in risk occurs, leading to a significant grid shutoff, and resulting in around 5% load shed for this day. On Oct 30th, the wildfire risk values return to moderate levels, and many lines are restored to avoid significant load shed. However, the total system risk is still reduced because many lines remain de-energized.
2) Geographical allocation of risk and load shed: Next, we analyze the geographical locations of load shed and wildfire risk in the system during the high risk days. Figure 3 shows the state of the grid (top) and the wildfire risk values for each line (bottom) on Oct 28, 29 and 30 (left to right).
We observe that on Oct 28 (left), there are several lines with risk values R ijt > V that are de-energized, but no load shed. On Oct 29 (middle), there is very high wildfire risk in the southern region of the grid, causing many of the lines in this region to be turned off and resulting in partial load shed at 2 buses and total load shed at 3 buses. Interestingly, we can see that some high risk lines remain energized to avoid further load shed. On Oct 30, the risk is reduced and many lines have been restored, but there is still partial load shed at 2 buses.
3) Solution time:
The baseline experiment involved solving the rolling horizon MOPSAR problem with a 4 day forecast horizon 22 times (for each of the 22 days), and solves in 29 seconds. However, the solve time is highly dependent on the problem parameters, in particular to the risk threshold V and α. In some instances (such as V = 0, α = 0.2) it can take more than 14 hours to solve the problem.
C. Impact of Forecast Horizon
We next investigate how the forecast horizon impacts solution time and solution quality by solving the rolling horizon problem with forecast horizons ranging from 1 to 7 days. 1) Solution time: The solution time increases from 1.93s for the 1-day horizon to 213.63s for the 7-day horizon (more than a 100 times increase). This indicates that the solve time may become prohibitively large for larger systems and long horizons, and highlights why it is important to understand how long the horizon needs to be to provide good solutions.
2) Objective function: We calculate the total load served, total system risk and total system vulnerability using the realized decisions and true wildfire risk for each time step and summing the values across the entire decision horizon. From these calculations, we found that the total objective function value improves by approximately 4.2% as the forecast horizon increases from 1 to 7 days, with 3.2% achieved already with a 3 day horizon. Figure 4 shows the different components of the objective function. The forecast horizon has a very small impact on the load shed, but the system risk increases and grid vulnerability decreases with a longer horizon.
3) Line status: We next assess how the forecast horizon changes line energization decisions. Table I(a) shows the total number of line energization and de-energization events that occur during the 21 day period. The number of de-energizations decreases from 93 de-energizations with a 1-day horizon to 74 de-energizations when using a 7-day horizon. The number and length of the restored lines show a less clear trend, with the number of re-energized lines remaining in the range from 61 to 54 across all horizons and the medium length horizon problems using a larger share of the restoration budget. Next, we consider the average, maximum and minimum risk level of energized and de-energized lines, shown in Table I some low-risk lines (risk below the threshold V = 100) are de-energized, as the restoration budget does not allow for restoration of all these lines. However, both the average and minimum line risk for de-energized lines is smaller for shorter forecast horizons, indicating that more low-risk lines (with risk below the threshold) remain de-energized due to an inadequate restoration budget and inability to plan further into the future. Overall, we conclude that a longer time horizon results in fewer de-energized lines because it better accounts for the slow restoration process, which may cause lines to remain deenergized after the risk has decreased, thus incurring future load shed and high vulnerability penalties.
D. Impact of Restoration Budget
We next investigate the impact of the restoration budget Y t . 1) Objective value: Table II(a) shows that the objective function value improves as the restoration budget increases. This is as expected, as a higher budget relaxes the problem. We further found that the load shed remains similar across all restoration budgets, while the wildfire risk increases and the vulnerability decreases with higher budgets.
2) Line status: Table II(b) shows the number of lines that were de-energized and re-energized, along with the total and average length of the restored lines. We observe that a larger restoration budget significantly increases both the number of de-energized and re-energized lines. Further, solutions with a small restoration budget de-energize many more lines than they re-energize, leaving a large number of lines still deenergized at the end of the study period. The average length of the restored lines increases from 11 miles/line with the lowest restoration to 28 miles/line with the highest restoration budget. This shows that the system operator is able to reenergize longer lines if more restoration capacity is available.
Table II(c) shows that the average, minimum and maximum wildfire risk of transmission lines change as we increase the restoration budget. The maximum risk of energized lines decreases and the minimum risk of de-energized lines increases as the restoration budget becomes higher. This is because the operator is able to react faster to changes in the wildfire risk when we have a higher restoration budget.
E. Impact of Risk Threshold
To demonstrate the benefit of including a risk threshold that penalizes the shutoff of low-risk lines, we compare the solutions for two different risk thresholds V = 0 (no penalty for shutoff of low-risk lines) and V = 100 (baseline). Figure 5(a) and (b) show the network status on October 29th, the highest risk day, for each of the two thresholds, respectively. The solution with risk threshold V = 0 turns off even low risk lines, leading to many de-energized lines and significant load shed. In comparison, the solution with V = 100 only disables a few lines and maintains some redundancy in the network. The two solutions serve 1413 MW and 2038 MW of load and have a wildfire risk of 4,920 and 114,220, respectively. We thus conclude that a non-zero risk threshold promotes more system redundancy and higher load served for a given value of α, but also has significantly higher wildfire risk.
IV. CONCLUSION This paper proposes the Multi-period Optimal Power Shutoff And Restoration (MOPSAR) problem, which co-optimizes preemptive power shutoffs and restoration efforts in power systems with high wildfire risk. The MOPSAR problem is implemented in a rolling horizon framework where the schedules are re-optimized on a daily basis as new information about wildfire risk become available. We apply the proposed method to the RTS-GMLC system and find that (i) a longer forecast horizon better accounts for the impact of de-energization on load shed, (ii) a larger restoration budget reduces risk by allowing for disabling and restoring more lines, and (iii) a higher risk threshold incentivizes more system redundancy, thus increasing operational security but also wildfire risk.
The proposed framework provide several avenues for future work. For example, there is a need to extend the model to consider N-1 security constraints and investigate the impact of
Fig. 1 :Fig. 2 :
12System Wildfire Risk Data: Top: Histogram of the wildfire risk of individual transmission lines, based on all realized wildfire risk observed from Oct 20th to Nov 10th. Bottom: Realized (black) and forecasted (orange lines) wildfire risk for the overall system, calculated as the sum of all wildfire risk values across all lines. Baseline MOPSAR solutions. Top: Comparison of wildfire risk with and without power shutoffs. Bottom: Total system load served with and without power shutoffs.
Fig. 3 :
3Powerline Risk on Oct 30 (a) Grid status on Oct 28 (b) Grid status on Oct 29 (c) Grid status on Oct 30 Power grid status and risk levels from Oct 28-30. Figs. 3a-3c show the transmission lines status and Figs. 3d-3f show the transmission line risk values for Oct 28 (left), 29 (middle) and 30 (right).
Fig. 4 :
4Objective value components for different forecast horizons.
(b). All solutions keep some high risk lines (risk greater than the threshold V = 100) in operation to serve load. Further,
Fig. 5 :
5System status on Oct 29th for two values of V = 0 (top) and V = 100 (bottom). using the full AC power flow model. Further, more efficient solution techniques are necessary to plan power shutoffs on a realistic scale power network. V. ACKNOWLEDGMENTS
TABLE I :
IResults for varying forecast horizons.(a) De-energization and Re-energization Decisions
Horizon (days)
1
2
3
4
5
6
7
De-energization
# Lines
93
85
84
85
79
78
74
Re-energization
# Lines
61
58
61
60
57
58
54
# Miles
1316 1346 1436 1381 1385 1373
1307
(b) Wildfire risk of Energized and De-energized Lines
Horizon (days)
1
2
3
4
5
6
7
Energized
Line Risk
Avg
50
52
54
55
56
57
57
Min
0
0
0
0
0
0
0
Max 198 208
206
206
208 208 208
De-energized
Line Risk
Avg 100 102
104
104
106 107 107
Min
1
1
17
8
40
40
40
Max 215 215
215
215
215 215 215
TABLE II :
IIResults for different restoration budgets. (a) Objective Function Values De-energization and Re-energization DecisionsRestoration Budget
25
50
75
100
125
Objective value
-0.402
-0.395
-0.391
-0.388
-0.385
% Change
0%
+1.74%
+1.77%
+3.48% +4.23%
(b) Restoration Budget
25
50
75
100
125
Total Budget
550 1100 1650 2200 2750
De-energization
# Lines
66
77
85
95
99
Re-energization
# Lines
28
45
60
75
83
# Miles
308
890
1381 1907 2325
Avg. length (Miles)
11
19.8
23.0
25.4
28.0
(c) Wildfire risk of Energized and De-energized Lines
Restoration Budget
25
50
75
100 125
Energized
Line Risk
Avg
54
54
55
55
56
Min
0
0
0
0
0
Max 208 208 206 206 206
De-energized
Line Risk
Avg
100 103 104 107 108
Min
1
8
8
40
48
Max 215 215 215 215 215
We recognize that expressing grid vulnerability on a line-by-line basis is less comprehensive and meaningful than using other metrics such as N-1 security. However, it does allow us to express a preference for keeping low risk lines in operation. A more in-depth modeling and investigation of grid vulnerability and operational security in the context of high wildfire risk is left for future work.
The authors would like to acknowledge Sofia Taylor for helping obtain wildfire risk data for the RTS-GMLC system.
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| sample_1330 | 0.7299 | arxiv | |
Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning
Thomas Vandal vandal.t@husky.neu.edu
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Evan Kodra evan.kodra@risq.io
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Jennifer Dy j.dy@neu.edu
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Sangram Ganguly sangram.ganguly@nasa.gov
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Ramakrishna Nemani rama.nemani@nasa.gov
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Auroop R Ganguly a.ganguly@neu.edu
Electrical and Computer Engineering Boston
Civil and Environmental Engineering Boston
Bay Area Environmental Research Institute / NASA Ames Research Center Moffett Field
NASA Advanced Supercomputing Division/ NASA Ames Research Center Moffett Field
Northeastern University, Civil and Environmental Engineering Boston
risQ Inc. Cambridge
Northeastern University
Northeastern University
MA, MA, MA, CA, CA, MA
Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning
CCS CONCEPTS • Computing methodologies → Neural networksReconstruc- tion• Applied computing → Earth and atmospheric sciencesKEYWORDS Bayesian Deep Learning, Uncertainty Quantification, Climate Down- scaling, Super-resolution, Precipitation Estimation
Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component, wellcharacterized uncertainty estimates must accompany predictions. However, S&E observations and model-simulations often follow heavily skewed distributions and are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean, likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture uncertainties from noisy observations, aleatoric, and from unknown model parameters, epistemic, provide us a foundation. Here we present a discrete-continuous BDL model with Gaussian and lognormal likelihoods for uncertainty quantification (UQ). We demonstrate the approach by developing UQ estimates on "DeepSD", a super-resolution based DL model for Statistical Downscaling (SD) in climate applied to precipitation, which follows an extremely skewed distribution. We find that the discrete-continuous models outperform a basic Gaussian distribution in terms of predictive accuracy and uncertainty calibration. Furthermore, we find that the lognormal distribution, which can handle skewed distributions, produces quality uncertainty estimates at the extremes. Such results may be important across S&E, as well as other domains such as finance and economics, where extremes are often of significant interest. Furthermore, to our knowledge, this is the first UQ model in SD where both aleatoric and epistemic uncertainties are characterized.
INTRODUCTION
Science and Engineering (S&E) applications are beginning to leverage the recent advancements in artificial intelligence through deep learning. In climate applications, deep learning is being used to make high-resolution climate projections [36] and detect tropical cyclones and atmospheric rivers [30]. Remote sensing models such as DeepSAT [3], a satellite image classification framework, also leverage computer vision technologies. Physicists are using deep learning for detecting particles in high energy physics [1] and in transportation deep learning has aided in traffic flow prediction [26] and modeling network congestion [27]. Scientists have even used convolutional neural networks to approximate the Navier-Stokes equations of unsteady fluid forces [29]. However, for many of these applications, the underlying data follow non-normal and discretecontinuous distributions. For example, when modeling precipitation, we see most days have no precipitation at all with heavily skewed amounts on the rainy days, as shown in Figure 1. Furthermore, climate is a complex nonlinear dynamical system, while precipitation processes in particular exhibit extreme space-time variability as well as thresholds and intermittence, thus precipitation data cannot be assumed to be Gaussian. Hence, for deep learning to be harnessed to it's potential in S&E applications, our models must be resilient to non-normal and discrete-continuous distributions.
Uncertainty quantification is another requirement for wide adoption of deep learning in S&E, particularly for risk management decisions. Twenty years ago, Jaeger et al. stated, "uncertainties in climate change are so pervasive and far reaching that the tools for handling uncertainty provided by decision analysis are no longer sufficient [18]." As expected, uncertainty has been a particular interest of climate and computer scientists to inform social and infrastructure adaptation to increasing weather extremes and natural disasters [19,25]. For example, Kay et al. studied six different sources of uncertainty of climate change impacts on a flood frequency model [20]. These uncertainties included future greenhouse gas scenarios, global climate models (GCMs) structure and parameters, downscaling GCMs, and hydrological model structure and parameters. Hence, quantifying the uncertainty from each of these processes is critical for understanding the system's uncertainty. This provides us with the problem of quantifying uncertainty in discrete-continuous and non-normal distributions. Recent work in Bayesian Deep Learning (BDL) provides a foundation for modeling uncertainty in deep networks which may be applicable to many S&E applications [10,12,22,39]. The simplicity of implementing BDL on an already defined deep neural network makes it an attractive approach. With a well-defined likelihood function, BDL is able to capture both aleatoric and epistemic uncertainty [22]. Epistemic uncertainty comes from noise in the model's parameters which can be reduced by increasing the dataset size. On the other side, Aleatoric uncertainty accounts for the noise in the observed data, resulting in uncertainty which cannot be reduced. Examples of aleatoric uncertainty are measurement error and sensor malfunctions. Aleatoric uncertainty can either be homoscedastic, constant uncertainty for different inputs, or heteroscedastic, uncertainty depending on the input. Heteroscedastic is especially important in skewed distributions, where the tails often contain orders of magnitude increased variability. Variants of these methods have already been successfully applied to applications such as scene understanding [21] and medical image segmentation [37].
While BDL has been applied to few domains, these models generally assume a Gaussian probability distribution on the prediction. However, as we discussed in S&E applications, such an assumption may fail to hold. This motivates us to extend BDL further to aperiodic non-normal distributions by defining alternative density functions based on domain understanding. In particular, we focus on a precipitation estimation problem called statistical downscaling, which we will discuss in Section 2. In section 3, we review "DeepSD", our statistical downscaling method [36], and Bayesian Deep Learning Concepts. In section 4, we present two BDL discretecontinuous (DC) likelihood models, using Gaussian and lognormal distributions, to model categorical and continuous data. Following in Section 5, we compare predictive accuracy and uncertainty calibration in statistical downscaling. Lastly, Section 6 summarizes results and discusses future research directions.
Key Contributions
(1) A discrete-continuous bayesian deep learning model is presented for uncertainty quantification in science and engineering. (2) We show that a discrete-continuous model with a lognormal likelihood can model fat-tailed skewed distributions, which occur often in science and engineering applications. (3) The first model to capture heteroscedastic, and epistemic, uncertainties in statistical downscaling is presented.
PRECIPITATION ESTIMATION
Statistical Downscaling
Downscaling, either statistical or dynamical, is a widely used process for producing high-resolution projections from coarse global climate models (GCMs) [? ? ? ]. Dynamical downscaling, often referred to as regional climate models, are physics based numerical models encoding localized sub-grid processes within GCM boundary conditions to generate high-resolution projections. Similar to GCMs, dynamical downscaling are computational expensive and simply cannot scale to ensemble modeling. Statistical downscaling is a relatively efficient solution which aims to use observed data to learn a functional mapping between low-and high-resolution GCMs, illustrated in Figure 2. Uncertainty in GCMs is exacerbated by both observational data and parameters in the functional mapping, motivating a probabilistic approach. GCMs through the Fifth Coupled Model Intercomparison Project (CMIP5) provides scientist with valuable data to study the effects of climate change under varying greenhouse gas emission scenarios [34]. GCMs are complex non-linear dynamical systems that model physical processes governing the atmosphere up to the year 2200 (some to 2300). GCMs are gridded datasets with spatial resolutions around 100km and contain a range of variables including temperature, precipitation, wind, and pressure at multiple pressure levels above the earth's surface. More than 20 research groups around the world contributed to CMIP5 by developing their own models and encoding their understanding of the climate system. Within CMIP5, each GCM is simulated under three or four emission scenarios and multiple initial conditions. This suite of climate model simulations are then used to get probabilistic forecasts of variables of interest, such as precipitation and temperature extremes [31]. While the suite of models gives us the tools to study large scale climate trends, localized projections are required for adaptation.
Many statistical models have been explored for downscaling, from bias correction spatial disaggregation (BCSD) [6] and automated statistical downscaling (ASD) [15] to neural networks [33] and nearest neighbor models [16]. Multiple studies have compared different sets of statistical downscaling approaches on various climate variables and varying temporal and spatial scales showing that no approach consistently outperforms the others [5,14,35]. Recently, Vandal et al. presented improved results with an alternative approach to downscaling by representing the data as "images" and adapting a deep learning based super-resolution model called DeepSD [36]. DeepSD showed superior performance in downscaling daily precipitation in the contiguous United States (CONUS) when compared to ASD and BCSD.
Even though uncertainty is crucial in statistical downscaling, it is rarely considered in downscaling studies. For instance, all the downscaled climate projections used in the latest US National Climate Assessment report (CSSR), produced on the NASA Earth Exchange, come with no uncertainty estimates. Though widely used in climate impact assessments, a recurrent complaint from the users is a lack of uncertainty characterization in these projections. What users often request are estimates of geographic and seasonal uncertainties such that the adaptation decisions can be made with robust knowledge [38]. Khan et al. presented one study that assessed monthly uncertainty from confidence based intervals of daily predictions [23]. However, this approach only quantifies epistemic uncertainty and therefore cannot estimate a full probability distribution. To the best of the authors' knowledge, no studies have modeled aleatoric (heteroscedastic) uncertainty in statistical downscaling, presenting a limitation to adaptation.
Climate Data
A wide variety of data sources exists for studying the earth's climate, from satellite and observations to climate models. Above we discussed some of the complexities and uncertainty associated with ensembles of GCMs as well as their corresponding storage and computational requirements. While the end goal is to statistically downscale GCMs, we must first learn a statistical function to apply a low-to high-resolution mapping. Fortunately, one can use observed datasets that are widely available and directly transfer the trained model to GCMs. Such observation datasets stem from gauges, satellite imagery, and radar systems. In downscaling, one typically will use either in-situ gauge estimates or a gridded data product. As we wish to obtain a complete high-resolution GCM, a gridded data product is required. Such gridded-data products are generally referred to as reanalysis datasets, which use a combination of data sources with physical characteristics aggregated to a well estimated data source. For simplicity, the remainder of this paper we will refer to reanalysis datasets as observations.
In SD, it is important for our dataset to have high spatial resolution at a daily time temporal scale spanning as many years as possible. Given these constraints, we choose to use precipitation from the Prism dataset made available by Oregon State University with a 4km spatial resolution at a daily temporal scale [8]. The underlying data in Prism is estimated from a combination of gauges measuring many climate variables and topographical information. To train our model, the data is upscaled from 4km to the desired low-resolution. For example, to train a neural network to downscale from 64km to 16km, we upscale Prism to 16km and 64km and learn the mapping between the two (see Figure 2).
For the reader, it may be useful to think about this dataset as an image where precipitation is a channel analogous to traditional RGB channels. Similarly, more variables can be added to our dataset which therefore increases the number of channels. However, it is important to be aware that the underlying spatio-temporal dynamics in the chaotic climate system makes this dataset more complex than images. In our experiments with DeepSD, we included an elevation from the Global 30 Arc-Second Elevation Data Set (GTOPO30) provided by the USGS.
BACKGROUND 3.1 DeepSD
The statistical downscaling approach taken by DeepSD differs from more traditional approaches, which generally do not capture spatial dependencies in both the input and output. For example Automated Statistical Downscaling (ASD) [15] learns regression models from low-resolution to each high-resolution point independently, failing to preserve spatial dependencies in the output and requiring substantial computational resources to learn thousands of regression models. In contrast, DeepSD represents the data as low-and high-resolution image pairs and adapts super-resolution convolutional neural networks (SRCNN) [9] by including high-resolution auxiliary variables, such as elevation, to correct for biases. These auxiliary variables allows one to use a single trained neural network within the training domain. This super-resolution problem is essentially a pixel-wise regression such that Y = F (X; Θ) where Y is high-resolution with input X = [X lr , X aux ] and F a convolutional neural network parameterized by Θ. F can then be learned by optimizing the loss function:
L = 1 2N i ∈S ∥F (X i ; Θ) − Y i ∥ 2 2 (1)
where S is a subset n examples. Based on recent state-of-the-art results in super-resolution [? ? ], we modify the SRCNN architecture to include a residual connection between the precipitation input channel and output layer, as shown in Figure 3. As discussed above, the resolution enhancement of 8x or more needed in statistical downscaling is much greater than the 2-4x enhancements used for images. DeepSD uses stacked SRCNNs, each improving resolution by 2x allowing the model to capture regional and local weather patterns, depending on the level. For instance, to downscale from 100km to 12.5km, DeepSD first trains models independently (or with transfer learning) to downscale from 100km to 50km, 50km to 25km, and 25km to 12.5km. During inference, these models are simply stacked on each other where the output of one plus the next corresponding auxiliary variables are inputs to the next. In the case of downscaling precipitation, inputs may include LR precipitation and HR elevation to predict HR precipitation. In this work, we focus on uncertainty quantification for a single stacked network which can then be translated to stacking multiple Bayesian neural networks.
Bayesian Deep Learning
In the early 1990's Mackay [28] introduced a Bayesian neural networks (BNNs) by replacing deterministic weights with distributions. However, as is common with many Bayesian modeling problems, direct inference on BNNs is intractable for networks of more than a one or two hidden layers. Many studies have attempted to reduce the computational requirements using various approximations [2,13,17]. Most recently, Gal and Ghahramani presented a practical variational approach to approximate the posterior distribution in deep neural networks using dropout and monte carlo sampling [10,11]. Kendall and Gal then followed this work for computer vision applications to include both aleatoric and epistemic uncertainties in a single model [22].
To begin, we define weights of our neural network as ω = {W 1 , W 2 , ..., W L } such that W ∼ N (0, I ) and L being the number of layers in our network. Given random outputs of a BNN denoted by f ω (x), the likelihood can be written as p(y| f ω (x)). Then, given data X and Y, as defined above, we infer the posterior p(ω|X, Y) to find a distribution of parameters that best describe the data. For a regression task assuming a predictive Gaussian posterior, p(y| f ω (x)) = N (ŷ,σ 2 ) with random outputs:
[ŷ,σ 2 ] = f ω (x).
Applying variational inference to the weights, we can define an approximate and tractable distribution q Θ (ω) = L l =1 q M l (W l ) where q M l (W l ) = M l × diag Bernoulli(1 − p l ) K l parameterized by Θ l = {M l , p l } containing the weight mean of shape K l × K l +1 , K l being the number of hidden units in layer l, and dropout probability p l . Following, we aim to minimize the Kullback-Leibler (KL) divergence between q Θ (ω) to the true posterior, p(ω|X, Y). The optimization objective of the variational interpretation can be written as [11]:
L(Θ) = − 1 M i ∈S logp(y i | f ω (x i )) + 1 N KL(q Θ (ω)||p(ω)) (2) =L x (Θ) + 1 N KL(q Θ (ω)||p(ω))(3)
where S is a set of M data points. To obtain well calibrated uncertainty estimates, it is crucial to select a well estimated p l . Rather than setting p l to be constant, we can learn it using a concrete distribution prior which gives us a continuous approximation of the Bernoulli distribution [12]. As presented by Gal et al., the KL divergence term is then written as:
KL(q Θ (ω)||p(ω)) = L l =1 KL(q M l (W l )||p(W l ))(4)KL(q M l (W)||p(W)) ∝ l 2 (1 − p l ) 2 ||M l || − K l H (p l )(5)
where
H (p) = −p log p − (1 − p) log (1 − p)(6)
is the entropy of a Bernoulli random variable with probability p. We note that given this entropy term, the learning dropout probability cannot exceed 0.5, a desired effect. For brevity, we encourage the reader to refer to [12] for the concrete dropout optimization. In the remainder of this paper, we will use this concrete dropout formulation within all presented models.
BAYESIAN DEEP LEARNING FOR SKEWED DISTRIBUTIONS
In this section we describe three candidate Bayesian deep learning models to quantify uncertainty in super-resolution based downscaling. We begin by formalizing the use of BDL within the SRCNN architecture assuming a normal predictive distribution, identical to the pixel-wise depth regression in [22]. This approach is further extended to a discrete-continuous model that conditions the amount of precipitation given an occurrence of precipitation. This leverages the domain knowledge that the vast majority of data samples are non-rainy days which are easy to predict and contain little information for the regression. Such a technique was used by Sloughter el al. using a discrete-continuous gamma distribution [32]. Lastly, we show that a lognormal distribution can be applied directly in BDL and derive its corresponding log-likelihood loss and unbiased parameter estimates.
Gaussian Likelihood
Super-resolution is an ill-posed pixel-wise regression problem such that BDL can be directly applied, as Kendall and Gal showed for predicting depth in computer vision [22]. As discussed in previous sections, it is crucial to capture both aleatoric and epistemic uncertainties in downscaling. As shown in section 3.1 of [22], we must measure the aleatoric uncertainty by estimating the variance, σ 2 , in the predictive posterior while also sampling weights via dropout from the approximate posterior, W ∼ q Θ (W). As before, we defined our Bayesian convolutional neural network f:
[ŷ,σ 2 ] = f W (X).(7)
and make the assumption that Y ∼ N (ŷ,σ 2 ). The Gaussian loglikelihood can be written as:
L x (Θ) = 1 2D iσ −2 i ||y i −ŷ i || 2 + 1 2 logσ 2 i(8)
where pixel i in y corresponds to input x and D being the number of output pixels. The KL term is identical to that in Equation 4. Given this formulation,σ i , the variance for pixel i is implicitly learned from the data without the need for uncertainty labels. We also note that during training the substiution s i := logσ 2 i is used for stable learning using the Adam Optimization algorithm [24], a first-order gradient based optimization of stochastic objective functions.
Unbiased estimates of the first two moments can the be obtained with T Monte Carlo samples,
{ŷ t ,σ 2 i }, from f W (x) with masked weights W t ∼ q(W): E[Y] ≈ 1 T T t =1ŷ t (9) Var[Y] ≈ 1 T T t =1μ 2 t − 1 T T t =1σ 2 t + 1 T T t =1μ t 2 .(10)
These first two moments provide all the necessary information to easily obtain prediction intervals with both aleatoric and epistemic uncertainties. For further details, we encourage the reader to refer to [22].
Discrete-Continuous Gaussian Likelihood
Rather than assuming a simple Gaussian distribution for all output variables, which may be heavily biased from many non-rainy days in our dataset, we can condition the model to predict whether rain occurred or not. The BNN is now formulated such that the mean, variance, and probability of precipitation are sampled respectively from f:
[ŷ,σ 2 ,φ] = f W (X)(11)p = Sigmoid(φ).(12)
Splitting the distribution into discrete and continuous parts gives us:
p y| f ω (x) = (1 −p) y = 0 p · N y;ŷ,σ 2 y > 0(13)
Plugging this in to 2 and dropping the constants gives us the loss function (for brevity, we ignore the KL term which is identical to
Equation 4): L x (Θ) = − 1 D i log 1 y i >0 ·p i · N y i ;ŷ i ,σ 2 i + 1 y i =0 · (1 −p i ) = − 1 D i,y i >0 logp i + log N y i ;ŷ i ,σ 2 i − 1 D i,y i =0 log(1 −p i ) = 1 D i 1 y i >0 ·p i + (1 − 1 y i >0 ) · (1 −p i ) − 1 2D i,y i >0σ −2 i ||y i −ŷ i || 2 + log σ 2 i(14)
where the first term is the cross entropy of a rainy day and the second term is the conditional Gaussian loss. Furthermore, we can write the unbiased estimates of the first two moments as:
E[Y] ≈ 1 T T t =1p tŷt (15) Var[Y] ≈ 1 T T t =1p 2 t ŷ 2 t +σ 2 t − 1 T T t =1p tμt 2 .(16)
Discrete-Continuous Lognormal Likelihood
Precipitation events, especially extremes, are known to follow fattailed distributions, such as lognormal and Gamma distributions [7,32]. For this reason, as above, we aim to model precipitation using a discrete-continuous lognormal distribution. It should be noted that the lognormal distribution is undefined at 0 so a conditional is required for downscaling precipitation. To do this, we slightly modify our BNN:
[μ,σ 2 ,φ] = f W (X) (17) p = Sigmoid(φ).(18)
whereμ andσ are sampled parameters of the lognormal distribution. Following the same steps as above, we can define a piece-wise probability density function:
p y| f ω (x) = (1 −p) y = 0 p · 1 yσ √ 2π exp − (log(y) −μ) 2 2σ 2 y > 0(19)
This gives us the modified log-likelihood objective:
L x (Θ) = 1 D i 1 y i >0 ·p i + (1 − 1 y i >0 ) · (1 −p i ) − 1 2D i,y i >0σ −2 i ||log y i −μ i || 2 + log σ 2 i(20)
In practice, we optimizeŝ := exp(σ ) for numerical stability. And lastly, the first two moments are derived as:
E[y] ≈ 1 T T t =1p t exp(μ + 1 2σ 2 ) (21) Var[Y] ≈ 1 T T t =1p 2 t exp(2μ + 2σ 2 )(22)
Given these first two moments, we can derive unbiased estimates of µ and σ :σ
= log 1 + 1 2 4Var[Y] E[y] 2 + 1 (23) µ = E[y] −σ 2 2(24)
that can be used to compute pixel-wise probabilistic estimates.
In the next section, we will apply each of the three methods to downscaling precipitation, compare their accuracies, and study their uncertainties.
PRECIPITATION DOWNSCALING
For our experimentation, we define our problem to downscale precipitation from 64km to 16km, a 4x resolution enhancement in a single SRCNN network. We begin with precipitation from the PRISM dataset, as presented in Section 2.2, at 4km which is then upscaled to 16km using bilinear interpolation. This 16km dataset are our labels and are further upscaled to 64km, generating training inputs. Furthermore, we use elevation from the Global 30 Arc-Second Elevation Datset (GTOPO30) provided by the USGS as an auxilary variable, also upscaled to 16km. In the end, our dataset is made up of precipitation at 64km and elevation at 16km as inputs where precipitation at 16km are the labels. In the discrete-continuous models, precipitation >0.5mm is considered a rainy day. Precipitation measured in millimeters (mm) is scaled by 1/100 for training when optimizing the Gaussian models. Elevation is normalized with the overall mean and variance. Our super-resolution architecture is defined with two hidden layers of 512 kernels using kernel sizes 9, 3, and 5 (see Figure 3). The model is trained for 3 × 10 6 iterations using a learning rate of 10 −4 and a batch size of 10. Three models are optimized using each of the three log-likelihood loss's defined above, Gaussian distribution as well as discrete-continuous Gaussian and lognormal distributions conditioned on a rainy day. 50 Monte Carlo passes during inference are used to measure the first two moments which then estimates the given predictive distribution's parameters.
Concrete dropout is used to optimize the dropout probability with parameters τ =1e-5 and prior length scale as l = 1 to improve uncertainly calibration performance [12]. For a pixel-wise regression the number of samples N is set as Days×Height×Width. These parameters were found to provide a good trade-off between likelihood and regularization loss terms. As shown in Figure 4, dropout rates for each model and hidden layer are close to 0.5, the largest possible dropout rate. We find that the Gaussian distribution has difficulty converging to a dropout rate while the discrete-continuous models quickly stabilize. Furthermore, the lognormal distribution learns the largest dropout rate, suggesting a less complex model. Validation is an important task for choosing a highly predictive and well calibrated downscaling model. In our experiments, we study each model's ability to predict daily precipitation, calibration of uncertainty, and width of uncertainty intervals. For reproducibility, we provide the codes for training and testing on github (https://github.com/tjvandal/discrete-continuous-bdl).
Predictive Ability
We begin by comparing each model's ability to predict the ground truth observations. Root Mean Square Error (RMSE) and bias are compared to understand the average daily effects of downscaling. To analyze extremes, we select two metrics from Climdex (http:// www.clim-dex.org) which provides a suite of extreme precipitation indices and is often used for evaluating downscaling models [4,35]:
(1) R20 -Very heavy wet days ≥ 20mm (2) SDII -Daily intensity index = (Annual total) / (precip days ≥ 0.5 mm).
In our analysis, we compute each index for the test set as well as observations. Then the difference between the predicted indices and observed indices are computed, ie. (SDII model -SDII obs ). These results can be seen in Table 1. We see a clear trend of the DC models performing better than a regular Gaussian distribution on all computed metrics. In particular, DC-Lognormal shows the lowest Bias, RMSE, and R20 error while DC-Gaussian has slightly higher errors but performs marginally better at estimating the SDII index. Furthermore, we study the predictability over space in Figure 5 by computing the pixel-wise RMSEs. Each model performs well in the mid-west and worse in the southeast, a region with large numbers of convective precipitation events. We see that the DC models, DC-Lognormal in particular, have lower bias than a regular Gaussian distribution. Similarly for RMSE, DC models, lead by a DC-Gaussian, have the lowest errors. Looking more closely, we see improved performance along the coasts which are generally challenging to estimate. The convolutional operation with a 5x5 kernel in the last layer reconstructs the image using a linear combination of nearby points acting as a smoothing operation. However, when this is applied to the conditional distributions, the gradient along this edge can be increased by predicting high Table 1: Predictive accuracy statistics computed pixel-wise and aggregated. Daily intensity index (SDII) and yearly precipitation events greater than 20mm (R20) measure each model's ability to capture precipitation extremes. R20-Err and SDII-Err measures the difference between observed indicies and predicted indicies (closer to 0 is better). and low probabilities of precipitation in a close neighborhood. This insight is particularly important when applied to coastal cities. Lastly, we look at each conditional model's ability to classify precipitous days with precision recall curves ( Figure 6). We see that recall does not begin to decrease until a precision of 0.8 which indicates very strong classification performance. It was assumed that classification of precipitation would be easy for such a dataset.
Uncertainty Quantification
The remainder of our analysis focuses on each model's performance in estimating well calibrated uncertainty quantification. We limit our analysis of uncertainty to only days with precipitation (≥ 0.5mm) as uncertainty on non-rainy days is not of interest. The calibration metric used computes the frequency of observations occurring within a varying predicted probability range:
c(z) = 1 N N i=1
I P (y i |f ω (x i ))>(0.5−z/2) * I P (y i |f ω (x i ))<(0.5+z/2) (25) where P is the cumulative density function of the predictive posterior and z ∈ [0, 1] defined the predictive probability range centered at 0.5. Ideally the frequency of observations will be equal to the probability. A calibration error can then be defined as:
RMSE cal = 1 K K i=1 (c(i/K) − i/K) 2(26)
where K is the number bins. In our analysis, we use K = 100. The calibration plots for each model can be seen in Figure 7. Right away we see from Figure 7 that the Gaussian distribution over-estimates uncertainty for most of the range with a wider range of variability between pixels. DC-Lognormal also overestimates uncertainty but has a lower range of variability between pixels, showing more consistent performance from location to location.
Overall, DC-Gaussian shows the lowest calibration error hovering right around x = y but underestimates uncertainty at the tails. Though DC-Lognormal is better calibrated at the tails, one could calibrate the tails by simply forcing the variance to explode. Taking this a step further, we present calibration RMSEs per pixel in Figure 7 (bottom row) to visualize spatial patterns of UQ. In the Gaussian model we find weakened and more variable results at high-elevations in the west and mid-west. Each of the DC models perform well, but DC-Lognormal also has areas of increased error in the west. In Figure 8 we aim to better understand these uncertainties for increasingly intense precipitation days. At these high rainfall days our models generally under-predict precipitation, but the Gaussian models often fail to capture these extremes. While the lognormal has wider uncertainty intervals, it is able to produce a well calibrated distribution at the extremes. Furthermore, these wide intervals indicate that the model becomes less confident with decreasing domain coverage at higher intensities. This may suggest that there exists a bias-variance trade-off between the Gaussian and Log-Normal distributions.
CONCLUSION
In this paper we present Bayesian Deep Learning approaches incorporating discrete-continuous and skewed distributions targeted at S&E applications. The discrete-continuous models contain both a classifier to categorize an event and conditional regressor given an event's occurrence. We derive loss functions and moments for Gaussian and lognormal DC regression models. Using precipitation as an example, we condition our model on precipitous days and predict daily precipitation on a high-resolution grid. Using the lognormal distribution, we are able to produce well-calibrated uncertainties for skewed fat-tailed distributions. To our knowledge, this is the first model for uncertainty quantification in statistical downscaling.
Through experiments, we find that this DC approach increases predictive power and uncertainty quantification performance, reducing errors with well calibrated intervals. In addition, we find that this conditional approach improves performance at the extremes, measured by daily intensity index and number of extreme precipitation days from ClimDex. Visually, we found that the DC models perform better than a regular Gaussian on the coasts, a challenge in statistical downscaling. These edge errors appear during reconstruction when the kernel partially overlaps with the coastal edge, acting as a smoothing operation. However, the DC models reduce this smoothing by increasing the expected value's gradients.
Overall, we find that the DC distribution approaches provides strong benefits to deep super-resolution based statistical downscaling. Furthermore, while the lognormal distribution uncertainty was slightly less calibrated, it was able to produce well understood uncertainties at the extremes. This presents a strong point, Bayesian Deep Neural Networks can well fit non-normal distributions when motivated by domain knowledge.
In the future we aim to extend this work to stacked superresolution networks, as used in DeepSD [36], which requires sampling of between networks. Some other extensions could be the addition of more variables, extension to other skewed distributions, and larger network architectures. Finally, incorporating these theoretical advances in uncertainty characterization, the NEX team plans to use DeepSD to produce and distribute next generation of climate projections for the upcoming congressionally mandated national climate assessment.
Figure 1 :
1Histogram of daily precipitation on the Contiguous United States from 2006 to 2015. A) All precipitation data points. B) Precipitation distribution on rainy days only. C) Log distribution of precipitation on rainy days.
Figure 2 :
2Prism Observed Precipitation: Left) Low resolution at 64km. Right) High resolution at 16km.
Figure 3 :
3Residual SRCNN Architecture used for DeepSD with a skip connection between precipitation and the output layer.
Figure 4 :
4Dropout probabilities learned using Concrete Dropout for both hidden layers.
Figure 5 :
5Daily Root Mean Square Error (RMSE) computed at each location for years 2006 to 2015 (test set) in CONUS. A) Gaussian, B) Conditional-Gaussian, and C) Conditional-Lognormal. Red corresponds to high RMSE while blue corresponds to low RMSE.
Figure 6 :
6Precision recall curve of classifying rainy days in conditional models.
Figure 7 :
7Calibration is computed as the frequency of predictions within a given probability range. This probability is varied on the x-axis with the corresponding frequency on the y-axis. Columns represent each model Gaussian, DC-Gaussian and Lognormal. Calibration plots on the first row compute per pixel with the shaded area representing the 80% confidence interval of calibration. The second row depicts calibration root mean square error (RMSE) per location.
Figure 8 :
8Uncertainty widths based on quantiles from their predictive distributions. The points are observations versus the expected value. The bands correspond to 50%, 80%, and 90% predictive intervals.
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| sample_1389 | 0.9148 | arxiv | |
Wind turbine power and land cover effects on cumulative bat deaths
Aristides Moustakas arismoustakas@gmail.com2
Infometrics Data Analytics Ltd
128 City RoadEC1V 2NXLondonUK
Natural History Museum of Crete
University of Crete
HeraklionGreece
Panagiotis Georgiakakis
Natural History Museum of Crete
University of Crete
HeraklionGreece
Elzbieta Kret
WWF Greece
Charilaou Trikoupi 119-124114 73AthensGRGreece
Eleftherios Kapsalis
Aris Moustakas
Society for the Protection of Biodiversity of Thrace
684 00Dadia, SoufliGRGreece
Wind turbine power and land cover effects on cumulative bat deaths
1 *Corresponding author,Data analyticswind turbine capacityturbine powerbat fatalitieswind energy facilitiesland use 3
Wind turbines (WT) cause bird and bat mortalities which depend on the WT and landscape features. The effects of WT features and environmental variables at different spatial scales associated to bat deaths in a mountainous and forested area in Thrace, NE Greece were investigated. Initially, we sought to quantify the most lethal WT characteristic between tower height, rotor diameter and power. The scale of interaction distance between bat deaths and the land cover characteristics surrounding the WTs was quantified. A statistical model was trained and validated against bat deaths and WT, land cover and topography features. Variance partitioning between bat deaths and the explanatory covariates was conducted. The trained model was used to predict bat deaths attributed to existing and future wind farm development in the region. Results indicated that the optimal interaction distance between WT and surrounding land cover was 5 km, the larger distance than the ones examined. WT power, natural land cover type and distance from water explained 40 %, 15 % and 11 % respectively of the total variance in bat deaths by WTs. The model predicted that operating but not surveyed WTs comprise of 377.8% and licensed but not operating yet will contribute to 210.2% additional deaths than the ones recorded. Results indicate that among all WT features and land cover characteristics, wind turbine power is the most significant factor associated to bat deaths. Results indicated that WTs located within 5 km buffer comprised of natural land cover types have substantial higher deaths. More WT power will result in more deaths. Wind turbines should not be licensed in areas where natural land cover at a radius of 5km exceeds 50%. These results are discussed in the climate-land use-biodiversity-energy nexus.
Introduction
The world is changing subject to land use and climate changes (Almond et al., 2022;IPBES, 2019). In an effort to mitigate anthropogenic carbon emissions related to energy production, wind as renewable energy resources is considered a plausible alternative. However, installing wind power facilities is directly related to land loss and habitat fragmentation, through land transformation and roads (Kati et al., 2021). In addition, the operation of wind turbines is considered as additional threat to many protected wildlife species (Cryan et al., 2014). We are thus facing a paradox of impacting biodiversity to modulate anthropogenic climatic impacts, as there are strong interaction effects between biodiversity, land use and climate (Peters et al., 2019;Ritchie et al., 2020).
Wind energy facilities are increasing worldwide (Global Wind Energy Council, 2021). After major investment efforts in recent years, in 2021 Greece had already reached 44% of the 2030 national target for wind harnessing (Kati et al., 2021). The country is an attractive target for wind energy investments as it exhibits high wind potential combined with very high percentage of public land, of which the vast majority (>77%) is forests and grasslands (Spanos et al., 2015) and a supportive national climate policy for RES deployment (Kati et al., 2021). Greece is a global biodiversity hotspot (Myers et al., 2000) with a high number of plant and animal species as well as endemism. Natura 2000, the network of protected areas in European Union, simultaneously protects habitats, animal, and plant species (OECD, 2020). In Greece, the Natura 2000 network consists of 446 sites, which cover approximately 28% of the country's land and 20% of the marine surface area (https://www.wwf.gr/en/our_work/nature/marine/protected_areas/natura_2000/). However, in Greece, wind energy facility development is permitted within Natura 2000 sites. Thus, the potential impacts of wind turbines (WT) merit detailed risk analysis as it might significantly contribute to habitat loss, fragmentation, and species decline.
Bats are long-lived mammals with low reproductive potential and thus high levels of adult individuals survivorship is important for maintaining a viable population (Wilkinson and South, 2002). All European bat species are strictly protected under the Habitats Directive (92/43/EEC, Annex IV) and the national legislation of many countries. Nevertheless, in the absence of specific, mandatory regulations, the effect of wind farm installation and operation on bat populations is rarely examined to a sufficient extent in environmental impact assessments, although increased mortality in wind turbines may increase extinction risk for frequently killed species (Frick et al., 2017).
Bat deaths depend upon characteristics of the environment around WTs such as cover of natural, agricultural, or artificial surface areas (Arnett and Baerwald, 2013;Arnett et al., 2008;Barré et al., 2023;Thompson et al., 2017). The interaction scale between bat abundance/deaths and the environmental characteristics varies between studies (Hartmann et al., 2021;Lehnert et al., 2014;Starbuck et al., 2022). In addition, the percentage of cover of each habitat type, the availability of water, trees, as well as topography is scale-specific (Starbuck et al., 2022). Furthermore, deaths depend on installed WT power (capacity) (MacGregor and Lemaître, 2020) and WT characteristics such as rotor diameter, speed, tower height, power, or produced energy that are correlated (Hartmann et al., 2021;Huso et al., 2021;MacGregor and Lemaître, 2020). Wind speed is a highly variable factor that significantly affects bat causalities in wind farms. Restricting nocturnal operation of WT to wind speeds above 5.0 to 6.0 m/s during the high risk periods has been proved to reduce dramatically the number of bat deaths with a minimum loss in produced energy (Arnett et al., 2011;Behr et al., 2017;Martin et al., 2017;Wellig et al., 2018).
Prediction is an elementary property of science (Medawar, 1984), yet ecology has traditionally focused on explaining patterns, rather than predicting beyond the range of the data, though this is changing (Evans et al., 2013). With modern online data repositories, censuring and monitoring methods such as remote sensing and acoustic or visual sensors, environmental data are more ubiquitous and richer than ever (Liu et al., 2021;Moustakas and Katsanevakis, 2018). In addition, modern computing capabilities and statistical methods facilitate the analysis of such data (Ma et al., 2017;Moustakas and Katsanevakis, 2018). More often than not, environmental data related to characteristics around the area of species of interest are easier to acquire than biological data, data of species per se (Daliakopoulos et al., 2017). Assuming that near features are more likely to be related than distant ones (Tobler, 1970), a locally trained model can be used to forecast biological patterns based on environmental and biological data in neighbouring locations (Daliakopoulos et al., 2017;Groom et al., 2018).
The use of statistical methods and modelling is of particular importance for the estimation of bats killed under WTs which might be often underestimated due to the fact that carcasses are of small size, not easily detected, quickly consumed by scavengers or destroyed from collisions (Smallwood, 2013). Death counts are improved by the use of detection dogs, cameras and digital technologies (Cryan et al., 2014;Smallwood et al., 2020), but these methods are costly and the scale and extent of their applications limited. A variety of methods have been tested to estimate bat mortalities, fatalities, or deaths based on existing data, including correction factors for scavenger removal, partial search of the WT surroundings and searcher efficiency (Arnett et al., 2005;Huso, 2011;Smallwood, 2013;Zimmerling and Francis, 2016), Stochastic Dynamic Methodology (Bastos et al., 2013), Bayes' theorem (Huso et al., 2015), habitat suitability modelling (Bastos et al., 2013) as well as complex statistical models and software tools (Maurer et al., 2020). Prediction of the cumulative effects of wind industry on a broader geographic scale has also challenged bat conservationists (Hayes, 2013;Roscioni et al., 2013;Voigt et al., 2012;Zimmerling and Francis, 2016).
In Greece, searches for bat deaths at wind farms are rarely undertaken and are based on variable search intensity and survey methodologies, in the absence of mandatory detailed guidelines. In one of the few studies, the results of intensive carcass searches in NE Greece were analysed with respect to species composition and temporal variation, but no inferences were made regarding WT features or environmental drivers of bat fatalities (Georgiakakis et al. 2012). In addition, surveys for killed bats in all neighbouring already operating wind energy facilities have not been conducted or had insufficient quality.
In this study we focused on modelling deaths at a set of WTs then predicting cumulative deaths across a larger region in a mountainous and forested area in Thrace, North East Greece. The main aims were: a) identification of WT and environmental features at different spatial scales associated to bat deaths, b) determine the most lethal WT feature, c) prediction of cumulative deaths in existing and future facilities, d) proposals for proper WT site selection related to landscape planning.
Methods
Study area
The study area is located in the Rhodope and Evros Regional Units, Thrace, Northern Greece. It is characterized as mountainous of rugged relief with slopes varying from gentle to steep (Vasilakis et al., 2008) and it is sparsely populated with scattered small villages and settlements. Altitude in the study area range from 659 m to 1020 m. Land cover is diverse including oak, junipers and endemic pine forests, as well as dry grasslands. Agricultural and artificial areas include mainly croplands and urban land covers. The climate is Mediterranean characterized by cold winters and mild/hot summers. Precipitation in winter ranges between 500 -800 mm while in the summer is often < 20 mm. The study area is one of the richest in Europe in bat diversity, with at least 24 species present (Papadatou, 2010). Furthermore, it has exceptional ornithological importance as it hosts habitats that are of European-wide significance, mainly for large birds of prey and aquatic birds (Catsadorakis and Källander, 2010). A large part of the region has been selected as priority area for the development of wind energy, as it is also one of the areas with the highest wind capacity in mainland Greece (EuropeanCommission, 2022). The highest values of wind speed are observed in higher altitudes as well as in the coastal zone (RAE, 2022).
Bat death data
Bat death data collected between August 2009 to July 2010 in the frame of Worldwide Wildlife Fund (WWF) Greece research project were used (Georgiakakis et al., 2012). We use the term 'death' instead of 'mortality' or 'fatality' since the last two refer to percentages calculated as the number of deaths relative to the population size or dying per WT, both unknown to us. , that are both unknown to us. During that period 88 WT from 9 wind farms were surveyed for bat carcasses. Each WT was visited five or six days a week, except the period between late December 2009 and early March 2010 where visits were rarer due to weather -related restrictions in accessibility (Georgiakakis et al., 2012). In total each WT was visited 305 days within a year (26,840 sampling events) and the number of bat deaths (N = 167 individuals from nine species) was recorded. In cases of multiple deaths in the same WT and day, each death would be recorded as a separate data entry (line in the data) so that data are always in a binary form (1 = death, 0 = no death). The sampling approach did not allow the use of estimators to assess the probability of detection and correct for searcher efficiency, scavenging and other sources of underestimation. Therefore, only the raw count data were used in the analyses.
WT data
Spatial data (Fig. 1a) as well as technical characteristics in terms of rotor diameter (m), tower height (m) and power (kW) for each examined WT were retrieved from Regulatory Authority for Energy (RAE) geoportal (RAE, 2022). Power is used sensu nameplate capacity of each WT as given by the manufacturer, and it is not identical with the energy produced. Three layers were downloaded (operation, installation and production licenses respectively) as shape files from RAE geospatial map and clipped in Evros and Rhodope region borders. Obtained data were grouped in five datasets. Dataset 1 follows the 88 operating WTs where bat deaths were recorded in detail 2009-2010 (Georgiakakis et al., 2012); (Table 1). Datasets 2 and 3 consist of fully operational WTs poorly surveyed (other studies) and not surveyed at all for bat deaths, comprised of 38 and 139 WTs respectively (Table 1). Dataset 4 consists of 11 WTs that have an installation, but not an operation license yet (have been installed or will be soon, but their rotors are not yet spinning) (Table 1). Dataset 5 consists of 56 WTs under the production license, but without an installation or operation license yet (their power, location and technical characteristics are approved, but may not be installed for various reasons, after excluding those without Environmental Terms Approval); (Table 1).
Environmental data & interaction scale
We estimated the percentage of each land cover class around each WT at 250, 1000, and 5000 m radius in Quantum GIS to inspect the effect of habitat composition on bat deaths (Fig. 1b). For each radius, classification was performed using the most detailed resolution available of the CORINE land cover (CLC2018, level 3, spatial resolution 100 m); (EEA, 2010), to record the percentage of every land cover (%) class around each WT. Distance from the nearest trees (m) and distance from water (m) as the minimum distance between the WT and the land cover class containing trees and water were recorded. In addition, tree canopy cover (%) was calculated as the sum of all land cover types containing forest trees. Elevation (m), aspect (degrees), and slope (degrees) around each WT were also recorded. All variables explored in the analysis are listed in Table 2.
Climatic data are publicly available at a resolution of 1 km (Worldclim, 2013). However, they were not used due to the fact that WTs in the same farm would have identical climatic values, and WTs in different farms distancing less than 1.42 km in a straight line (the diagonal of 1 km 2 cell) would also get identical values.
Selecting the land cover scale around WTs best explaining deaths
Bat deaths occurring at the location of WT depend upon characteristics of the environment nearby such as natural, agricultural, or artificial habitats around WTs (Roeleke et al., 2016;Santos et al., 2013). The interaction scale between bat abundance/deaths and the environmental characteristics varies between studies (Lehnert et al., 2014;Santos et al., 2013;Starbuck et al., 2022). In addition, the percentage of cover of each habitat type, or the availability of water, trees as well as the mean topography is scale-specific (Starbuck et al., 2022).
To quantify the optimal interaction scale between bat deaths and land cover characteristics around WTs, a data-driven approach was used (Moustakas et al., 2019) by comparing models between deaths and land cover classes across radii or 250, 1000, and 5000 m. Three generalized linear models (GLM) were fit with bat death events (0, 1) per day per WT (dependent binary variable) and land cover type percentage (independent variables) at 250, 1000, and 5000 m, in the absence of any other variables. Land cover data included the Corine level 3 (most detailed) land cover classes (Table 2). Models were fit with a binomial family error structure to account for the binary nature of the dependent variable. Model selection was performed using the Akaike Information Criterion (AIC); (Akaike, 1974;Burnham and Anderson, 2002). Analysis was conducted using the 'lme4' package in R statistical software (R Development Core Team, 2022).
Selecting the WT feature best explaining deaths
To quantify the WT feature that is best fitted with bat deaths (Huso et al., 2021;Smallwood, 2013), the correlation between the available WT features, rotor diameter, tower height and power was calculated using a Pearson's correlation matrix. We sequentially performed data-driven selection of the WT feature better fitted with bat deaths: three GLMs were fit with bat death events per day per WT and power or tower height, or rotor diameter were used as independent explanatory variable in the absence of any other variables. Models were fit with a binomial family error structure and model selection was performed by using the AIC. Analysis was conducted using the 'lme4' package in R (R Development Core Team, 2022).
WT and land cover effects on bat deaths
A GLM was built with bat death events per day per WT (dependent variable) at the optimal interaction scale, and the WT feature better fitted with deaths, distance from trees, distance from water, elevation, aspect, slope, forest cover, artificial land cover, agricultural land cover and natural land cover percentage (independent variables). All natural, agricultural, and artificial Corine land cover types (listed in Table 2) were combined into a single natural, agricultural, and artificial land cover percentage variable respectively which was further used in the analysis. The model was fit with a binomial family error structure. All independent variables were log(x+1) transformed prior to the analysis to successfully account for heteroscedasticity, as well as for facilitating comparisons among variables of differing levels of magnitude. Model selection of the most parsimonious model structure containing the most informative variables only was performed by the AIC (Burnham and Anderson, 2002). Any deletion of non-significant variables that did not increase AIC > 2 was deemed justified (Burnham and Anderson, 2002). The output of the model is the probability that a fatality will be found predicted by the independent variables. Sequentially, model outputs were categorized into two groups based on their predicted probabilities (p) of death. Cases with p above or equal to 0.5 are considered as deaths, while < 0.5 as not (Kassambara, 2018). The sum of deaths across all outputs indicates total deaths across the 88 WT in one year. Model outputs were compared with data to quantify the deviance in model fitting. Analysis was conducted using the 'lme4', 'nlme' 'MuMIn', 'effects' 'jtools', 'ggplot2', 'sjmisc' and 'lattice' packages in R (R Development Core Team, 2022).
Variance partitioning of variables explaining bat deaths
Hierarchical variance partitioning was performed between the independent variables of the optimal GLM and bat deaths with a binomial regressor to account for the contribution of each explanatory variable to the total variance (Chevan and Sutherland, 1991). Variance partitioning is a computational statistical technique capable of handling potentially correlated independent variables, whilst ranking the predictor importance of each variable (Chevan and Sutherland, 1991;Mac Nally, 2002). Variance partitioning is calculated from the AIC weights of each independent variable and based upon the number of times that a variable was significant among all possible combinations of the explanatory variables (Mac Nally, 2002). Results add to 100%. We performed 99 randomizations to extract confidence intervals and significance of variables. Analysis was conducted using the 'hier.part' package in R (R Development Core Team, 2022).
Predicting bat deaths
The most parsimonious GLM between bat deaths and the explanatory independent variables was used for predicting bat deaths into datasets 2 -5, where actual bat deaths are unknown, but the independent explanatory variables are available (Cameron and Trivedi, 2013;Chowell et al., 2020;Currie, 2016). The GLM input consisted of the values of each independent variable corresponding to the WT deaths to be predicted. The output of the model is death probability predicted by the independent variables. Sequentially, model outputs were categorized into two groups based on their predicted probabilities (p) of death. Cases with p above or equal to 0.5 are considered as deaths, while < 0.5 as not. The sum of deaths across all outputs indicates total deaths across all WTs in datasets 2 -5, in a year. Analysis was conducted using the 'lme4' package in R (R Development Core Team, 2022).
Results
WT features were highly positively correlated as indicated by Pearson's correlation coefficient (Corr P = 0.846 between power -tower height; Corr P = 0.99 between powerrotor diameter; Corr P = 0.848 between tower height -rotor diameter, all p-values <<0.001). The best model fit between deaths and WT features was power as quantified by the lowest AIC score, followed by rotor diameter, while tower height ranked last from the three available WT features (Table 3). The lowest AIC model (deaths -power) significantly differed from the second best (deaths -rotor diameter); ANOVA, deviance= -4.53, p-value <0.01.
The best model fit between deaths and land cover radius was at 5000 m as indicated by the lowest AIC score of the model at this scale, followed by 250 m, while the model containing land cover classes percentages at 1000 m ranked third (Table 4). The lowest AIC model (radius 5000 m) significantly differed from the second best (radius 250 m); ANOVA, deviance =40.97, p-value <<0.001.
The most parsimonious (final) model included the effects of power, distance from trees and water, aspect, slope, agricultural land cover percentage and natural land cover percentage ( Table 6). The inclusion of elevation, forest canopy cover percentage, and artificial land cover percentage were not justified by model selection and were thereby removed from the initial maximal model. The final model did not significantly differ from the initial maximal one, it was just simpler; ANOVA deviance = -0.947, p-value = 0.331 (Table 5). The mean of Artificial land cover percentage contained mainly zero values at the scale of 5000 m deployed in the final model, while elevation was highly correlated with slope, and forest canopy cover with natural land cover percentage (results not shown here).
In terms of model coefficients there is a negative fixed coefficient (-111.659) and the highest coefficient is fitted for the percentage of natural land within 5000 meters from each WT (mean coefficient = +17.345; Table 6, Fig. 2). The second and third highest coefficients were fit for distance from water (mean coefficient = +1.780) and power (mean coefficient = +1.260) respectively (Table 6, Fig. 2). The largest negative coefficient is fitted for slope (mean coefficient = -1.163; Table 6, Fig. 2). Sensitivity analysis of coefficients indicated that the effects of power, distance from water, slope and natural cover are robust as coefficients did not cross zero at a 95% confidence interval (Fig. 3).
Sensitivity analysis between the optimal model (after model selection) and the initial maximal one containing all variables indicated that 95% confidence intervals of coefficients of all three eliminated variables were crossing zero (results not shown here). In addition, 95% intervals of coefficients of variables included in the most parsimonious model and coefficients of the same variables before model selection did not significantly differ (results not shown here). We therefore did not proceed with model averaging across models and variables.
Variance partitioning indicated that power explained 40.22% of the total variance, the natural land cover percentage in 5000 m radius around each WT 15.93% and distance from water 11.52% (Figure 4). Slope explained 10.81%, agricultural cover 8.38%, aspect 8.22%, and distance from trees 4.88% of the total variance (Fig. 4). Randomizations indicated that all variables were significant ( Table 7).
The model predicted 169 deaths in dataset 1 when the actual recorded deaths were 167, and thus overestimated deaths by 1.2% (Fig. 5). Model predictions in dataset 2 indicated 152 deaths, 479 deaths in dataset 3, 79 deaths in data set 4, and 272 deaths in dataset 5 per year (Fig. 5). The total predicted number of bat deaths in the wind turbines of the study area is 1151 bats per year. In terms of percentages in comparison with recorded deaths (dataset 1), there is a higher probability of deaths of 377.8% in operating, but not sufficiently surveyed WTs (dataset 2 & 3). WTs not operating yet, but bound to (data set 4) or likely to operate soon (data set 5) together will contribute to 210.2% excess deaths than the ones recorded. Under the scenario that the WTs under production and installation licence proceed to operation, the total excess deaths will be 588% higher than the ones recorded.
Discussion
Deaths and wind turbine power
Results indicate deaths are significantly associated to wind turbine power. Power alone explained a third of the variance of bat deaths and it is more lethal than tower height or rotor diameter. Energy, the product of power and time, produced by WT is determined by the size of the turbine (tower height, rotor diameter), and rotor speed (Dixon and Hall, 2014). To that end decreasing rotor speed would need to be compensated by increasing WT size and vice versa for producing the same amount of energy. Thus, altering WT features will not minimize impacts on bats, as long as the energy produced remains the same or even increases. In addition, having several small or fewer large WT (Dabiri et al., 2015;Krijgsveld et al., 2009) is unlikely to minimize deaths as long as total produced energy remains constant. Avian and bat mortality was reported to be constant per energy unit produced across wind turbine power capacities (Huso et al., 2021), confirming that not simply the size of turbines but power is the factor better explaining deaths. In the same study, the actual energy produced by each WT, but not the nominal power which is the maximum power capacity was found as a more unbiased estimator of wildlife deaths (Huso et al., 2021). Since the actual energy produced by turbines in each wind farm is not disclosed in Greece, nominal WT power is still a better predictor of deaths than other WT features.
Another study also found power to be a significant explanatory variable with more installed capacity correlating with higher deaths (MacGregor and Lemaître, 2020). However the same study suggest that power 'was a poor predictor of estimated mortality' (MacGregor and Lemaître, 2020). One explanation why we found power (capacity) to be a strong predictor could be that all of the sampled WT were operating very similarly. This is plausible, because at the study area WTs are located in mountain or hill summits and relatively closely located at a straight line. Thus, there are few barriers that can obstruct or de-synchronize wind patterns during the year. In this case energy production, turbine operation and power will be highly correlated. The spatial synchrony of climate is also known to synchronize animal populations, the Moran effect (Moran, 1953), and synchronized populations suffer higher casualties (Hansen et al., 2013;.
Land cover and the interaction zone
Natural land cover was the second best predictor of bat deaths in terms of variance explained. It also had the steepest coefficient slope across all variables, deaths steeply increased for every unit (1%) of natural land cover increase. Thus, the 'perfect storm' for bat deaths needs a combination of high total power and WT installed in natural land cover areas. To that end our results confirm that 'the larger a facility is, the more important specific spatial and environmental context becomes in determining bat mortality' (MacGregor and Lemaître, 2020).
Deaths caused at operating WTs depend on land cover characteristics of coarser scales (Lehnert et al., 2014). Our results, in addition to previous studies (Dietz and Kiefer, 2016;Rodrigues et al., 2015b) suggest that in natural areas, wind turbines should not be licensed in areas where natural land cover at a radius of 5km exceeds 50%. . Natural land cover in terms of coniferous and broadleaved forests are associated with foraging areas and high mobility (Ferreira et al., 2015) which is reasonable to result in higher deaths. High bat collision rates with WTs are also reported in forested mountain ridge tops in the US (Kunz et al., 2007). . Installing of wind farms in disturbed areas instead of natural ones, is necessary in order to minimize cumulative impacts to wildlife (Kiesecker et al., 2011).
Outside these high-risk areas, environmental impacts assessment studies should extend the search range for important foraging, drinking and roosting sites in a sufficiently large area, typically no smaller than 5 km. The spatial cumulative effect of at least 5 km should be assessed as a combined effect of wind energy developments comprised of multiple WTs from different wind farms, taken together, rather just for a single WT. The interaction zone of at least or close to 5 km between the land cover and WT is deduced also from other studies: most processes regarding bat occupancy prediction were found to be most significant at 5760 m radius (Starbuck et al., 2022), the scale closest to 5 km from the ones examined in that study. Higher bat mortalities in WT located closer than 5 km from forests were also reported in Portugal , while Barré et al. (2023) found that bat activity around nacelles was positively affected by landscape characteristics at a radius of up to 10 km.
Other explanatory covariates such as agricultural land cover, aspect, slope, distance from trees and water yielded similar results with other studies (Ferreira et al., 2015;Roeleke et al., 2016;Roemer et al., 2019;Santos et al., 2013;Starbuck et al., 2022). The lack of significance of elevation can be explained by the fact that the data set is comprised of a mountainous landscape and thus there are few lower elevation values to allow for differentiating effects. It appears that in this case, slope is more important. Artificial land cover at a radius of 5 km around each WT was comprised in most cases of values very close to zero, and thus the lack of significance in the optimal model is based on the fact that WTs are located in a landscape that is mainly natural and agricultural at that scale.
Monitoring and public data repositories
In the absence of proper regulations for impact of WTs on bats in the postconstruction monitoring procedure, deaths that pass virtually unnoticed are several folds higher than the actual recorded ones. As bats have low reproduction rates, this is alarming as their population viability (Frick et al., 2017) or extinction debt numbers (Chattopadhyay et al., 2019) might subtly exceed reproductive population thresholds. To that end automated monitoring (McClure et al., 2018) together with field surveys should be systematically regulated together with the operational license to avoid severe population declines and regional or national scale extinctions (Rodrigues et al., 2015b). There is a need of high accuracy when monitoring the wind farm impacts, especially at large sites with steep and heavily vegetated areas. The use of detection dogs to effectively monitor bird and bat deaths at wind farms is becoming increasingly popular (Bennett, 2015). All studies to date agree that dogs outperform human searchers at finding bird and bat carcasses around wind turbines (Domínguez del Valle et al., 2020). According to decisions for the approval of environmental terms designed by the Greek authorities, carcass search area should be extended to 400 m around a turbine and a buffer zone of 300 m from roads connecting wind turbines within important bird areas and special protection areas sites, what makes it extremely difficult to be achieved by human researchers, thus the use of dogs should be obligatory implemented. In addition, online publicly accessible dataset repositories on species deaths by wind turbines should be established (Fernández-Bellon, 2020), regulated by European Commission as well as at national level. There is a need for publicly available data compiled in a comparable format, facilitates' cumulative risk assessment across regions, informed democratic decisions and social awareness (Murray-Rust, 2008). Such data are already available among others for road kills (Balčiauskas et al., 2020;Englefield et al., 2020) or invasive alien species (Deriu et al., 2017) and data-driven research is used to inform policy (Vanderhoeven et al., 2017).
Uncertainties and future research
Deaths were best explained in an interaction zone of 5 km which is the larger of the scales examined here. Further studies expanding that scale are needed to investigate the optimal distance -see e.g. (Moustakas et al., 2019) for an application in trees. It is worth noting that the relationship between deaths, WTs and land cover is not linear as the finer scale, 250 m exhibited a better model fit than the intermediate scale of 1 km. The analysis did not differentiate among bat species as models could not be fitted for each species separately . In addition, the interaction zone of 5 km between land cover and WTs needs to be cross-validated with bird species. In terms of data analytics, model validation was performed by comparing outputs of the trained GLM against the data that were used for training. Data scarcity did not permit in splitting the data into training and testing, with testing data not used for training (de Hond et al., 2022). The inclusion of climatic data especially at temporal resolutions within the year (months, weeks, etc) could provide valuable insights regarding WT synchronization as well as bat synchronization (Nicolau et al., 2022).
The number of bat deaths recorded in the field used for model fitting is an underestimate of the actual one. Although there are statistical models for estimating WT bat deaths number e.g. GenEst (Simonis et al., 2018), the sampling design did not permit using such methods to estimate deaths from raw count data. Obviously, the actual number of bat deaths in the study area is higher, even in WTs where no carcasses were found (Arnett, 2005;Huso et al., 2015), but a precise estimation was not possible.
Furthermore, although not examined in our study, landscape configuration in terms of mountain passes, linear elements suitable for commuting between habitat fragments (e.g. treelines, hedgerows, ravines), and water bodies too small to be classified into the Corine land cover, should be taken in account during the planning and licensing process (Arnett et al., 2008;Kelm et al., 2014;Piorkowski and O'Connell, 2010;Rodrigues et al., 2015a). Other configuration features such as habitat complexity has to been taken into account as bat deaths at WTs are expected to be higher in structurally rich landscapes (Hurst et al., 2016).
Landscape planning implications
The target of the new EU biodiversity strategy is to increase the protected area to at least 30 % of EU land by 2030 (EuropeanCommission, 2021;Hurst et al., 2016). Primary and old-growth forests and other carbon-rich ecosystems, such as grasslands will be the focus of conservation efforts, as well as soil conservation (EuropeanCommission, 2021). Rewilding EU is also core part of the plan (EuropeanCommission, 2021). On top of this plan, a second pioneering proposal aims to repair the 80% of European habitats that are in poor condition, and to bring back nature to all ecosystems (EuropeanCommission, 2022).
Installing WTs in protected areas or old forests and causing species decline is clearly contradicting both strategic plans. WTs are directly related with land loss and degradation by artificial base surfaces and road-induced fragmentation. Ranking of biodiversity threats in Europe indicates that historically threats deriving from land use changes are several folds higher than the ones from climatic changes (Almond et al., 2020), with comparable results in other studies (IPBES, 2019). In the most recent assessments, land-use change is still the biggest current threat to nature, destroying or fragmenting the natural habitats of many plant and animal species on land, in freshwater and in the sea (Almond et al., 2022). That is not meant to downplay climate-derived threats, but rather to disentangle the impact of land use changes and climatic changes on ecosystems.
A paradox emerges of impacting biodiversity to mitigate the climate: biodiversity is negatively affected by climate change, but biodiversity, through the ecosystem services it supports, makes an important contribution to both climate mitigation and adaptation (EuropeanCommission, 2009). Consequently, conserving and sustainably managing biodiversity is critical to addressing climate change (EuropeanCommission, 2009;Lloret et al., 2022). It thus needs to be prioritized what is the relative gain and loss of wind farm installation and operation in the climate-land-biodiversity-energy nexus. Table 1. Data sets used in the analysis. Data set 1: wind turbines surveyed for a full year (2009)(2010) and used for model training and variance partitioning; data sets 2 & 3: wind turbines in operation, but not adequately surveyed; data sets 4 & 5: licensed, but not in operation yet. Datasets 2 -5 were used for predicting bat deaths using the trained model in data set 1. The number of wind turbines (Nr of WT), total power (Sum of all WTs power; kW), and power per wind turbine (kW/WT) are listed in each data set.
Dataset
Windfarm category
Nr of WT
Figure 1 .
1a. Overview of the geographic location of datasets 1 to 5 in Thrace region, Northern Greece. b. (inner figure) Detail of land cover composition at scales of 250, 1000 and 5000 m (dashed outlines) around the WTs of Monastiri area (dataset 1, black dots). Different background colours depict land cover classification types.
Figure 2 .
2Effects of each covariate of the final model on bat deaths. Solid blue line indicates model fit, while shaded light blue envelopes indicate a 95% confidence interval. Vertical axis indicates probability of death for each variable, while horizontal axis the data range of each predictor in the final model. Thickness of black bars in the horizontal axis indicates data density.
Figure 3 .
3Sensitivity analysis of coefficients of the final model between bat deaths and explanatory covariates. Horizontal thin blue lines indicate a 95% confidence interval of the coefficient value of each parameter, while thick blue lines indicate a 90% confidence interval. Positive coefficient estimates indicate higher deaths while negative lower. The effects of distance from trees and agricultural land cover are crossing the dotted vertical zero line indicating that for some values their effects may not be consistent. All other effects are not crossing zero.
Figure 4 .
4Variance partitioning of the final model covariates on bat deaths. Variance partitioning is quantifying the percentage of variance explained by each variable, and ranking their relative importance. Results add to 100%.
Figure 5 .
5Bat deaths per year predicted in datasets 2 -5 by the trained optimal model in dataset 1. Circles indicate the mean while whiskers indicate a 95% confidence interval of the mean. The horizontal dotted red line indicates the actual recorded number of deaths in dataset 1 in a year.
Table 2 .Table 3 .Table 5 .
235Variables used in the analysis. Scale refers to the radius around each WT explored. WT features are the allometric and energy related characteristics of each WT. Topography refer to the physical landscape characteristics at the location of each WT and its distance to the nearest water sources and trees. Land cover follows the CORINE level 3 classification system. Land cover types are the ones that appeared in the classification around WTs. The sum of 'Broad leaved forest', 'Coniferous forest', and 'Mixed forest land cover' type percentages appears as the variable 'Forest land cover', that was also explored in the analysis Statistics of the three generalized linear models used to select the wind turbine feature best explaining bat deaths.Table 4. Statistics of the three generalized linear models used to select the land cover distance around wind turbines best explaining bat deaths. Statistics of the model selection used to remove variables based on AIC. The initial maximal model contained all variables while the final model did not include the effects of artificial land cover percentage, elevation, and forest canopy cover percentage.Table 6. ANOVA results of the final model between deaths (dependent variable) and WT power & environmental independent variables.Table 7. Randomizations of the variables used in variance partitioning. Variance partitioning was performed between the explanatory covariates of bat deaths in the optimal model. All variables were found to be significant after 99 randomizations.Category
Variables
Units
Mean
Scale
250 Radius
m
1000 Radius
m
5000 Radius
m
Wind Turbine
Power
kW
1208
Tower Height
m
54.132
Rotor Diameter
m
60.506
Topography
Elevation
m
867.95
Aspect
degrees 172.61
Slope
degrees 14.475
Distance from water
m
18372
Distance from trees
m
65.874
Land cover
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| sample_1396 | 0.8254 | arxiv | |
Bayesian reconstruction of past land-cover from pollen data: model robustness and sensitivity to auxiliary variables
3 Nov 2018
Behnaz Pirzamanbein
Department of Applied Mathematics and Computer Science
Technical University
Denmark
Centre for Mathematical Sciences
Lund University
Sweden
Centre for Environmental and Climate Research
Lund University
Sweden
Johan Lindström
Department of Applied Mathematics and Computer Science
Technical University
Denmark
Anneli Poska
Department of Physical Geography and Ecosystems Analysis
Lund University
Sweden
Institute of Geology
Tallinn University of Technology
Estonia
Bayesian reconstruction of past land-cover from pollen data: model robustness and sensitivity to auxiliary variables
3 Nov 2018* Corresponding author: Behnaz Pirzamanbein, bepi@dtu.dk 1
Realistic depictions of past land cover are needed to investigate prehistoric environmental changes, effects of anthropogenic deforestation, and long term land cover-climate feedbacks. Observation based reconstructions of past land cover are rare and commonly used model based reconstructions exhibit considerable differences. Recently Pirzamanbein et al. (Spatial Statistics, 24:14-31, 2018) developed a statistical interpolation method that produces spatially complete reconstructions of past land cover from pollen assemblage. These reconstructions incorporate a number of auxiliary datasets raising questions regarding the method's sensitivity to different auxiliary datasets.Here the sensitivity of the method is examined by performing spatial reconstructions for northern Europe during three time periods (1900 CE, 1725 CE and 4000 BCE). The auxiliary datasets considered include the most commonly utilized sources of past land-cover data -e.g. estimates produced by a dynamic vegetation (DVM) and anthropogenic land-cover change (ALCC) models.Five different auxiliary datasets were considered, including different climate data driving the DVM and different ALCC models. The resulting reconstructions were also evaluated using cross-validation for all the time periods. For the recent time period, 1900 CE, the different land-cover reconstructions were compared against a present day forest map.The validation confirms that the statistical model provides a robust spatial interpolation tool with low sensitivity to differences in auxiliary data and high capacity to capture information in the pollen based proxy data. Further auxiliary data with high spatial detail improves model performance for areas with complex topography or few observations.
Introduction
The importance of terrestrial land cover for the global carbon cycle and its impact on the climate system is well recognized (e.g. Claussen et al., 2001;Brovkin et al., 2006;Arneth et al., 2010;Christidis et al., 2013). Many studies have found large climatic effects associated with changes in land cover.
Forecast simulations evaluating the effects of human induced global warming predict a considerable amplification of future climate change, especially for Arctic areas (Zhang et al., 2013;Richter-Menge et al., 2011;Chapman and Walsh, 2007;Miller and Smith, 2012). The past anthropogenic deforestation of the temperate zone in Europe was lately demonstrated to have an impact on regional climate similar in amplitude to present day climate change (Strandberg et al., 2014).
However, studies on the effects of vegetation and land-use changes on past climate and carbon cycle often report considerable differences and uncertainties in their model predictions (de Noblet-Ducoudré et al., 2012;Olofsson, 2013).
One of the reasons for such widely diverging results could be the differences in past land-cover descriptions used by climate modellers. Possible land-cover descriptions range from static present-day land cover (Strandberg et al., 2011), over simulated potential natural land cover from dynamic (or static) vegetation models (DVMs) (e.g. Brovkin et al., 2002;Hickler et al., 2012), to past land-cover scenarios combining DVM derived potential vegetation with estimates of anthropogenic land-cover change (ALCC) (Strandberg et al., 2014;Pongratz et al., 2008;de Noblet-Ducoudré et al., 2012).
Differences in input climates, mechanistic and parametrisation differences of DVMs (Prentice et al., 2007;Scheiter et al., 2013), and significant variation between existing ALCC scenarios (e.g. Kaplan et al., 2009;Pongratz et al., 2008;Goldewijk et al., 2011;Gaillard et al., 2010) further contribute to the differences in past land-cover descriptions. These differences can lead to largely diverging estimates of past land-cover dynamics even when the most advanced models are used (Strandberg et al., 2014;Pitman et al., 2009). Thus, reliable land-cover representations are important when studying biogeophysical impacts of anthropogenic land-cover change on climate.
The palaeoecological proxy based land-cover reconstructions recently published by Pirzamanbein et al. (2014Pirzamanbein et al. ( , 2018 were designed to overcome the problems described above. And to provide a proxy based land-cover description applicable for a range of studies on past vegetation and its interactions with climate, soil and humans. These reconstructions use the pollen based land-cover composition (PbLCC) published by Trondman et al. (2015) as a source of information on past land-cover composition.
The PbLCC are point estimates, depicting the land-cover composition of the area surrounding each of the studied sites. Spatial interpolation is needed to fill the gaps between observations and to produce continuous land-cover reconstructions. Conventional interpolation methods might struggle when handling noisy, spatially heterogeneous data (Heuvelink et al., 1989;de Knegt et al., 2010), but statistical methods for spatially structured data exist (Gelfand et al., 2010;Blangiardo and Cameletti, 2015).
In Pirzamanbein et al. (2018) a statistical model based on Gaussian Markov Random Fields (Lindgren et al., 2011;Rue and Held, 2005) was developed to provide a reliable, computationally effective and freeware based spatial interpolation technique. The resulting statistical model combines PbLCC data with auxiliary datasets; e.g. DVM output, ALCC scenarios, and elevation; to produce reconstructions of past land cover. The auxiliary data is subject to the differences and uncertainties outlined above and the choice of auxiliary data could influence the accuracy of the statistical model. The major objectives of this paper are: 1) To draw attention of climate modelling community to a novel set of spatially explicit pollen-proxy based land-cover reconstructions suitable for climate modelling; 2) to present and test the robustness of the spatial interpolation model developed by Pirzamanbein et al. (2018);and 3) to evaluate the models capacity to recover information provided by PbLCC proxy data and to analyse its sensitivity to different auxiliary datasets.
Material and Methods
The studied area covers temperate, boreal and alpine-arctic biomes of central and northern Europe Four different model derived datasets, depicting past land cover, along with elevation were considered as potential auxiliary datasets. In each case potential natural vegetation composition estimated by the DVM LPJ-GUESS (Lund-Potsdam-Jena General Ecosystem Simulator; Smith et al., 2001;Sitch et al., 2003) were combined with an ALCC scenario to adjust for human land use (see Pirzamanbein et al., 2014, for details):
K-L RCA3 : Combines the ALCC scenario KK10 (Kaplan et al., 2009) and the potential natural vegetation from LPJ-GUESS. Climate forcing for the DVM was derived from RCA3 (Rossby Centre Regional Climate Model, Samuelsson et al., 2011) is based on a combination of satellite data and national forest-inventory statistics from 1990-2005 (Pivinen et al., 2001;Schuck et al., 2002) (Figure 1, column 1 row 1). All auxiliary data were up-scaled to 1 • × 1 • spatial resolution, matching the pollen based reconstructions, before usage as model input.
Statistical Model for Land-cover Compositions
A Bayesian hierarchical model is used to interpolate the PbLCC data; here we only provide a brief overview of the model, mathematical and technical details can be found in Pirzamanbein et al. (2018).
The model can be seen as a special case of a generalized linear mixed model with a spatially correlated random effect. An alternative interpretation of the model is as an empirical forward model (direction of arrows in Figure 2) where parameters affect the latent variables which in turn affect the data.
Reconstructions are obtained by inverting the model (i.e. computing the posterior) to obtain the latent variables given the data.
The PbLLC derived proportions of land cover (coniferous forest, broadleaved forest and unforested land), denoted Y PbLCC , are seen as draws from a Dirichlet distribution (Kotz et al., 2000, Ch. 49) given a vector of proportions, Z, and a concentration parameter, α (controlling the uncertainty:
V(Y PbLCC ) ∝ 1/α). Since the proportions have to obey certain restrictions (0 ≤ Z k ≤ 1 and 3 k=1 Z k = 1, were k indexes the land-cover types), a link function is used to transform between the Figure 1: Data used in the modelling. The first column shows (from top to bottom) the EFI-FM, SRTM elev , and the colorkey for the land-cover compositions, coniferous forest (CF), broadleaved forest (BF) and unforested land (UF). The remaining columns give (from left to right) the PbLCC (Trondman et al., 2015) and the four model based compositions considered as potential covariates: K-L RCA3 , K-L ESM , H-L RCA3 , and H-L ESM . Here K/H indicates KK10 (Kaplan et al., 2009) or HYDE (Goldewijk et al., 2011) land use scenarios and L RCA3 /L ESM indicates the climate -Rossby Centre Regional Climate Model (Samuelsson et al., 2011) or Earth System Model (Mikolajewicz et al., 2007) -used to drive the vegetation model. The three rows represent (from top to bottom) the time periods 1900 CE, 1725 CE, and 4000 BCE. Figure 2: Hierarchical graph describing the conditional dependencies between observations (white rectangle) and parameters (grey rounded rectangles) to be estimated. The white rounded rectangles are computed based on the estimations. In a generalized linear mixed model framework, η is the linear predictor -consisting of a regression term, µ, and a spatial random effect, X. The link function, f (η), transforms between linear predictor and proportions, which are matched to the observed land cover proportions, Y PbLCC , using a Dirichlet distribution. (Becker et al., 2009), K/H indicates KK10 (Kaplan et al., 2009) or HYDE (Goldewijk et al., 2011) land use scenarios and L RCA3 /L ESM indicates vegetation model driven by climate from the Rossby Centre Regional Climate Model (Samuelsson et al., 2011) or from an Earth System Model (Mikolajewicz et al., 2007).
Y PbLCC Data model Z LCRs = f (η) Z LCRs = f (η) Parameters Latent variables η µ X = + α β B Covariates κ ΣModel Covariates Intercept SRTM elev K-L ESM K-L RCA3 H-L ESM H-L RCA3 Constant x Elevation x x K-L ESM x x x K-L RCA3 x x x H-L ESM x x x H-L RCA3 x x x
proportions and the linear predictor, η:
Z k = f (η) = e η k 1+ 2 i=1 e η i for k = 1, 2 1 1+ 2 i=1 e η i for k = 3 η k = f −1 (Z) = log Z k Z 3 for k = 1, 2
Here f −1 (Z) is the additive log-ratio transformation (Aitchison, 1986), a multivariate extension of the logit transformation.
The linear predictor consists of a mean structure and a spatially dependent random effect, η = µ+X.
The mean structure is modelled as a linear regression, µ = Bβ; i.e. a combination of covariates, B, and regression coefficients, β. To aid in variable selection and suppress uninformative covariates a horseshoe prior (Park and Casella, 2008;Makalic and Schmidt, 2016) is used for β. The main focus of this paper is to evaluate the model sensitivity to the choice of covariates (i.e. the auxiliary datasets).
The PbLCC is modelled based on six different sets of covariates: 1) Intercept, 2) SRTM elev , 3) K-L ESM , 4) K-L RCA3 , 5) H-L ESM , and 6) H-L RCA3 ; illustrated in Figure 1. A summary of the different models is given in Table 1.
Finally, the spatially dependent random effect is modelled using a Gaussian Markov Random Field (Lindgren et al., 2011) with two parameters: κ, controlling the strength of the spatial dependence and
Testing the Model Performance
To evaluate model performance, we compared the land-cover reconstructions from different models for the 1900 CE time period with the EFI-FM by computing the average compositional distances (Aitchison et al., 2000;Pirzamanbein et al., 2018). This measure is similar to root mean square error in R 2 but it accounts for compositional properties (i.e. 0 ≤ Z k ≤ 1 and 3 k=1 Z k = 1).
Since no independent observational data exists for the 1725 CE and 4000 BCE time periods, we applied a 6-fold cross-validation scheme (Hastie et al., 2001, Ch. 7.10) to all models and time periods.
Results and Discussion
Fossil pollen is a well-recognized information source of vegetation dynamics and generally accepted as the best observational data on past land-cover composition and environmental conditions (Trondman et al., 2015).
Today, central and northern Europe have, at the subcontinental spatial scale, the highest density of palynologically investigated sites on Earth. However, even there the existing pollen records are irregularly placed, leaving some areas with scarce data coverage . The collection of new pollen data to fill these gaps is very time consuming and cannot be performed everywhere. All this makes pollen data, in their original format, heavily underused, since the data is unsuitable for models requiring continuous land-cover representations as input. The lack of spatially explicit proxy based land cover data directly usable in climate models has been hampering the correct representation of past climate-land cover relationship.
Regrettably, the commonly used DVM derived representations of past land cover exhibit large variation in vegetation composition estimates. The model derived land-cover datasets used as auxiliary data (Table 1) show large variation in estimated extents of coniferous and broadleaved forests, and unforested areas for all of the studied time periods (Figure 1). These substantial differences illustrate large deviances between model based estimates of the past land-cover composition due to differences in applied climate forcing and/or ALCC scenarios. Differences in climate model outputs (Harrison et al., 2014;Gladstone et al., 2005) and ALCC model estimates (Gaillard et al., 2010) have been recognized in earlier comparison studies and syntheses. The effect of the differences in input climate forcing and ALCC scenario on DVM estimated land-cover composition presented here are especially pronounced for central and western Europe, and for elevated areas in northern Scandinavia and the Alps ( Figure 1). In general the KK10 ALCC scenario produces larger unforested areas, notably in western Europe, compared to the HYDE scenario. Compared to the ESM climate forcing; the RCA3 forcing results in higher proportions of coniferous forest, especially for central, northern and eastern Europe. The described differences are clearly recognizable for all the considered time periods and are generally larger between time periods than within each time period. The purpose of the statistical model presented in Section 2.1 is to combine the observed PbLCC with the spatial structure in the auxiliary data to produce data driven spatially complete maps of past land-cover that can be used directly (as input) in others models.
To illustrate the structure of the statistical model, step by step advancement from auxiliary data Table 1) with different auxiliary datasets. Locations and compositional values of the available PbLCC data are given by the black rectangles. Middle row shows the compositional distances between each model and the Constant model. Bottom row shows the compositional distances between each model and the EFI-FM. Table 1) with different auxiliary datasets. Locations and compositional values of the available PbLCC data are given by the black rectangles. Third and fourth row show the compositional distances between each model and the Constant model.
for the areas with low observational data coverage (e.g. eastern and south-eastern Europe) is improved by including covariates that exhibit distinct spatial structures for the given areas (Figures 5 and 6).
Neither the DIC results nor the 6-fold cross-validation results show any advantage among the six tested models for the different time periods (Table 2). Analogous to the reconstructions, the predictive regions are very similar in both size and shape irrespective of the auxiliary dataset used, indicating similar reconstruction uncertainties across all models (Figure 7). Implying there is no clear preference among the models, i.e. that the results are robust to the choice of auxiliary dataset. Table 2: Deviance information criteria (DIC) and Average compositional distances (ACD) from 6-fold cross-validations for each of the six models and three time periods. Best value for each time period marked in bold-font.
DIC
Although a temporal misalignment exists between the PbLCC data for the 1900 CE time period (based on pollen data from 1850 to the present) and the EFI-FM (inventory and satellite data from 1990-2005); EFI-FM provides the best complete and consistent land cover map of Europe for present time, making it a reasonable choice for a comparison. The main differences between the EFI-FM and the PbLCC data for the 1900 CE time period are: 1) lower abundance of broadleaved forests for most of Europe, 2) higher abundance of coniferous forest in Sweden and Finland, and 3) higher abundance of unforested land in North Norway in the EFI-FM data than in the PbLCC data (Pirzamanbein et al., 2018). The average compositional distances computed between the land-cover reconstructions and the EFI-FM for 1900 CE show practically identical (1.47 to 1.48) distances between all six reconstructions and the EFI-FM, and small differences among the six presented models (Table 3).
These results clearly show that the developed statistical interpolation model is robust to the choice of covariates. The model is suitable for reconstructing spatially continuous maps of past land cover from scattered and irregularly spaced pollen based proxy data.
Conclusions
The statistical model and Bayesian interpolation method presented here has been specially designed for handling irregularly spaced palaeo-proxy records like pollen data and, dependent on proxy data availability, is globally applicable. The model produces land-cover maps by combining irregularly distributed pollen based estimates of land cover with auxiliary data and a statistical model for spatial structure. The resulting maps capture important features in the pollen proxy data and are reasonably insensitive to the use of different auxiliary datasets.
Auxiliary datasets considered were complied from commonly utilized sources of past land-cover data (outputs from a dynamic vegetation model using different climatic drivers and anthropogenic land-cover changes scenarios). These datasets exhibit considerable differences in their recreation of the past land cover. Emphasizing the need for the independent, proxy based past land-cover maps created in this paper.
Evaluation of the model's sensitivity indicates that the proposed statistical model is robust to the choice of auxiliary data and only considers features in the auxiliary data that are consistent with the proxy data. However, auxiliary data with detailed spatial information considerably improves the interpolation results for areas with low proxy data coverage, with no reduction in overall performance.
This modelling approach has demonstrated a clear capacity to produce empirically based land-cover reconstructions for climate modelling purposes. Such reconstructions are necessary to evaluate anthropogenic land-cover change scenarios currently used in climate modelling and to study past interactions between land cover and climate with greater reliability. The model will also be very useful for producing reconstructions of past land cover from the global pollen proxy data currently being produced by the PAGES (Past Global changES) LandCover6k initiative 1 .
Data availability
The database containing the reconstructions of coniferous forest, broadleaved forest and unforested land, three fractions of land cover, for the three time-periods presented in this paper, along with reconstructions for 1425 CE and 1000 BCE using only the K-L ESM are available for download from https://github.com/BehnazP/SpatioCompo. In addition the source code is available in the same
repository under the open source GNU General Public License.
Acronyms DVM Dynamical vegetation model.
ALCC
Anthropogenic land-cover change.
PbLCC
Pollen based land-cover composition.
LPJ-GUESS
The Lund-Potsdam-Jena General Ecosystem Simulator, a DVM.
EFI-FM
European Forest Institute forest map.
Notation
Y PbLCC
Observations, as proportions.
f Link function, transforming between proportions and linear predictor.
η Linear predictor, η = µ + X.
µ Mean structure; modelled as µ = Bβ using covariates, B, and regression coefficients, β.
X Spatially dependent random effect.
α Concentrated parameter of the Dirichlet distribution (i.e. observational uncertainty) Σ Covariance matrix that determines the variation between and within fields κ Scale parameter controlling the range of spatial dependency
( 45 •
45N to 71 • N and 10 • W to 30 • E). The PbLCC data published in Trondman et al. (2015) consists of proportions of coniferous forest, broadleaved forest and unforested land presented as gridded (1 • × 1 • ) data points placed irregularly across northern-central Europe. Altogether 175 grid cells containing proxy data were available for 1900 CE, 181 for 1725 CE, and 196 for the 4000 BCE time-period (Figure 1, column 2).
at annual time and 0.44 • × 0.44 • spatial resolution (Figure 1, column 3), K-L ESM : Combines the ALCC scenario KK10 and the potential natural vegetation from LPJ-GUESS. Climate forcing for the DVM was derived from the Earth System Model (ESM; Mikolajewicz et al., 2007) at centennial time and 5.6 • × 5.6 • spatial resolution. To interpolate data into annual time and 0.5 • × 0.5 • spatial resolution climate data from 1901-1930 CE provided by the Climate Research Unit was used (Figure 1, column 4), H-L RCA3 : Combines the ALCC scenario from the History Database of the Global Environment (HYDE; Goldewijk et al., 2011) and vegetation from LPJ-GUESS with RCA3 climate forcing (Figure 1, column 5), H-L ESM : Combines the ALCC scenario from HYDE and vegetation from LPJ-GUESS with ESM climate forcing (Figure 1, column 6).The elevation data (denoted SRTM elev ) was obtained from the Shuttle Radar Topography Mission(Becker et al., 2009) (Figure 1, column 1 row 2).Finally, a modern forest map based on data from the European Forest Institute (EFI) is used for evaluation of the model's performance for the 1900 CE time period. The EFI forest map (EFI-FM)
Σ
, controlling the variation within and between the fields (i.e. the correlation among different land cover types). Model estimation and reconstructions are performed using Markov Chain Monte Carlo (Brooks et al., 2011) with 100 000 samples and a burn-in of 10 000 (See Pirzamanbein et al., 2018, for details.). Output from the Markov Chain Monte Carlo are then used to compute land-cover reconstructions (as posterior expectations, E(Z|Y PbLCC )) and uncertainties in the form of predictive regions. The predictive regions describe the uncertainties associated with the reconstructions; including uncertainties in model parameters and linear predictor.
The cross-validation divides the observations into 6 random groups and the reconstruction errors for each group when using only observations from the other 5 groups are computed. To further compare predictive performance of the models Deviance Information Criteria (DIC; see Ch. 7.2 inGelman et al., 2014) were computed for all models and time periods. The DIC is a hierarchical modelling generalization of the Akaike and Bayesian information criteria(Hastie et al., 2001, Ch. 7).
(Figure 3 :
3model derived land cover) to final statistical estimates of land cover compositions for 1725 CE are given inFigures 3 and 4. The large differences in K-L RCA3 and K-L ESM are reduced by scaling with the regression coefficients, β, capturing the empirical relationship between covariates and PbLCC data. Thereafter, the land-cover estimates are subjected to similar adjustments due to intercept and SRTM elev , and finally similar spatial dependent effects.The impact of different auxiliary datasets was assessed by using the statistical model to create a set of proxy based reconstructions of past land cover for central and northern Europe during three time periods (1900 CE, 1725 CE and 4000 BCE; see Figures 5 and 6). Each of these reconstructions were based on the irregularly distributed observed pollen data (PbLCC), available for ca 25% of the area, together with one of the six models(Table 1) using different combinations of the auxiliary data (Figure 1).The resulting land-cover reconstructions exhibit considerably higher similarity with the PbLCC data than any of the auxiliary land-cover datasets for all tested models and time periods(Figures 5 and 6). At first the similarity among the reconstructions might seem contradictory, but recall that the model allows for, and estimates, different weighting (the regression coefficients, β:s) for each of the auxiliary datasets. Thus, the resulting reconstructions do not rely on the absolute values in the auxiliary datasets, only their spatial patterns. As a result, model performance for elevated areas and Advancement of the model for two locations at 1725 CE. Starting from the value of the K-L RCA3 and K-L ESM covariates ( * ), the cumulative effects of regression coefficients, β, (+); the intercept and SRTM elev covariates (•); and, finally, the spatial dependency structures (•), are illustrated. With the final points (•) corresponding to the land-cover reconstructions and marking the observed pollen based land-cover composition.
Figure 4 :
4Advancement of K-L ESM models for the 1725 CE time period: (a) shows the effect of intercept and SRTM elev , (b) shows the mean structure, µ, including all the covariates, (c) shows the spatial dependency structure and finally (d) shows the resulting land-cover reconstructions obtained by adding (b) and (c).
Figure 5 :
5Land-cover reconstructions using PbLCC for the 1900 CE time periods (top row). The reconstructions are based on six different models (see
Figure 6 :
6Land-cover reconstructions using local estimates of PbLCC for the 1725 CE (top) and 4000 BCE (bottom) time periods. The reconstructions are based on six different models (see
Figure 7 :
7The prediction regions and fraction of the ternary triangle covered by these regions are presented for three locations, the six models, and the 1900 CE, 1725 CE and 4000 BCE time periods.
Table 1 :
1Six different models and corresponding covariates. SRTM elev is elevation
EFI-FM Elevation K-L ESM K-L RCA3 H-L ESM H-L RCA31900 CE
Constant
1.48
0.08
0.18
0.20
0.17
0.19
Elevation
1.49
0.19
0.21
0.18
0.20
K-L ESM
1.48
0.09
0.07
0.09
K-L RCA3
1.48
0.11
0.06
H-L ESM
1.48
0.08
H-L RCA3
1.48
1725 CE
Constant
0.10
0.16
0.16
0.17
0.17
Elevation
0.14
0.11
0.14
0.13
K-L ESM
0.14
0.06
0.16
K-L RCA3
0.15
0.07
H-L ESM
0.15
4000 BCE
Constant
0.11
0.21
0.17
0.22
0.19
Elevation
0.19
0.12
0.20
0.15
K-L ESM
0.19
0.07
0.21
K-L RCA3
0.18
0.07
H-L ESM
0.20
Table 3 :
3The average compositional distances among the six models fitted to the data for each of the three time periods.
www.pastglobalchanges.org/ini/wg/landcover6k/intro
AcknowledgementsThe research presented in this paper is a contribution to the two Swedish strategic research areas Biodiversity and Ecosystems in a Changing Climate (BECC), and ModElling the Regional and GlobalEarth system (MERGE). The paper is also a contribution to PAGES LandCover6k. Lindström has been funded by Swedish Research Council (SRC, Vetenskapsrådet) grant no 2012-5983. Poska has been funded by SRC grant no 2016-03617 and the Estonian Ministry of Education grant IUT1-8. The authors would like to acknowledge Marie-José Gaillard for her efforts in providing the pollen based land-cover proxy data and thank her for valuable comments on this manuscript.
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| sample_1397 | 0.9839 | arxiv | |
Large time behavior of differential equations with drifted periodic coefficients and modeling Carbon storage in soil
20 Sep 2008
Stephane Cordier stephane.cordier@univ-orleans.fr
Fédération Denis Poisson, bât. Mathématiques
UMR CNRS 6628
University of Orléans
BP 6759, 45067 Orléeans Cedex 2France
University of Technical Education in HoChiMinh City
01Vo
Department of Mathematics and Computer Science
HoChiMinh City
Vietnam
University of Natural Science
Vietnam
Na-tional University HoChiMinh City
227 Nguyen Van Cu Str., Dist.5, HoChiMinh CityVietnam
Xuan Le
Truong
Thanh Nguyen
Long longnt@hcmc.netnam.vn
Alain Pham alain.pham@univ-orleans.fr
Ngoc Dinh
Fédération Denis Poisson, bât. Mathématiques
UMR CNRS 6628
University of Orléans
BP 6759, 45067 Orléeans Cedex 2France
University of Technical Education in HoChiMinh City
01Vo
Department of Mathematics and Computer Science
HoChiMinh City
Vietnam
University of Natural Science
Vietnam
Na-tional University HoChiMinh City
227 Nguyen Van Cu Str., Dist.5, HoChiMinh CityVietnam
Van Ngan Str
Thu Duc
Dist
Large time behavior of differential equations with drifted periodic coefficients and modeling Carbon storage in soil
20 Sep 2008Ordinary differential equationsT-periodic functionlinear driftCauchy sequenceseries' estimatesAMS subject classification: 34E0540A05
This paper is concerned with the linear ODE in the form y ′ (t) = λρ(t)y(t)+b(t), λ < 0 and which represents a simplified model of storage of the carbon in the soil. In the first part, we show that, for a periodic function ρ(t), a linear drift in the coefficient b(t) involves a linear drift for the solution of this ODE. In the second part, we give sufficient conditions on the coefficients to ensure the existence of an unique periodic solution of this differential equation. Numerical examples are given.
Introduction
A lot of phenomena of evolution are described using ordinary differential equations ODE or systems in which the coefficients and/or the source terms are periodic. Let us mention some applications in physics (e.g. the harmonic oscillator , the resonance phenomena due to oscillatory source terms), electricity (let us mention the famous RLC circuit with an oscillatory generator), in biology (circadian cycle), in agricultural studies (due to seasonal effects).
The main question which is addressed here is when or under which conditions a slow perturbation of the coefficient in the ODE will induce a similar behavior on the solutions, in large time. More precisely, we are looking for conditions to ensure that a linear drift in the (periodic) coefficients of the ODE will lead to a linear deviation (and thus unbounded) of the solutions or, on the contrary, what kind of perturbation in the coefficients are compatible with a stable (bounded, periodic in large time) solutions.
Although these questions can be applied to large number of applications, our original motivation concerned with the effect of climate change on the seasonal variations in the organic carbon contained in the soil as claimed at the end of the conclusion of Martin et al. [13].
Since the readers may be not familiar with this domain. Let us recall some basis about the issues of the soil organic carbon (SOC) modelling.
The spreading is one of opportunities for organic materials of human origin (sludge of filtering treatment station and derivative products) and agricultural (manure). The organic matter spread contain significant amounts of organic carbon which, after application, a fraction is permanently stored in the soil. ; The remainder is returned to the atmosphere as CO2. The spreading can be accessed through the storage of organic carbon in the soil, helping to reduce CO2 emissions (a major greenhouse gas effect) compared for example to the incineration of organic matter that returns all carbon into the atmosphere. The optimization of spreading of organic materials is important in reducing emissions of greenhouse gas effect.
The dynamics of carbon in the soil, which determines the amount of organic carbon stored in soil and returned in the form of CO2, depends on soil type, agricultural practices, climate and quantities spread. The soil organic carbon (SOC) plays an important role in several environmental and land management issues. One of the most important issues is the role that SOC plays as part of the terrestrial carbon and might play as a regulation of the atmospheric CO2. Many factors are likely, in a near future, to modify the SOC content, including changes in agricultural practices [3,18,2] and global climate changes [9,5,8,10,11].
Understanding SOC as a function of soil characteristics, agricultural management and climatic conditions is therefore crucial and many models have been developed in this perspective. These models are used in a variety of ways and after for long term studies [6,15,16,17]. The behavior of the SOC system, over a long term and assuming that the environment of the system (inputs of organic carbon, climatic conditions) is stable, is reported to tend towards steady or periodic state.
Some of he SOC models have been formulated mathematically [14,4,1,12,13]. Here we consider the RothC model [7,13] which consists in splitting the soil carbon into four active compartments. Under a continuous form it can be written as
dC(t) dt = ρ(t)AC(t) + B(t), (1.1)
where C (t) is a vector with 4 components, each corresponding to a compartment storage of carbon in the soil: DPM (decomposable plant material), RPM ( resistant plant material), BIO (microbial community) and HUM ( humus). These components indicate the amount of carbon stored at the moment t. In (1.1) i) ρ(t) is a function indicating the speed of mineralization of soil, which results in CO2 emissions. ii) A is a matrix that can represent the percentage of clay in the soil and speeds of mineralization in each compartment of C in the soil.
iii) B(t) indicates the amount of carbon brought in the soil (amount spread per unit time). Let us recall that the initial goal of this study was to understand how long term evolution on climatic data imply variation in large time on the solution of ODE with periodic coefficient and/or source terms with a (linear) drift. The mathematical tools involved in this paper are rather classical and simple but there are, up to our knowledge, very few literature on the subject.
In the reminder of this paper, we shall consider a simplified case with a single (scalar) equation but the extension to a diagonalizable system (as it is the case for the A matrix in [13], see eq (5)).
The main results in this paper are, first (section 2), to prove that a linear drift in the coefficients leads to a linear drift in the solution over a large time behavior. Second (section 3), we try to find sufficient conditions on the coefficients in order to get the existence of an unique periodic solution. These results are illustrated by numerical tests in section 4.
The extension to linear differential system is straightforward (by diagonalizing the system). The extension to partial differential equation are under study. For example, in the case of the linear heat equation, using Fourier Series, one can expect the same kind of results.
Asymptotic behavior of the solution
In this paper, we consider the linear differential equation
y ′ (t) = λρ (t) y (t) + b (t) , 0 ≤ t < +∞,(2.1)
where λ < 0, ρ(t) and b(t) are given functions satisfying the following conditions (A 1 ) ρ (t) is an T-periodic function, with T > 0 fixed.
(A 2 ) there exist the T-periodic function, β(t), such that b(t + T ) = b(t) + β(t), ∀t ∈ [0, ∞) . (2.2)
The general solution of (2.1) has the form
y(t) = e a(t) C 1 + t 0 b(s)e −a(s) ds , (2.3)
where C 1 is a constant and
a(t) def = λ t 0 ρ(s)ds. (2.4)
In this section, we prove that there exists a unique solution y ∞ (t) of (2.1) satisfying
y ∞ (t + T ) = y ∞ (t) + γ(t), ∀t ∈ [0, ∞), (2.5)
where γ(t) is an T-periodic function. Let first remark that
Lemma 2.1. Let b : R + −→ R. The following properties are equivalent : (a) ∃β(t) periodic with period T such that b(t + T ) = b(t) + β(t), ∀t ≥ 0 (b) ∃b(t) periodic with period T such that b(t) =b(t) + t T β(t), ∀t ≥ 0 Proof. Let us first prove (a)=⇒(b). Chooseb(t) = b(t) − t T β(t). Thenb(t) is periodic with period T sincẽ b(t + T ) = b(t + T ) − t+T T β(t + T ) = b(t) + β(t) − ( t T + 1)β(t) = b(t) − t T β(t) =b(t). Conversely (b)=⇒(a). Using b(t) =b(t) + t T β(t), we have b(t + T ) =b(t + T ) + t + T T β(t + T ) = b(t) + ( t T + 1)β(t) =b(t) + t T β(t) + β(t) = b(t) + β(t).
This concludes the proof.
Let us now prove the main result of this section. First, we state the some lemmas
Lemma 2.2. Let (A 1 ) hold. Then a(t + nT ) = a(t) + a(nT ) = a(t) + na(T ), ∀t ≥ 0, n ∈ N. (2.6) Proof. From (2.4) we deduce that a(t + nT ) = λ nT 0 ρ(s)ds + λ t+nT nT ρ(s)ds = a(nT ) + λ t+nT nT ρ(s)ds. (2.7)
On the other hand, by the assumption (A 1 ), we have Combining (2.7)-(2.9) we have (2.6).
λ t+nT nT ρ(s)ds = λ t 0 ρ(s + nT )ds = λ t 0 ρ(s)ds = a(t),(2.Lemma 2.3. Let assumptions (A 1 ), (A 2 ) hold. For n ∈ Z + and t ∈ [0, ∞), we put y n (t) = y(t + nT ) = e a(t+nT ) y(0) + t+nT 0 b(s)e −a(s) ds . (2.10) Then, y n (t) = y ∞ (t) + δ n (T ) + nγ(t), (2.11) where y ∞ (t) =e a(t) e a(T ) 1 − e a(T ) T 0 b(s)e −a(s) ds − e a(T ) 1 − e a(T ) 2 T 0 β(s)e −a(s) ds + t 0 b(s)e −a(s) ds , (2.12) δ n (T ) =e a(t) e na(T ) y(0) + e a(T ) 1 − e a(T ) T 0 b(s)e −a(s) ds + e a(T ) 1 − e a(T ) 2 T 0 β(s)e −a(s) ds , (2.13)
and
γ(t) = e a(t) e a(T ) 1 − e a(T ) T 0 β(s)e −a(s) ds + t 0 β(s)e −a(s) ds .
(2.14)
Proof. By the assumption (A 2 ), it follows from (2.10) and the lemma 2.2 that
y n (t) = e a(t) y n (0) + t 0 b(s)e −a(s) ds + n t 0 β(s)e −a(s) ds .
On the other hand, we have
y n (0) = y (nT ) = e a(nT ) y (0) + nT 0 b (s) e −a(s) ds = e na(T ) y (0) + n−1 k=0 T 0 b (s + kT ) e −a(s+kT ) ds = e na(T ) y (0) + T 0 b (s) e −a(s) ds n−1 k=0 e −ka(T ) + T 0 β (s) e −a(s) ds n−1 k=0 ke −ka(T ) .
By using the following equalities
n−1 k=0 e −ka(T ) = 1 − e −na(T ) 1 − e −a(T ) , and n−1 k=0 ke −ka(T ) = e −a(T ) e −a(T ) − 1 2 − e −(n+1)a(T ) e −a(T ) − 1 2 + n e −na(T ) e −a(T ) − 1 ,
thus we obtain
y n (0) = e a(T ) 1 − e a(T ) T 0 b (s) e −a(s) ds − e a(T ) 1 − e a(T ) 2 T 0 β (s) e −a(s) ds + e na(T ) y (0) − e a(T ) 1 − e a(T ) T 0 b (s) e −a(s) ds + e a(T ) 1 − e a(T ) 2 T 0 β (s) e −a(s) ds . + n e a(T ) 1 − e a(T ) T 0 β (s) e −a(s) ds
Combining previous equalities, we obtain (2.11). The proof of Lemma is complete. Now, we state the main theorem
Theorem 2.4. Let (A 1 ), (A 2 ) hold. Then, there exists a unique solution y ∞ (t) of (2.1) such that y ∞ (t + T ) = y ∞ (t) + γ(t), ∀t ∈ [0, ∞), (2.15)
where γ(t) is an T-periodic function, defined by
γ(t) = e a(t) e a(T ) 1 − e a(T ) T 0 β(s)e −a(s) ds + t 0 β(s)e −a(s) ds .
(2.16)
Proof. For n ∈ Z + and t ≥ 0, let us define Combining (2.20) and (2.21), we obtain
u n (t) def = y n (t) − nγ(t).y ∞ (t + T ) = lim n→+∞ u n+1 (t) + γ (t) = y ∞ (t) + γ (t) .
(2.22) Uniqueness Now, let y (t) be the solution of (2.1) corresponding to the initial value y (0) = A and
y (t + T ) = y (t) + γ (t) ,(2.23)
where γ (t) is an T-periodic function. Then y * (t) = y ∞ (t) − y (t) satisfy
y ′ (t) = λρ (t) y (t) , 0 < t < +∞, y (0) = L (T ) − A,(2.ρ(t + T ) = ρ(t) + α(t), ∀t ∈ [0, ∞) . (2.28)
In that case it is clear that there does not exist a solution which has the same property as the function ρ(t), for instance if we consider the example with b(t) = 0. Here the solution of (2.1) tends to 0 as t → +∞.
Sufficient conditions for the existence of periodic solutions
In this section, we consider the following assumptions for the functions ρ(t) and b(t) of the ODE (2.1) (B 1 ) ρ ∈ L 1 loc (0, ∞), ρ(t) > 0 and there exists a constant T > 0 such that
ρ(t + iT ) = ρ(t) + α i (t), ∀t ∈ [0, +∞), ∀n ∈ N, (3.1) (B 2 ) Assume that the function t → b(t)e −λ R t 0 ρ(s)ds belongs to L 1 loc (0, ∞) and b(t + iT ) = b(t) + β i (t), ∀t ∈ [0, +∞), ∀n ∈ N,(3.2)
where the functions sequences {α i (t)}, {β i (t)} satisfy some conditions specified later. Note that, by (3.1), (3.2) we also deduce that α i ∈ L 1 loc (0, ∞) and β i (·)e −λ R · 0 ρ(s)ds ∈ L 1 loc (0, ∞).
Let us define the function sequence {y n (t)} ∞ n=0 by
y n (t) = y(t + nT ),(3.3)
where y(t) is a solution of equation ( Combining (3.11) and (3.12), we obtain (3.9) -(3.10). The proof of lemma 3.6 is complete. Now, replace t = T in (3.9), we get y n+1 (0) = y n (T ) = µ n y n (0) + β n , (3.13) where µ n = e a(T )+λb αn , (3.14)
and
α i ≡ α i (T ), β i ≡ β i (T ), ∀i ∈ N. (3.15)
By the recurrent, from (3.13), we obtain the following corollary Now, to obtain the convergence of sequence {y n (0)} ∞ n=0 , we make the following assumptions Now, put
Corollary 3.3. Let (B 1 ), (B 2 ) hold. Then y n+1 (0) = n i=1 δ (n) i β n−i+1 + δ (n) n y(T ),(3.Assume that {α i (t)} ∞ i=1 and {β i (t)} ∞ i=1 satisfies 0 < α i+1 (t) ≤ α i (t), ∀t ≥ 0 and ∞ i=1 e −ia(T ) α i < +∞, (3.18) (B 3 ) 0 < β i+1 (t) ≤ β i (t), ∀t ≥ 0 and ∞ i=1 e −ia(T ) β i < +∞.Z n = n i=1 δ (n) i β n−i+1 . (3.28)
We shall prove that {Z n } is a Cauchy sequence. Let m, n ∈ Z + , m ≥ n, then
Z m − Z n = m i=n+1 δ (m) i β m−i+1 + n i=1 δ (m) i β m−i+1 − δ (n) i β n−i+1 def = J 1 + J 2 . (3.29)
It is clear that δ
(k) i = e ia(T ) .e λ(b α k +b α k−1 +···b α k−i+1 ) ≤ ρ i 1 , ∀k ∈ N, i = 1, 2, ...k,(3.30)
with ρ 1 = e a(T ) ∈ (0, 1) and by (3.18)-(3.19), we have
β i ≤ T 0 (|b(s)| + β 1 (s)) e −a(s)−λb α1(s) ds ≡ K(T ), ∀i ∈ N. (3.31) Estimate J 1 .
It follows from (3.30) and (3.31), that
|J 1 | ≤ m i=n+1 δ (m) i β m−i+1 ≤ K(T ) m i=n+1 ρ i 1 → 0, (3.32) when m, n → +∞, by ∞ i=1 ρ i 1 < +∞. Estimate J 2 .
By (3.30)-(3.31), we can estimate J 2 as follows
|J 2 | ≤ n i=1 δ (m) i β m−i+1 − β n−i+1 + n i=1 δ (m) i − δ (n) i β n−i+1 (3.33) ≤ n i=1 ρ i 1 β m−i+1 − β n−i+1 + K(T ) n i=1 δ (m) i − δ (n) i .
On the other hand, it follows from (3.10) that Using the following inequality
β m−i+1 − β n−i+1 = T 0 {b(s) + β m−i+1 (s)} e −e −X − e −Y ≤ |X − Y | , ∀X, Y ≥ 0,(3.β m−i+1 − β n−i+1 ≤ |λ| T 0 (|b(s)| + β 1 (s)) e −a(s) ( α n−i+1 (s) − α m−i+1 (s)) ds (3.36) + T 0 {β n−i+1 (s) − β m−i+1 (s)} e −a(s) .e −λb α1(s) ds ≤ |λ| T 0 (|b(s)| + β 1 (s)) e −a(s) ds α n−i+1 + e −λb α1 T 0 β n−i+1 (s)e −a(s) ds.
Hence,
n i=1 ρ i 1 β m−i+1 − β n−i+1 ≤ |λ| T 0 (|b(s)| + β 1 (s)) e −a(s) ds n i=1 ρ i 1 α n−i+1 + e −λb α1 n i=1 ρ i 1 T 0 β n−i+1 (s)e −a(s) ds (3.37)
On the other hand, we have
n i=1 ρ i 1 α n−i+1 = ρ n+1 1 n i=1 ρ −i 1 α i ≤ ρ n+1 1 ∞ i=1 ρ −i 1 α i → 0, (3.38) and n i=1 ρ i 1 T 0 β n−i+1 (s)e −a(s) ds = ρ n+1 1 n i=1 ρ −i 1 T 0 β i (s)e −a(s) ds ≤ ρ n+1 1 ∞ i=1 ρ −i 1 T 0 β i (s)e −δ (m) i − δ (n) i ≤ |λ| ρ i 1 n j=n−i+1 α j − m j=m−i+1 α j ≤ |λ| ρ i 1 n j=n−i+1 α j . (3.41)
Therefore, we deduce from (3.41) that
n i=1 δ (m) i − δ (n) i ≤ |λ| n i=1 ρ i 1 n j=n−i+1 α j = |λ| n i=1 i j=1 ρ n−j+1 1 α i (3.42) = |λ| ρ n+1 1 1 − ρ 1 n i=1 ρ −i 1 α i − n i=1 α i ≤ |λ| ρ n+1 1 1 − ρ 1 ∞ i=1 ρ −i 1 α i → 0, when m, n → ∞.
Combining we deduce that y ∞ (t) is a T-periodic function. We can also show as in section 2 that there is uniqueness of such a solution y ∞ (t).
Numerical results
In this section the following Cauchy problem (2.1) with the following choice
λ = −1, y 0 = 1, ρ(t) = sin 2 t, b(t) = t (6.1)
Clearly, ρ(t) and b(t) satisfy ρ(t + π) = ρ(t) and b(t + π) = b(t) + π i.e. the assumptions of section 2 with T = π and β(t) = π. Therefore the calculus of the different elements defined in section 2 give In fig.1 we have drawn the graph of the function t → γ(t), γ(t) = a 0 + t 0 β(s)e −a(s) ds e a(t) .
11
The fig.2 indicates the graphs t → y ∞ (t) and t → y ∞ (t + T ) where y ∞ (t) = l(T ) + The fig.2 fairly shows the drift property of y ∞ (t) just as the function b(t). The asymptotic behavior represented in fig.3 shows us the very fast convergence of the approximation z n (t) = y ∞ (t) + nγ(t) to the exact solution at the point t + nT i.e. y n (t) = y(t + nT ), y(t) being the solution of the Cauchy problem (6.1) and given by y(t) = y(0) + t 0 b(s)e −a(s) ds e a(t) .
So for n = 1 the two graphs coincide exactly for t ≥ 5! Finally in fig.4 we have put the graphs of the functions y n (t) and y n (t + π) with n = 5 and here we also note the drift property for the solution of (2.1) taking initial value y 0 = 1 at t = 0.
s)ds = na(T ).(2.9)
) 2 T 0 ββ
20n (t) = y ∞ (t) , ∀t ∈ [0, +∞) . (2.18) It is clear that y ∞ (t) is a solution of equation (2.1) satisfies the initial value y ∞ (0) = e a(T ) 1 − e a(T ) T 0 b (s) e −a(s) ds − e a(T ) 1 − e a(T (s) e −a(s) ds ≡ L (T ) . (2.19) By (2.18), we have y ∞ (t + T ) = lim n→+∞ u n (t + T ) = lim n→+∞ {y n (t + T ) − nγ (t + T )} . n+1 (t) − (n + 1) γ (t) + n [γ (t) − γ (t + T )] + γ (t)}On the other hand, by the periodicity of β(t), we get γ (t + T ) = e a(t+T ) e a(T ) 1 − e a(T ) (s) e −a(s) ds = γ (t) .
(t + T ) = y * (t) + γ * (t) , γ * (t + T ) = γ * (t) , y * (t) = (L (T ) − A) e a(t) , ∀t ≥ 0.(2.26) From (2.25) and (2.26) we deduce that γ * (t) = − (L (T ) − A) 1 − e a(T ) e a(t) , ∀t ≥ 0. (2.27) Combining (2.25), (2.27) we get A = L(T ). By the uniqueness of Cauchy problem, the proof of theorem 2.8 is complete. Remark If we consider the equation (2.1) where the assumptions (A 1 ) and (A 2 ) are replaced by (A ′ 1 ) b (t) is an T-periodic function, with T > 0 fixed (A ′ 2 ) there exist a T-periodic function, α(t), such that
y
2.1) corresponding to the initial value y(0) = C 1 and defined by (2.3). It can be proved that if ρ(t) and b(t) are the T-periodic functions then the function sequence {y n (t)} ∞ n=0 converge to y ∞ (t) where y ∞ (t) = e a(t) ∞ (t) being a unique T-periodic solution of equation (2.1).Now, we will extend this result to the case where ρ(t) and b(t) satisfy the conditions (B 1 ), (B 2 ), respectively.Let us now state some lemmas.
Lemma 3. 1 .
1Let (B 1 ) hold. Then we havea(t + nT ) = a(nT ) + a(t) s + nT )ds = a(nT ) + a(t) + λ t 0 α n (s)ds.Hence, we obtain (3.5). On the other hand, from (3.5) we can deduce that a ((n + 1)T ) = a(nT ) + a(T )
Lemma 3. 2 .
2Let (B 1 ), (B 2 ) hold. Then y n (t) = e a(t)+λb αn(t) y n (0) + β n (t) , (s)ds, and β i (t) =t 0 (b(s) + β i (s)) e −a(s)−λb αi(s) ds, i ∈ N. (3.10) Proof. From (3.3), (2.3) and (3.5), we deduce that y n (t) = e a(nT +t) (s)ds e a(nT ) C 1 + nT 0 b(s)e −a(s) ds + e a(nT ) nT +t nT b(s)e −a(s) ds = e a(t)+λ R t 0 αn(s)ds y n (0) + e a(nT ) nT +t nT b(s)e −a(s) ds .On the other hand, by change variable, it follows from the assumptions (B 2 ) and ((τ ) + β n (τ )) e −a(nT )−a(τ )−λ R τ 0 αn(s)ds dτ.
ia(T )+λ(b αn+b αn−1+...+b αn+1−i) , ∀i = 1, 2, ..., n. (3.17)
. 4 .. 5 .
45By the assumption (B 3 ) we deduce that the proof of (3.20) is straightforward and we omit it. From (3.10) we haveβ n (t) s) + β n (s)) e −a(s) e −λb αn(s) − 1 ds + t 0 β n (s)e −a(s) ds.(3.22) Using the following inequality e X − 1 ≤ |X| e |X| , ∀X ∈ R, Let (B 1 ) -(B 3 ) hold. Then, the sequence {y n (0)} ∞ n=0 is convergence and we have lim n→+∞ y n+1 (0) = e a(T ) 1 − e a(T ) T 0 b(s)e −a(s) ds ≡ L(T ). (3.25) Proof. From the assumption (B 3 ) and (3.17), we have δ (n) n = e na(T )+λ(b α1+b α2+...+b αn)
a(s) e −λb αm−i+1(s) − e −λb αn−i+1(s) m−i+1 (s) − β n−i+1 (s)} e −a(s) .e −λb αn−i+1(s) ds.
.
a(s) ds → 0. (3.39) By the assumption (B 3 ), it follows from (3.37)-(3.39) that n i=1 ρ i 1 β m−i+1 − β n−i+1 → 0, when m, n → ∞. It follows from (3.17) and the inequality (3.35) that
( 3 .
329), (3.32), (3.33), (3.40) and (3.42), we deduce that {Z n } is Cauchy sequence. Hence, it is clear that there exists the lim n→∞ y n+1 (0), by (3.16) and (3.26). Passing to the limit in (3.13) by (3.20)-(3.21), we have lim n→+∞ y n+1 (0) = e a(T ) 1 − e a(T ) T 0 b(s)e −a(s) ds ≡ L(T ).(3.43)The lemma 3.5 is completely proved.
Theorem 3. 6 .
6Let (B 1 )-(B 3 ) hold. Then there exists a unique T-periodic solution of equation (2.1), y ∞ Proof. First, by passing to the limit in (3.9), it follows from (3.20), (3.21) and (3.25) that lim n→∞ y n (t) = y ∞ (t), ∀t ≥ 0. It is clear that y ∞ (t) is a solution of equation (2.1) and satisfies the initial value y(0) = L(T ). Moreover, since y ∞ (t + T ) = lim n→∞ y n (t + T ) = lim n→∞ y(t + T + nT ) = lim n→∞ y n+1 (t) = y ∞ (t), ∀t ∈ [0, +∞),
s)e −a(s) ds ≈ 4.0912
Fig1.
The periodic function γ(t)
The asymptotic function y ∞ (t)
Fig3. Asymptotic behavior, n=1
Fig4. Drift property in asymptotic behavior
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| sample_1401 | 0.5028 | arxiv | |
Thermal Rectification in CVD Diamond Membranes Driven by Gradient Grain Structure
Zhe Cheng
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Brian M Foley
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Thomas Bougher
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Luke Yates
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Baratunde A Cola cola@gatech.edu
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
School of Materials Science and Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Samuel Graham
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
School of Materials Science and Engineering
Georgia Institute of Technology
30332AtlantaGeorgiaUSA
Thermal Rectification in CVD Diamond Membranes Driven by Gradient Grain Structure
1
As one of the basic components of phononics, thermal diodes transmit heat current asymmetrically similar to electronic rectifiers and diodes in microelectronics. Heat can be conducted through them easily in one direction while being blocked in the other direction. In this work, we report an easily-fabricated mesoscale chemical vapor deposited (CVD) diamond thermal diode without sharp temperature change driven by the gradient grain structure of CVD diamond membranes. We build a spectral model of diamond thermal conductivity with complete phonon dispersion relation to show significant thermal rectification in CVD diamond membranes. To explain the observed thermal rectification, the temperature and thermal conductivity distribution in the CVD diamond membrane are studied. Additionally, the effects of temperature bias and diamond membrane thickness are discussed, which shed light on tuning the thermal rectification in CVD diamond membranes. The conical grain structure makes CVD diamond membranes, and potentially other CVD film structures with gradient grain structure, excellent candidates for easily-fabricated mesoscale thermal diodes without a sharp temperature change.
Ⅰ. INTRODUCTION
Electron and phonon conduction are two main fundamental transport mechanisms in solid state materials, but all modern information computing processes are based on the flow of electrons in devices such as electronic transistors. 1,2 As their counterpart, phononics also has the potential to process information by manipulating heat flow like electron flow. 3 Thermal diodes are basic components of phononics, which aim to control heat current similar to electronic diodes in microelectronics. 4 For an electronic diode, its electrical resistance is small when applying a bias (electrical voltage) in one direction while the electrical resistance becomes very large when applying the bias in the other direction. This controls the electrical current to flow through the electronic diode asymmetrically. Similarly, when applying a bias (temperature difference) across a thermal diode in opposite directions, the thermal resistance is small when applying the bias in one direction while the thermal resistance becomes large in the other direction. Here, we define the thermal rectification as the ratio of the thermal resistance difference in the two directions and the smaller thermal resistance. 5,6 In the past two decades, interest in thermal rectification has been growing rapidly because of its potential applications in information computation, thermal control, and energy conversion. 1,2,4 Both theoretical and experimental explorations have been demonstrated by graded mass density, 7 two components with different materials, 8,9 asymmetric geometry, 10-14 phase change materials, 3,15,16 thermal radiation, 17-19 holes or graded doping. 20,21 Most of these demonstrations require very complicated nanofabrication techniques or have an interface which leads to a localized temperature drop. 20 These scenarios suggest that it would be interesting to observe large thermal rectification in a one-material configuration that can be fabricated easily.
Chemical vapor deposited (CVD) diamonds have been extensively studied to dissipate heat for applications of thermal management in power electronics. [22][23][24][25][26] To grow CVD diamond on a substrate, the substrate needs to be mechanically abraded with diamond powders as seeds.
Microwave-enhanced chemical vapor deposition method is used to grow diamond from these seeds by using a mixture of hydrogen and methane. 27 The diamond crystals grow in a columnar structure and expand laterally as the film thickness increases from the diamond-substrate interface. 28 Consequently, the diamond crystal size at the diamond-substrate interface is much smaller than that at the growth interface. This gradient grain structure results in different dominant phonon scattering mechanisms that have different temperature dependence in the two sides of the diamond membrane. When applying a temperature bias across the diamond membrane in two different directions, we can observe thermal rectification (different thermal resistances).
In contrast to the approaches of fabricated defects, holes, or asymmetric shapes, a CVD diamond membrane itself has conical grain structure and does not need extra fabrication. The gradient phonon confinement (grain boundary scattering) resulting from the gradient grain sizes makes it an excellent candidate for thermal rectification. In this work, we report a large theoretical thermal rectification in CVD diamond membranes by building a spectral thermal conductivity model based on complete phonon dispersion relation of diamond. This concept can be applied to other CVD growth materials where there is a strong change in the temperature dependence of thermal conductivity through the material.
Ⅱ. THERMAL CONDUCTIVITY MODEL
For mesoscale heat conduction modelling, the length scale is too large for Molecular Dynamics simulation and too small for assuming diffusive conduction. Empirical formulas or modified Callaway models were usually used to describe the thermal conductivity of CVD diamond. Sood et al. used a gray kinetic model to model thermal conductivity by assuming an effective mean free path. 29 Several modified Callaway models were also used to model diamond thermal conductivity with assumptions of constant phonon velocity, and an ideal Debye-type phonon spectrum. [30][31][32][33] Here, we model the thermal conductivity of CVD diamond with complete phonon dispersion relation without these assumptions, similar to the method used by Mingo
1 2 BE v j j k f C k dk T ,(1)22 2 1 6 BE j j j j k f v k dk T ,(2)
where is the thermal conductivity, j is the phonon polarization index, v is the phonon group velocity, is the total scattering rate, is the angular frequency, BE fT is the temperature derivative of Bose-Einstein distribution function, and k represents the phonon wavevector. 35 We chose (100) direction of the phonon dispersion relation of diamond to do all the calculations because this direction is highly symmetric which can be assumed as isotropic Brillouin zone. 36 The temperature dependent specific heat of diamond was calculated and agreed excellently with experimental values, 37 as shown in FIG. S1. The total scattering rate is determined by the Matthiessen's rule, 38 given as 29 ). The local scattering rate for cross-plan thermal conduction is given by
1 11 j j imp u v d ,(3)1 11 () ( ) ( ) jj j imp u zeff reff vv z d z d z ,(4)
where, effective cross-plane grain size ()
zeff dz =0.75 () z dzt/(1-t), effective in-plane grain size () reff dz = () r dz(1+p)/(1-p).
t and p are constants related to transmission and specularity. We take t=0.56 and p=0.33 which are fitted from experimental data in Ref. 28 . For impurity scattering, we assume the impurity scattering at the nucleation interface is ten times larger than the isotope scattering ( Here, the heat transfer in the diamond membrane is a one-dimensional steady-state heat conduction. To obtain the thermal resistance = ∆ ⁄ , if we fix the temperature of one side of the membrane as T1, we need to find a certain heat flux to make the temperature of another side of the membrane as 2000 = 1 + ∆ . We know the distance from nucleation interface of each layer once we know the membrane thickness. The temperature of all layers are initialized as T1.
For every layer (i), its thermal conductivity (i) can be obtained after we know its distance from the nucleation interface (zi) and its temperature (Ti). By guessing a value of heat flux q, the temperature of each layer is updated with = −1 − × ∆ ⁄ . Here ∆ is the thickness of each layer. Repeat updating Ti and i until they are self-consistent. After that, the temperature
R1
R2
Growth side Nucleation side difference between layer 1 and layer 2000 is obtained and compared with the needed value as feedback to change the value of q. After we find the heat flux that makes the temperature difference between layer 1 and layer 2000 as the needed value, the thermal resistance can be obtained. This procedure also works for calculating thermal resistance in the opposite direction.
We only need to change the heat flux to a negative value. The thermal rectification is the ratio of the thermal resistance difference for two opposite directions and the smaller thermal resistance. Only for a small part in the middle of the membrane, its thermal conductivity has the opposite trend, which decreases the thermal rectification. These differences in thermal conductivity distribution results in the preferential heat flow moving from different sides of the membrane. The total thermal resistance when heat flux flows from the nucleation side to the growth side is smaller than that when heat flux flows from the growth side to the nucleation side.
As a result, the thermal rectification of this diamond membrane configuration reaches to 25%.
FIG. 4. Temperature (a) and thermal conductivity (b) distribution along thickness direction with a temperature bias of 175-375 K. "Nucleation cold" represents the nucleation side of the diamond membrane has a lower temperature than that at the growth side. "Nucleation hot"
represents the nucleation side of the diamond membrane has a higher temperature than that at the growth side. When the membrane is thin, grain boundary scattering plays an important role in impeding thermal transport even at growth side of the membrane. Unlike phonon-phonon scattering, structural imperfection scatterings like grain boundary scattering are elastic scatterings which are temperature independent. When grain boundary scatterings are dominant over phonon-phonon scatterings, the thermal conductivity is less temperature dependent. When the temperature bias is applied, thermal rectification becomes small because the thermal conductivity is weakly temperature dependent and does not change much with different temperature distribution. As the thickness increases, the large grain size impedes phonon transport to a diminishing degree.
Phonon-phonon scattering becomes the dominant mechanism affecting thermal transport, which is highly temperature dependent. This leads to an increasing rectification ratio. But as the membrane thickness keeps increasing, the temperature gradient across the membrane thickness direction becomes increasingly small. The middle part of the membrane does not contribute to thermal rectification. This leads to a slow decrease of thermal rectification when the membrane thickness keeps increasing. Additionally, the thermal rectification increases with the applied temperature bias. The thermal rectification with temperature bias of 100 K is close to twice as that with temperature bias of 50 K. However, the thermal rectification with temperature bias of 200 K is larger than twice of that with temperature bias of 100 K. This is due to the very large temperature dependence of diamond thermal conductivity at low temperatures (175-225 K). To observe thermal rectification in the diamond membranes, high heat flux is required (several kW/mm 2 ). Additionally, to distinguish the effects of grain boundary and defects near the nucleation interface we added in the model on the thermal rectification, we calculate the thermal
the distance from the nucleation interface (z).20 Then the thermal conductivity of CVD diamond is a function of distance from nucleation interface z and temperature T.FIG. 1. Schematic diagram of grain structure of the CVD diamond membrane. R1 and R2 are thermal resistances of the diamond membrane when heat flux goes from the nucleation side to the growth side and from the growth side to the nucleation side. A finite element method is easily used to obtain the temperature and thermal conductivity based on Fourier's law, as shown in FIG. 2. The diamond membrane is divided into 2000 layers.
FIG. 2 .
2Schematic diagram of the iteration process of calculating thermal rectification.Ⅲ. RESULTS AND DISCUSSIONFIG. 3 shows the temperature dependent local cross-plane thermal conductivity of the CVD diamond membrane with different distances from the nucleation interfaces (z). If taking the curve of z=100 μm as an example, the diamond is polycrystalline but has very large grains so phononphonon scatterings will dominate over grain boundary scatterings. As a result, the thermal conductivity increases with increasing temperature at low temperatures because of the sharp temperature dependence of specific heat (T 3 ). The thermal conductivity decreases with increasing temperature at high temperatures because of phonon-phonon scattering. At a given temperature,(z1, T1) (z i , T i ) (z 2000 , T 2000 ) κi=function (z i , T i ) q 1. Initialize Ti=T1 to calculate every κi 2. Guess q 3. Update T i =T i-1 -q *Δz/ κ i and κ i until self-consistent 4. Calculate ΔT= T 1 -T 2000Adjust q to obtain the needed ΔT the local thermal conductivity increases with z because the grain size increases with z. The temperature where peak thermal conductivity occurs shifts to higher temperatures with smaller z because structural imperfection like grain boundary scattering and impurity scattering impedes phonon transport significantly at low temperatures. Elastic scatterings like grain boundary scatterings and impurity scatterings are temperature independent while phonon-phonon scatterings are strong temperature-dependent. So we can see strong temperature dependence of thermal conductivity for large z values and weak temperature dependence for small z values.This is the phenomenon we leverage here to observe thermal rectification in CVD diamond membranes. In the temperature range of 200-300 K, thermal conductivity for z=1 μm increases with temperature while thermal conductivity for larger z values decreases with temperature.These opposite trends facilitate thermal rectification in CVD diamond membranes.FIG. 3. Temperature dependent local cross-plane thermal conductivity of a CVD diamond membrane for different distances from nucleation side (z). 10 The value of thermal rectification is defined as (R2-R1)/R1, as shown in FIG. 1. R1 and R2 are thermal resistances of the whole diamond membrane with heat flux flowing in the two opposite directions (i.e. R1 from the nucleation side to the growth side, and R2 from the growth side to the nucleation side). FIG. 4 shows the temperature and thermal conductivity distribution along thickness direction when applying a temperature bias of 175-375 K to a 100 μm thick diamond membrane. The slope of temperature change with z is large near nucleation interface because of its low thermal conductivity, especially when the nucleation side is on the low temperature side of the bias. When the nucleation side is the cold side and the growth side is the hot side, the thermal conductivity of both the cold and hot sides are small, resulting in a large thermal resistance. When the growth side is the cold side and the nucleation side is the hot side, the thermal conductivity of both the nucleation and growth sides are large, resulting in a small thermal resistance.
and temperature bias affect the thermal rectification of CVD diamond membrane significantly. FIG. 5 shows thickness dependent thermal rectification with different temperature biases of 50 K, 100 K, and 200 K. The average temperature of all these three cases is 275 K. The thermal rectification increases with membrane thickness rapidly before reaching a peak. Then it decreases slowly with increasing thickness. FIG. 5. Thickness dependent thermal rectification of a CVD diamond membrane with 50 K, 100 K, and 200 K temperature biases.
rectification in both cases (with and without the extra defects), as shown in FIG. 6. The two lines overlap with each other for both cases so the added defects in the model does not affect the thermal rectification. The observed thermal rectification is mainly due to gradient grain structure. FIG. 6. Thermal rectification for diamond membranes with and without considering added defects near the nucleation interface in the model. The temperature bias is 175-375 K.As one of the basic components of phononics, thermal diodes transmit heat current asymmetrically similar to electronic rectifiers and diodes in microelectronics. In this work, we report an easily-fabricated mesoscale chemical vapor deposited (CVD) diamond thermal diode without sharp temperature change driven by the gradient grain structure of the CVD diamond membrane. We developed a spectral thermal conductivity model of the thermal conductivity of CVD diamond with complete phonon dispersion relation to show significant thermal rectification in CVD diamond membranes. With the use of our model we find thermal rectification reaches 5%, 11%, and 25% with temperature biases of 50K, 100K, and 200K, which suggests that CVD diamond could serve as practical thermal diodes. To explain the observed thermal rectification, we studied the temperature and thermal conductivity distribution in the CVD diamond membrane. Additionally, we discussed the effects of temperature bias and diamond membrane thickness, which shed light on tuning thermal rectification in CVD diamond membranes. The conical grain structure makes CVD diamond membranes, and potentially other CVD film structures with gradient grain structure, excellent candidates for easily-fabricated mesoscale thermal diodes without a sharp temperature change. Wang, L. & Zhang, Z. Thermal rectification enabled by near-field radiative heat transfer between intrinsic silicon and a dissimilar material. Nanoscale and Microscale Thermophysical Engineering 17, 337-348 (2013).
et al. for silicon nanowires and Foley, et al. for nano-grained SrTiO3 thin films. 34,35 The specific heat and thermal conductivity are calculated by2
2
For CVD diamond, the grain sizes change with distance from the nucleation side z, as shown inFIG. 1. We calculate the in-plane and cross-plane crystal sizes as same as Ref.where, relaxation time for impurity is
41
()
imp
j
A
, relaxation time for Umklapp scattering is
2
/
1
() CT
uj BT e
, d is the sample size. By fitting calculated thermal conductivity to previously
reported experimental values 32
, we can obtain constants A, B, and C as 1e -48
s 3
, 2.03e -20
s/K, and
425 K. The fitting plot is shown in FIG. S2.
28,29
(Formulas
7 and 8 in Ref.
Review Letters 104, 154301 (2010).
ACKNOWLEDGEMENTSThe authors would like to acknowledge the funding support from DARPA Thermal Transport in Diamond Thin Films for Electronic Thermal Management initiative under contract no.FA8650-15C-7517.
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| sample_1432 | 0.7484 | arxiv | |
UNIVERSIDAD CENTRAL DE LAS VILLAS FACULTAD DE MATEMÁTICA, FÍSICA Y COMPUTACIÓN DEPARTAMENTO DE FÍSICA LA FOTO-BIOFILIA DE LA VÍA LÁCTEA
DrJorge Ernesto Horvath
Santa Clara
UNIVERSIDAD CENTRAL DE LAS VILLAS FACULTAD DE MATEMÁTICA, FÍSICA Y COMPUTACIÓN DEPARTAMENTO DE FÍSICA LA FOTO-BIOFILIA DE LA VÍA LÁCTEA
Autor: Lic. OSMEL MARTÍN GONZÁLEZ Tutores: Dr. Rolando Cárdenas Ortiz
Tesis presentada en opción al grado científico de Doctor en Ciencias Físicas. OSMEL MARTÍN GONZÁLEZ Santa Clara 2010 UNIVERSIDAD CENTRAL DE LAS VILLAS FACULTAD DE MATEMÁTICA, FÍSICA Y COMPUTACIÓN DEPARTAMENTO DE FÍSICA LA FOTO-BIOFILIA DE LA VÍA LÁCTEA Tesis presentada en opción al grado científico de Doctor en Ciencias Físicas.2010AGRADECIMIENTOSAgradecer a todos los que de una forma u otra han hecho posible la materialización de este proyecto escrito en condiciones tan adversas. Primero que todo, agradecer a mi familia por el apoyo y cariño durante todos estos años. A mi esposa por haber compartido conmigo las vicisitudes propias del trabajo y de la vida, a los viejos por contribuir siempre e incondicionalmente a mi formación profesional, a mis dos hermanos por su ejemplo, por estimularme y apoyarme durante todo este tiempo. Al resto de mi buena familia por apoyarme, implícita o explícitamente, siempre.Agradecer a la dirección del departamento de Física y fundamentalmente a Jesús, a todos mis compañeros de trabajo, por el cariño y consideración de Villar y Arturo, a Yoelsy, Genly, al Monte, al profesor Ricardo Grau por solo citar algunos.Un agradecimiento especial para los amigos de la vieja guardia a Humbertico, Juan, Michel y particularmente a Alcides, el otro hermano, presente e indispensable a la hora cero.Para terminar, agradecer infinitamente el apoyo y la confianza depositada por mis dos excelentes tutores. A Jorge, por el valor y profundidad de sus ideas, por ese espíritu jovial y siempre solidario con que me acogió no solo en su institución sino en el seno de su cariñosa familia. Por esa identidad latinoamericana y progresista implícita en su segundo nombre. A Rolando, por el apoyo incondicional en la concepción de este proyecto, por sus cualidades de comunicador y organizador, por su humanismo y honestidad, por ser un enamorado de la ciencia en su concepción más amplia, por esa fructífera amistad que ya casi alcanza las dos décadas.DEDICATORIA … , a mis dos amorosas princesitas: Lianet y LisetSINTESISEn el presente trabajo se aborda de manera integral las implicaciones que tiene el régimen fotobiológico y particularmente la radiación ultravioleta (RUV) en el origen, extensión y evolución de la vida fotosintética en nuestra galaxia. En esta concepción se abordan elementos a escalas espacio temporales notablemente diferentes que incluyen desde aspectos cosmológicos del problema, pasando por aspectos de la estabilidad estelar y planetaria, hasta considerar elementos de la biosfera a una escala mucho más regional o local pudiendo alcanzar, incluso, el nivel celular. Un énfasis particular se presta al papel que pueden potencialmente desempeñar las explosiones estelares y particularmente los brotes de rayos gamma BRG sobre la biosfera terrestre. En este punto, se discuten algunos criterios de daño por radiación UV establecidos en la literatura y se introducen algunos criterios adicionales. Aspectos característicos de estas perturbaciones a nivel de ecosistema son discutidos cuantitativamente para el caso de algunos ecosistemas acuáticos, resaltando las complejidades inherentes a los mismos. Para finalizar, se introducen algunas nociones sobre la extensión e importancia de los ritmos circadianos para los seres vivos permiten un acercamiento a aquellas teorías que abordan los problemas relacionados con el propio proceso del surgimiento de la vida y su definición.INDICE
1
INTRODUCCIÓN
El surgimiento de la Vida ha sido, sin lugar a dudas, uno de los tópicos más polémicos y menos comprendidos en toda la historia de la humanidad. Con raíces tan antiguas como la propia civilización humana y alcanzando representaciones que van desde lo meramente artístico o religioso hasta alcanzar aspectos fundamentales de carácter filosófico, el tema aparece como un elemento recurrente en casi todas las culturas.
Sin embargo, la inclusión formal de este tópico en el campo de la ciencia no sería probablemente hasta el año 1862 con los trabajos del químico francés Louis Pasteur. En ellos y bajo condiciones de laboratorio bien controladas, Pasteur refutaría definitivamente las ideas sobre la generación espontánea demostrando la utilidad del método científico y particularmente del enfoque experimental en este tipo de estudios. Aunque los trabajo de Pasteur constituyeron un notable paso de avance sus resultados confirmaron el carácter sumamente complejo de la Vida y la imposibilidad, al menos desde el punto de vista científico, de ofrecer una respuesta simple para explicar su origen. En correspondencia con las dificultades anteriores, los estudios sobre el origen de la Vida en la Tierra se dividen en lo que podríamos llamar dos corrientes fundamentales; las que consideran a la Vida como un fenómeno originario de nuestro planeta y las que no.
Dentro del marco de las que consideran a la vida como un fenómeno originario se encuentran las teorías de la evolución química como son el -Mundo ARN‖ y -El metabolismo primero‖ (consultar Lazcano, 2010). En este contexto, la vida surge a partir de elementos químicos 2 sencillos, que van generando bloques moleculares cada vez más complejos. Así la materia evolucionaría desde las formas inorgánicas inertes hasta la materia orgánica viva.
Dentro de las teorías que consideran la vida como un proceso no originario se encuentra la Panspermia, introducida originalmente por el también químico y ganador del premio Nobel Svante Arrhenius en 1903. Su dogma central es que la vida se formó inicialmente en el espacio exterior pudiendo llegar a nuestro planeta gracias a los meteoritos u otros objetos que colisionaron con la Tierra sobre los eones Hadeico o Arcaico. Estos objetos portarían células u organismos simples, que fueron depositados sobre la superficie de la Tierra, y que se revitalizarían cuando las condiciones ambientales fueran las adecuadas, desarrollándose, sembrando la vida en el planeta y evolucionado a lo largo de millones de años para dar lugar a las formas actuales de vida. Aunque esta teoría no resuelve directamente el problema del surgimiento de la vida, el hallazgo de moléculas orgánicas complejas en el espacio y la composición química de meteoritos como el de Murchison han hecho que esta teoría se reconsidere una y otra vez.
Por otro lado, tanto en correspondencia con las teorías de la evolución química como en el de la panspermia, las condiciones climáticas de la llamada tierra temprana (eones Hadeico o Arcaico) desempeñan un papel fundamental para comprender los procesos de instauración, diseminación y posterior evolución de la vida en nuestro planeta. Numerosos son los trabajos referidos en la literatura especializada sobre esta temática (Grenfell y colaboradores, 2010;Kasting y Catling, 2003). Dentro las variables climáticas consideradas, una buena parte de estos trabajos se centran en las condiciones radiativas de la atmosfera arcaica, el hábitat y los posibles niveles de 3 irradiación (particularmente en la región del RUV) a que estaban sometidos estos primeros organismos (Cockell, 2000;Cockell y Raven, 2007).
El interés motivado por la RUV se debe en buena medida a los efectos directos que pueden ocasionar la exposición a niveles moderados de RUV sobre los organismos vivos y fundamentalmente sobre el material genético. Dicha influencia ha motivado que algunos autores la consideren como uno de los posibles promotores de la evolución biológica (ejemplo ver Hessen, 2008). Sin embargo, es de esperar que dicho papel haya variado sensiblemente durante toda la historia biogeoquímica de nuestro planeta. Probablemente los altos niveles de la RUV en el eón arcaico hayan ejercido como un factor más bien restrictivo a la vida durante esta etapa, condición esta que pudo suavizarse ya en el proterozoico con niveles de O 2 alrededor del uno por ciento que garantizaban un bloqueo parcial por parte del ozono. Por otro lado, si bien el incremento en los niveles de oxígeno en la atmósfera disminuye sensiblemente los niveles de RUV, este incremento favorece el daño foto-oxidativo por formación de radicales libres. Este parece un hecho notable si tenemos en cuenta que la llamada explosión del Cámbrico (~550 Ma), periodo en el cuál se diversificó considerablemente el número de especies que habitaban el planeta, coincide aproximadamente con la instauración de la atmósfera moderna.
De las consideraciones anteriores se reafirma el criterio de considerar la vida como un fenómeno complejo, no solo en su esencia, sino por la continua co-evolución con otros factores que conforman el clima y le confieren la mayor parte de las propiedades distintivas que exhibe nuestro planeta. Este hecho, fundamenta una buena parte de los programas que se llevan a cabo hoy en día con el objetivo de detectar vida en otros planetas como es el caso de las misiones -Terrestrial Planet Finder‖ y Darwin ( Kaltenegger, 2010). En este sentido, considerar la Tierra 4 como un exo-planeta permite definir y calibrar criterios específicos para medir o inferir algún nivel de actividad biológica. Entre los criterios más aceptados se encuentran la presencia de determinados gases como el oxígeno, metano y óxido nitroso, así como la presencia del llamado límite rojo alrededor de 0.7 um, típico de la extensión de las formas de vida fotosintéticas (Consultar por ejemplo DesMarais y colaboradores, 2002).
Por otro lado, pese al papel preponderante del sol sobre nuestro planeta, no es descartable considerar el efecto estocástico de otras fuentes de radiación a escala galáctica. Un cúmulo importante de investigaciones en los últimos años han sido dirigidas en este sentido. El objetivo fundamental de estos trabajos consiste en estimar los posibles impactos sobre la atmósfera y biosfera de nuestro planeta de eventos astrofísicos muy intensos, así como sus posibles consecuencias sobre el proceso de evolución biológica (Smith y colaboradores, 2004b). Dentro de este grupo se destacan por su intensidad las explosiones de supernovas (ESN) y los llamados brotes de rayos gamma (BRG) (Thomas y colaboradores, 2005;Galante y Horvath, 2007). Por la magnitud de estos eventos y teniendo en cuenta el carácter mutagénico o incluso letal que pueden tener los altos niveles de RUV existen hipótesis que los relacionan con algunas de las grandes extinciones masivas que han tenido lugar en el pasado de nuestro planeta (Mellot y colaboradores, 2004). La importancia de estos eventos puede trascender el propio marco de la Tierra y ser un elemento negativo a considerar en la habitabilidad de determinada región como en el caso de la zona galáctica habitable introducida por (González y colaboradores, 2001) y explorada por otros autores como (Lineweaver y colaboradores, 2004) 5
La novedad y actualidad del tema
Este trabajo se enmarca en una serie de investigaciones y estudios recientes centrados fundamentalmente en la influencia potencial que pueden ejercer tanto la radiación solar como la asociada a eventos astrofísicos intensos como son las explosiones estelares sobre el medio ambiente y la biosfera. En él se abordan varios elementos y herramientas que permiten una mejor comprensión y evaluación de los efectos nocivos asociados al incremento de la radiación ultravioleta (RUV) y permiten abordar problemas científicos de gran vigencia como el manejo, cuidado y protección de ecosistemas o el cambio climático global. En este contexto se discuten además aspectos referentes a la complejidad intrínseca de los sistemas biológicos y el carácter fenomenológico del propio proceso de modelación.
Por otro lado, el trabajo a diferencia con otros, ayuda a establecer de manera integral el papel de la radiación sobre el origen, distribución y evolución de la vida alcanzando incluso una escala cosmológica. Se proponen escenarios probables para la llamada tierra temprana como el eón Hadeico o el principio del Arcaico, aspectos discutidos por su importancia en la literatura especializada. En el trabajo además, se analizan aspectos relacionados con la propia esencia de la vida como fenómeno auto-organizado y lejos del equilibrio. En este sentido, se discute la importancia de los ritmos circadianos y de las oscilaciones bioquímicas de manera general con la introducción de un modelo dinámico simple para la célula primitiva.
Los resultados fundamentales que conforman esta tesis se encuentran publicados en: (12): 2117-2143 (2005) Adicionalmente sobre esta temática se encuentra aún en proceso de arbitraje el trabajo (por invitación) para conformar el capítulo de un libro sobre la génesis de la Vida que publicará la editora Springer 5) Martín O., Peñate, L., Cárdenas R., Horvath J.E. The Fotobiological regime in the very early Earth and the emergence of life. Para capítulo del libro ‗'Origins of Life'' de Springer.
El objeto de la investigación: El entorno de radiación en nuestra galaxia y su influencia sobre las formas de vida fotosintéticas y sobre la biosfera de manera general.
Sus objetivos:
-Estimar las condiciones del Universo en general, y de la Vía Láctea en particular, que contribuyen a la aparición de la vida.
-Estimar las repercusiones fundamentales que tiene el régimen fotobiológico y sus posibles alteraciones sobre los productores primarios fotosintéticos.
-Explorar el comportamiento de las biosferas planetarias ante grandes perturbaciones del régimen fotobiológico asociados a la ocurrencia de eventos estelares intensos como las explosiones estelares. 7 La hipótesis de trabajo: El régimen fotobiológico y sus alteraciones constituyen un elemento clave para comprender el origen, evolución y distribución de la vida, no solo en el ámbito terrestre, sino en un contexto general. Por tanto el Universo en general, y en particular nuestra galaxia, muestran un determinado grado de foto-biofília.
El fundamento metodológico y los métodos utilizados para realizar el trabajo de investigación: Dado lo interdisciplinar del tema, se hizo una extensa revisión bibliográfica y se consultó a diversos especialistas nacionales y extranjeros, para posteriormente seleccionar las herramientas que se usaron para cumplir los objetivos. Estas herramientas estaban dentro de diversas áreas, tales como Astrofísica Teórica, Física Atmosférica (interacción radiaciónatmósfera), Ecología Teórica (dinámica de ecosistemas bajo estrés radioactivo), Fotobiología (estimación de daño biológica de las radiaciones UV) y Ciencia de la Complejidad (probables efectos no lineales en el comportamiento de la biosfera, tanto a nivel de ecosistema como celular 1 LA VIDA FOTOSINTÉTICA EN EL CONTEXTO COSMOLÓGICO El objetivo de este capítulo es examinar las potencialidades del Universo en general, y de nuestra galaxia en particular, para la emergencia de vida fotosintética.
Modelo general de Vida
Astrobiología es el nombre moderno con que se designa la ciencia que estudia el origen, evolución, distribución y destino de la vida en la Tierra y en el Universo. Es un área interdisciplinar donde confluyen Astronomía, Física, Biología, Geología y otras ciencias.
Para estudiar la vida en el contexto cosmológico, es necesario guiarse por un modelo de vida lo más general posible, que rebase las limitaciones de la vida tal y como la conocemos en la Tierra.
Nos adherimos a un modelo en que como mínimo se exigen tres condiciones para la emergencia de vida: a) Elementos químicos biogénicos. Ejemplo: C, H, O, N b) Solvente en que los elementos puedan mezclarse y reaccionar para formar moléculas biológicas complejas. Ejemplo: H 2 0 c) Una fuente de energía que guíe la bioquímica mencionada en el inciso anterior. Ejemplo: Luz y el proceso de fotosíntesis en los productores primarios en la Tierra Es bueno señalar que en la Tierra, si bien todas las especies conocidas se incluyen en los ejemplos de los dos primeros puntos, no todas las formas de vida dependen de la luz solar y la fotosíntesis (los seres humanos dependemos de la fotosíntesis indirectamente, mediante la ingestión de alimentos). Los organismos quimiosintéticos que viven en los respiraderos 10 hidrotérmicos en las profundidades oceánicas no dependen en lo absoluto de la luz solar, ya que ellos elaboran sus alimentos a partir de sustancias químicas presentes en tales ecosistemas. Así las cosas, en nuestro planeta conocemos dos formas de vida: a) Vida que depende de la luz (directa o indirectamente): Organismos fotosintéticos (fitoplancton, algas, plantas superiores) y animales herbívoros, carnívoros, detritívoros, omnívoros, etc. b) Vida independiente de la luz: Organismos quimiosintéticos (los cuales representan la minoría en nuestro planeta).
En este trabajo nos concentramos en el estudio de la vida dependiente de la luz, o sea, dependiente del proceso de fotosíntesis. Esta elección responde fundamentalmente a la notable repercusión de este proceso en la evolución biogeoquímica de nuestro planeta y a la disponibilidad de energía. Actualmente la fotosíntesis supera en varios órdenes a otras formas de producción primarias y se estima que en la tierra temprana, alrededor de 380 Ma, su contribución a la productividad global fuera similar a la de los organismos quimiosintéticos (Raven 2009;Canfield, 2006).
Una perspectiva cosmológica al problema
Al menos en principio, es posible abordar el problema del surgimiento de la vida y particularmente de la vida fotosintética desde una perspectiva tan general como la cosmológica (Davies, 2004). Si uno examina cuidadosamente los requerimientos asumidos en la sección anterior, salvo la condición de existir un solvente adecuado, las naturaleza de las restantes dos condiciones pueden trascender el marco puramente estelar o galáctico donde se desarrolla la 11 vida. Desde esta perspectiva, dichas condiciones aparecen ligadas directamente a las leyes más generales que rigen nuestro universo y que han permitido la formación de estructuras tales como las propias galaxias, estrellas, planetas, nubes moleculares gigantes alrededor de las cuales se originara y evolucionara la vida.
En este sentido, una importancia particular se le confiere a los procesos de formación de estrellas debido a sus múltiples roles en el contexto astrobiológico. Además de ser la fuente de energía por excelencia para el proceso de fotosíntesis y proveer una plataforma climática relativamente estable, en su interior se sintetizan los elementos químicos indispensables (biogénicos) que son expulsados violentamente en las etapas finales de su ciclo de vida. De hecho, las abundancias actuales de estos elementos en el Universo, en la galaxia y particularmente en el sistema solar implican la existencia de otras generaciones de estrellas. Se estima que estas primeras estructuras se formaron a expensas del material primigenio (H y He fundamentalmente) y se caracterizaron por ser extremadamente masivas y de gran luminosidad así como por tener ciclos de vida extremadamente cortos del orden de unos 3 millones de años. El estudio y caracterización de estas primeras formaciones constituye hoy en día un campo activo de investigación tanto desde el punto de vista observacional como teórico (Consultar por ejemplo Yoshida y colaboradores, 2003;Wise y Abel, 2008).
Es conveniente señalar que el proceso de formación de elementos químicos también ocurrió en los primeros segundos de nuestro universo en la llamada nucleosíntesis primordial. Sin embargo, las condiciones de este proceso favorecieron mayoritariamente la formación de los elementos químicos más ligeros del sistema periódico tales como el hidrógeno, el helio y en menor cuantía el litio. Elementos más pesados como el carbono o el nitrógeno quedaron limitados únicamente 12 al nivel trazas haciendo despreciable su contribución frente a los procesos ordinarios de nucleosíntesis estelar.
La expansión del Universo y el proceso de formación de estructuras
En el marco del modelo cosmológico estándar, el universo actual no es más que el resultado de un largo proceso evolutivo (expansión adiabática) a partir de un estado inicial, caracterizado por una densidad y temperatura extremas. En correspondencia con este modelo, la forma en que se ha llevado el proceso de expansión del Universo es clave para comprender los procesos de formación de estructuras y por consiguiente para estimar la biofilia de este. Típicamente, para un universo plano, homogéneo e isótropo, la tasa de expansión se expresa mediante el llamado
0 4 2 G H (1.3) 13
donde G es la constante gravitacional. El segundo término del miembro izquierdo es el análogo a la fricción viscosa y realmente contribuye a la amortiguación de las sobredensidades. Si la expansión universal tuviera una tasa por encima de cierto umbral H u (dependiente del modelo cosmológico), entonces la formación de estructura no hubiese procedido, o sea, no se hubieran formado galaxias, nubes moleculares gigantes etc. Lo que sucede en la realidad es que la magnitud H es variable en el tiempo, dependiente del modelo cosmológico y del inventario total de materia y energía del universo. Para el modelo cosmológico estándar, que presupone que a gran escala el universo es homogéneo e isótropo, la ecuación (3) tiene dos posibles soluciones: una en la que sobredensidad es eliminada conforme el tiempo avanza según una relación del tipo (δ≈1/t); en la otra la sobredensidad crece proporcional a la expansión (δ≈a) contribuyendo al proceso de formación de estructuras hasta conformar el Universo en su apariencia actual.
El proceso de formación de estructuras desde una perspectiva local
Si bien el principio cosmológico estándar ha resultado una herramienta extremadamente útil para estudiar nuestro universo, su validez se encuentra limitada a escalas considerablemente grandes del orden de 100-300 Mpc. A estas escalas, el universo se puede considerar prácticamente homogéneo y su dinámica se encuentra determinada fundamentalmente por la influencia de un fluido exótico mayoritario de presión negativa: la energía oscura. Este componente, de naturaleza aún poco comprendida, constituye prácticamente dos tercios del contenido material de universo y se considera el responsable de su expansión acelerada en correspondencia con los datos observacionales provenientes de las supernovas tipo Ia.
Por otro lado, para realizar estudios a escalas inferiores resulta imposible obviar el carácter no homogéneo en la distribución de la materia agrupada en galaxias, cúmulos y supercúmulos de galaxias. A estas escalas la dinámica aparece dominada por otro componente exótico mayoritario: la materia oscura. Ocupando prácticamente un tercio de todo el contenido material del universo la materia oscura, a diferencia de la energía oscura, parece agruparse significativamente por debajo de la llamada escala de homogeneidad (100-300 Mpc) y sus efectos pueden ser notables incluso en la dinámica galáctica. Aún sin un candidato bien establecido, la materia oscura se considera el ingrediente indispensable para explicar la dinámica de las grandes formaciones estelares así como el comportamiento anómalo encontrado en las curvas de rotación típicas de muchas galaxias incluyendo la nuestra.
Con vistas a modelar la evolución de la sobredensidad a nivel local (un observador en ella) Sussman, Quirós y el autor (Sussman, Quirós y Martín, 2005) proponen un modelo alternativo que generaliza en varios aspectos trabajos anteriores sobre esta temática. La construcción del modelo descansa sobre el caso esféricamente simétrico de las llamadas soluciones de Szafron-Szekeres para las ecuaciones de Einstein y reconoce en su definición una interacción explícita entre los dos componentes mayoritarios: la energía oscura (modelada como un fluido homogéneo) y la materia oscura (considerada como un fluido no homogéneo).
La aplicación un esquema como este presenta algunas ventajas pues permite reducir formalmente el estudio de la sobredensidad, dependiente del tiempo y de las coordenadas espaciales, a un escenario clásico del tipo FLRW de mucha menor complejidad al depender únicamente de la variable temporal. El método permite además explorar el impacto que pueden tener a nivel local varios formalismos plausibles en la literatura para la energía oscura como es el caso de los 15 campos escalares. Para este fin basta solo con proponer una relación adecuada entre la densidad y la presión (ecuación de estado) para describir el comportamiento de la energía oscura. La elección conveniente de la dependencia espacial y las condiciones de frontera permite describir la dinámica de agrupamientos de materia oscura a una escala arbitraria que ajusten convenientemente a las restricciones observacionales.
Por otro lado, el hecho de proponer una interacción explicita (no gravitacional) entre la materia oscura y la energía oscura puede ser un elemento cuestionable dentro del modelo. Sin embargo, la naturaleza relativamente desconocida de ambos componentes podría justificar en alguna medida este tipo de suposición. De cualquier manera, un escenario como este podría ser interesante, tanto en el ámbito teórico como práctico, y apropiado para describir el embrión de grandes formaciones estelares, cuna posterior de la vida. En este sentido y aunque de manera paradójica, la vida, enmarcada como un fenómeno a nivel de las interacciones electromagnéticas en el seno la materia ordinaria, emerge bajo los designios de un Universo gobernado por dos componentes de naturaleza tan exótica y tan poco comprendida como pueden ser la energía y materia oscuras.
Con vistas proseguir en nuestro análisis y aunque hasta el momento hemos dirigido nuestra atención a aspectos generales relacionados con la vida y sus condicionamientos en la gran escala, en los próximos epígrafes acercaremos nuestro estudio a escalas considerablemente menores, próximas al escenario donde la vida, tal y como la conocemos se desarrolla. 16
Emergencia de vida fotosintética en planetas tipo terrestre que orbitan estrellas medianas
En este epígrafe particularizamos el modelo de vida que utilizaremos, a partir del modelo más general esbozado en el epígrafe 1.1. Consideraremos que la lista mínima de elementos biogénicos está integrada por CHON, el solvente es el agua y la fuente de energía es la luz proveniente de una o varias estrellas. Consideraremos que la zona foto-habitable de un sistema estelar es aquella en la que el agua puede estar en forma líquida en la superficie de un planeta con presión atmosférica similar a la terrestre. Con este modelo, se considera que las estrellas medianas (F, G y K) son las más adecuadas para que en sus sistemas planetarios emerja la vida fotosintética, pues las estrellas grandes (O y B) tienen tiempos de vida relativamente cortos, del orden de millones o decenas de millones de años, como para que pueda emerger la vida. Por otro lado, las estrellas pequeñas (M) obligan a sus planetas a acercarse demasiado para que el agua pueda estar líquida en su superficie, y entonces los planetas sufren anclaje de marea, dando siempre la misma cara a la estrella. La anterior situación puede implicar congelamiento de la atmósfera en el hemisferio oscuro y el arrastre hacia éste de la atmósfera del hemisferio iluminado, lo que pudiera terminar en un estado de congelación total de la atmósfera. Sin embargo el tema no está exento de debate, si tenemos en cuenta que algunos estudios recientes sugieren que esta situación no sucedería necesariamente en todos los casos. Para una discusión más detallada de estos tópicos consultar (Lammer, 2007).
Otro elemento importante a tener en cuenta en el caso de la vida fotosintética es la temperatura de la estrella. Teniendo en cuenta que en primera aproximación los espectros de emisión de estos sistemas se ajustan aceptablemente a un cuerpo negro, la longitud de onda y por consiguiente la energía de los fotones en la región de mayor emisión va a depender directamente de la temperatura en correspondencia con la conocida ley de Wien T b . Esto implica, teniendo en cuenta que la reducción del CO 2 y el H 2 O en la fotosíntesis es un proceso energéticamente costoso, la necesidad de emplear etapas (reacciones fotoquímicas) adicionales con vistas a un mejor aprovechamiento de la energía. Esta consideración podría ser importante para aquellos sistemas estelares con temperaturas más bajas que nuestro Sol como es el caso de las ya mencionadas estrellas M (Wolstencroft and Raven, 2002;Cockell and Raven 2004).
En este trabajo y de manera simplificada, podríamos decir que la vida fotosintética puede emerger en planetas tipo terrestre orbitando estrellas medianas (F, G o K) y en los cuales hay agua líquida e irradiancia suficiente en la superficie planetaria como para que se pueda realizar la fotosíntesis.
Emergencia de vida en la Tierra
La historia natural de nuestro planeta se divide en eones, según se muestra en la Tabla 1.1 (Schopf, 1987). Se ha considerado tradicionalmente qué anterior a estas fechas, durante el eón Hadeico, la Tierra era un mundo inhóspito con océanos de magma y sometido a intenso bombardeo de asteroides (Shoemaker, 1983). Sin embargo, el reciente descubrimiento de zircones (rocas que necesitan de agua líquida para formarse) que datan de ese eón ha abierto la posibilidad de que dentro del Hadeico hubiera un período de relativa calma, precisamente en la era que podríamos bautizar como Hadeico intermedio (entre 4400 y 4000 Ma antes del presente) (Valley y colaboradores, 2002 El rango de longitudes de onda útiles para la fotosíntesis es aproximadamente el mismo que podemos ver: 400-700 nm. A esta banda típicamente se le llama Radiación Fotosintéticamente Activa (RFA). Asumiremos que toda esta banda favorece la fotosíntesis, mientras que la radiación ultravioleta (RUV) la inhibe, debido a que causa daños en el aparato fotosintético y a que daña los ácidos nucleicos (ADN y ARN) obligando a la célula a invertir energía en repararlos. Detalles sobre estos tópicos pueden encontrarse en (Cockell, 2000;Hader y Worrest, 1991;Neale y colaboradores, 1993;Cullen y Neale, 1994;Vincent y Roy, 1993).
Eón Tiempo antes del presente en Ma
Tanto durante el Hadeico intermedio como durante el Arcaico temprano, la atmósfera carecía de bloqueadores de radiación ultravioleta como el ozono, aunque existe la hipótesis de la probable existencia de smogs de hidrocarburos (Pavlov y colaboradores, 2001). En esas condiciones es de esperar que la vida fotosintética emergiera en el agua (Cockell, 2000;Cockell y Raven, 2007), para así aminorar el crudo régimen fotobiológico existente en la superficie continental (que además solo cubría un 10% del planeta durante el Arcaico).
La parte superior del océano, en que la irradiancia es suficiente para hacer posible la fotosíntesis, es llamada zona fótica. Hoy día alcanza hasta 200 metros de profundidad en las aguas más claras en las cuencas centrales oceánicas, y hay razones para pensar que el océano Arcaico era así de transparente. La parte superior de esta zona es típicamente influenciada por la circulación de Langmuir si los vientos soplan a más de 3 m/s, algo típico en el Arcaico temprano. Estas corrientes circulares y verticales mezclan las aguas de la parte superior del océano, haciendo sus propiedades físicas (temperatura, densidad) constantes, de ahí el nombre de capa mezclada. Por debajo de ésta, la circulación es detenida por gradientes de densidad y temperatura (picnoclinas y termoclinas), y se establece una estratificación de las aguas. La profundidad de la capa mezclada hoy día es de decenas de metros, y depende de la localidad.
20
Considerando el crudo régimen fotobiológico durante el Hadeico y Arcaico temprano (Cockell, 2000), es razonable asumir que la biota viviente en la capa mezclada del océano fuera resistente a las radiaciones, especialmente considerando efectos como la circulación de Langmuir. Estas corrientes circulares periódicamente expondrían a los organismos unicelulares a la superficie, donde recibirían altas dosis de RUV. De modo que esperaríamos una biota de baja diversidad, debido a la restricción ultravioleta. Además, estos organismos deberían tener buenas capacidades de reparación, de modo que empleamos el llamado modelo E que aparece en (Fritz y colaboradores, 2008) para estimar las tasas de fotosíntesis en la capa mezclada del océano.
La tasa de fotosíntesis P en este modelo se calcula mediante:
inh pot E P P
* 1 1 (1.4)
Donde inh E * es la irradiancia inhibitoria adimensional, dada por la radiación ultravioleta, mientras que pot P es la tasa de fotosíntesis en ausencia de fotoinhibición, dada por: s PAR E E s pot e P P / 1 (1.5) En la expresión anterior, P s es la tasa de saturación de la fotosíntesis en ausencia de inhibición; E PAR (en W.m -2 ) es la irradiancia de la luz visible, mientras que E s (en W.m -2 ) es un parámetro del modelo. La irradiancia inhibitoria adimensional de radiación ultravioleta está dada por: Donde E (en W -1 .m 2 ) son los pesos biológicos que cuantifican la efectividad de la exposición espectral E (en W -2 .m -2 .nm), es decir, E representa la inhibición de la fotosíntesis causada por la radiación ultravioleta de longitud de onda .
Sustituyendo la ecuación (1.5) en la (1.4) y normalizando respecto a P s obtenemos:
* 1 1 inh E E S E e P P S PAR (1.7)
Ahora queda claro que la tasa de fotosíntesis es una combinación de dos factores: el numerador en la ecuación anterior favorece la fotosíntesis (pues la irradiancia de la radiación fotosintéticamente activa está allí), mientras que el denominador la inhibe, debido a la presencia del factor inhibitorio de irradiancia ultravioleta. La emergencia de la fotosíntesis es aún un tema abierto, pero parece razonable asumir las mismas rutas fotosintéticas y aproximadamente tasas similares durante toda la historia de la vida. Esto nos permite estimar la influencia del régimen fotobiológico sobre la fotosíntesis, es decir, la influencia de diferentes irradiancias solares y tramitancias atmosféricas.
Dividimos la zona fótica en dos capas para estimar las tasas fotosintéticas: la capa mezclada y el resto de la zona fótica. La profundidad de la capa mezclada, donde existe la circulación de Langmuir, depende de la velocidad del viento que sopla en la superficie. Para el Arcaico temprano es razonable asumir profundidades iguales o mayores de 30 metros (Cockell, 2000). En este trabajo, como ejemplo para nuestros cálculos, asumimos una capa mezclada de 40 metros de profundidad, en gran medida porque en la referencia anterior hay multitud de datos hasta esa profundidad. Realmente, para calcular las tasas de fotosíntesis en la capa mezclada, en la 22 ecuación (1.7) usamos E PAR y E * inh como se reportan en (Cockell, 2000), y promediamos E s de los datos para fitoplancton en 16 estaciones antárticas (Fritz y colaboradores, 2008). Por otro lado, para estimar E RFA y E * inh por debajo de la capa mezclada se extrapolaron los resultados reportados en (Cockell, 2000) hasta las profundidad de 200 m.
Cuando la irradiancia de la radiación fotosintéticamente activa E RFA toma el valor del parámetro E s , entonces el numerador en el miembro derecho de la ecuación (1.7) se iguala a 0,63, es decir, el parámetro E s representa la irradiancia de la radiación fotosintéticamente activa E RFA que asegura el 63 % de la tasa máxima de fotosíntesis ( % 63 S P P
). Así, mientras menor sea el valor de E s , más eficiente es el organismo que realiza la fotosíntesis, puesto que alcanza el 63%
de la tasa máxima con una irradiancia menor.
Podemos preguntarnos si existirían apreciables diferencias en el potencial fotosintético de los organismos del Arcaico temprano comparados con los unicelulares actuales. consecuentemente, las corrientes circulares de Langmuir llegarían a decenas de metros de profundidad. Estas corrientes hundirían y subirían organismos unicelulares capturados en la capa mezclada, de manera que las irradiancias promedio recibidas por una célula durante un ciclo completo en una celda de Langmuir serían:
L z z E nm nm inh z z z E E L 0 400 200 * ) ( ) , ( (1.8) L z z nm nm RFA z z z E E L 0 700 400 )
, ( (1.9) donde z L es la máxima profundidad a la que la circulación de Langmuir se extiende. Como mencionamos anteriormente, por debajo de esta capa mezclada aparece la estratificación del agua como resultado de gradientes de temperatura y/o densidad (termoclinas y picnoclinas), lo cual no permite la circulación y mezcla.
En la Figura 1.1 presentamos curvas de la tasa de fotosíntesis relativa vs. Profundidad en el océano Arcaico, para tres valores del parámetro E s . Como en (Cockell, 2000), consideramos ángulos solares zenitales de 0 y 60 grados (ver figura 1.2). El primero proporciona máxima irradiación con el Sol directamente sobre nuestras cabezas, mientras que el segundo da irradiancias similares a las actuales durante el mediodía en altas latitudes.
P/P 0 (%) Z (m ) Es=20W.m -2 Es=15W.m -2
Es=25W.m -2
25
Como era de esperar, en ambos casos a menor valor de E s , mayor valor de tasa de fotosíntesis (ver ecuación 1.7). También vemos que las condiciones para la máxima tasa de fotosíntesis se dan a profundidades de alrededor de 75 m para ángulo solar zenital de 0 grados; y a 50-60 m para 60 grados, pues en este último caso la menor presión ultravioleta permite a las células acercarse más a la superficie oceánica para captar más radiación fotosintéticamente activa.
Sin embargo, enfatizamos que las figuras anteriores pueden falsear nuestras conclusiones si ignoramos el papel de la circulación de Langmuir en el océano. Las figuras muestran las tasas de fotosíntesis como si los organismos unicelulares planctónicos estuvieran a profundidad fija todo el tiempo, pero en realidad esas células viviendo en la capa mezclada pueden ser fácilmente capturadas por las corrientes circulares de Langmuir, experimentando hundimiento y emergencia cíclicas.
A modo de ejemplo, consideramos esa circulación con una profundidad máxima de 40 metros, y calculamos las irradiancias promedio recibidas por un organismo atrapado en ésta usando las ecuaciones (1.8) y (1.9). Entonces sustituimos en la ecuación (1.4) para obtener la tasa fotosintética promedio en un ciclo completo. Los resultados de dicho procedimiento se muestran Obtenemos pequeñas tasas promedios de fotosíntesis, de alrededor del 7%, para los tres valores de E s usados en este trabajo cuando el Sol está en el zenit, y valores de 15% para el ángulo solar zenital de 60 grados. Como podemos ver al comparar con las figuras 1.1 y 1.2, ser capturado en la circulación de Langmuir reduce considerablemente las posibilidades fotosintéticas de los organismos que viven en la capa mezclada, especialmente cuando hay una muy intensa irradiancia. Esto se debe a la cruda exposición a la radiación ultravioleta mientras el organismo está circulando en la parte superior del océano. Por debajo de la capa mezclada, la fotosíntesis sería razonablemente buena hasta 150 m y se extendería incluso a profundidades mayores que 200 m.
Emergencia de vida en nuestra vecindad cósmica
Es probable que la primera sonda no tripulada en probar a existencia de vida fotosintética en nuestra vecindad cósmica sea enviada a nuestro sistema planetario más cercano: el que pertenece a la estrella α de la constelación Centauro (α Centauri). Este sistema se encuentra a 4,37 años luz de nuestro Sol. Con la tecnología actual llegar allí tomaría varios milenios, pero no es 27 descartable que tecnologías en desarrollo tales como la vela espacial o la fusión nuclear por pulsos podrían reducir este tiempo de manera considerable (Hearnshaw, 2010).
Realmente, α del Centauro es un sistema binario compuesto por dos estrellas bastante similares a nuestro Sol. α del Centauro A es una estrella G2V, como nuestro Sol, mientras que α del Centauro B es una estrella K1V. La masa de la estrella A es un 10% mayor que la del Sol mientras la masa de la B es alrededor de 10% menor. Las observaciones han descartado la existencia de planetas tipo Júpiter (gigantes gaseosos) y enanas pardas en este sistema, haciendo más probable la existencia de planetas tipo terrestre (Guedes y colaboradores, 2008). Sin embargo, éstos son más difíciles de detectar. Las simulaciones computacionales para la formación de planetas alrededor de α del Centauro B predicen de uno a cuatro planetas tipo terrestre en órbitas estables, uno o dos de ellos dentro de la zona estelar habitable (es decir, donde puede existir agua líquida en la superficie planetaria).
Utilizando las ecuaciones del epígrafe anterior, se puede hacer un cálculo aproximado para la tasa de fotosíntesis de un hipotético planeta tipo terrestre en la zona habitable de α del Centauro B (situado a 0,7 unidades astronómicas de esta estrella, lo cual asegura temperaturas superficiales similares a las de la Tierra Vemos entonces que las condiciones para la tasa fotosintética máxima están más cerca de la superficie si se compara con la Tierra Arcaica (compare con la Fig. 1 La situación hipotética descrita para (α Centauri) podría ser válida y extensible para otros sistemas más alejados dentro de nuestra galaxia. Si consideramos el número de sistemas estelares con características similares, incluso dentro de la llamada zona galáctica habitable, es posible
Z (m) Es=20W.m -2 Es=15W.m -2 Es=25W.m -2 P/P 0 (%) 29
estimar las posibilidades reales para el desarrollo de formas de vida fotosintéticas como un hecho nada despreciable.
La rotación planetaria y el régimen fotobiológico
Las condiciones para la vida en un planeta que orbita estrellas medianas (F, G, K) son radicalmente distintas a las de un planeta que orbita estrellas pequeñas (M). En este último caso el planeta deberá estar muy cerca de la estrella madre para que haya agua líquida en su superficie, pero entonces caerá en la zona de anclaje de marea y no podrá rotar sobre su propio eje, dando siempre la misma cara a la estrella. Esto implicará una ausencia de ciclicidad en el régimen fotobiológico; siempre habrá luz en el hemisferio que enfrenta la estrella y siempre oscuridad en el que queda detrás.
Por otro lado, para las estrellas medianas la zona habitable queda fuera de la zona de anclaje de marea, por lo que los planetas orbitantes podrán rotar sobre su propio eje y entonces habrá alternancia luz oscuridad. Es de esperar que esta ciclicidad del régimen fotobiológico impondrá ritmos circadianos (de cada día) en algunos de los procesos biológicos. En el caso de la Tierra, estos ritmos se observan en casi todos los organismos incluso en los seres humanos, siendo un ejemplo típico de este comportamiento la alternancia sueño vigilia. Investigaciones recientes (Uchida y colaboradores, 2010) muestran que estos ritmos alcanzan el nivel celular pudiendo estar representados tanto en la funcionabilidad de algunas estructuras foto-receptoras, como en el marco del propio código genético. Hoy se conoce que bajo determinadas condiciones los ritmos circadianos (originados por el régimen fotobiológico) modulan otros ritmos tales como el ciclo celular e incluso el ciclo de la glucólisis. La importancia biológica de los ritmos y particularmente del proceso de glucólisis se examinará en detalle en el capítulo III en un acercamiento a aquellas teorías que intentan explicar el origen de la vida.
Conclusiones
A lo largo de este capítulo hemos discutido varios aspectos relacionados directa o indirectamente con la emergencia de la vida y sus condicionamientos. En nuestro análisis hemos considerado elementos a escalas considerablemente diferentes que involucran aspectos importantes de la dinámica galáctica y cosmológica hasta particularizar en aquellos aspectos que rigen la vida fotosintética a escala planetaria en el marco de un sistema estelar determinado. Pese a las complejidades inherentes a un enfoque tan general, un análisis de esta naturaleza permite acercarnos desde una perspectiva polifacética, y por ende, más adecuada a la hora de abordar un fenómeno tan complejo y tan poco entendido como es la vida. Las conclusiones básicas derivadas de este capítulo podrían resumirse de la siguiente forma:
1. La velocidad de expansión del Universo ha permitido condiciones para la emergencia de vida, porque ha sido suficientemente moderada como para que se formen las estructuras necesarias (galaxias, estrellas, planetas).
2. La interacción entre los componentes mayoritarios energía y materia oscuras juegan un rol fundamental en el proceso de formación de estructuras a gran escala y por ende sobre el fenómeno de la Vida. 31 3. Existen mejores condiciones para la emergencia de vida en general, y fotosintética en particular, en los planetas que orbitan estrellas medianas (F, G y K), aunque no es En el caso de las estrellas medianas y pequeñas, todavía en secuencia principal (o sea, que aún tienen hidrógeno como combustible nuclear), también hay tormentas de consideración que implican eyecciones de grandes cantidades de radiación al espacio. Por su relativa cercanía y elevada frecuencia, el efecto de estas tormentas puede llegar a ser importante para la vida en aquellos planetas tipo terrestres dentro la llamada zona estelar habitable.
Otros objetos compactos tales como las magnetoestrellas (un tipo de estrellas de neutrones, que por tanto no está en secuencia principal), también pueden liberar importantes dosis de radiación (Woods, 2004). Una de esas explosiones, provenientes de una distancia de 50 000 años luz, perturbó la ionosfera terrestre en el 2004 de manera medible. Alrededor de unas 12 magnetoestrellas han sido observadas en nuestra galaxia, pero podría haber más que aún no hemos detectado.
Se piensa que las explosiones estelares imponen restricciones a la habitabilidad de la Vía Láctea (González y colaboradores, 2001). Por ejemplo, no se espera vida en las cercanías del centro de la galaxia, pues la gran concentración de estrellas hace que la frecuencia de supernovas sea muy alta. Por otro lado, diversos autores han lanzado hipótesis sobre el probable rol de explosiones estelares en algunos descensos de biodiversidad en la Tierra (Smith y colaboradores, 2004b El pasaje de un planeta por los brazos espirales de la galaxia también ha sido argumentado como relativamente peligroso para la vida tal y como la conocemos, debido en parte a la mayor cantidad de estrellas y por tanto de explosiones estelares. De hecho, algunos autores muestran que el Sistema Solar ha estado dentro de alguno de los brazos espirales durante casi todas las extinciones masivas del Fanerozoico (Leitch y Shavith, 1998).
Los principales efectos ambientales que una explosión estelar puede ocasionar sobre nuestro planeta (Scalo y Wheeler, 2002;Smith, Scalo & Wheeler, 2004a;Thomas y colaboradores, 2005) son espectros tipo aurora que depositan a nivel del mar un flash ultravioleta extremadamente intenso pero de corta duración (flash UV), formación de óxidos de nitrógeno que reducen la capa de ozono (con el consiguiente incremento del ultravioleta solar) y que bloquean parcialmente la luz visible con probable enfriamiento global. Otros de los efectos estimados son las lluvias ácidas, resultado de la combinación de los óxidos de nitrógeno con el agua atmosférica. Con la excepción del flash UV, los demás efectos pueden persistir por alrededor de una década, con importantes consecuencias para la biosfera, por supuesto en dependencia de la distancia a la que explota la estrella y a la energía liberada. Precisamente al cálculo de las distancias críticas para algunos de estos efectos dedicamos el próximo epígrafe. 36
Principales efectos a corto plazo
En este acápite estudiaremos los aspectos fundamentales asociados al flash UV y sus implicaciones potenciales sobre la biosfera.
Interacción de los fotones gamma con las atmósferas planetarias
Hemos seleccionado dentro de las explosiones estelares a aquellas que son las más energéticas, y por ende con mayor potencial para alterar considerablemente el régimen fotobiológico en un planeta tipo terrestre. Nos referimos a las explosiones o brotes de rayos gamma (BRG), en los que se emiten en escasos segundos o minutos energías del orden de 10 44 J. Como ya hemos mencionado con anterioridad, la radiación de los BRG's sale colimada de la estrella progenitora bajo un ángulo relativamente variable en correspondencia con el tipo de evento. En este trabajo lo consideraremos aproximadamente de 0.01 srad en correspondencia con los trabajos de (Frail y colaboradores, 2001).
El proceso de interacción primario de los fotones gamma con la atmósfera desencadena toda una serie de fenómenos transitorios (ionización, excitaciones electrónicas, vibracionales, etc.) capaces de inducir incluso ionosferas secundarias y que culminan con la deposición progresiva de la energía original del haz en las diferentes capas de la atmósfera. Básicamente, el proceso de interacción para energías menores de 3 MeV se puede describir como la combinación de un proceso dispersivo de Compton y otro de foto-absorción, si tenemos en cuenta que otros procesos posibles, como la formación de pares, se encuentran considerablemente limitados a estas energías.
Por otro lado, si tenemos en cuenta que la energía de los fotones gamma supera considerablemente la energía de ionización típica de las moléculas, y que a su vez, estas últimas son aproximadamente similares para cualquier candidato atmosférico razonable (alrededor de unos 30-35 eV), es posible inferir que el proceso de interacción primaria con la atmósfera prácticamente no dependa de su composición: ellos ven un mar de electrones enlazados dentro de las moléculas y simplemente desprenden a muchos de ellos al interactuar con estas. Estos fotoelectrones a su vez interactúan de diversas maneras excitando otras moléculas, las cuales al regresar a estados de menor energía emiten un espectro tipo aurora, en el que una fracción de la energía incidente llega al nivel del mar en forma de radiación ultravioleta: este es el vigoroso flash UV de unos 10 segundos de duración, primer efecto ambiental de un BRG. (Consultar Smith y colaboradores, 2004a para una descripción detallada de este proceso).
Para calcular la dependencia del efecto con la distancia a la estrella, primeramente asumimos un espectro del BRG (Smith y colaboradores, 2004a) la siguiente parametrización:
0 exp 100 E E keV E k dE dN para 0 E E (2.1) keV E e keV E k dE dN 100 100 0 para 0 E E , (2.2) donde 250 0 E keV, 9 . 0 y 3 . 2 .
El rango de energías para los fotones gamma de 50 keV < E< 3 MeV. Este espectro original fue dividido en 100 intervalos "monocromáticos" igualmente espaciados logarítmicamente, con un valor correspondiente de energía media y flujo asociado a cada intervalo.
Para todos los modelos atmosféricos se consideró una atmósfera exponencial y con constituyentes bien mezclados (excepto el ozono), con una escala de altura Ho = 8 km y una densidad ρ = 1,3 x 10 -3 g/cm 3 .
Para la deposición de energía gamma (liberación de electrones y posterior excitación de las moléculas), se asumió la composición actual de la atmósfera, pues como dijimos anteriormente estos procesos poco dependen de la composición. Entonces se empleó el procedimiento general descrito en (Gehrels y colaboradores, 2003 (2.3) El proceso de posterior emisión del espectro tipo aurora (que incluye el flash UV) sí depende de la composición atmosférica, por lo que se tomaron cinco modelos de paleo-atmósferas; con 10 -5 , 10 -4 , 10 -3 , 10 -2 y 10 -1 naa (nivel atmosférico actual) de O 2 , respectivamente. También se tomó la atmósfera moderna con 10 0 naa. Podemos considerar que a grandes rasgos nuestros modelos de 39 atmósferas coinciden con razonable aproximación a aquellas existentes en los tiempos geológicos que se muestran en la tabla 2.1. Para implementar la columna de ozono en cada una de las atmósferas se siguieron dos procedimientos. El primero fue un simple re-escalado de la atmósfera estándar USA 76, y el segundo implicó una bajada en altura de todo el perfil del ozono y un posterior re-escalamiento al caso apropiado. Se conoce que la depresión del oxígeno no sólo hace la capa de ozono más delgada, sino más cercana a la troposfera (Segura y colaboradores, 2003;Kasting y Catling, 2003). El segundo procedimiento intenta mimetizar a grandes rasgos el último efecto.
Contenido de oxígeno en nivel
Considerando lo anterior, la reemisión de la parte ultravioleta del espectro tipo aurora se asume que sigue la ley empírica (Smith y i Fdep, es la energía total depositada en la capa i-ésima. Los valores max y min se asocian a los límites típicos de las bandas del nitrógeno y se fijaron a 130 y 600 nm respectivamente. Si tenemos en cuenta que el nitrógeno es actualmente un componente mayoritario en la atmósfera y que al parecer, su columna no ha variado notablemente durante la evolución geológica de la Tierra, tal elección parece justificada. De cualquier manera, probablemente la expresión 2.4 sea ajustable para describir, al menos groseramente, el comportamiento espectral de otras especies moleculares importantes. Finalmente, para obtener los flujos de radiación UV en la superficie de la Tierra, se tuvieron en cuenta los efectos de la absorción y de la dispersión de Rayleigh para cada uno de los modelos de paleo-atmósferas propuestos. El efecto neto en la superficie se calcula como la suma de los efectos de emisión de cada capa.
La tabla 2.2 muestra la energía UV que alcanza el suelo, expresada como fracción de la energía gamma originalmente incidente en el tope de la atmósfera para algunas bandas representativas, mientras en la Fig. 2.1 se muestra los espectros UV en función de la longitud de onda que alcanzan la superficie terrestre para los distintos modelos convenientemente normalizados respecto al flujo total que deposita el BRG en el tope de la atmósfera. De análisis de ambos se puede apreciar que incluso llegan fotones de la banda UV-C al suelo, o sea, con longitudes de 41 onda por debajo de 280 nm, lo cual no sucede típicamente con la irradiancia solar por la atenuación atmosférica. La banda UV-C es particularmente dañina desde el punto de vista biológico entre otros factores por contener el pico de máxima absorción del ADN y por la marcada formación de radicales libres.
Efectos biológicos y distancias críticas
A partir de los resultados derivados en la sección anterior es posible estimar a que distancias el progenitor de un BRG, con las características antes mencionadas, pueda considerarse potencialmente peligroso para la vida en nuestro planeta. Para calcular estas distancias críticas recurriremos a algunos criterios e índices reportados en la literatura sobre el tema así como a estudios que evidencian el impacto negativo que tienen incluso los niveles moderados de RUV solar sobre una buena parte de los productores primarios.
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Con ese fin y similar al tratamiento realizado en el primer capítulo para el eón arcaico, calculemos las irradiancias biológicas efectivas E* asociadas al BRG para cada modelo de paleoatmósfera considerado. Para ello convolucionaremos el espectro de acción biológica e( ) para daño al ADN con la irradiancia espectral UV incidente E( ) según la expresión (Cockell 2000;Cockell y Raven 2007).
E* e( )E( ) (2.5)
Definamos entonces las fluencias biológicas efectivas F* como:
F* E * t ,(2.6)
donde t es el tiempo de exposición a la radiación UV. Esta magnitud estima el efecto de la radiación integrado en el tiempo y suele ser conveniente en aquellos casos donde la contribución de los mecanismos intrínsecos de reparación de daños (por ejemplo, los mecanismos reparadores del ADN) sea poco significativa. De esto no ser cierto, el daño biológico estimado directamente a partir de la magnitud F * podría estar seriamente sobredimensionado. Conviene señalar en este punto que tanto para el caso particular de F * como de cualquier otra expresión matemática que se introduzca en lo que sigue, el subíndice BRG denotará siempre el UV producto de la explosión estelar, mientras que el subíndice Sol denotará el UV proveniente del Sol.
En lo que respecta a la resistencia a las radiaciones, la enorme variabilidad encontrada entre las especies hace que definir un criterio de daño biológico significativo se considere un problema borroso. Con vistas a solventar en alguna medida estas dificultades consideraremos, al menos por el momento, valorar la acción en los productores primarios más abundantes, que son los Esto significa que durante el tiempo de exposición de 10 s al flash UV, las células de fitoplancton en la superficie acuática estarían expuestas a una fluencia biológica efectiva n veces mayor que la que están acostumbradas a recibir desde el Sol en un día entero. Parece razonable esperar mortalidad significativa incluso para n=1, especialmente considerando que durante los 10 s del UV flash no habrá tiempo para los mecanismos de reparación del ADN. Por supuesto, la mortalidad no solo ocurrirá durante el breve tiempo de exposición, sino también con posterioridad a medida que las secuelas irreversibles inducidas sobre los organismos se vayan evidenciando. Otro elemento que refuerza esta elección son los estudios recientes que muestran 45 que una buena parte de los productores primarios, especialmente el llamado pico-fitoplancton, recibe dosis de UV solar significativas durante el día, responsables de la elevada tasa de mortalidad reportada para estos organismos. O sea, incluso bajo las condiciones relativamente suaves de irradiación de la era moderna, al parecer un número considerable de especies que habita nuestro planeta se encuentran notablemente estresadas por efecto del UV solar.
Otra cuestión a considerar es la duración del día en los diferentes eones. Aun cuando hay incertidumbres, una duración de 15 horas en el Arcaico temprano parece bien fundamentada, así como una de 20 horas en el Proterozoico, la que ha ido aumentando hasta las 24 horas actuales.
Tomamos un valor promedio de 20 horas y suponemos un fotoperiodo promedio de 10 horas para la exposición diaria real al Sol. Las diferencias en cuanto a eón y latitud geográfica no cambian apreciablemente nuestros resultados, pues se trata de modelaciones a escala planetaria y no regional.
Definamos ahora la irradiancia biológica efectiva en una forma adimensional según la expresión: Como era de esperar, cuanto menor sea el contenido de oxígeno, mayor será el daño en el ADN causado por el BRG, ya que la atmósfera tendría menos ozono para proteger los organismos del UV retransmitido. Los resultados graficados en la figura 2.2 constituyen un primer paso para explorar la importancia relativa del flash. Tengamos en cuenta que por lo general, los autores que trabajaron en la modelización de los efectos de la GRB en la Tierra tienden a ignorar el flash UV, en gran parte basado en el argumento de que los efectos a largo plazo son más importantes.
Además, en ambientes que poseen un escudo protector de oxígeno-ozono, la banda UV-C es absorbida casi en su totalidad, y su efecto biológico eficaz es relativamente pequeño, como puede verse en las dos curvas inferiores de la Fig. 2.2. Sin embargo, con la disminución progresiva del contenido de oxígeno, aparece una fracción notable en la región del UV-C que alcanza la superficie del planeta y que contribuye de manera muy negativa, no solo sobre el ADN, sino sobre la mayoría de los procesos biológicos. Por lo tanto, para las atmósferas que tienen de 3 10 a 5 10 naa (probablemente durante el Arcaico y Proterozoico temprano) el pico de la irradiancia biológicamente efectiva cae en la región UV-C, como puede verse en las tres curvas de la parte superior de la Fig. 2 Si tenemos en cuenta que la fluencia del BRG en el tope de la atmosfera se puede escribir como:
I BRG top t BRG E D 2 ,(2.10)
donde E =5x10 43 J es la energía gamma, es el ángulo sólido, fijado a 0,01 srad de acuerdo a (Frail y colaboradores, 2001) y D es la distancia a la estrella. La absorción en el medio interestelar no se incluyó en nuestro análisis debido a ser este prácticamente transparente a los fotones de alta energía (Galante y Horvath, 2007).
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Sustituyendo la ecuación (2.10) en la (2.9) y resolviendo para D obtenemos la expresión para calcular las distancias críticas a partir de la cual una estrella emisora de un BRG causaría mortalidad superficial significativa al cumplimentarse la condición (2.7):
D E E ad * t Sol n E Sol * (2.11)
Para estimar E Sol * para nuestras atmósferas proponemos el siguiente procedimiento aproximado:
consideramos que la atmósfera Arcaica estudiada en (Cockell, 2000) se corresponde a nuestro modelo de atmósfera con 10 -5 naa O 2 . De la Fig. 5 Proterozoico y el Arcaico temprano la biota más resistente a las radiaciones residía en tierra firme. Por lo tanto, un BRG la hubiera podido afectar menos que a la biota posterior que solía vivir en entornos fotobiológicamente más amenos, tales como los de la mitad del Proterozoico hasta el presente.
Principales efectos a largo plazo
Incrementos persistentes de los niveles del UV solar asociados a un BRG.
Se conoce de las secciones anteriores que un BRG puede afectar los niveles típicos de radiación UV que alcanzan el suelo en al menos dos formas diferentes, el ya estudiado flash UV y por el aumento del UV solar asociados a la disminución de la capa de ozono (Galante y Horvath, 2007).
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La importancia relativa de estos efectos parece ser una función fuerte del contenido de oxígeno libre en la atmósfera.
Para atmósferas contemporáneas, similares a la de la Tierra (rica en O 2 ), la principal influencia estimada del BRG es el de la disminución de la capa de ozono y el consecuente incremento del UV solar en superficie, siendo ambos efectos consecuencia directa de la formación de grandes cantidades de óxidos de nitrógeno. La recuperación total de la capa de ozono estará determinada principalmente por fenómenos de transporte con una escala de tiempo estimada de alrededor de una década (Thomas y colaboradores, 2005). Según este estudio, el llamado -destello típico más cercano‖ que hipotéticamente ocurrió en los últimos 1000 millones de años podría causar, a nivel mundial, una disminución en la capa de ozono de hasta un 38% y una fracción importante de esta (por lo menos 10%) se mantendría hasta por siete años implicando:
-Una mayor irradiación de la superficie del planeta con la radiación solar ultravioleta (RUV), -Aumento de la opacidad de la atmósfera reduciendo la luz del sol visible en unos pocos %, debido a la formación de NO2, con potencial enfriamiento global (Melott y colaboradores, 2005) -Depósito de nitratos por lluvias ácidas en cantidades algo mayores que las causadas por los rayos cósmicos en la actualidad.
Es evidente que los dos primeros efectos podrían afectar a muchas especies fotosintéticas: más UV solar puede dañar el ADN e inhibir la fotosíntesis hasta cierto punto, mientras que la reducción de luz del sol en el visible (es decir, la radiación activa fotosintéticamente activa, RFA) podría reducir la energía disponible para realizar la fotosíntesis y por lo tanto para la producción primaria. Sin embargo, el tercer efecto puede compensar, al menos parcialmente, la 52 mencionada inhibición de la fotosíntesis, y podría incluso causar la eutrofización (enriquecimiento de nutrientes en exceso) en algunos ecosistemas de agua dulce y costeros. Es cierto que la lluvia ácida podría tensionar sectores de la biosfera, pero después de una titulación, el aumento del nitrato depositado podría ser útil para los organismos fotosintéticos, especialmente para las plantas terrestres.
Indicadores globales de daño biológico
Con vistas a estudiar los efectos del flash UV, en las secciones anteriores habíamos considerado varios criterios cuantitativos para evaluar los daños provocados por la radiación. Aunque estos criterios son igualmente aplicables al incremento persistente de la RUV solar, es conveniente en cualquier caso, estudiar la posibilidad de definir algunos criterios de daños que nos permitan tener una perspectiva global de esta influencia sobre la biosfera. Sobra reiterar las múltiples dificultades y factores que conspiran contra establecer un criterio de esta naturaleza. Sin embargo, una idea aproximada de estos efectos desde una perspectiva global es dada por el llamado factor de amplificación de la radiación (FAR), relacionando las irradiaciones biológicamente efectivas * E (solares) con las columnas de ozono N , antes y después del evento ionizante.
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Por otro lado y aunque no han sido considerado explícitamente, bajo la acción de la RUV los organismos pueden revertir las reacciones fotoquímicas utilizando enzimas especializadas o volver a sintetizar las moléculas afectadas. Estos procesos, conocidos genéricamente como de reparación, no dependen sólo de la especie, sino también de las variables ambientales. Por ejemplo, consideremos la relación de reparación-temperatura conocida para varias especies de fitoplancton: a muy bajas temperaturas la reparación es muy lenta, mientras que a temperaturas más altas la reparación es eficiente. Otro factor climático a considerar es la propia irradiación luminosa, fundamentalmente en la llamada banda de foto-reactivación sobre los (350-450 nm) que incluye la luz azul y parte de la banda UV-A. La importancia de esta banda se debe a que la fotoliasa, enzima que garantiza uno de los mecanismos de reparación más eficientes y extendidos entre los organismos, precisa de este rango para activarse. En una reacción química ultra-rápida, dicha enzima es capaz de eliminar lesiones como los dímeros de timina, una de las más mutagénicas y tóxicas inducidas por la radiación ultravioleta al ADN (para más detalles consultar Sinha y Hader, 2002). Adicionalmente a la foto-reactivación que utiliza una única enzima, la célula dispone de varias estrategias y mecanismos de reparación en cadena que involucran a múltiples enzimas y que no precisan de la luz visible por lo que suelen denominarse genéricamente como reparación en oscuro.
Como en general, dichos mecanismos no se tiene en cuenta a la hora de medir las FPB, es el factor de amplificación biológico (FAB) la cantidad que nos da una información más precisa sobre los efectos biológicos de la RUV: Dicha tabla sugiere que el daño al ADN es, en general, la principal influencia de un BRG sobre la biosfera y que las plantas terrestres pueden sufrir incluso más que el fitoplancton. Sin embargo, debe tenerse en cuenta que los FAR se miden en condiciones de control muy diferentes 55 a las condiciones naturales en las cuales viven los organismos. Por lo tanto, el uso de factores de amplificación biológicos (FAB) o curvas de respuesta a la exposición (CRE) debe darnos una idea mucho mejor de la respuesta de la biosfera a las perturbaciones de la RUV.
Desafortunadamente, muy pocos FAB o CRE se han medido para los productores primarios más comunes en la biosfera, tales como las principales especies de fitoplancton marino. Por lo tanto, nos faltan datos biológicos de campo para efectuar cálculos más precisos de los posibles efectos globales de un BRG en la biosfera. Por suerte varios estudios están en marcha que proporcionarán datos biológicos de utilidad, por lo que el futuro próximo parece bastante prometedor.
Reducción de los niveles de irradiación en superficie asociados al NO 2
Para tener en cuenta la reducción del espectro de la irradiación en la superficie del planeta debido a la formación de NO 2 , se utilizó el espectro de energía solar I 0 (λ) en la superficie que figura en la norma ASTM G173-03e1 (Http://www.astm.org/Standards/G173.htm). Así, teniendo en cuenta que en (Thomas y colaboradores, 2005) se reporta una reducción de la irradiación total en el rango (0-10)% debido a la formación NO 2 , calculamos el valor de las columnas de NO 2 que llevarían a una reducción de la irradiación total I para varios valores de la fracción f según: donde τ es el camino óptico de los fotones en la columna de NO 2 . Esta magnitud da la clave para estimar la cantidad de NO 2 necesaria para reducir la irradiación total en un factor f dado.
Los resultados de aplicar dicha metodología se muestran en la tabla 2.5 para algunas bandas de interés seleccionadas. En ella se muestra la presencia de una tenue banda de absorción en la banda visible (RFA), mientras que una absorción más pronunciada aparece en la región del UV-A y en la banda de foto-reparación biológica (350-450 nm). Los efectos sobre esta última puede ser importantes si tenemos en cuenta que la luz en este rango (azulada) como ya se discutió es necesaria para ejecutar la foto-reparación (Sinha y Hader, 2002 El procedimiento anterior no considera el aumento de la irradiación debido a la reducción del ozono, pero como el Sol tiene su máximo en la parte visible del espectro, la contribución a la irradiancia total es muy pequeña. Esta afirmación fue confirmada mediante el uso del código de transporte radiativo NCAR / ACD TUV: Tropospheric Ultraviolet & Visible Radiation Model (http://cprm.acd.ucar.edu/Models/TUV/). Valiéndonos del citado código pudimos comprobar que un 30% de disminución de la columna de ozono standard de 340 unidades Dobson implicó un aumento del 22% de la radiación UV-B, pero un incremento de sólo 0,37% en la región del UV-A. Este resultado confirma que la contribución al aumento de la radiación UV-A asociado al descenso del ozono resulta prácticamente despreciable frente al efecto de disminución asociado a la formación de NO 2, que en este caso está en torno del 10%.
Resumiendo los resultados anteriores, podemos apreciar que el efecto global neto de un BRG en atmósferas contemporáneas (ricas en O 2 ) sugiere una combinación de varios tipos de daños.
Básicamente tendríamos un incremento de la R UV (disminución de la capa de ozono), y una eficiencia menor en los mecanismos de reparación del daño al ADN. Además, las reducciones en el visible implican que menos luz (RFA) estará disponible para la fotosíntesis. Por último, la reducción total de la luz solar en los porcentajes calculados en este trabajo podría indicar un enfriamiento global, hecho que de por sí merece consideración en futuras investigaciones.
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Conclusiones
Durante el transcurso de este capítulo se han discutido varios aspectos sobre las posibles influencias que una explosión estelar tan intensa como un BRG puede tener sobre la vida en nuestro planeta y particularmente sobre los productores primarios más extendidos. Hemos empleado, discutido y definido criterios que nos permiten estimar la importancia relativa de algunos efectos asociados a este tipo de eventos como son el flash UV, los indicadores de daño global o el incremento de la opacidad asociada al NO 2 . Parte de los resultados fundamentales, como los derivados en la sección 2.3 (efectos a largo plazo), son aplicables también en el contexto de otros eventos estelares como pueden ser las explosiones de supernovas. Básicamente las conclusiones fundamentales derivadas en el capitulo podrían resumirse así:
1. Perturbaciones intensas del régimen fotobiológico asociadas a eventos astrofísicos como un BRG pueden potencialmente afectar la biosfera en correspondencia con la distancia al progenitor y al nivel de oxígeno atmosférico libre.
2. Los ecosistemas que habitan en atmósferas con contenido de oxígeno relativamente alto (similar al actual) aparecen potencialmente como los más afectados tanto por los efectos directos del flash como por el efecto persistente del UV solar.
3. Entre las principales afectaciones de un BRG sobre la biosfera se encuentran el daño al ADN y los procesos de inhibición a los productores primarios tanto en el fitoplancton marino y como para el caso de las plantas terrestres. 59 4. La opacidad asociada al NO 2 en la región visible podría potenciar el efecto dañino del incremento del UV solar al inhibir, en alguna medida, el papel de los mecanismos reparadores fundamentalmente el de foto-reactivación.
aproximada de lo que podría ocurrir en una considerable fracción de las aguas continentales y los ecosistemas costeros después de la incidencia de la perturbación debida al BRG, ya que muchos de estos sistemas, a menudo, muestran ya un cierto grado de eutrofización debido fundamentalmente a los arrastres de materia orgánica y suelo de las tierras aledañas.
Por otro lado, pese a su carácter marcadamente local, un proceso como el de la eutrofización muestra una dinámica considerablemente compleja donde son posibles estados alternativos (biestabilidad), oscilaciones, histéresis, etc., comunes en otros ecosistemas de mayor relevancia global. Estas características los sitúan como un modelo adecuado para sondear desde un punto de vista cualitativo, posibles respuestas de otros ecosistemas bajo perturbaciones similares.
Admitimos que un modelado más exacto de la acción de un exceso de radiación ultravioleta a nivel de los ecosistemas requiere modelos específicos y de un elevado nivel de información para cada sistema en cuestión, tanto para el caso de los ecosistemas acuáticos como terrestres, tarea que se propone complementar en trabajos futuros.
El modelo integral de simulación acuática
El Modelo Integral de Simulación Acuática (CASM en la literatura) ha descrito con éxito las características principales del proceso de eutrofización en lagos reales (Amemiya y colaboradores, 2007). Este proceso está asociado, como dijimos, al sobre-enriquecimiento por nutrientes, principalmente fósforo y nitrógeno, con el consiguiente aumento de los niveles de fitoplancton, mientras que otras especies, tales como peces y zooplancton pueden escasear considerablemente bajo estas condiciones. Como dijimos en el punto anterior, la eutrofización por la deposición de nitratos es una de las posibles consecuencias de un BRG incidente en 64 nuestra atmósfera, haciéndolo un proceso atractivo para nuestros propósitos. En este modelo hay una entrada externa del nutriente limitante para el ecosistema N I , el cual en nuestro caso incluiría la deposición atmosférica de nitratos por lluvia posterior al evento. La ecuación (3.1) a continuación representa la dinámica de nutrientes en el ecosistema, donde r N es la tasa de pérdida de nitrógeno por diversas causas (por ejemplo, sedimentación, flujo, etc.), mientras que el tercer término de la derecha modela el consumo de nutrientes por parte de los consumidores primarios (fitoplancton X). La forma de este término se inspira en la cinética de Michaelis-Menten, comúnmente aplicada para modelar de manera sencilla algunos procesos enzimáticos. En nuestro caso, es el cociente de la masa de nutrientes (masa de nitrato) a la biomasa, 1 r es la máxima tasa de crecimiento del fitoplancton y 1 k una constante de media-saturación (cuando 1 k N , todo el término se dividirá por dos después de cancelar N , de ahí la denominación de -media-saturación‖). Por último, el cuarto término del lado derecho de la ecuación (3.1) representa la entrada de nutrientes N , a través de la descomposición de detritos D , teniendo en cuenta que
D d N k NX r r I dt dN N N 4 1 1 (3.1)
La producción primaria del ecosistema está representada por la ecuación (3.2) a continuación, donde el fitoplancton X consume nutrientes a través del primer término del lado derecho (se compárese con el tercer término del lado derecho de (3.1)), y el segundo término muestra cómo el zooplancton Y se alimenta del fitoplancton. En este término, 1 f es la tasa de alimentación de zooplancton y 2 k es la constante de media-saturación para este término (porque cuando 2 2 k X , la cancelación de 2 X asegura que todo el término se divide por dos). El último término del lado derecho de la ecuación contiene la mortalidad del fitoplancton 1 d y su velocidad de eliminación del ecosistema 1 e . Tenemos así
X ) e d ( X k Y X f N k NX r dt dX 1 1 2 2 2 1 1 1 (3.2)
La ecuación (3.3) a continuación representa la dinámica del consumidor primario, el zooplancton Y . El primer término del lado derecho muestra cómo se alimenta del fitoplancton (compárese con el segundo término del lado derecho de la ecuación anterior), mientras que el tercer término dice cómo el zooplancton es depredado por el consumidor secundario, los peces zoo-planctívoros Z . El parámetro representa la eficiencia de la asimilación del zooplancton, y el sentido de los otros parámetros se puede deducir fácilmente de las explicaciones dadas para las dos primeras ecuaciones. Escribimos que
Y ) e d ( Y k Z Y f X k Y X f dt dY 2 2 2 3 2 1 2 2 2 1 (3.3)
La dinámica de los consumidores secundarios, los peces zoo-planctívoros, se indica en la próxima ecuación. Aquí la introducción de un nuevo parámetro * Z , la biomasa inferior de equilibrio de los peces zoo-planctívoros, evita la situación irreal de versiones anteriores del CASM, en los que los peces pueden aparecer de los estados en los que ya estaban extinguidos.
) Z Z )( e d ( Y k Z Y f dt dZ * 3 3 2 2 2 (3.4)
Por último, debemos considerar que hay fuentes de detritos D en el ecosistema (materia fecal y cadáveres Y , X y Z ), cuya descomposición devuelve los nutrientes al ecosistema. Esto es muy importante en todos los ecosistemas: una importante fracción de los nutrientes se devuelve al ecosistema a través de la descomposición de las heces y los seres muertos, como se indica en la
ecuación 3.5 D ) e d ( Z d Y d X d Y k Z Y f ) ( X k Y X f ) ( dt
La inclusión del transporte radiativo en el Modelo Integral de Simulación Acuática
La formulación del modelo CASM anterior no tiene en cuenta la distribución vertical de los seres vivos en la columna de agua. Esta es una omisión importante a la hora de considerar cualquier situación de estrés de RUV, dada la atenuación de la radiación debida a la absorción y dispersión en la columna de agua. Para tener en cuenta esto consideramos al fitoplancton como el único nivel trófico necesariamente bajo tensión por la radiación UV, ya que está obligado a tener una adecuada exposición solar con el fin de realizar la fotosíntesis (Neale y colaboradores, 2003).
Podemos entonces imaginar todo el fitoplancton a una cierta profundidad efectiva estará expuesta al aumento de los niveles de RUV después de un BRG. Así, para incluir el papel de algunos componentes del ecosistema como cobertores del UV en la columna de agua (detritos y fitoplancton en sí mismos), hemos modificado el modelo CASM haciendo que el coeficiente de la tasa de mortalidad del fitoplancton ( i d ) ya no una constante, sino una función explícita de esos componentes de la forma (3.6) La dependencia exponencial anterior es motivada por la conocida ley de Beer para la absorción de la luz por soluciones líquidas X h y D h son los coeficientes de atenuación de la radiación UV por fitoplancton y detritos, mientras que d es un coeficiente de tasa de letalidad del fitoplancton cuando no se considera el bloqueo de rayos UV.
D h X h i D X e d d
La forma propuesta para modelar la atenuación del UV (ecuación 3.6) está en consonancia con los resultados de una larga lista de estudios experimentales realizados con este fin (ver para este y otros efectos, Lange y colaboradores, 2003). Hoy en día, se encuentra bien establecido el papel como agentes bloqueadores de la RUV que tienen pequeñas concentraciones de compuestos orgánicos disueltos (COD) o particulados (COP). Los niveles de estos compuestos pueden influir directamente en las distribuciones no solo del fitoplancton sino de organismos superiores en la cadena trófica como el zooplancton y los peces. Es importante destacar, que en el caso de los organismos superiores son comunes las estrategias de migración vertical con vistas a disminuir los daños asociados al UV (Hylander y Hansson, 2010;Leech y colaboradores, 2005). Esta situación suele ser mucho más notable en el caso de los lagos cristalinos debido a la mayor penetrabilidad del UV en la columna de agua. 68 3.1.3 Principales resultados para escala regional.
Para tener en cuenta los efectos combinados de la disminución de la capa de ozono y la reducción espectral de la luz solar, nuestra modificación del modelo CASM para los lagos se exploró con incrementos del coeficiente de la tasa de mortalidad del fitoplancton ( i d ) sin considerar aún los efectos de fotoprotección explícitamente. Los resultados de esta exploración se expresan mediante un diagrama de bifurcaciones. Un análisis del transporte radiativo en los regímenes de oscilación parece interesante debido a que las propiedades ópticas de la columna de agua están continuamente variando en el tiempo.
Algunos de los componentes materiales como el detritos (D ) y el fitoplancton ( X ) tienen el papel de protección adicional contra el UV para las principales especies subacuáticas. Teniendo en cuenta nuestra expresión modificada para el coeficiente de la tasa mortalidad (ecuación 3.6) y 70 considerando contribuciones iguales para la atenuación de los fotones UV por el fitoplancton y detritos ( h = X h = D h ), encontramos el comportamiento mostrado en la Figura 3.2. Fig. 3.2 Efectos de la auto-protección al UV sobre la dinámica del estado cristalino.
Ahora, de acuerdo con la figura 3.2, si la auto-protección no es demasiado alta, el régimen oscilatorio alrededor del estado cristalino persiste, con pequeñas correcciones en la amplitud y período de oscilación. Si la auto-protección alcanza cierto valor umbral, la población de fitoplancton en el tiempo sufre una recuperación progresiva regresando el ecosistema al régimen turbio original.
Los resultados anteriores ilustran la complejidad del proceso de predicción de cómo los ecosistemas terrestres se recuperarían si fuesen alcanzados por un BRG. El estado hacia el que en alguna etapa (Cleaves y Miller, 1998). En algunos casos, la producción de estos compuestos podría haber alcanzado niveles notables llegando a crear una densa niebla capaz de cubrir el planeta (Pavlov y colaboradores, 2001).
Adicionalmente, los efectos directos de la radiación podrían estar conectados con el origen de la homoquiralidad (Fitz y colaboradores, 2007), propiedad distintiva de moléculas biológicas consideradas claves como los azúcares y aminoácidos. La homoquiralidad se basa en la propiedad de especies moleculares idénticas, no superponibles (enantiomeros), de girar el plano de polarización de la luz en un sentido bien determinado, siendo los azúcares biológicamente activos únicamente derechos y los aminoácidos izquierdos. Hechos astronómicos como la identificación de una intensa fuente de luz circularmente polarizada en una de las nubes de polvo de la constelación Orión (Baley y colaboradores, 1998), similar a la que dio origen a nuestro sistema solar, sustentan este tipo de conjeturas.
Sin embargo, probablemente el efecto más notorio de la radiación es su ya mencionado carácter cíclico en días y noches. Ciclos que se traducen en la mayor parte de las reacciones atmosféricas que comienzan en procesos fotoquímicos y en los ya mencionados ritmos circadianos que tienen lugar en los organismos vivos.
Oscilaciones químicas y bioquímicas. Origen y Clasificación
Hoy día, la presencia de oscilaciones químicas o bioquímicas puede ser entendida al menos de dos formas, como un proceso exógeno o endógeno. Los primeros son propiciados por agentes externos que pueden incluir fluctuaciones de parámetros ambientales tales como la iluminación, 74 temperatura, pH u otros sobre un sistema de reacciones químicas determinado, no necesariamente de naturaleza biológica. Entre estos, las contribuciones más importantes parecen estrechamente relacionadas con la extensión del ciclo diario de luz y oscuridad (de 15 h al inicio del arcaico y 24 h ahora). Tal influencia, de efectos notables en la dinámica del ozono y de otras muchas especies en la química atmosférica, parece decisiva en la expansión de los ritmos circadianos en plantas, animales y microorganismos como cianobacterias (Para más elementos de los ritmos circadianos ver Mihalcescu y colaboradores, 2004;Lakin-Thomas y Brody, 2004;Liebermeister, 2005). Su origen, conjuntamente con el de las proteínas fotosensibles, aparece tempranamente en las células primitivas con el propósito de proteger la replicación de DNA de altas dosis de radiación ultravioleta durante el día en el eón Hadeico o Arcaico. En consecuencia con tales criterios, el ritmo emerge como un factor clave en la regulación de procesos bioquímicos dentro de un individuo, así como en la coordinación ante las fluctuaciones medio ambientales. Otras fuentes de ciclicidad a escalas de tiempo considerablemente mayores, podrían tener alguna repercusión directa o indirecta en el origen, distribución y evolución de la vida como pueden ser los ciclos solares, los llamados ciclos de Milankovich o el tránsito del sistemas solar por lo brazos espirales de nuestra galaxia.
A diferencia de las anteriores, las llamadas oscilaciones endógenas se originan como el resultado de la compleja red de interacciones (metabólica en el caso de los seres vivos) con múltiples rutas y lazos de retroalimentación entre los diferentes componentes (metabólicos, enzimas, etc) y estructuras (ver Micheva y Roussel, 2007).
Aunque inicialmente introducido en la química con la reacción de Belousov-Zhabotinsky (BZ) para describir el curso de la oxidación de los iones Ce 3+ y BO 3 en solución ácida, el término 75 reacciones oscilantes rápidamente alcanzó sus mejores aplicaciones en los sistemas bioquímicos y biológicos.
Las oscilaciones, tanto de carácter exógeno como endógeno, aparecen como procesos genéricos
Estableciendo un modelo Vida.
Basados en las consideraciones citadas anteriormente podemos dar por supuesto que las oscilaciones son una propiedad ancestral de los sistemas vivos, y esta suposición nos permite (en forma más bien drástica) clasificar un sistema simple como vivo (oscilando) o muerto (nooscilando). De hecho esta definición sabemos resulta demasiado simplificada para organismos modernos, pero creemos que podría ser de ayuda para estudiar y clasificar algunos sistemas simples, probablemente parecidos a la primeras expresiones -abióticas ‖ de la vida.
Elegir un esquema como este evita, en buena medida, los problemas relacionados con establecer una definición universalmente aceptada del concepto de vida (ver Joyce y Orgel, 1993 ;Lazcano, 2010) acercándose a una línea de pensamiento introducida inicialmente por (Kauffman, 1995) y 76 a escenarios del tipo -El metabolismo primero‖. Conjuntamente con el fenómeno de las oscilaciones, la capacidad de sincronización (Bier y colaboradores, 2000), la homoquiralidad (Plankensteiner y colaboradores, 2004) Aunque en principio es posible implementar las ideas discutidas con anterioridad en cualquier oscilador hipotético o real, por su importancia consideraremos básicamente el llamado oscilador glucolítico.
La glucólisis como un caso particular
Consideremos una modificación de la versión mínima del modelo propuesto originalmente por (Bier y colaboradores, 2000) con la meta de modelar la sincronización oscilatoria del proceso glucolítico en células de levadura (ecuaciones 3.7, 3.8)
dt dV G GT k V dt dG in 1 (3.7) dt dV T T K T k GT k dt dT m p 1 2 (3.8)
El último término en cada ecuación se incluye con el objetivo de considerar explícitamente el efecto de un volumen variable sobre la dinámica en correspondencia con los trabajos previos de 78 (Pawlowski y Zielenkiewicz, 2004). La forma específica del término dV/dt puede ser estimada a partir de la velocidad con que cambia la concentración total de la especies oscilantes dN/dt, donde el valor de N será la suma de las diferentes concentraciones en el sistema anterior, en este caso N=G+T. En correspondencia con esto, considerando el sistema anterior (ecuaciones 3.14-3.15) y después de algunos pasos algebraicos, es posible encontrar una expresión para el término
como T K T k GT k V G T r r dt dV m p in 1 ) ( 1 / (3.9)
En esta expresión, el parámetro r tiene la función de codificar el comportamiento específico de la membrana frente a cambios de volumen o a procesos difusivos a través de ella. Si superponemos que su valor es pequeño, es posible, considerando un desarrollo en series de potencias encontrar una expresión simplificada para el término de cambio de volumen de la forma
T K T k GT k V r dt dV m p in 1 / (3.10)
A partir de razonamientos similares, es posible realizar estimaciones de otros efectos como la magnitud y el sentido de los flujos de solvente en función del comportamiento de la presión osmótica, teniendo en cuenta que para soluciones diluidas se cumple que
T R C P J N osm solv
. (3.11) dónde P osm es la presión osmótica. ∆C N es la diferencia de concentración dentro y fuera la célula de las especies oscilantes, R = 8.314 J K -1 mol -1 es la constante universal del gas y T es la 79 temperatura expresada en grados Kelvin (K). Varios son los análisis que se pueden hacer a partir de la ecuación entre los que se destacan la existencia de un flujo límite cuando la presión osmótica sobrepase determinado umbral o cuando la frecuencia de las oscilaciones sea demasiado elevada para que la condición de equilibrio referida en la ecuación anterior llegue a ser aplicable. Básicamente, con la introducción del nuevo parámetro, nuestro objetivo se limita ahora a explorar sus efectos sobre las oscilaciones originales del sistema. Para ello consideraremos primeramente el uso de la expresión aproximada (ecuación 3.9) y con posterioridad mediante el empleo de la expresión general (ecuación 3.10). La parametrización empleada en ambos casos se corresponde a la originalmente empleada por (Bier y colaboradores, 2000) consistente con un estado oscilante (consultar tabla 3.2 en el Anexo B), coincidente con la nueva versión para el valor del parámetro 0 r
Un análisis aproximado
Exploremos entonces, desde el punto de vista numérico, el comportamiento del modelo aproximado (ecuación 3.9) para valores crecientes del parámetro r. Los resultados de este procedimiento se muestran en la figura 3.3. En correspondencia con el comportamiento exhibido en el gráfico, el modelo aproximado sugiere que las membranas con baja rigidez o con poca resistencia al paso del solvente, limitan la viabilidad de los estados oscilantes o vivos según nuestro criterio. En este caso se puede observar como el periodo crece, mientras la amplitud de las oscilaciones decrece ante incrementos pequeños del parámetro. Nótese además, que por encima de determinado umbral el sistema pierde completamente sus características oscilantes pasando a lo que llamaríamos un estado muerto.
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El Caso general
Pese a que los resultados obtenidos para el caso anterior son razonables, recordemos que su validez puede encontrarse limitada a las regiones donde el parámetro r pueda considerarse realmente pequeño. Si analizamos las implicaciones sobre la dinámica de la expresión general (ecuación 3.10) obtenemos un comportamiento algo diferente. Nuevamente los incrementos del parámetro r conspiran contra el carácter oscilatorio del sistema que se traducen en un incremento paulatino del periodo de las oscilaciones (ver figura 3.4). Sin embargo, a diferencia del caso aproximado, no llegan a ocurrir cambios cualitativos de las soluciones (bifurcaciones) para incrementos notables del parámetro. Este comportamiento implica, al menos en este tipo de construcción, la robustez del fenómeno de las oscilaciones frente a los procesos de cambio de volumen o del transporte pasivo a través de la membrana. Fig. 3.4 Incremento paulatino del periodo de las oscilaciones con el incremento del parámetro r 82 Sin embargo, si tenemos en cuenta el presumible rol que desempeñan las oscilaciones en la dinámica celular y consideramos además la vida como un fenómeno limitado en el tiempo, entonces un incremento considerable del período de las oscilaciones puede considerarse, en un sentido práctico, como un estado no oscilante, o sea, muerto en nuestro criterio.
Si uno extiende este estudio para incluir otros osciladores químicos o bioquímicos (para el caso de la mitosis consultar Goldbeter, 1991 ) bien establecidos y hace un análisis algo más cuidadoso mediante el estudio numérico (Dhooge y colaboradores, 2006;Doedel, 1986) de posibles bifurcaciones asociadas al parámetro r, descubre una tendencia general a la pérdida del comportamiento oscilatorio. Sin embargo, los efectos sobre los patrones de la oscilación si pueden variar sustancialmente de un oscilador a otro sin mostrar una regla o tendencia bien establecida (Martín y colaboradores, 2009).
Las motivaciones en considerar la glucolisis como caso distintivo se debe fundamentalmente a su presencia en casi todos los organismos como una fuente principal de energía química y ser, quizás, la más antiguas vía metabólica (Fell y Wagner, 2000). Estas características la convierten en un proceso particularmente interesante del punto de vista del astrobiológico. El proceso en sí mismo consiste en la ruptura gradual de las reservas de glucosa para liberar energía en forma de moléculas ATP. Está bien documentado el hecho que durante el proceso, las concentraciones de los diferentes metabolitos (ATP, glucosa) exhiben oscilaciones respecto a cierto valor de concentración medio. Se conoce además que dichas oscilaciones poseen la habilidad de sincronizarse entre células diferentes. Para este trabajo, hemos elegido uno de los varios modelos 83 que se han propuesto para estudiar y reproducir los patrones oscilatorios y los posibles mecanismos de sincronización.
Para terminar es bueno considerar dos elementos adicionales. Primero debe quedar claro que en nuestro análisis describimos sólo membranas pasivas, en el sentido que no están directamente acopladas al propio metabolismo de la célula. Obviamente, éste no es el caso de organismos modernos donde las estructuras de membrana se regeneran y crecen continuamente, pero aceptable en los comienzos, cuando su papel principal pudo estar limitado a actuar como simples receptáculos para los procesos -bioquímicos‖ incipientes.
El segundo elemento se relaciona con algunos aspectos termodinámicos de la vida y nuestros criterios específicos de vida y muerte. Desde un punto de vista estrictamente termodinámico, ambos estados estarían vivos en el sentido que los dos se encuentran fuera del equilibrio, existiendo flujos netos de masa y energía. Si nuestro criterio fuera acertado, entonces los sistemas vivos formarían una clase más bien limitada dentro de otra, mucho más general, que incluiría a todos aquellos sistemas alejados del equilibrio.
Conclusiones
Los resultados obtenidos en este capítulo muestran como la modelación de los sistemas biológicos es una tarea altamente compleja, no solo por el elevado número de variables involucradas o la carencia de datos sino por el carácter marcadamente no lineal de su comportamiento. Particularmente para el caso regional, hemos explorado los posibles impactos que provocan el efecto combinado de los excesos de radiación UV y el sobre-enriquecimiento de 84 nutrientes vinculados a eventos como las BRG o las supernovas cercanas. En correspondencia con estos resultados, los efectos al parecer importantes sobre los ecosistemas estudiados, podrían exhibir un comportamiento más bien variado, dependiendo entre otros factores de la resistencia de las especies presentes (fundamentalmente del fitoplancton) y de la posibilidad de efectos de apantallamiento al exceso de UV en la columna de agua que reduzcan de manera considerable los niveles de exposición. Por otro lado hemos discutido el papel de los ciclos, importancia y modulación por efecto del transporte pasivo a través de las membranas. Las conclusiones fundamentales que se derivan de los análisis anteriores podrían resumirse como:
1. Las perturbaciones intensas en el régimen fotobiológico pueden alterar sensiblemente la dinámica de los ecosistemas llegando incluso a inducir cambios irreversibles en el estado de estos.
2. Las complejidades inherentes a los sistemas biológicos, tanto a nivel de sistemas (biosfera, ecosistema) como de organismos unicelulares, la carencia de datos fidedignos así como aspectos específicos del método de modelación ecológica, limitan en buena medida el alcance de este tipo de estudios.
3. Las propiedades de las membranas primitivas y el transporte pasivo pueden modular la emergencia de ciclos, elementos interesantes desde el punto de vista astrobiológico si tenemos en cuenta su importancia y extensión entre los organismos vivos.
CONCLUSIONES
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CONCLUSIONES
El papel de las radiaciones sobre el origen, instauración y evolución de la vida ha sido por varias décadas un tema activo de investigación, no solo en el marco de las investigaciones puramente astrobiológicas, sino en una buena parte de los trabajos astrofísicos y de las llamadas Ciencias de la Tierra. Enmarcado en este contexto, nuestro trabajo tiene la peculiaridad de abordar esta problemática desde una perspectiva general que involucra tanto los aspectos cosmológicos o galácticos del problema hasta aquellos de carácter planetario alcanzando incluso elementos de índole local o regional.
Desde el punto de vista más general posible, el fenómeno de la vida parece estar condicionado directamente con la dinámica y las leyes más generales que rigen nuestro universo y que han dado lugar a la formación de estructuras como nuestra galaxia. Es importante acotar que este carácter biofílico, expresado en otros conceptos como los de zona estelar o galáctica habitable, son consecuencia directa de la dinámica y no de un intervalo temporal específico. Tengamos en cuenta que las condiciones del universo temprano no eran en lo absoluto favorables para la vida.
Un razonamiento similar es igualmente extensible tanto a la evolución de nuestra galaxia como a los orígenes del sistema solar.
Ya en un contexto planetario, el régimen fotobiológico emerge como una variable climática significativa en el comportamiento de la biosfera como sistema y particularmente en el caso de los productores primarios. Bajo las condiciones del régimen fotobiológico estacionario establecidas por una estrella como el Sol, las contribuciones relativas en las regiones UV y visible del espectro en superficie aparecen como elementos determinantes que condicionan, junto a otros factores tales como la circulación o presencia de bloqueadores del UV en el agua, la GLOSARIO Principales términos de corte cosmológico y astrofísico empleados Brotes de rayos gamma (BRG): Las mayores explosiones reportadas en el universo con fluencias del orden de unos 10 44 J y una duración promedio del orden de algunos segundos a minutos. Se asocian a la interacción de sistemas binarios o al colapso de estrellas muy masivas.
Se caracterizan además por que las emisiones ocurren fundamentalmente en la región gamma del espectro y son colimadas.
Energía Oscura: Componente mayoritario de naturaleza aún no establecida que representa prácticamente dos tercios del contenido de materia-energía del universo. Se considera el responsable de la aceleración expansiva de nuestro universo.
Materia Ordinaria: Denominación empleada para la materia de naturaleza bien establecida como son los bariones, fotones y neutrinos con vistas a diferenciarla de la llamada Materia Oscura.
Materia Oscura: Componente mayoritario de naturaleza poco establecida, de carácter atractivo y que representa la mayor parte de la materia no radiante que se agrupa en las galaxias, cúmulos y supercúmulos de galaxias. Sus efectos son ya notables en la dinámica galáctica.
Modelo Cosmológico Estándar:
Criterio introducido originalmente por Einstein y ampliamente asumido por la cosmología moderna para describir las propiedades y evolución del universo a gran escala. En correspondencia con este, nuestro universo hoy en día puede considerarse plano, homogéneo e isótropo a escalas considerables.
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Principales términos de corte astrobiológicos
Borde rojo: Comportamiento espectral típico exhibido por la atmósfera como consecuencia directa de la absorción de los pigmentos de la clorofila alrededor de los 0.7 µm (luz roja). Es considerado como una bioseñal superficial importante en los programas de búsqueda de vida extrasolar.
Mundo ARN: Forma parte de las teorías que intentan explicar el origen de la vida y pese a sus muchas limitaciones, se considera entre las alternativas más aceptadas por la comunidad científica. Desarrollada en sus orígenes por H.J. Muller (1926) supone que la información juega un papel preponderante y que inicialmente pudo estar codificada preferentemente en el ARN.
Metabolismo Primero: Forma parte de las teorías que intentan explicar el origen de la vida suponiendo que el metabolismo es un factor clave para este proceso. Sus fundamentos iniciales descansan sobre los trabajos de A. Oparin (1938) sobre los coacervados.
Panspermia: Teoría popularizada por Arrhenius (1903) que supone a la vida como un fenómeno no originario de nuestro Planeta, cuya semilla provino del espacio exterior con el impacto de asteroides o cometas.
Zona estelar habitable: Región alrededor de una estrella considerada favorable para la emergencia de vida introducida por J.F. Kasting. Entre los requerimientos más aceptados se encuentran los niveles de irradiancia adecuados sobre un planeta rocoso, capaz de retener atmósfera y agua líquida.
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Zona galáctica habitable: Puede considerarse una extrapolación del concepto de zona galáctica habitable. Supone que las condiciones de vida en la galaxia varían significativamente siendo favorables en una zona intermedia del disco. Los criterios se basan fundamentalmente en la estabilidad (menor número de supernovas) y al nivel de metalicidad (entiéndase elementos diferentes al H y He).
Términos de corte ecológico
Biosfera: Términos de implicaciones planetarias usado para referirse a la interacción de todos los organismos vivos organizados en ecosistemas.
Biota: Denominación genérica usada para referirse a todos los organismos vivos sin especificaciones.
Capa mezclada: Se denomina a la región del océano con propiedades químico físicas homogéneas debido a los procesos de transporte de diferente naturaleza. Puede extenderse de escasos metros hasta profundidades considerables de cientos de metros.
Detritus: Nombre con que se designa la materia orgánica residual dentro de ecosistema determinado integrada fundamentalmente por las heces, organismos muertos, hojas y otras materias orgánicas en descomposición.
Ecosistemas: Relaciones que se establecen a escala regional o local entre las diversas especies y comunidades y con el medio ambiente. El cuidado y manejo de estos sistemas se considera un elemento indispensable en todas las políticas ambientales.
102 Eón: Intervalo de tiempo del orden de los Ga en que se divide la historia geológica de nuestro planeta para su estudio. Se reconocen cuatro eones que en orden cronológico ascendente serían Hadeico, Arcaico, Proterozoico y el Fanerozoico (actual) Eutrofización: Proceso asociado al exceso de nutrientes fundamentalmente nitrógeno y fósforo y que se caracteriza por un incremento desmedido del fitoplancton. La eutrofización es la causa de la turbidez que exhiben muchos lagos y áreas costeras en la actualidad debido al uso excesivo de fertilizantes.
Fitoplancton: Integrado por un gran número de especies y organismos unicelulares entre los que se destacan diferentes tipos de cianobacterias y algas. Por ser los productores primarios más extendidos se consideran un elemento indispensable tanto dentro del ecosistema como a nivel climático global.
Relaciones tróficas: Dependencias de depredación (alimentación) que establecen diferentes especies de organismos, usualmente con grados de organización diferentes.
Ritmos circadianos: Periodicidad que manifiestan una amplia generalidad de procesos que ocurren en los organismos vivos motivadas fundamentalmente por la alternancia diaria de luz oscuridad entre otras variables climáticas. Es considerada como una estrategia adaptativa importante frente a los excesos de radiación UV.
Términos de corte fotoquímico o fotobiológico
Factor de Amplificación Biológica (FAB): Función de ponderación biológica que se construye con vistas a estimar los efectos del UV sobre determinado proceso orgánico. Incluye la acción de los mecanismos de reparación celulares.
Factor de Amplificación de la Radiación (FAR): Función de ponderación biológica construida con vistas a estimar los daños por el incremento de UV asociados a las variaciones en el contenido de ozono. No incluye en su definición la acción de los mecanismos de reparación celulares.
Fotoreactivación: Es uno de los mecanismos más extendidos y eficientes de reparación de los daños al ADN por efecto del UV. El proceso depende de una enzima denominada fotoliasa y de luz en el rango de 350-450 nm (azulada)
Funciones de Ponderación Biológica (FPB):
Funciones matemáticas construidas generalmente a partir de estudios experimentales para cuantificar los efectos de determinado agente (ejemplo UV) sobre determinada estructura o proceso orgánico como pueden ser el ADN o la fotosíntesis respectivamente.
Radiación Fotosintéticamente Activa (RFA): Intervalo de longitudes de onda comprendido aproximadamente entre 400-700 nm que contribuye activamente al proceso de fotosíntesis.
Zona Fótica: Término empleado para referirse aquella región con niveles de luz suficiente como para realizar el proceso de fotosíntesis. Su amplitud depende directamente de aquellos factores que afectan la transparencia de la columna del agua.
1 )
1Martín O., Cárdenas R., Guimarais M., Peñate L., R. Horvath J.E., Galante D. ´´Effects of gamma rays bursts in Earth´s biosphere''. Astrophysics and Space Science (2010) 326: 61, O., Galante, D., Cárdenas, R. Horvath, J.E ‗'Short-term effects of gamma rays bursts on Earth''. Astrophysics and Space Science (2009) 321: 161-167 4) Sussman R., Quiros I., Martin O. ‗'Inhomogeneous models of interacting dark matter and dark energy''. General Relativity and Gravitation 37
24 Fig. 1 . 1
2411Tasa relativa de fotosíntesis vs. profundidad en el océano Arcaico, para (azs = 0 0 ) Fig. 1.2 Tasa relativa de fotosíntesis vs. profundidad en el océano Arcaico para (azs = 60
modelo estudiadas en el tiempo geológico En los demás aspectos seguimos a(Segura y colaboradores, 2003): adoptamos sus datos para la columna de ozono, fijamos la presión atmosférica a 1 atm y en las paleo-atmósferas reemplazamos el O 2 faltante por CO 2 , al ser este un gas que probablemente abundó en los paleoambientes de nuestro planeta.
42 Fig. 2. 1
421UV que alcanza el suelo expresada como fracción de la energía gamma originalmente incidente en el tope de la atmósfera. Irradiancias UV que alcanzan el suelo para distintas atmósferas y longitudes de onda, normalizadas respecto al flujo completo del BRG en el tope de la atmósfera.
organismos fotosintéticos unicelulares: el fitoplancton. Cualquier afectación importante sobre el fitoplancton repercutirá sobre gran parte de la biosfera(Behrenfeld y colaboradores, 2005) por su transmisión a través del ensamblaje trófico (alimentario) y mediante otros mecanismos indirectos. En nuestro caso modificamos el criterio en(Thomas y colaboradores, 2005), pues en vez irradiancias o flujos biológicos efectivos, introducimos el concepto de fluencias biológicas efectivas para describir el potencial daño del BRG. La razón para esta elección está en que durante el corto e intenso flash UV de 10 s de duración no habrá tiempo suficiente para que los mecanismos de reparación del ADN funcionen, y por ende los daños serán acumulativos, propiamente descritos por una fluencia (J/m 2 ) y no por un criterio de flujo o irradiancia (W/m 2 ), más adecuado para escenarios en los que la reparación del ADN funciona. Basados en esto, asumimos la siguiente condición para tener una significativa mortalidad de fitoplancton superficial bajo la acción del UV flash:
de lãs FAR son dependientes tanto del grupo de especies como del proceso orgánico a considerar (representada por una función de ponderación biológica o FPB). Dichas funciones son típicamente medidas en condiciones controladas de laboratorio, de modo que tienen un valor limitado para estimar la respuesta real de los seres vivos a la RUV.
partir de ahora los subíndices antes y después denotan los valores posterior y anterior del impacto del BRG. Se utilizaron los valores de f de 0.98, 0.96, 0.94 y 0.92, los cuales 56 representan reducciones en la irradiación de 2
sistema. Como puede verse de las ecuaciones (3.1) -(3.5), CASM posee cinco variables dinámicas y 19 parámetros (consultar Tabla 3.1 en el Anexo A para la parametrización empleada). En general, referimos al lector interesado al trabajo de Amemiya y colaboradores (2007) para más detalles.
En la Figura 3.1 se muestra cómo el comportamiento cualitativo del modelo cambia en función del parámetro i d donde las líneas sólidas representan estados estables u oscilatorios mientras las de trazos representan estados transitorios. De su análisis se desprende que cuando el parámetro i d aumenta hasta 0,105, sólo un 5% superior al valor de referencia de 0,1 utilizado por Amemiya y colaboradores (2007), el estado estacionario surge claramente como oscilatorio en una llamada bifurcación de Hopf. Para valores más altos (alrededor de 0,125), la bi-estabilidad del sistema se rompe y el estado oscilatorio surge como la única posibilidad. Tales estados alternativos son exhibidos por el CASM para otras regiones de los parámetros (Amemiya y colaboradores, 2007). 69 Fig. 3.1 Diagrama de bifurcaciones para el modelo CASM en función del parámetro de tasa de mortalidad del fitoplancton (d 1 ).
(
McKane y colaboradores, 2007) en los sistemas biológicos, ocurriendo las mayoría de la veces de manera combinada, o sea, por ejemplo una oscilación endógena modulada por una fuente exógena. Quizás de los mejores ejemplos de este comportamiento sea la fluctuación periódica exhibida por ATP y glucosa durante el ciclo de glucólisis. De manera general, las oscilaciones se consideran como un componente crucial de importantes procesos celulares que no solo comprenden las rutas metabólicas, sino también la reproducción e inclusive la señalización (Igoshin y colaboradores, 2004).
80 Fig. 3 . 3
8033Patrones de oscilación para valores crecientes del parámetro r en el caso del oscilador glucolítico. La línea roja, paralela al eje temporal, implica la existencia de un estado muerto (nooscilante)
).LA VIDA
FOTOSINTÉTICA EN
EL CONTEXTO
COSMOLÓGICO
9
). Este escenario ha sido llamado una Tierra Temprana Fría (TTF).Si realmente existió, quizá su régimen fotobiológico difería poco del que existió en el Arcaico
temprano: el Sol ya había terminado su fase T de Tauro (Cnossen y colaboradores, 2007) (por lo
que sus emisiones en el ultravioleta y el visible serían similares en ambas eras). Con respecto a la
atmósfera, la composición exacta está aún en debate (Catling y Claire, 2005; Catling y
colaboradores, 2001), aunque parece razonable suponer niveles de N 2 similares a los actuales asi
como importantes cantidades de gases de efecto invernadero tales como CO 2 y CH 4 . En ambas
eras la rotación más rápida del planeta implicaría fuertes vientos superficiales de más de 150
km/h. Esta situación generaría, entre otros patrones complejos, corrientes verticales circulares
(circulación de Langmuir) en el océano que se extenderían hasta decenas de metros de
profundidad. Como veremos posteriormente, este hecho jugará un papel crucial en la eficiencia
de la fotosíntesis.
). Usamos los datos de irradiancias ultravioletas para una Centauro B, que es una estrella K1V. Los resultados de este procedimiento se muestran en la figura 1.3. Figura 1.3 Tasa de fotosíntesis vs. Profundidad en el océano, para un ángulo solar zenital de 60 grados, en un planeta tipo terrestre a 0,7 UA de Alfa del Centauro Bestrella K2V dados en (Segura y colaboradores, 2003), como un modelo aproximado para α del
28
.2). Esto se puede explicar porque Alfa del Centauro B es más fría que el Sol, emitiendo entonces una menor proporción de radiación ultravioleta. Al comparar las tasas máximas de fotosíntesis (Figs. 1.2 y 1.3), se infiere que hay condiciones similares o quizás, ligeramente más favorables para la emergencia de vida fotosintética en un planeta tipo terrestre localizado a 0,7 UA de Alfa del Centauro que en la Tierra Arcaica, si las demás condiciones ambientales son más o menos similares.
de descartar la probable emergencia de vida en los sistemas de estrellas pequeñas LAS PERTURBACIONES DEL RÉGIMEN FOTOBIOLÓGICO EN LA VÍA LÁCTEA El objetivo de este capítulo es examinar algunas perturbaciones en el régimen fotobiológico a que puede estar sometida la vida fotosintética en nuestra galaxia particularizando en el caso terrestre.2.1 Explosiones estelares y la habitabilidad en la Vía LácteaEn todas las estrellas existe la posibilidad de emisión de grandes dosis de radiación ionizante al espacio. Los mecanismos son variados y con frecuencia implican reajustes en los campos magnéticos estelares, colapso gravitacional y/o establecimiento de reacciones nucleares muy energéticas.Las explosiones estelares más energéticas que se conocen son los brotes de rayos gamma (BRG), en los que se emiten en escasos segundos o minutos energías del orden de 10 44 J. Otro tipo de explosiones muy energéticas tienen lugar en las supernovas de diversos tipos. De hecho, existe una conexión directa entre algunos tipos de BRG y supernovas(Zhang y Meszaros, 2004). Estos conforman los llamados BRG de tipo II asociados al colapso de estrellas masivas (tipos O y B) como en el nacimiento de una supernova tipo 1b/c y se caracterizan por tener menor intensidad, mayor duración y una colimación más acentuada del haz. A diferencia de estos, los llamados BRG del tipo I se asocian a la fusión de sistemas binarios compactos como una estrella de neutrones y un agujero negro, o en los que una enana blanca incorpora materia de una gigante roja hasta alcanzar la masa crítica para que ocurra la explosión. Los brotes del tipo I se caracterizan por ser eventos muy energéticos, de menor duración así como un menor grado de colimación en el haz emergente si se comparan con sus homólogos del tipo II (Gao y Dai, 2009).(M).
PERTURBACIONES
DEL RÉGIMEN
FOTOBIOLÓGICO EN
LA VÍA LÁCTEA
2.
) .
)Ejemplos son las hipótesis de que la extinción masiva del Ordovícico(Melott y colaboradores, 2004; Melott y Thomas, 2009), ocurrida hace unos 450 millones de años, fue causada por un BRG y que la extinción menor de moluscos bivalvos tropicales en la transición Pleistoceno-Plioceno fue causada por una supernova de la asociación Escorpión-Centauro (Benítez, Maíz-Apellániz y Canelles, 2002). En esta última asociación de estrellas masivas ocurrieron varias supernovas en los últimos 10 millones de años, y es intrigante la coincidencia de que las anomalías de Fe 60 en el lecho oceánico fijan como mejor fecha para una supernova cercana en unos 2,8 millones de años atrás, mientras que la extinción transcurre en varias fases, pero con un pico hace 2,6 millones de años. No obstante, se requiere de más estudio para demostrar fehacientemente a una supernova como la causa única, o más bien contribuyente junto a otras, de esta extinción.35
, de acuerdo a su propio flujo y energía media, donde) . La atmósfera se dividió en 90 capas desde la altura
0 (nivel del mar) hasta 180 km, y el rango de longitudes de ondas se dividió en 100 haces
-monocromáticos‖. Cada haz normalmente incidente fue atenuado por una ley exponencial de
Beer de la forma
j
i x
i
j
i
e
N
N
0
,
j
i
N , es el
flujo de fotones remanente del haz monoenergético incidente
0
i
N ; x
j es la densidad de columna
(en g/cm 2 ) de la capa y
I es el coeficiente de atenuación másico correspondiente, tomado de
(Berger y colaboradores, 2005). La energía depositada en cada capa fue determinada usando la
diferencia de los flujos totales de capas adyacentes:
100
1
1
,
,
,
j
j
i
j
i
N
N
i
Fdep
estimador para todos los efectos del UV. Esto implicara alguna subestimación en E La magnitud de las distancias reportadas en la tabla anterior posibilitan hacer algunas conclusiones generales sobre la posibilidad y magnitud que un evento de este tipo pudo haber tenid en algún momento de la evolución biológica de nuestro planeta y por ende aplicables a Distancias críticas para que el flash UV que llega a nivel del mar supere un número determinado de veces la fluencia biológica efectiva del UV solar.Como primer elemento tenemos que, las biosferas del Fanerozoico, del meso-Proterozoico y Proterozoico tardío serían, a corto plazo, las más estresadas por un flash de UV de un GRB procedente de varios kpc. Para esto tengamos en cuenta que incluso, para causar un daño 16 veces mayor que el asociado al UV solar (última columna), las distancias críticas para esas épocas son similares a las estimadas para el "último estallido cercano típico" a la Tierra, o sea de 1 a 2 kpc en los últimos 1000 millones de años. Por lo tanto, podría ser interesante la inclusión del flash UV dentro del modelado detallado de los efectos a largo plazo de un BRG durante el eón Fanerozoico, tal como se presenta en Thomas y colaboradores del 2005.efectiva de un BRG, pero sus efectos serían menos significativos al recibir mayores fluencias biológicamente efectivas durante el día. Por lo tanto, es atractivo pensar que durante elde dicho artículo se puede inferir valores
aproximados de 80 W/m 2 y 20 W/m 2 para ángulos zenitales solares de 0 y 60 grados,
respectivamente. Como un promedio aproximado usamos E
Sol
*
50W /m 2 . Seguidamente
utilizamos la Tabla 3 de (Segura y colaboradores, 2003), donde los E
Sol
* para las mismas paleo-
atmosferas aparecen normalizados al valor actual, lo cual nos permite estimar E
Sol
*
para todas
nuestras atmósferas. En el mencionado artículo los autores usan el rango 295-315 nm como un
Sol
* debido a
la absorción de la banda UV-C (200-280nm) por el ozono. Por tanto, a menor contenido de
oxígeno, dicha subestimación será mayor. Sin embargo, consideramos que los errores
introducidos serán relativamente pequeños, especialmente si se tiene en cuenta que se está
trabajando con valores relativos (normalizados) para inferir los E
Sol
*
correspondientes a cada
atmósfera.
En la Tabla 2.3 a continuación se resumen los principales resultados derivados del esquema
anterior y al empleo de la expresión (2.11).
49
cualquier otro planeta similar al nuestro en la galaxia. Destacamos las siguientes:
O 2 naa
*
ad
E
)
/
(
*
m
W
E
Sol
)
(
D 2 kpc
)
(
D 4 kpc
)
(
D 8 kpc
)
(
D 16 kpc
10 0
0.005
0.009
4.45
3.14
2.22
1.57
10 -1
0.010
0.0141
5.07
3.58
2.53
1.79
10 -2
0.043
0.095
4.00
2.83
2.00
1.42
10 -3
0.085
1.961
1.25
0.88
0.63
0.44
10 -4
0.128
33.454
0.37
0.26
0.18
0.13
10 -5
0.172
50
0.35
0.25
0.17
0.12
Tabla 2.3 50
Por otro lado, si nos enmarcamos en una distancia dada al progenitor del BRG, los ecosistemas
que viven en atmósferas del orden de unos 10 -1 naa serían entonces los más estresados. Este
hecho corresponde aproximadamente a una atmósfera anterior a la mitad del período
Proterozoico.
Se desprende además un hecho que a primera vista puede parecer sorprendente. Los ecosistemas
menos protegidos, en correspondencia con el análisis las tres últimas filas de la Tabla 2.3, no son
necesariamente los más afectados. Ciertamente, recibirían una mayor fluencia biológicamente
donde P es la tasa de un proceso orgánico (por ejemplo, fotosíntesis). Aunque muy pocos FAB se han medido experimentalmente, conjuntamente con la FAR, estos podrían ser útiles para una primera estimación del daño global en la biosfera por un BRG, aunque una modelización más*
*
antes
después
antes
después
E
E
FAB
P
P
(2.5)
54
detallada implica que uno debe estudiar ecosistemas específicos, las unidades básicas para la
construcción de la biosfera.
Los resultados de aplicar estos criterios al caso de un BRG típico descrito en Thomas y
colaboradores, (2005) se recogen en la Tabla 2.4, mostrándose el aumento de la fracción efectiva
de irradiación biológica para diferentes valores de la disminución del ozono y varias funciones
de ponderación biológica.
Funciones de peso biológico
RAF
*
*
antes
después
E
E
para disminuciones del ozono en (%)
38
30
20
10
Foto-inhibición
del fitoplancton marino
0.31
0.31
1.12
1.07
1.03
Foto-inhibición en
plantas terrestres
0.51
0.51
1.20
1.12
1.05
Daño al ADN
1.67-2.2 2.22-2.85 1.82-2.20 1.45-1.63 1.19-1.26
Tabla 2.4 Factores de amplificación de la radiación y el incremento fraccional de las
irradiancias biológicas efectivas para reducciones de la columna de ozono de 38, 30, 20, 10
porciento.
). Cocientes de irradiación antes y después del BRG para algunas bandas seleccionadas.f
fUV-A
f PAR
f 350-450 nm
0.98
0.92
0.98
0.92
0.96
0.85
0.95
0.84
0.94
0.78
0.93
0.77
0.92
0.71
0.90
0.70
Tabla2.5 57
No está completamente claro si el antepasado de la célula primitiva tuvo una pared celular o no, pero parece un hecho probable teniendo en cuenta las múltiples funciones que esta asume en los organismos modernos. Varios compuestos han sido propuestos como posibles candidatos para conformar la membrana en las células primitivas (Ourisson y Nakatani 1994; Deamer y colaboradores, 2002 para ver detalles). Desafortunadamente no hay una alternativa clara hasta ahora para este cuadro, y la estabilidad de las estructuras formadas se sabe son extremadamente dependientes de parámetros ambientales como el pH del medio. También se ha alegado en los últimos años, que algunos de los más importantes compuestos para formar estas estructuras pudieron tener un carácter exógeno, condicionados por la transferencia de material orgánico proveniente del espacio exterior(Bernstein y colaboradores, 2001(Bernstein y colaboradores, , 2002; Muñoz Caro y colaboradores. 2002; Dworkin y colaboradores 2001).Básicamente nuestro modelo rudimentario de célula primitiva estaría conformado por un sistema de reacciones químicos capaz de oscilar, limitado por una membrana semipermeable y flexible que permite el transporte pasivo de determinadas sustancias. El volumen de la célula viva, a semejanza de las células reales, será de magnitud variable en correspondencia con los gradientes específicos (presión osmótica) a través de la membrana afectando la dinámica del sistema original (ver Zonia y Munnik, 2007). En este sentido, las propiedades intrínsecas de la membrana determinarán la factibilidad del estado oscilante (célula viva).y la emergencia de complejas redes de interacción (Fell y
Wagner, 2000) aparecen como características distintivas de todos los seres vivos, sugiriendo una
conexión mucho más intrínseca y profunda con el fenómeno de la vida en sí mismo.
Otro elemento clave que consideremos en nuestro modelo es la existencia de una membrana o
pared celular. En las células modernas dicha membrana es indispensable para el funcionamiento
celular, controlando el flujo de agua, el intercambio de sustancias y delimitando las dimensiones
efectivas de la célula. Entre los roles de la membrana se encuentra además, el resguardo de las
estructuras internas de la célula de la influencia nociva del medio ambiente (para más detalles
Zonia y Munnik, 2007).
. Incluso para los escenarios más favorecidos dentro de la zona estelar habitable los niveles de radiación ultravioleta RUV conjuntamente con los efectos de la circulación vertical oceánica pueden limitar en buena medida las posibilidades reales de los organismos fotosintéticos dentro de la llamada zona fótica.5. La temperatura de la estrella, la presencia o no de bloqueadores activos a la RUV tanto en la atmósfera como en el océano y las capacidades de reparación de la biota existente, emergen como parámetros claves a considerar en este tipo de estudios.
3. LA COMPLEJIDAD DE LA VIDAEn este capítulo se examinan aspectos referentes a la dinámica de los ecosistemas estresados por los excesos de RUV que pueden ser, consecuencia directa de un BRG o de la explosión de una supernova cercana. Adicionalmente, se introducen también elementos sobre el origen e importancia de los ciclos biológicos en el contexto de las teorías sobre el surgimiento de la vida, resaltando las complejidades inherentes en este tipo de estudios.3. 1 Brotes de rayos gamma a nivel de los ecosistemasEn los capítulos anteriores hemos restringido nuestra atención, fundamentalmente, a la acción de un exceso de radiación ultravioleta sobre los llamados productores primarios. Sin embargo, resulta prácticamente imposible establecer una modelación más detallada de este fenómeno sin reconocer explícitamente la estructuración de la biosfera en ecosistemas y su continua interrelación con el clima. Muchos son los factores que conspiran contra un estudio de esta naturaleza destacándose, la elevada variabilidad en la sensibilidad a la radiación reportada para diferentes especies, pudiendo variar incluso, dentro de los organismos de una misma especie, el nivel de conocimiento muchas veces limitado que se dispone y los posibles umbrales y efectos no lineales asociados a este tipo de sistemas(Scheffer colaboradores, 2001; Van nes yScheffer, 2004). Si bien y como una primera aproximación, pudiera ser aceptable considerar que las principales alteraciones ocurran inicialmente sobre los productores primarios de las biosfera (fitoplancton, algas, plantas superiores), al constituir estos la base de la cadena alimenticia, cualquier perturbación en ellos debe reflejarse de una manera más bien complicada en los niveles tróficos superiores (herbívoros, carnívoros, omnívoros). Es importante aclarar, que los excesos 62 de radiación ultravioleta pueden afectar directamente a organismos expuestos a la radiación pertenecientes a otros niveles tróficos, fundamentalmente a aquellas en estado larvario o adulto(Vincent y Neale, 2000), ocasionando directamente la muerte o enfermedades tan extendidas como el eritema o el cáncer de piel. Pese a ser un problema científico bien establecido, la amplia diversidad de ecosistemas y las complejidades intrínsecas de este problema hacen que las posibles respuestas ante un exceso de radiación ultravioleta sea considerada, hasta hoy, una cuestión abierta(Hader y colaboradores, 2007).En otro ámbito, como la biosfera regula en buena medida los niveles atmosféricos de importante gases tipo invernadero como son el CH 4 , el CO 2, y los propios niveles de O 2 en escalas geológicas, las perturbaciones por exceso de radiación ultravioleta tanto de origen solar o extrasolar, pueden potencialmente llevar a cambios climáticos globales (Thomas y colaboradores, 2005) con las consecuencias ecológicas correspondientes. De hecho, reconocer la compleja interacción biosfera clima se convierte en un elemento clave para comprender con claridad, la evolución biogeoquímica de un planeta como la Tierra.Para estudiar los efectos de la incidencia de un BRG a nivel regional o local, es importante dada su amplia diversidad, el modelado del exceso de radiación ultravioleta en varios ecosistemas. En este trabajo en particular se han elegido los lagos. Una de las razones para esta elección es que el modelo seleccionado de lago describe con éxito el proceso de eutrofización (exceso de enriquecimiento por los nutrientes, principalmente nitrógeno y fósforo) y se ha previsto, que uno de los efectos atmosféricos de un BRG sería una lluvia de compuestos de nitrógeno, lo que contribuiría a la eutrofización de los ecosistemas terrestres(Thorsett, 1995; Thomas y colaboradores, 2005). Esperamos entonces que nuestros resultados puedan resultar una medida
d es la tasa de descomposición de D. Llegamos así a
un lago dado evolucionará podría depender de varias variables y parámetros, donde el fitoplancton parece jugar un papel preponderante. Sin embargo, un modelado más exacto de la recuperación de los ecosistemas acuáticos después de un BRG necesita un estudio más detallado del comportamiento de las especies más comunes de fitoplancton bajo estrés RUV, y también de la inclusión de otras variables ambientales en consideración.Por otro lado, transiciones abruptas o cambios de regímenes entre posibles estados alternativos a escala global pueden generar un conjunto de serias implicaciones ecológicas a escala planetaria.La posibilidad de un cambio irreversible en la biosfera a nivel global podría tener consecuencias catastróficas para muchos ecosistemas terrestres incluyendo a la especie humana y debe ser un aspecto fundamental en la mayor parte de las políticas y estrategias de protección y recuperación de ecosistemas y del medio ambiente en general, que en una buena parte de ellas, presuponen un carácter lineal (Van Nes y Scheffer, 2004).3.2 Complejidad a nivel celularLa riqueza en el comportamiento exhibido por los sistemas biológicos puede considerarse, en última instancia, como una expresión de la naturaleza compleja de los seres vivos. Aunque en el primer capítulo se introdujo el tema, básicamente abordamos condiciones generales para el surgimiento de la vida en un contexto astrofísico o cosmológico, sin dedicar mayor atención al fenómeno de la vida y a las principales ideas acerca de su surgimiento. La inclusión de estos tópicos, de trascendencia universal, nos permite ganar en completitud de nuestro trabajo teniendo 72 en cuenta que consideramos escenarios terrestres en el periodo Arcaico o Hadeico hace unos 3.5 o 4.0 Ga atrás.Particularmente en el ámbito terrestre, pese al éxito posterior de los organismos fotosintéticos, existe cierto consenso en que las primeras formas de vida empleaban la quimio-síntesis como vía primaria para obtener la energía. Anterior a estos periodos, comienza lo que se ha dado a conocer la era prebiótica, marcada por la ausencia de cualquier forma o expresión de vida, independientemente del grado de organización.Grande es el nivel de incertidumbre con respecto a esta etapa, no solo en lo referentes a aspectos climáticos no resueltos aún, como la conocida paradoja del sol pálido (aspectos del tema en Grenfell y colaboradores, 2010), sino también a los procesos físico-químicos y de autoorganización que dieron lugar a la emergencia de un fenómeno, tan complejo y tan poco entendido, como es la vida. Varios son los enfoques recogidos en la literatura sobre esta problemática que van desde los más clásicos, como la formación de compuestos orgánicos claves en línea con el famoso experimento de(Miller y Urey, 1953), hasta los que implican principios aún no establecidos que involucran áreas fundamentales de la mecánica cuántica, los sistemas complejos y la teoría de la información (para una discusión general sobre estas temáticas consultarDavies, 2004).Durante esta etapa, la radiación juega un papel decisivo en la mayor parte de los procesos de síntesis y degradación de compuesto orgánicos que se establecen fundamentalmente en la atmosfera y en el océano. Es notable el número de mecanismos de reacción propuestos en la literatura donde la interacción con la radiación, básicamente con el UV, aparece explícitamente
extensión, el hábitat de los organismos fotosintéticos así como la eficiencia del propio proceso de la fotosíntesis.Por otro lado, las alteraciones bruscas del régimen fotobiológico asociados a eventos astrofísicos intensos como un BRG cercano puede ejercer un impacto significativo sobre varios componentes de la biosfera y particularmente sobre los productores primarios, variando en correspondencia de otros factores climáticos como los niveles de oxígeno y ozono libres en la atmósfera. Sin embargo, pese a ser un hecho factible, es muy difícil estimar de una manera clara, la posible repercusión que un evento de esta naturaleza sería capaz de desencadenar sobre la biosfera a nivel global, si tenemos en cuenta las complejidades intrínsecas manifiestas no solo a nivel de ecosistemas sino a nivel de la propia vida, interpretada como un fenómeno complejo. Los aspectos discutidos con anterioridad podrían resumirse a modo de conclusiones en: -La dinámica del Universo en general y de la Vía Láctea en particular condicionan cierto nivel de biofilia que se manifiesta, de manera más notable, en aquellas regiones dentro de las llamadas zona estelar habitable y zona galáctica habitable.-El régimen fotobiológico y sus posibles perturbaciones condicionan en buena medida la viabilidad, extensión y hábitat de los productores primarios fotosintéticos así como la eficiencia de procesos claves como es el caso de la fotosíntesis.-Modelar de manera detallada el impacto que tienen eventos como los BRG sobre la biosfera constituye una tarea extremadamente difícil si tenemos en cuenta, además de las considerables incertidumbres climáticas aparejadas a estos fenómenos, el comportamiento altamente complejo que exhiben todos los sistemas biológicos y particularmente los ecosistemas.
Apéndice AParámetros empleados en el modelo CASM. Los valores fueron tomados de(Amemiya y colaboradores, 2007).ParámetroValor Unidades
Extender los estudios sobre la influencia de las explosiones estelares en la tierra temprana con vistas a estimar posibles efectos fotoquímicos en atmósferas con composiciones variables de CO2 y metano fundamentalmente. Extender los estudios sobre la influencia de las explosiones estelares en la tierra temprana con vistas a estimar posibles efectos fotoquímicos en atmósferas con composiciones variables de CO2 y metano fundamentalmente.
Continuar el desarrollo de nuevos índices y criterios de daño biológico apropiados para este tipo de escenario. Continuar el desarrollo de nuevos índices y criterios de daño biológico apropiados para este tipo de escenario.
Explorar otros ecosistemas modernos de interés bajo el efecto sostenido de un incremento de las radiaciones ultravioletas. Explorar otros ecosistemas modernos de interés bajo el efecto sostenido de un incremento de las radiaciones ultravioletas.
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| sample_1445 | 0.9851 | arxiv | |
The modeling of the ENSO events with the help of a simple model
February 20, 2007
Vladimir N Stepanov
Proudman Oceanographic Laboratory
MerseysideEngland
The modeling of the ENSO events with the help of a simple model
February 20, 2007
The El Niño Southern Oscillation (ENSO) is modelled with the help of a simple model representing a classical damped oscillator forced by external forcing. Eastern Pacific sea surface temperature (SST) and the mean equatorial Pacific thermocline depth correspond to the roles of momentum and position. The external forcing of the system is supplied by short-period meridional mass fluctuations in the Pacific sector of the Southern Ocean due to the joint effect of the atmospheric variability over the Antarctic Circumpolar Current (ACC), bottom topography and coastlines, and also by the variability of westerly winds in the tropics. Under such conditions the ENSO-like oscillations arise as a result of propagation of signals due to both initial signals appeared in the Southern Ocean and the tropical westerly wind anomaly, that propagate then across the equatorial Pacific by means of fast wave processes. The external forcings are the main factor in establishing the oscillation pattern.
Introduction
Alvarez-Garcia et al. 2006 from a coupled global climate model simulation have identified three classes of ENSO events. The first two classes are characterized by well known paradigms: the first is the delayed oscillator where equatorial coupled waves produce a delayed-negative feedback to the warm sea surface temperature SST anomalies in the tropics (e.g., see Suarez and Schopf 1988); the second model is the recharge oscillator where fast wave processes adjust the thermocline tilt as a result of wind stress variability (see, e.g., Jin 1996). There is a strong coincidence between the minimums and maximums of this mass variability in the Pacific, and cold and warm ENSO events, respectively, i.e., short-term fluctuations in M(t) are related to the onset of ENSO events (the correlation coefficient between the mean summer's mass variability M(t) presented on Fig. 1 has not yet transformed into baroclinic ones. These anomalies can be transferred to low latitudes by the wave mechanism described by Ivchenko et al. 2004, henceforth IZD04, that subsequently interact with stratification changing the tropical thermocline tilt which can amplify an ENSO event. IZD04 showed that signals due to salinity anomalies generated near to Antarctica can propagate almost without changes of disturbance amplitude in the form of fast-moving barotropic Rossby waves. Such waves propagate from Drake Passage (where the ACC is constricted to its narrowest meridional extent) to the western Pacific and are reflected at the western boundary of the Pacific before moving equatorwards and further northwards along the coastline as coastally trapped Kelvin waves. Such signals propagate from Drake Passage to the equator in only a few weeks and through the equatorial region in a few months (henceforth denote via T B the period needed for anomalies from the Southern Ocean to reach low latitudes). In a more realistic coupled ocean-atmosphere general circulation model, Richardson et al. 2005 observed a similar rapid response of the Pacific to a similar density anomaly in the ACC. In reality, as it was described earlier, the density anomalies defining the ocean dynamics in the vicinity of the equator propagate very fast meaning that an equatorial Kelvin wave would take about 2 months to cross the whole Pacific and therefore, any density/pressure disturbances appeared in western tropics will be revealed in eastern ones very quickly by means of propagation of internal (baroclinic) Kelvin waves (see, e.g., Blaker et al. 2006).
Hence we can directly investigate the tropical variability at short periods by using the shorter period and decay time parameters than in BJO05 assuming that the propagation of short time scales of Kelvin waves and associated SST reaction lead to rise to interannual fluctuations that are only dependent on external forcing describing the variability of dynamics in the Southern Ocean and in the tropics.
Method and Results
The recharge oscillator of BJO05 is based on two equations for the T E and the h. A third equation describing the variability of bottom water thickness anomaly in the tropical western Pacific, z, is added here to parameterize the variability of the thermocline depth h due to the fluctuations of meridional fluxes in the Southern Ocean. For this case, the equations of BJO05 system can be rewritten as:
∂ t T E = -2γ T E + ω o h,(1)∂ t h = -ω o T E -2γ B h + ω B z,(2)∂ t z = -2γ B z + F ex ,(3)
where T=2πω -1 and T B =2πΩ -1 are the periods, and γ -1 and γ B -1 are the decay times describing the processes in the tropics and the middle latitudes respectively;
ω 2 =ω o 2 -γ 2 ; Ω 2 =ω B 2 -γ B 2 ;
and F ex denotes the external forcing. Bold font in (1) -(2) denotes the terms of the original BJO5 model. The terms with subscript "B" describe the processes of interaction between the Southern Ocean and the tropics, that are due to fast-moving barotropic Rossby wave processes from the Southern Ocean to low latitudes (see IZD04) and they are added in equations (1)-(3) similar processes for the tropics that will be described below.
The external forcing added in the equation (3) The statistical significance of all correlation coefficients presented in the paper is statistically significant at the 99% level that was determined via an effective sample size following
The effect of westerly wind variability in the model
It has been established that the onset of ENSO depends on equatorial wind anomalies in the western Pacific during the preceding spring and summer, though these wind anomalies can trigger the ENSO when the oceanic conditions in the tropical Pacific are favourable to the development of the ENSO (see e.g. Lengaigne et al., 2004). ). It can also be seen from Figure 2 that the short-period meridional mass variability in the Southern Ocean can be considered as a "favourable" condition to set up the ENSO. Figure 3 shows the correlation between the wind stress zonally averaged over the Pacific from the ECMWF reanalysis, <τ (1984) to maximize the signal-to-noise ratio) were used. However, model results slightly depend on the choice of these data.
The additional external tropical force F T which parameterizes the effect of westerly wind variability was added to the right side of equation (2) Besides, the Δτ T should be chosen in such a way that it is greater than the time delay due to the propagation of the signal in the tropics as the thermocline tilt adjusts to the variability of wind stress by means of wave processes. The SOI-index is defined as having the opposite sign to F T from convention since it corresponds to setting up a warm ENSO event when the wind in the tropics is weakened. This negative SOI is denoted SOI -.
Hence equation (2) becomes: Δτ T =4 months has no significant effect on the correlation between T E and NINO4-index.
∂ t h = -ω o T E -2γ B h + ω B z + F T ,(6)
Thus, this simple ENSO model is able to reproduce ENSO events very well.
The simplified forecast ENSO model
The modified system of the ENSO model (1)
∂ t h = -ω o T E + F ex + F T ,(7)
where t F ex (t,
Δτ) = C o /Δτ ∫ M(t) dt. (8) t-Δτ
Here C o is a scale factor and Δτ is the time delay due to the propagation of the signal from the Southern Ocean to the equator (IZD04). Thus, the effects of variability due to both M(t) and the westerly wind variability in the tropics averaged for the previous Δτ and Δτ T months will be used in the following numerical experiments.
Relying on IZD04's estimate of 4-6 months as the time needed for anomalies from the Southern Ocean to reach the low latitudes of the Pacific, the parameter Δτ in experiments was varied from 1 to 6 months. As in experiment E2, the parameter Δτ T =4 months was used.
The values of the scaling factors C o =6.3 and C T =12.6 were also adopted in this experiment so that the maximum amplitude of the total variability of T E is 1.6 o C and the contribution of both external forcings is comparable (it is about 1 o C for both F T and F ex ). The parameters T and γ in these experiments varied as in experiment E1
The equation system (1), (5) and (7)-(8) was solved numerically from 1951 onwards with the initial conditions T E | t=1951+Δτ =0, h| t=1951+Δτ =0 (henceforth experiment E3). A time shift in the initial conditions is determined by the lag between the external forcing in the Southern Ocean (see Fig. 1) and in the tropics (Fig. 3), and the onset of an ENSO event. The force F ex describing the effect of dynamic variability in the Southern Ocean, appeared in the system after 1985 that due to available model data for M(t). With model parameters T=2 months, γ -1 = 7 months, and Δτ T =Δτ=4 months the oscillations with the periods corresponding to ENSO were established in the system and reproduced all warm and cold ENSO events.
Summary
List of Figure Captions
However, Kessler 2002, argued that ENSO events are like disturbances with respect to a stable basic state, requiring an initiating impulse not contained in the dynamics of the cycle itself, and the initiation might be carried out by some other climate variation. The third class of ENSO events identified by Alvarez-Garcia et al. 2006 is characterized by a relatively quick development of ENSO events (less than 9 months after the changes of the above mentioned plausible exciting forcings in the tropics) and it supports the conclusion of Kessler 2002 about some initiating impulse. This article considers the variability arising from the joint effect of bottom topography, coastlines and atmospheric conditions over the ACC as an amplifier/trigger for ENSO events. Numerical experiments with the help of a barotropic ocean model (Stepanov and Hughes 2004) forced by 6-hourly global atmospheric winds and pressures from the European Centre for Medium-Range Weather Forecasts (ECMWF), have demonstrated that changes in wind strength over the ACC together with the effect of bottom topography induce some pressure/density anomalies in the Southern Ocean (Stepanov and Hughes 2006; Stepanov, submitted manuscript 2006 (see, also http://arxiv.org/abs/physics/0702159 , henceforth S06). These anomalies lead to short-period variations of meridional flows in the Pacific sector of the Southern Ocean to the north of 47 o S, that result in the mean value of daily water mass variability M(t) in the Pacific about of 500 Gt (Gigatonns) for a summer period preceding the cold or warm ENSO events (although the real water exchange between the Pacific and the Southern Ocean is more than an order of magnitude higher because of the link between the total meridional flux and mass flux in the western portion of the Pacific obtained in these numerical experiments). These mass variations are anticorrelated with the strength of the wind over the ACC at the 99% confidence level. All these above described features are clear seen from Figure 1, where the transport through Drake Passage and the daily mass variability in the Pacific Ocean M(t) ~ o ∫ t Q P (t) dt due to meridional transport fluctuations Q P through the latitude of 40 o S, averaged for July-September from the model's 20-year time series, are shown.
and the winter's NINO4-index (dashed line on Fig. 1) is 0.84 at the 99% confidence level). This meridional flux variability in the Pacific sector of the Southern Ocean can induce some short-period density anomalies in the vicinity of these regions with high meridional flux variability at the time scales of several months when the effect of barotropic changes
The above described mass variability in the Southern Ocean can significantly influence the tropics. The value of daily mass variability in the Pacific about 5000 Gt obtained by S06 (it takes into account the link between the total meridional flux and mass flux in the western portion of the Pacific) gives an estimate of the typical size of the signal arriving in the tropical Pacific. This signal is substantial, as a positive (negative) mass change corresponds to thermocline elevation (depression) in the tropics about 50 m over an area of 10 degree by 100 degrees in the period of 3 months. This signal propagates across the equatorial Pacific by means of short time scales of Kelvin waves and influences the tropical SST via the deepening (shallowing) of thermocline depth. Thus these wave interactions can define the interannual SST fluctuations in the tropics via the variability of dynamics in the Southern Ocean, i.e., as it was shown by S06, these interannual SST fluctuations are associated with the interannual variability of atmospheric conditions over the ACC in the preceding 4-6 months, which in turn, is initiated by the variability in the tropics in the preceding couple months. S06 proposed a plausible explanation of coupled interaction of the tropics and high latitudes and their influence on ENSO events which includes the following processes. Upper ocean warming (cooling) in the tropics (that, e.g., could be associated with a seasonal cycle) leads to an enhanced (decreased) heating in the upper troposphere over the tropical ascending region in the Pacific. It means warmer (colder) air is transferred by the Hadley cell from the tropics to the descending regions in the subtropics that slows down (speeds up) here the atmospheric downwelling which then weakens (strengthens) wind over the Southern Ocean. As it was mentioned earlier (due to the anticorrelation between mass variations in the Pacific and the strength of wind over the ACC), the weak (strong) wind over the Southern Ocean is associated with equatorward (poleward) mass flux in the Southern Ocean to the north in the vicinity of 47 o S that leads to the amplification of a warm (cold) ENSO signal via propagation of pressure/density anomalies from the Southern Ocean to the tropics by means of fast wave processes. The interaction between the tropics and the Southern Ocean depends on the stochastic processes of ocean-atmospheric interactions in these regions. A substantial role in these stochastic processes, as it was shown by S06, can be due to the mass flux variability in the Southern Ocean associated with the changes in atmospheric forcings over the ACC, and would the interaction between the tropics and high latitudes lead to the ENSO event or usual seasonal variability, depends on the processes in the Southern Ocean. Burgers et al. 2005, henceforth BJO05, presented the simplest form of the ENSO recharge oscillator model which is based on two equations: one for the eastern Pacific sea surface temperature anomaly T E and the other for the mean equatorial Pacific thermocline depth anomaly h with the damping on T E much stronger than the damping on h. The interaction between T E and h is characterized by the time delay between the east and the west of the Pacific that is due to both finite Kelvin wave speed and SST dynamics. In this paper authors have taken into account a parameterization of the fast wave process by which the thermocline tilt adjusts to the wind stress into the recharge oscillator. The parameters of the recharge oscillator model were obtained from two different methods, but both are based on a standard fit, that minimizes the rms error of model forecasts for the model variables and the observed values. This fit gives an oscillation period T and decay time γ -1 of about 3 and 2 years, respectively, since the observed periods of ENSO lie in the range from 2 to 4 years.
is defined as being proportionate to the scaled monthly averaged mass variability of M(t) in the Pacific Ocean due to meridional transport fluctuations through the latitude of 40 o S (i.e., | M(t)|≤1) from 1985 to the end of 2004 (S06) with the coefficient C o (F ex = C o M(t)). In the model this forcing describes the short period mass variability in the Pacific due to meridional transport fluctuations through the latitude of 40 o S which lead to the appearance of a cold (warm) temperature anomalies in the Southern Ocean (described by F ex in (3)), that are transferred to low latitudes by the wave mechanism by IZD04 (having the time scale of T B ). This increases (decreases) the bottom water thickness in the western Pacific, z, that leads to the elevation (depression) of the thermocline in the west equatorial Pacific. This mass surplus (lack) near the equator begins to disperse eastward as a so-called downwelling (upwelling) Kelvin wave resulting in deepening (shallowing) of the mean thermocline depth via the last term ω B z in (2) (it is similar to the term ω o h in (1) which describes the dependence of T E variability on the mean thermocline depth (with the time scale of T)). The terms with γ B define damping processes. Thus, the terms of equations (1)-(3) with subscript "B" properly describe processes in the model: the high (low) value of F ex (i.e., M(t)) leads to an increase (decrease) of variable z that increases (decreases) h, and T E increases (decreases) too. The periods and decay times in the experiments were varied across a broad range: from 1 till 10 for the period and from 1 till 36 months for the decay time. The SST anomalies averaged over the region between latitudes 5 o S and 5 o N, and between longitudes 160 o E and 150 o W of the Pacific (NINO4-index from http://climexp.knmi.nl) have been used for a comparison with the model T E .
Figure 2a .
2avalues for the M(t) and the NINO4-index for the model's period are presented in The correlation coefficient between the monthly averaged values of M(t) and NINO4 is 0.27. The positions of major peaks for these curves are consistent, though the M(t) curve displays more high frequency fluctuations than NINO4. The equation system (1)-(3) was solved numerically from 1985 onwards with the initial conditions: T E | t=1985 =0, h| t=1985 =0 (henceforth called experiment E1). With model parameters T=2 months, γ -1 = 7 months, and T B =5 months, γ B -1 = 10 months the oscillations with periods corresponding to ENSO were excited in the system. The value of parameter C o =1.3 was chosen in the experiment that corresponds to the maximum amplitude of variability of T E ∼ 1 o C. The upper solid and the middle lines on Figure 2a correspond to the scaled model SST T E and thermocline depth h obtained in this experiment. The oscillation of h leads that of T E by about 2 months and the majority of its variability is due to the M(t): the correlation of M(t) with h is 0.84. The correlation between model T E and NINO4 is 0.68. The percentage of variance explained was calculated to be about 43%. Figure 2b shows winter's T E and the NINO4-index (averaged during the three months from December to February when the warm or cold ENSO events usually achieve the maximum phase of their development) and, for comparison, the preceding scaled summer's mass variability of M(t) in the Pacific Ocean due to meridional transport fluctuations through the latitude of 40 o S. The latter is from the model's time series (S06), averaged from July to September. The correlation coefficient between winter's T E and the NINO4-index is 0.72 and the percentage of variance explained is about 48%. Experiments in which the values of the model parameters were varied show that the model results have little dependence on the choice of the period T B or the damping coefficient γ, but they are sensitive to the decrease of γ B -1 and the increase of T. The correlation between T E and NINO4 decreases with increasing of T (decreasing γ B -1 ) and drops to about 0.5 when T (γ B -1 ) equals to 6 (5) months. An increase in the parameter γ -1 leads to noisier behaviour of the variable h, but these changes are not significant for T E . It is seen clearly from Figure 2b that the warm ENSO events of 1986-87, 1991-92, 2003 and partly for 1997, along with the cold ENSO events of 1988-89 and 1998-2000 can be reproduced by this simple model. The warm and cold ENSO events occurred when the maximums and minimums of the ocean model's summer meridional flow from the Southern Ocean were observed, so the joint effect of atmospheric conditions over the ACC and bottom topography in the Southern Ocean could be considered as the mechanism amplifying (or may be triggering, since there is no other external forcing in the model) ENSO events. However, the warm ENSO event in 1994-95 was omitted by the model that demonstrates the nature of ENSO events is more complicated than this simple model, due to the interaction between the ocean and atmosphere over a much broader area.
) and winter's NINO4-index (averaged December-February). There are high correlations between ENSO and winds in the tropics, in the Trade Wind region and over the ACC. The interpretation of these high correlations is that weak winds in southern hemisphere set up warm ENSO events (for clarity the dashed line onFigure3 represents the scaled profile of time averaged <τ x >). As mentioned above, there is an anticorrelation between the strength of the wind over the ACC and the variability of meridional mass fluxes in the Pacific which in turn, is significantly correlated with winter's NINO4-index in the latitude band from 45 o to 35 o S (dotted line in Figure 3). From the value of correlation coefficient between the mean summer's M(t) and winter's NINO4 (~0.8), it can be calculated that the mean summer's M(t) describes about half of winter's NINO4-index variance. Thus the variability of wind over the ACC in the ENSO model is taken into account via M(t). To account for the effect of westerly wind variability in the tropics, the SOI-index will be used in the following experiments.
F
T (t,Δτ T )= -C T /Δτ T ∫ SOI(t) dt ≡ C T /Δτ T ∫ SOI -T is a scale factor; SOI is the scaled value, i.e. |SOI|≤1. The SOI contains both the long time scale component of the ENSO signal and noise components. To minimize the influence of noise on model results, the SOI averaged on the preceding interval Δτ T is used.
way to experiment E1. The value of parameter C T =5.1 was chosen in this experiment, so that the maximum amplitude of variability in T E corresponds to 1.6 o C and so the contribution of both external forcings to this variability would be comparable (that follows from the correlation coefficient between the M(t) and NINO4-index). The correlation between SOIand NINO4 for the period from 1985 to 2005 is 0.38 (though for 1950-2005 this coefficient is 0.57), increasing up to 0.62 at 4 months lag, where the SOIleads the NINO4-index (0.70 for 1950-2005). On this basis the parameter Δτ T =4 months was chosen and after that the correlation between the forcing F T (t, Δτ T =4) and NINO4 increased. The solution of the modified ENSO system is presented in Figure 4. All warm and cold ENSO events (including the warm ENSO event in 1994-95 omitted before) are now reproduced by this simple model. The analysis of the SOI-index and M(t) for 1994 shows that the previous failure to reproduce the ENSO of 1994-95 in experiment E1 was due to the presence of weak winds in southern hemisphere having low variability on time almost continuously during whole of 1994, that minimizes the joint effect of the variability of atmospheric conditions over the ACC on ocean dynamics in the Southern Ocean. However, the long-term weakness of westerly winds in the tropics leads to the onset of ENSO, which is now taken into account by the parameterization of the external tropical forcing. The correlation coefficient between the model T E and NINO4 is 0.83. The percentage of NINO4 variance explained by T E is more than 65%. The correlation coefficient between winter's T E and NINO4-index is 0.87, and the percentage of variance explained in this case is about 76%. Note that for the case of Δτ T =0 the correlation between the model T E and NINO4-index is 0.72 and the percentage of NINO4 variance explained by T E is 46%, i.e., the model results are similar to the results of experiment E1, when only forcing due to the effect of the Southern Ocean was taken into account. The choice of a larger scale factor C T for the model forcing due to the SOI, to obtain results comparable with the Southern Ocean contribution to variability in the eastern Pacific SST anomaly, demonstrates that the variability of ocean dynamics in the Southern Ocean makes a major contribution to the variability of tropical SST. Experiments in which the values of the model parameters (T and γ) were varied demonstrated a similar dependence to experiment E1. The variation of Δτ T (±2months) from
, (3) and (5)-(6) can be reduced for the forecast of ENSO events (similar to the model of BJO05) by the following representation of the expression for external forcings in the Southern Ocean:
The scaled values for SOI -(with a time lag of 4 months) and NINO4-index for the period from 1951 to 2005 are shown inFigure 5a. The behaviour of these curves are very similar (correlation coefficient is 0.70) though the original SOIcurve contains more noise than NINO4, that is natural for atmospheric pressure variability in comparison with SST. The upper (solid) and middle lines onFigure 5acorrespond to the model scaled values of SST, T E , and thermocline depth h obtained in experiment E3 for the period from 1951 to 2005. The variability in T E and h is observed to increase after 1985 when F ex is included.Figure 5bshows the curves of T E and h from 1985 in more detail. It can be seen that the oscillation of h leads that of T E by about 2 months, similar to experiment E1.The correlation coefficients for SOIand M(t) with model T E at 4-months lag, for the period of 1985-2005, are about 0.65 (SOIand M(t) lead T E ). In comparison, the correlation coefficient obtained for this period between the model T E and NINO4 is 0.82 (0.78 for 1951-2005). The percentage of variance explained is about 60% which is slightly less than in experiment E2. The correlation between the winter T E and the NINO4-index for 1985-2005 is 0.92 and the percentage of variance explained is about 84% that is slightly better than the results of experiment E2. Thus, this simple ENSO model is able to forecast ENSO events for 4 months in advance by using the model M(t) and SOI-index averaged for the previous 4 months. Experiments in which the values of the model parameters (T and γ) were varied demonstrated a similar dependence to experiment E1. Variation of Δτ from Δτ=4 months slightly decreases the correlation coefficient between T E and NINO4-index, decreasing by about 0.2 and 0.1 for Δτ=2 and Δτ=6, respectively. Hence, the Δτ=4 months is the optimum choice.
A modified version of the simple model of BJO05 which is a classical damped oscillator, with eastern Pacific SST and the mean equatorial Pacific thermocline depth representing momentum and position respectively, was used to model ENSO events. The main difference between the original BJO05 and the modified model is the presence of external forcings and the use of shorter period and decay time parameters meaning that the propagation of short time scales of Kelvin waves and associated SST reaction lead to rise to interannual fluctuations that are completely dependent on external forcings describing the variability of dynamics in the Southern Ocean and in the tropics. The external forcings in the model are parameterized by the short period mass variability in the Pacific sector of the Southern Ocean due to meridional transport fluctuations through the latitude of 40 o S, and the SOIindex (defined with the opposite sign to convention). The first forcing describes the variability due to the joint effect of the atmospheric variability over the ACC, bottom topography and coastlines in the Southern Ocean; the second forcing describes westerly wind variability in the tropics. Both forcings are results of coupled interactions between the tropics and high latitudes. Under such conditions oscillations arise in the ENSO system as a result of propagation of signals due to both initial signals appeared in the Southern Ocean and the tropical westerly wind anomaly, that propagate then across the equatorial Pacific by means of fast wave processes. The external forcings are the main factor in the establishment of the oscillation pattern in the ENSO forecast. To obtain results comparable with the Southern Ocean contribution to variability in the eastern Pacific SST anomaly, a larger scale factor for the model forcing due to the weakness of westerly winds in the tropics was chosen. It demonstrates that the variability of ocean dynamics in the Southern Ocean makes a major contribution to the variability of tropical SST though it is initiated by the variability in the tropics in the preceding couple months. However, the westerly wind variability in the tropics becomes more important when weak westerly winds established in the tropics during very long periods (about year) leading to the onset of ENSO, while weak winds in southern hemisphere having low variability on time minimize the joint effect of the variability of atmospheric conditions on ocean dynamics in the Southern Ocean. It was shown that this simple ENSO model is able to forecast the ENSO events for 4 months in advance by using the short period model mass variability in the Pacific sector of the Southern Ocean due to transport fluctuations through its open boundary, along with the SOIindex, each averaged over the previous 4 months. A model skill of 0.92 for a four-month lead forecast of the December-February ENSO is comparable with the correlation between August-September NINO4-index and the subsequent December-February NINO4-index and it may be seemed not so impressive. The most important point of these model results is the establishment of two major and comparable feedbacks (in a system with so many feedbacks and connections) responsible for the onset of ENSO, accounting for about 84% of the percentage of variance explained: -short-period meridional mass fluctuations in the Pacific sector of the Southern Ocean due to the joint effect of the atmospheric variability over the ACC, bottom topography and coastlines;-the variability of westerly winds in the tropics.
Fig. 1 -
1The values of transport through Drake Passage in Sv (thin solid line) and daily mass variability M(t) in the Pacific Ocean due to meridional transport fluctuations through the latitude of 40 o S in Gt (Gigatonns) (thick solid line) averaged for July-September. Symbols EL and LA denote warm and cold ENSO events, respectively. Dashed line corresponds to scaled winter's NINO4-index.
Fig. 2 a
2-Mass variability M(t) due to meridional transport fluctuations through 40 o S in the Pacific Ocean (the lowest line), scaled by a maximum of its value, the thermocline depth anomaly, h (middle line), the SST anomaly, T E (upper solid line) and the NINO4-index (upper dashed line) for the period from 1985 to 2005; the value of NINO4-index is scaled by a factor of 1.6; bthe winter T E (solid line) and NINO4-index (averaged from December to February) (dashed line) and the preceding summer's M(t), averaged from July to September (dashed-dotted line).
Fig. 3
3The correlation coefficient: dotted line for the meridional summer's mass fluxes averaged from July until September and solid line for the zonal wind stress over the Pacific averaged from June to September, each with winter's NINO4-index (averaged during three months from December until February). The dashed line represents the scaled profile of time averaged zonal wind stress. The positive sign corresponds to the eastern direction.
Fig. 4
4As Figure 2 but for experiment E2.
Fig. 5 a
5-the scaled values for SOIindex with a 4 months time lag (the lowest line), the thermocline depth anomaly, h (the middle line), the SST anomaly, T E (upper solid line) and the NINO4-index (the upper dashed line) for the period from 1951 to 2005; the value of NINO4-index and T E are scaled by a factor of 1.6; bthe scaled winter's T E and NINO4index with preceding mean summer's model M(t) and SOIindex (top); h, T E and the NINO4-index for the period from 1985 to 2005 (bottom).
Figure 1
Figure 5
5Figure 3
The SOI-index is defined as the normalized atmospheric pressure difference between Tahiti and Darwin, i.e. the higher SOI-index, the stronger tropical wind. There are several slight variations in the SOI values calculated at various centres. In following experiments the series from 1950 onwards calculated by the method ofRopelewski and Jones (1987) (obtained from the website http://climexp.knmi.nl) and data by Trenberth (http://www.cgd.ucar.edu/cas/ catalog/climind, where the standardizing is done using the approach outlined by Trenberth
Acknowledgments. This work was funded by the Natural Environment Research Council.Thanks to Simon Holgate for commenting on this manuscript.
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| sample_1452 | 0.7557 | arxiv | |
Future climate trends from a first-difference atmospheric carbon dioxide regression model involving emissions scenarios for business as usual and for peak fossil fuel
April 2014
L M W Leggett
Global Risk Policy Group Pty Ltd
D A Ball
Global Risk Policy Group Pty Ltd
Future climate trends from a first-difference atmospheric carbon dioxide regression model involving emissions scenarios for business as usual and for peak fossil fuel
April 2014
This paper investigates the implications of the future continuation of the demonstrated past strong correlation between first-difference atmospheric CO2 and global surface temperature. It does this, for the period from the present to 2050, for a comprehensive range of plausible future fossil fuel energy use scenarios. The results show that even for a business-as-usual (the mid-level IPCC) fossil fuel use estimate, global surface temperature will rise at a slower rate than for the recent period 1960-2000. Concerning peak fossil fuel, for the most common scenario the currently observed temperature plateau will in the near future turn into a decrease. The observed trend to date for temperature is compared with that for global climate disasters: these peaked in 2005 and are notably decreasing. The temperature and disaster results taken together are consistent with either a reduced business-as-usual fossil fuel combustion scenario into the future, or a peak fossil fuel scenario, but not with the standard business-as-usual scenario. If the future follows a peak fossil fuel pathway, a markedly decreasing trend in global surface temperature should become apparent over the next few years. If entertained, these results are evidence that the climate problem may require less future preventative action. If so, the same evidence is support for the case that the peak fossil fuel problem does require preventative action. This action is the same as it would have been for climatethe rapid transition to a predominantly renewable global energy system.
Introduction
Energy from fossil fuel is of fundamental importance to the functioning of society. It is axiomatic therefore that estimation of the range of possible future trends in fossil fuel production is essential for planning worldwide (OECD 1999;International Energy Agency 2013). First, the amount of future fossil fuel estimated to be available affects the mix of energy sourcesfossil fuel or non-fossil fuelestimated to be required for combustion for energy provision. If the future amount of fossil fuel is estimated as less than global demand, the gap between supply and demand must be closed. This can be achieved by demand reductionsocietally difficultor by supply increase, from nonfossil fuel sources. Second, negative externalities from emissions from fossil fuel burning -local (respiratory) and/or global (climate change) -will also vary depending on the future trend trajectory.
This last question, of the character of climate change expected from the atmospheric carbon dioxide contributed to by fossil fuel combustion, has taken on further complexity since Leggett and Ball (2014) showed that the rate of change of atmospheric carbon dioxide leads and is closely correlated to global surface temperature. The rate-of-change relationship means that temperature, and possibly other aspects of climate, are more sensitive to the change of atmospheric carbon dioxide than if the sensitivity were simply linear. For this reason, the question of future scenarios concerning atmospheric carbon dioxide deserves revisiting, because the same atmospheric-CO2 future scenarios may have a more dynamic and immediate effect on climate variables than previously entertained. This paper addresses these questions. It does so by the following means.
For the period up to 2050 the paper first from the literature outlines (a) a cross-section across the full range of proposed anthropogenic emissions scenarios; and (b) using these, by linear regression analysis derives indicative future atmospheric CO2 levels. The paper then depicts future global surface temperature levels which have been published from previous modelling analyses; Finally, for the afore-mentioned range of indicative future atmospheric CO2 levels, translates these into rates of change (in terms of the first derivative (first difference)). For the period 1850 to 2050, these past results to 2012 and future projections are compared with trends in climate observations, first for global surface temperature and second for global climate disasters.
Methods
To make it easier to visually assess the relationship between the key climate variables, most data are normalised using statistical Z scores (also known as standardised deviation scores) (expressed as "Relative level" in the figures). In a Z-scored data series, each data point is part of an overall data series that sums to a zero mean and variance of 1, enabling comparison of data having different native units. See the individual figure legends for details on the series lengths. The period covered by the specific Z-score is shown on the figure as, for example, "Relative trend Z1960-2013".
In the study, no attempt is made to translate results from Z-scores back to levels of temperature or numbers of climate disasters. This is because the aim is primarily to show trends and turning points, not, for example, to project specific values for global temperature.
The investigation is conducted using linear regression. Global atmospheric surface temperature and the annual number of global climate disasters are the dependent variables. For these two variables, we tested the relationship between (1) the level of atmospheric CO2 and (2) the change in the level of atmospheric CO2. We express these CO2-related variables in terms of the first finite difference, which is a convenient approximation to the first derivative (Hazewinkel, 2013). It is noted that there is a considerable background to the use of the rate of change of atmospheric CO2including in first difference formin climate studies -for example, Kaufmann et al. (2006).
When change in a data series is expressed as the result of subtracting the value for the previous year from that of the current year, the resulting series is termed a first differences series. It is noted that a first differences series differs from one involving percentage change in that the first differences series preserves the relative scale of the change.
Variability is explored using both intra-annual (monthly) data and interannual (yearly) data. The period covered in the figures is shorter than that used in the data preparation because of the loss of some data points due to calculations of differences and of moving averages.
The quantification of the degree of relationship between different plots was carried out using regression analysis to derive either the correlation coefficient (R) or the coefficient of determination (R 2 ) for each relationship. Student's t-tests were used to determine the statistical significance of the correlations.
Annual data is presented unsmoothed. For monthly data, smoothing methods are used to the degree needed to produce similar amounts of smoothing for each data series in any given comparison. Notably, to achieve this outcome, series resulting from higher levels of differences require more smoothing. Smoothing is carried out initially by means of a 13-month moving averagethis also minimises any remaining seasonal effects. If further smoothing is required, then this is achieved by taking a second moving average of the initial moving average (to produce a double moving average). This is performed by means of a further 13 month moving average, to produce a 13 x 13 moving average.
Data sources
The following are the data series used in this analysis and their sources. Unless otherwise stated, as long time series as reasonably practicable are used in this analysis. At its maximum, this period is 1850-2050. This perspective can provide the fullest possible indication of (i) the existence of common patterns and (ii) the relative scale of changes and their relative long-run frequency -including their relative unprecedentedness or otherwise.
Further details of data sources are given in Table 1.
Results
In what follows, for clarity: (i) results are cumulated iteratively, one result at a time; and (ii) in the figures each new result added to the pre-existing group of curves is depicted in red.
Results are grouped under three subheadings: global surface temperature; global climate disasters; and future scenarios for global fossil fuel consumption.
Global surface temperature The group of curves in Figure 1 shows the very close agreement between the model for CO2 and both the two models CIMP3 (earlier) and CIMP5 (more recent). The graph shows the dominance of the temperature projections by the linear level of CO2. Given Figure 2 illustrates the start point of this study: the familiar and much discussed topic that over the last 10 years or so the temperature trend has started to statistically significantly diverge from the average projection of current climate models (Fyfe et al. 2013). Figure 2 shows that the trend in observed atmospheric carbon dioxide to 2012 does not throw light 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0
Relative trend (Z1861-2050)
Proj. atmos. CO2 (RCP4.5 CMIP5 model)
Proj. temp. (RCP4.5 CMIP3 model) Proj. temp. (RCP4.5 CMIP5 model)
on this point: it closely followsin fact is slightly higher than -the IPCC temperature trend. A range of models other than the IPCC projections exist. An illustrative example is the model of Lean and Rind (2009). The trend projected for this model is added to the suite of trends from the previous figures in Figure 3. This trend is lower than the IPCC midrange projections, but higher than the observed temperature trend in recent years. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0
Relative trend (Z1960-1998)
Proj. atmos. CO2 (RCP4.5 CMIP5 model)
Observed temp.
Observed atmos. CO2 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 The relationship in monthly terms between first-difference atmospheric carbon dioxide and global surface temperature is shown from 1958 to 2013 in Figure 5. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 As shown in Leggett and Ball (2014), but with data now updated to early 2013, the enlarged figure shows clearly the very close similarity between the first-difference carbon dioxide and the temperature signatures. Visual inspection leaves very much the impression that the one curve may depart from the other from time to time but that if this happens the curves soon come back into synchronisation again. This is true over the entire period of the data involving some 600 data points. Using an accepted convention (Comer and Gould, 2011) the degree of correlation is considered strong (R = 0.70), and the statistical significance of the correlation is extremely high (P=7.02E-98). Correcting for autocorrelation with the Cochrane-Orcutt procedure leads after four iterations to a Durbin-Watson statistic of 2.08 (showing little or no remaining autocorrelation) and a lower statistical significance, but one which is still high, of 0.00011. 1958 1960 1963 1965 1968 1970 1973 1975 1977 1980 1982 1985 1987 1989 1992 1994 1997 1999
Global climate disasters
Next, what is the situation for the trend concerning climate outcome categories other than temperature? One such group is climate disasters, for which the standard categories are wildfire, heat wave, drought, flood and storm (EM-DAT, 2013). In considering the trend for climate disasters it is recognised (for example, Guha-Sapir and Below, 2002) that for earlier decades due to poorer reporting there may be greater amounts of missing data.
To minimise issues concerning possible missing data in earlier decades, based on an empirical assessment (see Supplementary 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2
Number of climate disasters
Drought Flood Storm Wildfire
Heat wave Total
The figure shows that, although the number of events per year and timing of peaks vary, all disaster types without exception show a peak and then a decrease.
The counts for individual OECD climate disaster types are summed into a total category termed OECD climate disasters. In Figure 7 this trend is superimposed over those depicted in Figure 4. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0
Relative trend (Z1960-2013)
Proj. atmos. CO2 (RCP4.5 Figure 8 illustrates the data for the period. Correlation coefficients for and the statistical significance of the relationships between the trends in Figure 8 are displayed in Tables 2 and 3. Table 2 shows that the largest correlation coefficient (R=0.734) between a CO2 model and temperature is for the correlation between temperature and the first-difference atmospheric CO2 model. This correlation is statistically significant (P= 0.0012). Table 3 shows that the relationships between aggregate climate disasters and all but firstdifference atmospheric CO2 display strong correlations but have negative coefficients.
Each of these relationships is highly statistically significant. As climate disasters are count data, results are from log-linear regression (Poisson distribution selected). Table 3. Correlation coefficients for and the statistical significance of the relationships between temperature models and the observed and the observed trend in global climate disasters. Green: substantial correlation and/or statistically significant; orange: correlation of wrong sign or not statistically significant. Figure 8 show that there is little correlation between climate disasters and temperature and first-difference CO2 for the period after the 1998 peak. For the full period for which climate disaster data is used however -1960 to 2013a clear similarity in trend is seen (Figure 9). The correlation coefficient for this relationship is high (Pseudo R² (Cox and Snell) = 0.998), and the relationship is highly statistically significant (P<0.0001)). 3.00 1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 9 1 9 7 2 1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 2 0 0 2 2 0 0 5 2 0 0 8 2 0 1 1
Independent variable
relative value (Z-score)
Global surface temperature
Global climate disasters (OECD)
This study has shown, then, statistically significant evidence that, after 1998, two climate outcomesglobal surface temperature and global climate disasters -on the one hand no longer increase with the increasing linear atmospheric CO2 trend and on the other -for temperature -do follow the first-difference atmospheric CO2 trend. For climate disasters the trend decreases statistically significantly as linear CO2 increases. It is also shown that, as for temperature, it is likely that climate disasters are also following first-difference CO2.
Effect of future scenarios for global fossil fuel consumption
With this evidence presented for links between climate outcomes and rate of change of CO2, what might plausible future scenarios look like, first for the trend for atmospheric CO2, and then for resulting climate outcomes under a first-difference CO2 model?
The major modern source of atmospheric CO2 is emissions from the combustion of fossil fuels. The RCP4.5 atmospheric CO2 trend reflects the notion that fossil fuel production into the future will roughly follow demand and continue to rise (Meinshausen et al., 2011). Other business-as-usual models also exist.
A key element of current modelling is the extent to which "unconventional" fossil fuels such as gas generated by hydraulic fracturing and oil from sources such as tar sands may change future expected global fossil fuel production. One business as usual study which explicitly incorporates unconventional fossil fuels is that of BP (2013). There has been a substantial and statistically significant linear correlation between anthropogenic CO2 emissions and atmospheric CO2 from 1959 to 2012 (Supplementary Information Figure 9). If the proposed BP (2013) output per year to 2030 translates by the relationship to date to the amount of carbon dioxide per year present in the atmosphere (for derivation see Supplementary Information, section 2), the following curve (red) in Figure 10 results.
It can be seen that this current (2013) estimate is -even allowing for unconventional fossil fuels -for lower emissions growth than expected in the RCP4.5 model. As well, a slightly but steadily decreasing growth rate is projected in the BP (2013) study. The alternate view to that of the IPCC and BP (2013) is that fossil fuel production will peak. Figure 11 adds to the trends depicted in previous figures one (red curve) based on a peak fossil fuel scenario. This scenario is that of Nel and Van Zyl (2010) modified for the present study after Laherrere (2012) to allow for recent amended estimates of fossil fuel production from unconventional sources of the types assessed by BP (2013). Even with the addition of unconventional fuels, the Laherrere (2012) projection is that global fossil fuel is expected to peak in the mid-2020s and then to show a gradual decline. This peak fossil fuel trajectory is given in Figure 11.
It is noteworthy that the peak fossil fuel scenario shows a peak like that of the climate events, but it is some 20 years into the future (and see below). 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 Figure 11. Data as for Figure 9 except that projected atmospheric CO2 derived from projected anthropogenic CO2 emissions (BP 2013) is depicted in mid blue and projected atmospheric CO2 (peak fossil fuel model) (see text) is added (red curve).
The following figures take the linear atmospheric CO2 future level in Figure 8 and previous figures and express these as growth in first difference terms analogous to that shown for the actual data for the period 1958 to 2013 in Figures 8 and 9.
In Figure 12 the first difference of the IPCC atmospheric CO2 estimated trajectory for the RCP 4.5 is given. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 Figure 12 shows that the first difference RCP 4.5 trajectory reaches a maximum at about 2030 and then shows a slight decrease thereafter. It is noted that the RCP4.5 future trajectory is modelled as a smooth curve and thus its first difference shows less interannual variation than generated from the observed atmospheric CO2 data introduced in figure 8. That said, this is not important for the purpose of this paper, which is to estimate broad trajectories into the futureup or down, more or less, not year on year change.
In Figure 13 the first-difference of the BP 2013 scenario to 2030 is given. This firstdifference trend is markedly different to that for RCP 4.5, with a decrease shown from as soon as 2013 on. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 Figure 13. Data as for Figure 11 except that the first-difference transformation of the RCP4.5 (CIMP5) model is depicted in light blue and the first-difference transformation of projected atmospheric CO2 from projected anthropogenic CO2 emissions (BP 2013) is added (red curve).
In Figure 14, the first-difference trend for the peak fossil fuel scenario to 2050 is added. 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 -2 0 2 4 6 8 10 12 1 8 6 1 1 8 7 0 1 8 7 9 1 8 8 8 1 8 9 7 1 9 0 6 1 9 1 5 1 9 2 4 1 9 3 3 1 9 4 2 1 9 5 1 1 9 6 0 1 9 6 9 1 9 7 8 1 9 8 7 1 9 9 6 2 0 0 5 2 0 1 4 2 0 2 3 2 0 3 2 2 0 4 1 2 0 5 0 This first-difference peak fossil fuel scenario shows the most marked decrease of all the first-difference scenarios shown. The scenario seems on the face of it hard to entertain.
Yet it should be borne in mind that never before over the whole period depicted from 1850 has the absolute amount of CO2 in the atmosphere decreased, as happens in the peak fossil fuel scenario.
Concerning temperature, Figure 14 overall shows that it has shown considerable variation over the period from the 1850s to the present so that its change in trend since 1998 is not unprecedented. For climate disasters, however, the situation is different. Albeit over the shorter period from 1960 to the present, the decrease since 2005 is unprecedented. When the correlation between temperature and disasters and between temperature and first difference CO2 from 1960-2013 is then recalled, this suggests that, taken together, the two climate categories studied -global atmospheric surface temperature and total climate disasters -have tended to follow either the first-difference BP or the first-difference peak fossil fuel future scenarios. Entertaining this, the long time-perspective given by the figure --commencing in 1850 -enables the observation that, the global climate is about to enter an unprecedented period.
Discussion
In this section, the following is considered: the implications of the results for current scientific stances; precedents for use of first difference rate of change in public policy;
implications of the results for scenario-based risk analysis; and implications for energy policy.
Implications of this work for current scientific stances
While generating differences, a strong case can be made that this work is nonetheless consistent with current climatology.
The differences are twofold.
First, the concept that the rate of change of atmospheric CO2 has a role in the trend in climate event frequency can be seen to be consistent with current climatology. This is because it is possible that the rate effect has not been revealed until now because there has not in the modern era until now been in existence a previously large monotonically increasing forcing which has started to decrease. So it would seem that climatology might develop because of this --it would not be that part of current climatology was "wrong".
A second point is that the first difference view provides some very clear signature matchesstatistically significant correlationsbetween anthropogenic inputs and climate variable outputs. This provides additional strong evidence supporting the notion of the dominant effect of human activity on current climate.
In particular, much of short term climate variation that might have been considered noise (for example, Karl et al., 2009) can now be considered signal. (While beyond the scope of this paper, the noise-like appearance of this signal opens the possibility that it might be noise from the plant biosphere photosynthesis system. In other words, noise from one system acting as a signal to another system.)
Precedents for use of first difference rate of change in public policy
The fact that the climate curves match the atmospheric CO2 trend in first-difference form The above excerpt shows a rate of change series being used by a well-established mainstream organisation, the OECD, to predict a future trend change in the raw series a substantial number of periods ahead.
Translating this thinking to the present topic could mean the following. If future climate event trends follow 2012 along the peak fossil fuel scenario trajectory, this will mean observed real-world climate trends will be acting as a leading indicator that peak fossil fuel is arriving within the timeframe predicted by published studies such as Nel and Cooper (2010).
Considering first-difference CO2 as a leading indicator potentially enables two major insights. First, it is an answer to the question of why this hinge of history-like turn is happening now. Second, so answered, the trends are also a harbinger that peak fossil fuel is a scenario to take seriously.
Implications of results for scenario-based risk analysis
The use of scenario-based risk-analysis perspectives is widely supported including by the IPCC (Klein et al, 2007): "… a robust decision framework is suitable for analysing the array of future vulnerabilities to climate change." The above trends would enable a recommendation that there would be benefit from including the first-difference scenario alongside the pre-existing scenarios shown in the earlier figures in monitoring future climate outcomes and that public policy planning and implementation was such that it would be robust against the first-difference potential outcome as well as other existing potential outcomes.
It must be admitted that it is hard to believe that the proposed future trajectory from 2014 for first difference peak fossil fuel could possibly happen. But yet, in 1950, it would have been hard to believe that the rapid rise which was to come up to the year 2000 would happen, yet it did.
In the same way that some IPCC models predict an unprecedented 8 degrees hotter by 2100 , and that is not on trend to coming true, the first-difference peak fossil fuel prediction also may not come true. Nonetheless, the IPCC had to report what their model said, and so must we.
It is noted that it can be claimed that the mean IPCC model is so far not coming true (Fyfe 2013)possibly because of unforseen feedbacks (Leggett and Ball 2014). The future may show that the same may turn out to be true for the first-difference peak fossil fuel model.
All the above said, and noting it is important to stress that the future rate of change of CO2 scenario is a scenario not a prediction (not a guarantee), it can now be monitored.
Forewarned is forearmed.
Implications for energy policy
A feature of the first differencing method is the evidence it provides that climate trends in existence now may be leading indicators to a forthcoming peak in fossil fuel production.
As stated above, this possibility suggests that climate trends should be monitored against both first difference modelsbusiness as usual and peak fossil fueluntil which of the two pathways being followed becomes clear.
If future events lean to the peak fossil fuel pathway, with the implications for future climate depicted above, it is stressed that peak fossil fuel is itself a global risk. If such implications for future climate come about, it will be so because there is a new plank in the case that the peak fossil fuel risk is real.
A metaphor therefore is that you are at your doctor's. You are told that you do not have the heart disease it was thought you had. So you are happily entertaining not having to undergo the stringencies of the diet and exercise treatment which had been prescribed.
But just as you do, your doctor then goes on to say that he has found you have a cancer.
And the treatment for that is --exactly the same as for the heart disease! 4) accounting bias, which underreports indirect, uninsured, and others losses; 5) geographic bias, which generates a spatially distorted picture of losses by over-or underrepresented certain locales; and 6) systemic bias, which makes it difficult to compare losses between databases due to different estimation and reporting techniques.
With the above background, the EM-DAT disaster events database (Centre for Research on the Epidemiology of Disasters, Ecole de Sante Publique, Universite Catholique de Louvain, Brussels, Belgium) (EM-DAT 2013) is chosen as it is, as mentioned, widely used, for assessment of the extent in the database of the biases listed by Gall (2009).
In the EM-DAT database, climate disaster types are coded into four main categories: extreme temperature, flood, storm, drought and wildfire. The extreme temperature category is further is made up of two main sub-typesheat wave and cold wave. In this study the heat wave sub-type is used. Trends in theses categories are assessed against the six bias risks listed by Gall (2009).
1) Hazard bias; 2) Temporal bias; 5) Geographic bias
If there is temporal bias it should be less apparent in countries with on average higher GDP per capita. The following figures show relative phasings of peaks in event time series by continent and climate disaster type.
Supplementary figure 1. Flood disasters by continent: relative trend (Z scores) and polynomial curve of best fit (total cases: 3726) 3.00 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2 The preceding figures show that climate disaster categories tend to show single peak years. These peak years tend to differ by disaster type, but per disaster type, with a minority of exceptions, to coincide across continents. This tendency is greater for disasters for which there is the largest number of cases. These results are summarised in Supplementary table 1. 2) Temporal bias Barredo (2009) noted that a simple assessment of the number of damaging events included in the flood data he studied built up from the EM-DAT database and other sources revealed that in the first half of the assessment (1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988) there were 32 events, whereas in the period 1989-2006 there were 90. He suggested that this difference went reasonably beyond natural variability or societal changes and could therefore be attributed to inaccuracies in the accounting of the events.
This question is explored further by comparing the disaster event trend with that of an external trend.
In doing so, we note that it is considered that records are reasonably complete for major disaster types in some countries from 1970, so similarity with a valid external comparator should occur at least from this start date.
It can be seen that in Supplementary figure 6 covering the period 1960 to 2003 climate disasters show a relationship to the level of CO2 which is very close to linear. This supports the above statement of reliable data from 1970, and further is support for taking that view back at least to 1960. Hence this start year is used in this study. Atmospheric CO2
Climate disasters
How does data from the rest of the world compare? Supplementary figure 7 shows that both curves increase monotonically to the early 2000s, and as expected the non-OECD curve is somewhat more non-linear that the OECD curve. Nonetheless both curves show a decrease as the 2000s wear on (see main account).
Figure 1
1shows data for the mid-range (van Vuuren et al. 2011) IPCC representative concentration pathway RCP4.5 scenario. The figure shows: modelled atmospheric carbon dioxide; and the projected global surface temperature for the multi-model means for models run (a) during 2005 and 2006 (http://cmippcmdi.llnl.gov/cmip3_overview.html?submenuheader=1) for the 2007 Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) (phase 3 of the Coupled Model Intercomparison Project (CMIP3) and (b) up to generally 2012 for the Fifth Assessment Report (AR5,2013) (CMIP5). (The Representative Concentration Pathways (RCPs) are a set of four new pathways developed for the climate modelling community as a basis for long-term and near-term modelling experiments The four RCPs together span the range of radiative forcing values calculated to year 2100 found in the open literature.)
this close similarity, for simplicity in the following figures the linear RCP4.5 CO2 projection is used to indicate the broad trajectory of the IPCC mid-range bundle of curves. The figure shows that both the earlier model averages run in the 2006-7 period and the later from 2012 are closely similar to each otherthe later model average being slightly higher to 2030 -and that both the overall models are throughout dominated by the level of atmospheric CO2.
Figure 1 .
1The relative trend (Z-scores) in historic and simulated time series of atmospheric carbon dioxide and the anomalies in annual global-mean surface temperature for the mid-range (van Vuuren et al. 2011) IPCC representative concentration pathway RCP4.5 scenario. All simulations use historical data up to and including 2005 and use RCP4.5 after 2005. The figure shows: modelled atmospheric carbon dioxide (blue curve); and the projected global surface temperature for the multi-model means for models run (a) during 2005 and 2006 (http://cmippcmdi.llnl.gov/cmip3_overview.html?submenuheader=1) for the 2007 Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) (phase 3 of the Coupled Model Intercomparison Project (CMIP3) (purple curve) and (b) up to generally 2012 for the Fifth Assessment Report (AR5,2013) (CMIP5)(yellow curve).
Figure 2
2utilises the RCP4.5-scenario-modelled atmospheric carbon dioxide from Figure 1 to represent both itself and, given their demonstrated close similarity shown in Figure 1, the two RCP4.5 temperature series. Added to this in Figure 2 are the observed global surface temperature and the observed seasonally adjusted level of atmospheric carbon dioxide as measured at the Mauna Loa atmospheric station (NOAA, 2013).
Figure 2 :
2RCP4.5-scenario-modelled atmospheric carbon dioxide fromFigure 1(blue curve) standing for itself and, given their demonstrated close similarity, the two RCP4.5 temperature series shown inFigure 1; observed seasonally adjusted level of atmospheric carbon dioxide as measured at the Mauna Loa atmospheric station (light blue curve); and observed global surface temperature (Hadcrut4; ref) (red curve) for the period 1850 to 2013.
Figure 3 .
3Data as for Figure 2 except that the curve for observed global surface temperature (Hadcrut4; ref) 1850 to 2013 is now depicted in lilac; and the global surface trend projected to 2030 from the regression model of Lean and Rind (2009) is added (red curve).
Figure 4
4shows however(Leggett and Ball 2014), that the annual change in atmospheric carbon dioxide --expressed in terms of first differences --does show a levelling off similar to that of temperature.
Figure 4 .
4Data as for Figure 3 except that the global surface trend projected to 2030 from the regression model of Lean and Rind(2009)is depicted in light blue; and the smoothed (13 month moving average) first difference of observed atmospheric CO2 is added (red curve).
Information), data used in the following section is (i) limited to OECD countries and (ii) commences in 1960. That said, the series for both OECD countries and the rest of countries are similar, and in particular (Supplementary Figure 7) each shows peaking in climate disasters between 2000 and the present.
Figure 6
6shows the trend in counts per year for OECD countries from 1960 to 2013 for each of wildfire, heat wave, drought, flood and storm (EM-DAT 2013).
Figure 6 .
6OECD countries: number of disasters per year from 1960 to 2013 for each of wildfire, heat wave, drought, flood and storm (EM-DAT 2013
Figure 7 .
7Data as for Figure 4 except that the smoothed (13-month moving average) first difference of observed atmospheric CO2 is depicted in mid blue; and observed total OECD climate disasters are added (red curve).
Figure 7
7shows that the OECD climate disaster trend for 1960 to 2013 shows a clear peak (around 2005) followed by a steady decrease since then. Such a peak and decline is unprecedented over the half-century period depicted. The slope of this decreasing trend since 2005 is seen to depart even further from the linear CO2 trend and that proposed for temperature byLean and Rind (2009) than the previously shown global surface temperature and atmospheric CO2 curves.
Figure 8 .
8Depiction of annual data from 1998 to 2013 used for linear regression analysis to assess statistical significance of differences between observed and modelled climate trends
Figure 9 .
9Annual tropical surface temperature and global climate disasters 1960
Figure 10 .
10Data as forFigure 6except that total observed OECD climate disasters is depicted in pink and projected atmospheric CO2 derived from projected anthropogenic CO2 emissions (BP2013) is added (red curve).
Figure 12 .
12Data as forFigure 10except that projected atmospheric CO2 (peak fossil fuel model) (see text) is depicted in purple and the first-difference transformation of the RCP4.5 (CIMP5) model is added (red curve).
Figure 14 .
14Data as forFigure 12except that the first-difference transformation of projected atmospheric CO2 from projected anthropogenic CO2 emissions (BP 2013) is depicted in light blue and first-difference projected atmospheric CO2 (peak fossil fuel model) is added (red curve).
is of interest because rate-of-change curves of this type are used in public policy as leading indicators of the future performance of real world events. For example, from the OECD-published volume OECD Composite Leading Indicators: a tool for short-term analysis: http://www.oecd.org/fr/std/indicateursavancesetenquetesdeconjoncture/15994428.pdf A number of different derived measures are available in different OECD publications. These measures assist users in the analysis and interpretation of recent developments in the Composite Leading Indicator (CLI). These are… The 12-month percent change of the composite indicator and the 12-month trend rate for the reference series. The 12-month percent change of the indicator is a rate where the initial value is a 12month centred average (the rate is calculated by dividing the figure for a given month by the 12-month moving average centred on m-12). This rate gives early warnings of turning points in the CLI. The timing of the peaks/troughs corresponds to the local maximum/minimum of the rate. For perfectly well-behaved cycles, this gives signals about 12 months ahead (in practice however, time series are not perfectly wellbehaved)... … An assessment of the ability of these measures to predict turning points has been done for the United States over the period 1980-1998. Signals given by the measures have been compared to the turning points in the reference series. Different statistics have been calculated including the: number of leads/lags in months and the number of missing and extra signals… The 1-month percent change gives early signals of all turning points, except in January 1989. The 12-month percent change gives signals of all the turning points with a longer lead. Both measures give extra signals of turning points. Over the period 1980-1998, there are no missing signals.
We used the Hadley Centre-Climate Research Unit combined land SAT and SST (HadCRUT) version 4.2.0.0 tropics (30S-30N) average http://www.metoffice.gov.uk/hadobs/hadcrut4/data/download.html. This series is used because (Leggett and Ball 2014) it shows the highest correlation with first-difference atmospheric CO2. It is noted (Leggett and Ball 2014) that HADCRUT4 tropics is closely correlated with HADCRUT4 global surface temperature. Atmospheric CO2 data is from the U.S. Department of Commerce National Oceanic & Atmospheric Administration Earth System Research Laboratory Global Monitoring Division Mauna Loa, Hawaii monthly CO2 series (annual seasonal cycle removed) ftp://ftp.cmdl.noaa.gov/ccg/CO2/trends/CO2_mm_mlo.txt. Disaster information is from the WHO Collaborating Centre for Research on the Epidemiology of Disasters (CRED) Emergency Events Database EM-DAT (EM-DAT 2013). In the EM-DAT database, climate disaster types are sorted into four main categories: extreme temperature, flood, storm and wildfire. The extreme temperature category is further is made up of two main sub-typesheat wave and cold wave. In this study the heat wave sub-type is used. The number of events per year for each of the preceding categories is added to produce an annual climate disaster time series.
Table 1 .
1Data sourcesData
series
Content
Source
Internet location
Atmos.
CO2
(RCP4.5
scenario)
Atmos. CO2
RCP4.5 scenario
RCP DATABASE:
http://www.iiasa.ac.at/web-
apps/tnt/RcpDb
Lean and
Rind
temperatu
re model
Lean, J. L. & Rind D. H. How will
Earth's surface temperature
change in future decades?
Geophys. Res. Lett. 36 L15708
(2009).
BP world
energy
use
projection
Christof Ruhl: 'BP Energy
outlook 2030' Statistical Review
of World Energy;
http://www.bp.com
Proj temp
mip5_glob
al
tas_Amon
_modmea
n_rcp45
IPCC RCP4.5
temperature
projection
http://climexp.knmi.nl/data/tsicmip5_tas_
Amon_modmean_rcp45_0-360E_-90-
90N_n_+++.txt
Anthro.
CO2
(Peak
fossil fuel
scenario)
Z1860-2011
Anthro. CO2
BP 2013, Nel and Cooper 2009,
Laherrere 2012)
http://www.bp.com/statisticalreview,
Nel and Cooper 2009, Laherrere 2012
IPCC A2
temperatu
re
projection
IPCC TAR SRES
A2 temperature
projection
WDCC -World Data Center for
Climate Hamburg
http://cera-
www.dkrz.de/WDCC/ui/Compact.jsp?acr
onym=HADCM3_SRES_A2
Total
climate
forcing
incl. volc.
(RCP4.5
scenario)
Z1860-2011
TOTAL_INCLVOL
CANIC_RF
RCP DATABASE:
http://www.iiasa.ac.at/web-
apps/tnt/RcpDb
IPCC
20C3M
temperatu
re dataset
Temperature
dataset between
1765 and 2005
Timespan: For convenience,
RCP3PD, RCP45, RCP6 and
RCP85 datasets, as well as two
supplementary extension files
include datasets between 1765
and 2005, identical to the
provided 20c3m dataset.
Drought
EM-DAT: The OFDA/CRED
International Disaster Database
-www.emdat.net -Université
catholique de Louvain -Brussels
-Belgium (EM-DAT 2013)
http://www.emdat.be/disaster-list
Cold
wave
Heat
wave
Wildfire
Figure 5. 1958 to 2013 monthly: First-difference atmospheric carbon dioxide (smoothed by a 13 month moving average) (dark blue curve) and global surface temperature (purple curve)Relative trend (Z1960-1998)
Proj. atmos. CO2 (RCP4.5 CMIP5
model)
Observed temp.
Proj. temp. (Lean and Rind (2009)
model)
Observed atmos. CO2
1st diff. observed atmos. CO2
With the trends depicted above visually in terms of descriptive statistics, statistical tests are now carried out on the strength and statistical significance of the relationships between the trends.model)
Observed temp.
Proj. temp. (Lean and Rind
(2009) model)
Observed atmos. CO2
1st diff. observed atmos. CO2
Observed global climate
disasters
Two characterisations are made: each of the two outcomes of temperature and climate
disasters is assessed against both linear and 1 st difference atmospheric CO2.
What are the equivalent statistical results for the range of models depicted in the earlier
figures? To avoid use of non-linear models, linear regressions are conducted for the year
from peak first-difference atmospheric CO2 and temperature -1998 -for the succeeding
years up to the latest year available -2013. Annual data is used.
Table 2 .
2Correlation coefficients for and the statistical significance of the relationships between the observed and modelled temperature trend. Green: substantial correlation and/or statistically significant; orange: not statistically significant.Observed global climate disasters
Proj. atmos. CO2 (RCP4.5 CMIP5 model)
Proj. temp. (RCP4.5 CMIP5 model)
Proj. temp. (RCP4.5 CMIP3 model)
1st diff. atmos. CO2 RCP4.5 model
Proj. temp. (Lean and Rind (2009) model)
Observed atmos. CO2
1st diff. observed atmos. CO2
Table 3 and
3
Supplementary table 1. Disaster types: total reported and peak years by continent: per cent alignedNo.
reported
disasters
globally
1980-
2013
Peak
years by
continent:
per cent
aligned
Flood
3726
80
Storm
2763
80
Drought
499
60
Wildfire
332
100
Heat
wave
140
40
Z1981-2011 Anthro. CO2 emissions from Fossil fuels (MtC) (PFF projection) plus LU Z1981-2011 Atmos CO2 Mauna Pred atmos CO2 from anthro PFF scenario Atmos. CO2 by anthro. CO2 1959-2012-7.2
-5.2
-3.2
-1.2
0.8
2.8
y = 0.908x -0.0166
R 2 = 0.9774
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Supplementary informationTwo matters are dealt with in this section: (i) an investigation of the adequacy of climate disaster trend data; and (ii) the calculation of future atmospheric CO2 projections from anthropogenic CO2 emissions. For references, see References above.Gall (2009)draws the conclusion that current global and national databases for monitoring losses from national hazards suffer from a number of limitations, which in turn lead to misinterpretation of hazard data. These biases include: 1) hazard bias, which produces an uneven representation and distribution of losses between hazard types;Investigation of the adequacy of climate disaster trend data2) temporal bias, which makes it difficult to compare losses across time due to less reliable loss data in past decades;3) threshold bias, which results in an underrepresentation of minor and chronic events; 3.00 4.00 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2 3.00 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2 Supplementary figure 4. Wildfire disasters by continent: relative trend (Z scores) and polynomial curve of best fit (total cases: 332)Supplementary figure 5. Heatwave disasters by continent: relative trend (Z scores) and polynomial curve of best fit (total cases: 140) 4.00 5.00 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4 2 0 0 6 2 0 0 8 2 0 1 0 2 0 1 2 3.00 4.00 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8 2 0 1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 9 1 9 7 2 1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 2 0 0 2 2 0 0 5 2 0 0 83) Threshold bias; 4) accounting biasEM-DAT focuses on major disasters. These are more likely to show up in records, hence reducing threshold and accounting bias.Conclusion to section on disaster dataFrom the positive results from the above eight tests, it is considered that the OECD climate disaster data from the EM-DAT database is fully adequate for use as an extra climate outcome alongside global surface temperature in the assessment of climate trends and their relationship to atmospheric CO2. In the assessment, as for the preceding tests, the number of events per year for each of the categories of flood, storm, drought, wildfire and heat wave is added to produce an annual aggregate climate disaster time series.Calculation of future atmospheric CO2 projections from anthropogenic CO2 emissionsCalculation of future atmospheric CO2 projections from anthropogenic CO2 emissions is done by simple regression from the prior relationship between anthropogenic CO2 emissions and atmospheric CO2. Supplementaryfigure 8shows the data used. It can be seen that for the different estimates available there is a broadly linear relationship over the period of overlap. Supplementaryfigure 10shows the predicted future atmospheric CO2 based on the relationship shown in Supplementary figure 9. This is the data used in the analysis in the paper proper.-8 -6-4-2 0 2 4 6 1 8 5 0 1 8 6 0 1 8 7 0 1 8 8 0 1 8 9 0 1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 2 0 3 0 2 0 4 0 2 0 5 0Supplementary referencesFor references, see References above.
Normalised flood losses in Europe. J I Barredo, Nat. Hazards Earth Syst. Sci. 9Barredo, J. I., 2009: Normalised flood losses in Europe: 1970-2006. Nat. Hazards Earth Syst. Sci., 9, 97-104.
. British Petroleum (BP). BP Energy OutlookBritish Petroleum (BP), 2014. BP Energy Outlook 2035.
CDIAC (Carbon dioxide information analysis center. CDIAC (Carbon dioxide information analysis center) (2012)
Em-Dat, The OFDA/CRED International Disaster Database. Available online at www.em-dat.net. Accessed. EM-DAT: The OFDA/CRED International Disaster Database. Available online at www.em-dat.net. Accessed December 2013.
Overestimated global warming over the past 20 years. J C Fyfe, N P Gillett, F W Zwiers, Nature Climate Change. 3Fyfe, J. C., Gillett N. P. & Zwiers F. W. Overestimated global warming over the past 20 years. Nature Climate Change 3, 767-769 (2013)
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Supplementary figure 2. Storm disasters by continent: relative trend (Z scores) and polynomial curve of best fit (total cases: 2763). Supplementary figure 2. Storm disasters by continent: relative trend (Z scores) and polynomial curve of best fit (total cases: 2763)
. Americas Asia Africa Europe Oceania Poly. Europe) Poly.Americas Asia Africa Europe Oceania Poly. (Americas) Poly. (Asia) Poly. (Africa) Poly. (Europe) Poly. (Oceania)
Wildfire Americas Wildfire Asia Wildfire Europe Wildfire Oceania Wildfire Africa Poly. (Wildfire Americas) Poly. (Wildfire Asia) Poly. (Wildfire Europe) Poly. (Wildfire Oceania) Poly. Wildfire AfricaWildfire Americas Wildfire Asia Wildfire Europe Wildfire Oceania Wildfire Africa Poly. (Wildfire Americas) Poly. (Wildfire Asia) Poly. (Wildfire Europe) Poly. (Wildfire Oceania) Poly. (Wildfire Africa)
Scatter plot of the relationship between anthropogenic CO2 emissions and atmospheric CO2 for the period. Supplementary figure 9Supplementary figure 9. Scatter plot of the relationship between anthropogenic CO2 emissions and atmospheric CO2 for the period 1959 to 2012
Predicted future atmospheric CO2 based on the relationship shown in 1850 1859. Supplementary figure 10Supplementary figure 10. Predicted future atmospheric CO2 based on the relationship shown in 1850 1859 1868 1877 1886 1895 1904 1913 1922 1931 1940 1949 1958 1967 1976 1985 1994 2003 2012 2021 2030 2039 2048
| sample_1456 | 0.9937 | arxiv | |
SF2A 2022 THE CARBON FOOTPRINT OF ASTRONOMICAL RESEARCH INFRASTRUCTURES
J Richard
A Siebert
E Lagadec
N Lagarde
O Venot
J Malzac
J.-B Marquette
M N'diaye
D Briot
J Knödlseder
SF2A 2022 THE CARBON FOOTPRINT OF ASTRONOMICAL RESEARCH INFRASTRUCTURES
Observatoriesspace telescopesspace probescarbon footprintclimate change
We estimate the carbon footprint of astronomical research infrastructures, including space telescopes and probes and ground-based observatories. Our analysis suggests annual greenhouse gas emissions of 1.2 ± 0.2 MtCO2e yr −1 due to construction and operation of the world-fleet of astronomical observatories, corresponding to a carbon footprint of 36.6±14.0 tCO2e per year and average astronomer. We show that decarbonising astronomical facilities is compromised by the continuous deployment of new facilities, suggesting that a significant reduction in the deployment pace of new facilities is needed to reduce the carbon footprint of astronomy. We propose measures that would bring astronomical activities more in line with the imperative to reduce the carbon footprint of all human activities. * We estimated that there are ∼ 1000 optical or near infrared telescopes with diameters smaller than 3 metres in the world, which largely dominates the number of observatories but provides only a modest contribution to the aggregated carbon footprint.
Introduction
The Intergovernmental Panel on Climate Change (IPCC) is a body created in 1988 by the World Meteorological Organization (WMO) and the United Nations Environment Programme (UNEP) with the objective to provide governments at all levels with scientific information that they can use to develop climate policies. The IPCC authors assess thousands of scientific papers published each year to provide a comprehensive summary of what is known about the drivers of climate change, its impacts and future risks, and how adaptation and mitigation can reduce those risks. According to the 6 th IPCC assessment report (IPCC 2021), it is unequivocal that human influence has warmed the atmosphere, ocean and land. The scale of recent changes across the climate system as a whole -and the present state of many aspects of the climate system -are unprecedented over many centuries to many thousands of years. Global warming of 1.5 • C and 2 • C will be exceeded during the 21 st century unless deep reductions in carbon dioxide (CO 2 ) and other greenhouse gas (GHG) emissions occur in the coming decades. Many changes due to past and future GHG emissions are irreversible for centuries to millennia, especially changes in the ocean, ice sheets and global sea level. From a physical science perspective, limiting human-induced global warming to a specific level requires limiting cumulative CO 2 emissions, reaching at least net zero CO 2 emissions, along with strong reductions in other GHG emissions.
There is growing recognition in the astronomy and astrophysics community that it must assume its share in the global effort to reduce GHGs. Like many other institutes we have therefore undertaken at the Institut de Recherche en Astrophysique et Planétologie (IRAP) an estimate of our GHG emissions so that we can devise an action plan that meets the challenge to drastically reduce emissions. In doing this exercise, we aimed in including all relevant sources of GHG emissions, comprising the purchase of goods and services and the use of data from research infrastructures, such as space telescopes and probes and ground-based observatories. While these sources were generally omitted in other works, the Bilan Carbone © method that we used for our estimate prescribes to include all sources for which our laboratory is responsible and on which our activity depends on. In other words, to identify the sources that need to be included in the estimate, the question to ask is whether our activity will be impacted if a given source is removed. Obviously, removing purchase of goods and services and use of data from observing facilities would make our activity impossible. In addition, research infrastructures are often invented, eventually built, and sometimes operated by researchers from our lab, hence as astronomers we also share the responsibility for their existence.
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In total we found that IRAP's GHG emissions in 2019 were 51.5 ± 6.0 tCO 2 e per astronomer of which 27.4 ± 4.8 tCO 2 e were attributed to the use of observational data (Martin et al. 2022). Interestingly, the sources that were so far neglected in GHG emission estimates of other research laboratories dominate IRAP's GHG emissions, with 55% due to the use of observational data and 18% due to the purchase of goods and services, of which a substantial fraction is related to instrument developments. The next most important source of GHG emissions was professional travelling (16%), all remaining contributions sum up to only 11%. So IRAP's carbon footprint is largely dominated by inventing, developing, constructing and using research infrastructures, which is the core business of our institute. To understand whether this is specific to IRAP, or whether this is a general feature of astronomy, we went one step further and estimated the total carbon footprint of the world-fleet of astronomical observatories that were operating in 2019.
2 Estimate of the carbon footprint of the world-fleet of astronomical research infrastructures
Method
We estimated the carbon footprint of astronomical research infrastructures using primarily a monetary method that relates cost to GHG emissions. This approach is known to have large uncertainties due to the aggregation of activities, products and monetary flows that may vary considerably from one facility or field of activity to another. An alternative life-cycle assessment (LCA) methodology is recommended by key space industry actors (ESA LCA Working Group 2016) as the optimal method to assess and reduce the carbon footprint of space missions, but it is difficult to implement in practice (especially for comparative or discipline-wide assessments) due to the confidential nature of the required input activity data (Maury et al. 2020). At present, a monetary method analysis is thus the only feasible way to assess the combined carbon footprint of the world's spaceand ground-based astronomical research infrastructures. For space missions, we complemented the monetary method by an alternative approach based on the payload launch mass. We adopted throughout this study an uncertainty of 80% for the carbon footprint estimate of individual facilities, as recommended by the French Agency for Ecological Transition (ADEME) for a monetary analysis (Breitenstein 2021).
For our estimate we followed the standard method of multiplying activity data with emission factors, including GHG emissions from constructing and operating the facilities. We started with considering a list of facilities from which data were used in peer-reviewed journal articles made by IRAP researchers in 2019. The list includes 46 space missions and 39 ground-based observatories. For space missions, we estimated the carbon footprint by multiplying mission cost or payload launch mass with appropriate emission factors. Owing to their longer lifetimes compared to space missions, we separated construction from operations for ground-based observatories and estimated the carbon footprint by multiplying construction and operating costs with appropriate emission factors. The full list of cost and mass data that we gathered from the literature and the internet can be found in the Supplementary Information of Knödlseder et al. (2022).
To derive the carbon footprint of the world-fleet of astronomical facilities we only considered the infrastructures that were still operating in 2019, reducing our initial list from 85 to 75 facilities. We then used a bootstrap method to extrapolate the carbon footprint of the facilities in our list to an estimated number of 55 active space missions and 1142 ground-based observatories. * In short, the bootstrap method randomly selects M facilities from a reduced list of N infrastructures, selecting on average each infrastructure M/N times (with M ≥ N ). Summing up the carbon footprints of all selected infrastructures provides then a linear extrapolation of the carbon footprint from N to M infrastructures. Yet bootstrapping goes beyond a linear extrapolation in that it preserves the discrete character of the facilities, and by repeating the sampling process it provides a probability density distribution for the aggregated carbon footprint of the M facilities. We repeated the random sampling 10,000 times and used the mean and standard deviation of the results to provide an estimate of the value and uncertainty of the aggregated carbon footprint. In order to reduce the bias that may arise from the specific 75 facilities in our initial list, and to avoid mixing infrastructures with hugely different carbon footprints (such as small and large optical telescopes), we divided the facilities in our list into broad categories that reflect scientific topic and observatory type. Details of the method and estimates for the number of worldwide active facilities per category are provided in Knödlseder et al. (2022).
Activity
Emission factor Space missions (based on payload launch mass) 50 tCO 2 e kg −1 Space missions (based on mission cost) 140 tCO 2 e Me −1 Ground-based observatory construction 240 tCO 2 e Me −1 Ground-based observatory operations 250 tCO 2 e Me −1 Insurance, banking and advisory services 110 tCO 2 e Me −1 Architecture and engineering, building maintenance 170 tCO 2 e Me −1 Installation and repair of machines and equipment 390 tCO 2 e Me −1 Metal products (aluminum, cupper, steel, etc.) 1700 tCO 2 e Me −1 Mineral products (concrete, glass, etc.) 1800 tCO 2 e Me −1
Emission factors
We estimated dedicated emission factors for our study using existing carbon footprint estimates for space missions and ground-based observatories. Specifically, life-cycle carbon footprints of space missions were estimated from the case studies of Wilson (2019) which covered the entire mission including the launcher and a few years of operations. From these studies, we infered mean emission factors of 140 tCO 2 equivalent (CO 2 e) per million e (Me) of mission cost and 50 tCO 2 e kg −1 of payload launch mass. Emission factors of ground-based observatories were derived using existing carbon footprint assessments for the construction of two facilities and the operations of three facilities. We found a mean emission factor of 240 tCO 2 e Me −1 for construction and of 250 tCO 2 e Me −1 for operations. A lower monetary emission factor for space missions is supported by the fact that space missions are much less material intensive compared with ground-based observatories after normalizing by cost. For example, the liftoff mass of a e1 billion space mission launched with Ariane 5 ECA is about 790 tonnes, while the European Extremely Large Telescope (E-ELT), which has a similar cost, has a mass of about 60,000 tonnes. The space sector is in fact unique, and is characterized by low production rates, long development cycles and specialized materials and processes (Geerken et al. 2018).
The emission factors used in this study are summarised in Table 1 where they are compared to monetary emission factors selected from Breitenstein (2021), covering the range of values encountered for economic activity sectors in France. The comparison shows that emission factors for astronomical research infrastructures are at the low side of other economic activity sectors, implying that decarbonising observatory construction and operations will be challenging within the current socio-economic system. Office work is an important contributor to the carbon footprint of the space sector (Chanoine et al. 2017), which is in agreement with the observation that its emission factor is close to that of office work activities such as insurance, banking and advisory services. As explained above, constructing ground-based observatories is considerably more material intensive than building a space mission, hence a larger emission factor for ground-based observatory construction with respect to space missions is plausible.
Due to the lack of published information we were not able to derive a specific emission factor for space mission operations, yet since the underlying infrastructures and activities are similar to operations of groundbased observatories it seems plausible that their emission factors are comparable. We note that the emission factor of operations depends sensitively on the carbon intensity of electricity generation (which is an important contributor to the overall operations footprint) and the number of persons needed for operations (which is an important contributor to the overall operating costs). Consequently, the operations emission factor for a specific facility may deviate significantly from our estimated average value, yet since we are considering here only the aggregated carbon footprint of astronomical facilities such deviations should average out.
Results
The aggregated results of our estimation are summarised in Table 2. Two set of values are presented: the first where we bootstrap-sampled all research infrastructures in each of the categories, and the second where we bootstrap-sampled all except the facilities with the largest carbon footprint in each category (the footprints of the non-sampled facilities were simply added to the bootstrap result). The latter approach is motivated by the possibility that the largest carbon footprint in a given category arises from a facility that is unique in the world, hence excluding this facility from the sampling avoids that the bootstrap sampling selects this unique facility multiple times. Examples for such unique facilities in our initial list are the Hubble space telescope SF2A 2022 or the ALMA observatory which have annual carbon footprints of several tens of ktCO 2 e yr −1 . So the second approach is more conservative, plausibly bracketing together with the first approach the true value of the carbon footprint of astronomical research infrastructures. Table 2 gives both the lifecycle and the annual footprints. The lifecycle footprint includes the contributions from construction and operations until 2019, while the annual footprint is the sum of the lifecycle footprint of each facility divided by its lifetime, defined as the time since start of operations, or ten years, whatever is longer. While the lifecycle footprint aggregates carbon footprints over different time periods, and hence is of limited use, the annual footprint is an estimate of the yearly GHG emissions of the considered research infrastructures. The last row provides the average results between both bootstrapping approaches, with the differences between the results added to the quoted uncertainties. Our analysis hence suggests that the world-fleet of astronomical facilities that were operating in 2019 had an annual carbon footprint of 1.2 ± 0.2 MtCO 2 e yr −1 .
Dividing the annual carbon footprint by an estimated number of 30,000 astronomers in the world gives a footprint of 42.8 ± 7.7 tCO 2 e yr −1 per average astronomer for the first bootstrapping approach and 35.1 ± 4.6 tCO 2 e yr −1 for the second. These results are a bit larger than the estimated footprint of 27.4 ± 4.8 tCO 2 e yr −1 related to the use of observational data for an average IRAP astronomer, yet the IRAP estimate is based on a restricted list of facilities which may tend to underestimate the true footprint. Taking nevertheless all these results at face value, we derive an estimate of 36.6 ± 14.0 tCO 2 e yr −1 for the annual carbon footprint of the world-fleet of astronomical facilities per average astronomer that comprises all individual results and their uncertainties.
Consequences
According to our analysis, astronomical research infrastructures appear to be the single most important contributor to the carbon footprint of an average astronomer. Additional contributions include purchase of goods and services, travelling and commuting, supercomputing, running the office building and meals, that for IRAP add up to an additional carbon footprint of 23 tCO 2 e yr −1 per astronomer, resulting in a total professional annual footprint of an average astronomer of about ∼ 50 tCO 2 e yr −1 . Adding also the astronomer's lifestyle footprint, estimated to 10 tCO 2 e yr −1 for upper class consumers in France (Lenglart et al. 2010), leads to an estimated annual footprint of about ∼ 60 tCO 2 e yr −1 for an average astronomer in France.
Keeping global warming with a reasonable chance below a level of 1.5 • C or 2 • C requires GHG emission reductions by 84% or 63% in 2050 with respect to 2019 (IPCC 2022), corresponding to annual average emission reductions of about ∼ 6% or ∼ 3%. GHG emissions are not equally distributed between regions, activities and humans, requiring more than average reductions by important emitters to assure the social acceptability of the efforts. Our analysis suggests that astronomers are important emitters, and asking consequently for an order of magnitude reduction effort of GHG emissions over the coming 30 years is not implausible. Obviously, astronomy has not only an environmental but also a societal impact, and finding the right balance between these impacts needs to be subject of public debate. Yet this applies to all sectors of human activity, be it any scientific sector, or sectors that satisfy basic human needs, such as agriculture, housing, health care, dressing and transport. Exempting astronomy from significant GHG emission reductions seems thus difficult to justify.
Taking action
Coming back to astronomical research infrastructures, reducing their carbon footprint requires first that each planned or existing facility performs a detailed environmental lifecycle analysis, informing quantified action plans to reduce their emissions. Progress in the implementation of the action plans need to be monitored, and plans be adapted if needed. LCA results, action plans and achievements need to be made public, so that the progress on GHG emission reductions is transparent and fairness can be assured.
For proposed facilities LCA results should inform implementation decisions, while for existing facilities LCA results should inform decarbonisation plans. Possible actions include switching to renewable energies for observatory operations, reducing air-travelling and avoiding air-shipping, moving to electric vehicle fleets, and extending equipment lifetime. With such measures, the European Southern Observatory (ESO) plans to reduce its operations-related GHG emissions of 28 ktCO 2 e yr −1 in 2018 by up to 4.4 ktCO 2 e yr −1 over the next years, corresponding to a reduction of 15%. † This is an important step, yet falls short of the required reduction levels mentioned above. In addition, ESO is currently building the E-ELT with an estimated construction carbon footprint of at least 63.7 ktCO 2 e (ESO, personal communication), corresponding to about 15 years of GHG emission savings. Operating the E-ELT will add additional GHG emissions, as illustrated by the past and predicted annual carbon footprint of electricity consumption at the ESO observatory sites in Chile, shown in Fig. 1. While between 2016 and 2022 a reduction of GHG emissions from electricity consumption by ∼ 50% was achieved (by swapping at Paranal from liquid petrol gas generators to a grid connection in 2018 and adding photovoltaic power plants in 2022), the additional electricity needs of E-ELT will have annihilated all the reductions by the end of this decade; despite important efforts, the GHG emissions due to electricity consumption will exceed in 2030 those of 2016. This illustrates an obvious but inconvenient truth: it is extremely difficult to decarbonise while ramping up! ESO is so far the only organisation that provides public information on carbon footprint estimates and reduction plans, exposing the organisation obviously to be used as a casestudy. There are no reasons to believe that the situation is different for other organisations, at least as long as they continue to expand. It's up to these other organisations to prove us wrong, yet until this is done, we should accept that reducing the GHG emissions of astronomy is challenging while continuing with the deployment of new facilities at the current pace.
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Towards sustainable astronomy
Obviously, all this calls for deep changes in how astronomy is done in the future, but given the required order of magnitude reductions in GHG emissions, how could it be otherwise? A first step would be to use what we already have and move towards a more extended and deeper analysis of existing astronomical data archives. It is well recognised that archives are valuable resources for astronomy, and a significant fraction of discoveries is made by exploring already existing data (e.g. White et al. 2009;De Marchi 2022). Use of archival data should be actively promoted and be considered when evaluating operation extensions. Resources should be allocated according to carbon footprint, having in mind that remaining carbon budgets that keep global warming below 1.5 • C or 2 • C shrink rapidly. Today, no funding agency is investing significantly into decarbonising research infrastructures; tomorrow, decarbonising existing facilities must become their funding priority! This also means that less money will be available to build new infrastructures, yet is this really a problem? Stoehr et al. (2015) argue that, in the future, observatories will compete for astronomers to work with their data, which if true seems to indicate that we may have already too many facilities. There is no requirement per se on the deployment pace of new facilities or missions, and slowing down the current pace will lead to less GHG emissions, free resources for investing into decarbonisation and give more time for in-depth analyses of existing data. Another measure is moving away from competition towards more collaboration. If we really believe that astronomers are working for mankind, there is no need to build the same kind of facility several times on the globe. For example, one 40-m class telescope in the world should be sufficient to make the discoveries to be made with such an instrument. And there is no scientific justification for having a new space-race towards the planets, a few well-coordinated international missions should be sufficient to gain the knowledge we are after. Of course, astronomy is not the root cause of climate change, nor can astronomy alone fix it, but astronomy with its significant per capita GHG emissions must be exemplary and take its fair share, leading the way towards a sustainable future on Earth.
The author would like to thank R. Arsenault, S. Brau-Nogué, M. Coriat, P. Garnier, A. Hughes, P. Martin and L. Tibaldo for useful discussions. This work has benefited from discussions within the GDR Labos 1point5.
Fig. 1 .
1Past and predicted annual carbon footprint of electricity consumption at the ESO observatory sites in La Silla, Paranal and Armazones (data from Filippi et al. 2022).
Table 1 .
1Emission factors.
Table 2 .
2Carbon footprint of world-fleet of astronomical research infrastructures active in 2019.Category
Lifecycle footprint (MtCO 2 e) Annual footprint (ktCO 2 e yr −1 )
All facilities sampled
Space missions (cost-based)
8.4 ± 2.0
596 ± 111
Space missions (mass-based)
6.4 ± 1.2
455 ± 74
Ground-based observatories
14.2 ± 1.5
757 ± 131
Total
21.6 ± 3.2
1283 ± 232
Facility with largest footprint excluded from sampling
Space missions (cost-based)
7.1 ± 1.4
490 ± 79
Space missions (mass-based)
5.8 ± 0.9
417 ± 65
Ground-based observatories
12.6 ± 1.0
600 ± 70
Total
19.0 ± 2.3
1054 ± 137
Total (average)
20.3 ± 3.3
1168 ± 249
† https://www.eso.org/public/about-eso/green/
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| sample_1459 | 0.9915 | arxiv | |
OFFSHORE-WIND ENERGY | RENEWABLE ENERGY Wind energy potential of the German Bight Limits and consequences of large-scale offshore wind energy use
Axel Kleidon
OFFSHORE-WIND ENERGY | RENEWABLE ENERGY Wind energy potential of the German Bight Limits and consequences of large-scale offshore wind energy use
10.1002/piuz.202201654Translated version Originally published in German -Cite as: Kleidon, A. (2023) "Windenergie in der Deutschen Bucht", Physik in unserer Zeit, 54(1), 30-36.
The wind blows stronger and more reliably over the sea than over land. Thus, offshore wind energy is expected to make a major contribution to the energy transition in Germany, especially in the German Bight. But what happens when a growing number of wind farms extract more and more wind energy from the atmosphere?The challenges of the energy transition for the next decades in Germany are enormous. It is true that 15.9 % of primary energy demand was already covered by renewable energy in 2021 [1], and a lower energy demand is expected in the future due to more modern technologies such as heat pumps and electromobility. However, the transition to a complete, sustainable energy system that is free of fossil fuels is still a long way off.Many energy transition scenarios focus on the expansion of a combination of solar and wind energy. These two types of renewable energy have the greatest potential in Germany [2] and complement each other very well over the course of the year: while the Sun can supply a particularly large amount of renewable energy in summer, it fails in winter. This can be compensated for by wind energy, as the dark winter months are usually stormier than the summer.Wind power generation at sea plays a special role in these scenarios. Wind blows stronger and more continuously at sea than on land, so it can generate electricity more efficiently and reliably. In Germany, expansion is planned mainly in the German Bight of the North Sea, where the exclusive economic zone -i.e. the part of the sea that is administered by Germany beyond the territorial sea -offers considerably more surface area than the Baltic Sea. For example, wind farms with 6.7 GW of installed capacity are currently located in the North Sea, compared to only 1.1 GW in the Baltic Sea (as of 2021, [3]). In 2021, these wind farms contributed about 24 TWh/a or 4.9 % to the German electricity demand of 491 TWh/a, which means that the turbines were utilized to an average of 35 % -the so-called capacity factor [3]. Wind turbines at sea were thus almost twice as productive as on land, where the capacity factor was only 18 %.By 2050, it is assumed that the use of offshore wind energy will increase significantly more than on land, i.e. onshore. In its coalition agreement, the German government has targeted the expansion of offshore wind energy to 70 GW, i.e. roughly a tenfold increase in currently installed capacity. Onshore, there is already 56 GW of turbine capacity, and an expansion to around 200 GW is expected here, distributed over 2% of the country's surface area. However, with 357,000 km 2 there is considerably more space than in the exclusive economic zone of the North Sea, which is only 28,600 km 2 in size. So the plans envisage a much more intensive use of wind energy at sea than on land. And because each wind turbine draws energy from the atmosphere and thus weakens the winds, the question arises whether, with such a strong expansion, the turbines could take the wind away from each other and thus endanger the high yields. of 1 10
Wind energy in the German Bight
This question was examined in a report by Agora Energiewende on the wind energy potential of the North Sea [5]. I worked scientifically on this report and want to present the results here in a comprehensible way. This study has also already been taken into account in the current, official planning of offshore wind energy in Germany. In the following, I will go through the steps necessary to determine the potential for electricity generation by wind energy use in the German Bight. In particular, I want to make the effect of wind extraction by the turbines physically plausible.
In the first step, we determined the areas that are potentially available for the expansion of wind energy (Figure 1). There is a whole range of different uses of the sea. These include, of course, shipping, which needs routes, certain areas are designated as nature reserves, there are areas used for military purposes, and areas are needed for submarine cables and supply lines. These areas preclude wind energy use, which significantly reduces the total area available. The usable areas can be roughly divided into two areas separated by a wide route for shipping: the coastal area 1 (blue in Figure 1) with 2767 km 2 and the far-from-the-coast area 2 (red) with 4473 km 2 .
Next, we need technical information on the turbines that will be placed in these areas. For this purpose, we choose a hypothetical 12 MW turbine with a rotor diameter of 200 m, which corresponds to the specifications of the currently most powerful turbines. The power generation of a single turbine is described by the so-called power curve. It shows how much electricity an isolated turbine produces at a prevailing wind speed, the so-called wind yield (Figure 2c). The dependence on the wind speed can be roughly divided into four ranges: In calm conditions below the cut-in velocity of 3 m/s, the turbine produces no electricity. In the second range up to the rated velocity of 11.5 m/s, the output increases proportionally to the kinetic energy flux density given by (1/2) ρ v 3 , with the air density ρ = 1.2 kg/m 3 and the wind speed v in m/s. The energy flux density is then multiplied by the cross-sectional area spanned by the rotor and the power coefficient of about 0.42 (that is, 42% of the kinetic energy flux density can be used) to determine the yield in this range. In the third range above the rated wind speed up to the cut-out velocity of 28 m/s, the yield is determined by the capacity of the generator. Above this wind speed, the turbine is shut down to protect against damage and does not generate any electricity.
The average yield of the wind turbine is then determined by combining the power curve with the frequency distribution of wind speeds. For this purpose, we used the frequency distribution of wind speeds (Figure 2a) measured by the FINO-1 measuring station in the German Bight at a height of 100 m in the period 2004-2015. Its position is marked in Figure 1. These data show that the absence of wind is relatively rare with an average of 5.8 %, the second range where the yield depends directly on the wind speed is the most frequent with 61.5 %, 32.6 % of the time the turbine operates at its capacity. In only 0.1 % of the time the turbine has to be shut down due to excessive wind speeds.
In total, the turbine generates an average of 6.8 MW of electrical power or 59.1 GWh of electrical energy per year. The efficiency of the energy generation can be described on the one hand by the full load hours, with which the annual yield is simply described by the product with the capacity of the turbine. The annual yield is thus calculated as 12 MW * x h/a = 59.1 GWh/a with x = 4928 full of 3 10
Wind conditions in the German Bight and their use by an isolated standing wind turbine. a) Frequency distribution shows wind measurements 2004-2015 at 100 m height on FINO-1 in the North Sea [4], position of this measuring station see Figure 1. b) The seasonal course of wind speeds over the months is shown by the median, where the area highlighted in blue covers 25-75 % of the distribution. c) Yield of an isolated 12 MW wind turbine as a function of wind speed and d) its seasonal variation in the North Sea. Highlighted in light grey on the left is the range where wind yield increases with wind speed (61.5% of the time), while in the range highlighted in dark grey the turbine operates at its capacity limit (32.6% of the time).
FIG. 2 WIND IN THE GERMAN BIGHT
load hours per year. On the other hand, the efficiency can be described by the capacity factor, which describes the ratio of the average yield to the capacity of the turbine. In our case, the capacity factor is 6.8 MW/12 MW = 56.7 %. The efficiency -or the capacity factor -is not only described by the technical specification of the turbine, but also by the wind conditions. For example, the capacity factor in Germany on land is only about 20 % [6]. In principle, the yield is also subject to seasonal fluctuations, with higher yields in winter than in summer ( Figure 2d).
Next, we considered different scenarios in which the two areas 1 and 2 are equipped with different numbers of wind turbines. Three scenarios rely solely on the use of Area 1 for wind energy because of its proximity to the coast makes the costs of installation, supply, and connection to the power grid less expensive. These scenarios consider different installation densities of 5, 10 and 20 MW per square kilometre. With an area of 2767 km 2 , this corresponds to 1153, 2306, and 4612 turbines with 12 MW capacity each.
In five other scenarios, we consider both areas with installation densities of 5, 7.5, 10, 12.5, and 20 MW/km 2 , with 3017 to 12067 turbines distributed evenly over the 7240 km 2 of both areas combined. This gives us a total of eight scenarios, covering a range of 14 to 145 GW of installed capacity. The German government's expansion target of 70 GW is thus well covered.
Wind yield estimation
Next, we determined the total yield of the installed turbines for the different scenarios. A seemingly obvious way to do so would be to simply multiply the yield of the isolated turbine by the number of turbines. This gives us theoretical results for yields as shown by the light bars in Figure 3. This type of estimation is currently widely used. Sometimes it is reduced by an empirically determined park loss factor of 10 %, but sometimes it is even expected that technological progress will actually increase turbine efficiency. The scenarios then result in a wind yield of 7.8 to 82.1 GW or 68.2 to 713.6 TWh/a. By comparison, electricity consumption in Germany in 2021 was around 491 TWh/a [3].
However, this way of calculating yields does not take into account that wind turbines extract a considerable amount of kinetic energy from the atmosphere. This weakens the wind and thus the average efficiency of the turbines in the region. We can easily see this by looking at the kinetic energy fluxes of the region (Box "KEBA: Kinetic Energy Balance of the Atmosphere" on p. 7). On the one hand, there are the two inputs into the lower atmosphere of the region, the so-called boundary layer, which over the North Sea is about 700 m thick: The first contribution comes from the horizontal flow into the region, the second comes from above through vertical mixing.
Area 1 in Figure 1 has an area of 2767 km 2 . We consider it simplified as a square in the following, with a length of about 52.6 km. If we assume a wind speed of 9.4 m/s, which corresponds to the median of the frequency distribution in Figure 2a, this is in the range where the wind yield increases with wind speed (Figure 2c). Thus, about 52.6 x 10 3 m x 7 x 10 2 m x (0.5 x 1.2) kg/m 3 x (9.4 m/s) 3 ≈ 18.3 GW flows into the area, while the vertical replenishment is relatively small at about 2.8 GW (see equations (2) and (3) in the Box "KEBA: Kinetic Energy Balance of the Atmosphere"). Thus, 21.1 GW of kinetic energy enters Area 1 at this wind speed, which is already quite close to the installed capacity of 14 GW for the smallest scenario for Area 1 with 1153 turbines. So we can see that the wind turbines will extract an appreciable amount of kinetic energy from the region and their effect must be taken into account.
For estimating the yields of different scenarios, we can take the balance of kinetic energy fluxes in our virtual box (box "KEBA: Kinetic energy balance of the atmosphere" [7], and Figure 4). The estimates from this approach are shown by the blue bars in Figure 3. The orange bars come from calculations using a much more complex numerical weather prediction model. As we can see, the results from both methods are very similar. So looking at the energy fluxes in the atmosphere is the key to understanding the reduced yields from strong wind energy use.
For a complete balance of the kinetic energy flows, we also need to look at the loss terms. In addition to the extraction of energy by the turbines, there is also the friction loss in the wake of the turbines, surface friction as well as the export of kinetic energy into the areas downwind of the wind farms. The effect of wind extraction can be represented comparatively simply with a reduction factor, since all these components depend on the kinetic energy flux density.
Electricity yield of different offshore wind energy expansion scenarios in the German Bight without (light) and with (dark) the extraction of wind energy by the turbines. The blue estimates are based on the KEBA approach (see "KEBA: The Kinetic Energy Balance of the Atmosphere"), while the orange estimates are based on calculations with a much more complex numerical weather prediction model (WRF). The vertical black line represents Germany's average electricity consumption in 2021. As a comparison: the German government's expansion target for offshore wind energy for 2030 is 30 GW of installed capacity, in 2050 it is 70 GW (data from [5]).
FIG. 3 ELECTRICITY YIELD OF DIFFERENT SCENARIOS
This factor depends primarily on the size of our virtual box and the number of turbines (see formula (10) in the box "KEBA: Kinetic energy balance of the atmosphere"). It reduces the yield especially at low wind speeds, since it then depends strongly on wind speed. At high wind speeds, much more kinetic energy enters into our box, since the kinetic energy fluxes depend on the third power of the wind speed. In this case, the turbines operate at their capacity, which means that lowering the wind speed does not affect their yield as much. Figure 5 shows an example of the change in the various contributions in the kinetic energy balance for the scenarios. The natural case without wind energy use is also included. Here, the input of kinetic energy is balanced with surface friction and downwind export. The more wind energy is used in the areas, the more the terms shift towards electricity generation (yellow in Figure 5) and frictional losses to the wakes (orange). This is at the expense of surface friction and export. These two terms are directly coupled to wind speed, so wind speed must decrease. This can clearly be seen in the frequency distribution of wind speeds (Figure 6), which shifts towards lower values with greater use.
Kinetic energy balance of the atmosphere over the region in which wind energy is used and from which an effective wind speed can be calculated. See box "KEBA: Kinetic energy balance of the atmosphere" for explanation of symbols and how this calculation is done.
FIG. 4 KINETIC ENERGY BALANCE OF THE ATMOSPHERE
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The effect of wind extraction by turbines can be described quite simply and physically with the help of the kinetic energy balance of the lower atmosphere [7]. For this purpose, we consider the air volume above the area of the planned wind farms (Figure 4), with width W and length L, as well as a height H. This height comprises the boundary layer in which the lower atmosphere is well mixed. Over the North Sea this is usually around 700 m high.
We now consider the components that contribute, export, or convert kinetic energy in this volume. These are the kinetic energy inputs from upwind areas and from above, Jin,h (dark blue arrow in the figure) and Jin,v (light blue arrow), the export Jout,h downwind (purple arrow), the frictional loss due to surface friction Dfric (red arrow), the extraction by the turbines for power generation Gturb (yellow arrow), and the frictional losses in the wakes due to the mixing of surrounding air masses Dwake (orange arrow).
Jin,h + Jin,v = Jout,h + Dfric + Gturb + Dwake .
(1)
The horizontal input of kinetic energy is described by:
Jin,h = [(ρ/2) vin 3 ] * W * H.(2)
The expression in the brackets describes the kinetic energy flux density, with the air density ρ of about 1.2 kg/m 3 near the sea surface and the wind speed vin. We can describe the input of kinetic energy from the free atmosphere, which is above the boundary layer, by vertical mixing through the friction loss at the surface when there are no wind turbines, because then these two terms balance. This is described by:
Jin,v = ρ Cd vin 3 x W x L(3)
where Cd represents the drag coefficient and which is typically about 0.001 over sea.
If wind turbines are present, we describe the wind speed within the volume by an effective speed v. It will be lower than vin, because the wind turbines change the kinetic energy balance of the volume. We use this effective wind speed to describe the other four terms of the balance. We write the export of kinetic energy into downwind areas analogous to (2) as
Jout,h = [(ρ/2) v 3 ] x W x H.(4)
For the friction loss we write similar to (3):
Dfric = ρ Cd v 3 x W x L.(5)
The power generation, or yield, of the wind turbines in the range when power depends on the wind speed, is given by
Gturb = [(ρ/2) v 3 ] x η x Arotor x N,(6)
where η is the power coefficient of the turbine, typically η 0.42, Arotor is the cross-sectional area spanned by the rotor blades, in the case of our 12 MW turbine this is 31415 m 2 , and N is the number of wind turbines.
For the friction loss in the turbine wakes, we assume 50% of the power extracted from the wind by the turbines as a realistic value. Thus it follows:
Dwake = 0,5 x Gturb .(7)
The four terms of the right-hand side of the kinetic energy balance (1) all depend on v 3 , so we can easily obtain the effective wind speed by rearranging the equation. This can then be described as
v = fred 1/3 vin,(8)
and the amount of electricity generated by
Gturb = fred [(ρ/2) vin 3 ] x η x Arotor x N.(9)
Here, fred is a reduction factor describing the effect of wind extraction from the volume:
.
(10)
Note that for an isolated turbine (N = 1) this factor is 1, so there is no yield reduction. The higher the number of turbines and the larger the rotor area, the smaller the factor becomes, the wind is weakened and the yield is reduced. In the case where the turbines operate at their capacity, a similar expression can be derived.
The application to the 72 GW scenario is briefly illustrated here: With H = 700 m, W = L ≈ 85 090 m, Cd = 0.001, η = 0.42, and N = 6033, this results in a factor of fred = 870 m/ (870 m + 1404 m) = 0.38. When yields depends on wind speed, this factor implies that wind extraction causes the yields to drop to 38%, a 62% reduction, while wind speeds have only dropped by 28%. However, this is only a partial aspect of the overall yield, as there are still times when the turbines operate at their capacity. Therefore, the reduction in Figure 3 is less dramatic at 40%. The various components of the kinetic energy balance can then be determined by combining the observed energy flux density (505 W m -2 in the median at vin = 9.4 m/s) with the parameters and equations.
These KEBA calculations are available as a spreadsheet for yield estimates on the Internet [8]. Install Areas Figure 4, explanation of the symbols in the legend and box "KEBA: Kinetic energy balance of the atmosphere").
f red = H + 2C d ⋅ L H + 2C d ⋅ L + 3/2 ⋅ η A rotor ⋅ (N − 1)/
Components of the kinetic energy balance for the scenarios of Figure 3, the upper light blue section again applies to Area 1 alone, the lower white section to Area 1 and 2 together. The values are estimated with the KEBA approach (colouring as in
FIG. 5 KINETIC ENERGY COMPONENTS
Conclusions
Overall, this gives us a differentiated picture of the contribution that offshore wind energy can make to the energy transition: On the one hand, the potential to generate electricity is huge, even with the associated, significant reductions due to wind extraction from the turbines. For example, the 72 GW scenario can cover more than a third of Germany's current electricity consumption. On the other hand, the use is much more efficient if wind farms are less dense and distributed over larger areas. This can be seen in a direct comparison of the scenarios 55 GW installed in Area 1 and 54 GW installed in both areas (Figures 3 and 5). In the latter case, the reduction effect is much smaller, as the turbines are distributed over a much larger area.
This weakening effect will therefore play an increasingly important role in the expansion of offshore wind energy. It is independent of the technology, the size of the turbines or the positioning of the turbines in the wind farm. After all, the main effect has to do with what the turbines are there to do: To extract energy from the wind in order to generate electricity with it.
FIG. 6 WIND SPEEDS
Summary A significant contribution to the energy transition is expected from offshore wind energy in the German Bight. Due to the strong and steady winds, offshore electricity generation appears to be very efficient. For 2050, the German government assumes an installed capacity of 70 gigawatts, a tenfold increase compared to today. But what happens when so many wind turbines draw their energy from the wind? This can be easily determined with the help of the kinetic energy balance of the atmosphere above the wind farms. Since the input of kinetic energy is limited, the more wind energy is used, the lower the wind speeds in the region must be, and with them the efficiency of the turbines. So less electricity is generated than would be expected without this effect. At 70 GW, that would reduce electricity generation by as much as 40%. Still, it could meet a large part of the current electricity demand. For the efficient use of wind energy at sea, it is therefore advisable to plan wind farms as widely dispersed as possible in order to reduce their influence on the wind fields.
Keywords
Wind energy, offshore, energy transition, renewable energy, full load hours, kinetic energy, wind speed, power rating, capacity factor, kinetic energy balance of the atmosphere (KEBA).
Frequency distribution of wind speeds of three scenarios illustrating the shift to lower wind speeds with more wind energy use. The numerical values indicate the median of the respective distributions.
Abbildung 2 :
2Flächen der Deutschen Bucht, die zum Ausbau der Windenergie genutzt werden können. Die küstennahen Flächen in dunkelblau werden hier als "Gebiet 1" bezeichnet, während die roten, küstenfernen Flächen als "Gebiet 2" zusammengefasst werden. Die Lage der FINO-1 Messstation ist durch den weissen Kreis markiert. Karte modifiziert nach[5].Areas of the German Bight that can be used for the development of wind energy. The areas close to the coast in dark blue are referred to here as area 1, the red areas far from the coast as area 2. Black and white circle: position of the FINO-1 measuring station(map modified according to[5]).3°4°
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Abbildung 1: Windbedingungen in der deutschen Bucht sowie deren Nutzung für Windenergieerzeugung durch eine isoliert stehenden Turbine. a. Die Häufigkeitsverteilung zeigt Windmessungen auf 100m Höhe von der FINO-1 Messplattform in der Nordsee für die Jahre 2004-2015 [4]. Die Position dieser Messstation ist in der Karte in Abbildung 2 markiert. b. Der saisonale Verlauf von Windgeschwindigkeiten über die Monate ist gezeigt durch den Median, wobei der farbig unterlegte Bereich 25-75% der Verteilung zeigen. c. Der Ertrag einer isoliert stehenden 12 MW Windturbine als Funktion der Windgeschwindigkeit sowie d. den saisonalen Gang in der Nordsee. Links hellgrau markiert ist der Bereich, wo Windertrag mit der Windgeschwindigkeit ansteigt (61.5% der Zeit), während im dunkelgrau markierten Bereich die Turbine an ihrer Kapazitätsgrenze operiert (32.6% der Zeit).Month
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Stromertrag verschiedener Ausbauszenarien der Offshore Windenergie in der Deutschen Bucht ohne (hell) un (dunkel) dem Entzug von Windenergie durch die Turbinen. Die blauen Abschätzungen basieren auf dem KEBA Ansatz (sieh während die orangen Abschätzungen auf Berechnungen mit einem wesentlich komplexeren, numerisches Wettervorhersag ("WRF") basieren. Die vertikale, schwarze Linie stellt den mittlere Stromverbrauch Deutschlands des Jahres 2020 dar. Als Das Ausbauziel der Bundesregierung für die Offshore Windenergie für 2030 sind 30 GW installierte Kapazität, in 2050 bei 70 Daten aus [5].of
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The author Axel Kleidon studied physics and meteorology at the University of Hamburg and Purdue University, Indiana, USA. He received his doctorate from the Max Planck Institute for Meteorology in 1998 for his work on the influence of deep-rooted vegetation on the climate system. He subsequently conducted research at Stanford University in California and at the University of Maryland. Since 2006, he has headed the independent research group "Biospheric Theory and Modelling" at the Max Planck Institute for Biogeochemistry in Jena. His research interests range from the thermodynamics of the Earth system to the natural limits of renewable energy sources.
Physik in unserer Zeit. A Kleidon, https:/onlinelibrary.wiley.com/doi/abs/10.1002/piuz.20190154050120A. Kleidon, Physik in unserer Zeit 2019, 50(3), 120.
. S Germer, A Kleidon, https:/journals.plos.org/plosone/article?id=10.1371/journal.pone.0211028PLoS ONE. 20192211028S. Germer, A. Kleidon, PLoS ONE 2019, 14(2), e0211028.
. A Kleidon, L M Miller, 10.5194/gmd-13-4993-2020Geosci. Model Dev. 4993A. Kleidon, L. M. Miller, Geosci. Model Dev., 2020, 13, 4993.
The Kinetic Energy Budget of the lower Atmosphere (KEBA) Model: Files from the project 'Making the most of offshore wind. A Kleidon, 10.17617/3.3hAgora Energiewende and Agora VerkehrswendeA. Kleidon, The Kinetic Energy Budget of the lower Atmosphere (KEBA) Model: Files from the project 'Making the most of offshore wind', commissioned by Agora Energiewende and Agora Verkehrswende, 2020, https://doi.org/ 10
| sample_1465 | 0.9685 | arxiv | |
September 2005
309September 2005
Comments by William M. Gray (Colorado State University) on the recently published paper in Science byWebster, et al., titled "Changes in tropical cyclone number, duration, and intensity in a warming environment" ABSTRACT Recent US major landfalling hurricanes Katrina and Rita and last year's four U.S. landfalling major hurricanes have spawned an abundance of questions concerning the role that global warming might be playing in these events. This idea has been given added credence by the September 2005 Science paper of Webster, Holland, Currie and Chang (Vol. 304, pp. 1844-1846) showing that the global number of Category 4-5 hurricanes have increased in the last 15 years (1990-2004) in comparison with the prior 15-year period of 1975-1989. They report 171 Category 4-5 hurricanes in the earlier 15-year period vs. 269 (56% increase) in the later 15 year period. Global mean surface temperature in the later period has been about 0.3 o C higher than in the earlier period. The authors'imply that their measured rise in global Category 4-5 hurricanes is likely related to these higher global temperatures.Having been involved with hurricane research and forecasting for nearly 50 years, I feel I have an obligation to offer comments on this paper's primary finding on the recent rise of global Category 4-5 hurricanes. I do not agree that global Category 4-5 tropical cyclone activity has been rising, except in the Atlantic over the last 11 years. The recent Atlantic upsurge has explanations other than global temperature rise.
DISCUSSION
The near universal reference to this paper over the last few weeks by most major media outlets is helping to establish a false belief among the general public that global hurricane intensity has been rising and that global warming may be a contributing factor. I cannot accept the accuracy of the authors' measurements of global Category 4-5 hurricanes during 1975-1989 as indicated in their Table 1.
This earlier 15 year global data set would not have been able to accurately delineate Category 4-5 hurricanes from Category 3 hurricanes or even at times from Category 1-2 hurricanes. It was just not possible to confidently distinguish the dividing line between maximum sustained surface winds above or below 130 mph (110 knots) in most global storm basins during the 1975-1989 period.
In the late 1970s I visited all the global tropical cyclone centers and observed their satellite capabilities and the training of their forecasters as part of a World Meteorological Organization (WMO) tropical cyclone survey trip that I was commissioned to make. The satellite tools and forecaster training in the tropical cyclone regions of the Indian Ocean and Southern Hemisphere during the 1975-1989 period was not adequate for the task of objectively distinguishing Category 4-5 hurricanes from Category 3 hurricanes or to always be able to confidentially distinguish Category 4-5 hurricanes from Category 1-2 hurricanes.
DETERMINATION OF TROPICAL CYCLONE MAXIMUM WIND SPEEDS
There always has been, and there probably always will be, problems in assigning a representative maximum sustained surface wind to a hurricane. As technology advances and the methods of determining a tropical cyclone's maximum sustained surface winds change, different values of maximum winds will often be assigned to hurricanes than the values that would have been assigned in previous years.
With the availability of new aircraft deployed inertial dropwindsondes and the new step-frequency surface wind measurement instruments in the Atlantic, it is being found that Atlantic hurricanes and some Northeast Pacific hurricanes that were flown have sustained surface winds that are often stronger than would have been estimated from wind values extrapolated from aircraft altitude. Due to these recent and continuing changes in measurement techniques (Franklin et al. 2003), Saffir-Simpson category numbers in the Atlantic have and likely will continue to creep upward. These changes will likely be translated to other global tropical basins.
CHANGE IN INTENSITY MEASUREMENT TECHNIQUES IN THE
NORTHWEST (NW) PACIFIC
The Northwest Pacific basin is the most active of all tropical cyclone basins. It had aircraft reconnaissance center fixes during the period 1945-1986 but has not had aircraft reconnaissance since. The satellite has been the only tool to track NW Pacific typhoons since 1987.
There was an anomaly in the measurement of typhoon intensity in the 14-year period of 1973-1986 when the Atkinson-Holliday (1977) technique for typhoon maximum wind (V max ) and minimum sea-level pressure (MSLP) was used. The Atkinson-Holliday (AH) technique is known to have significantly underestimated the maximum winds of typhoons in comparison with their central pressures. This interpretation has been supported by a combination of comparative satelliteaircraft data from the Atlantic; by pre-1973 NW Pacific aircraft-measured windpressure, and by the pure satellite measurement since 1987. This topic has been extensively reviewed by Knaff and Zehr (2005). Table 1 (1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986) used the Atkinson-Holliday (1977) Category 4-5 data.
VARIATION IN MAJOR HURRICANE NUMBERS DURING THE LAST TWO
DECADES OF GLOBAL WARMING
As tropical cyclone maximum wind (V max ) observational techniques are frequently not adequate to distinguish between Category 4-5 and Category 3 hurricanes, it might be more representative to observe the increase of major hurricanes By contrast, the Atlantic has seen a very large increase in major hurricanes during the last 10-year period in comparison to the previous 10-year period (38 between 1995-2004 vs.14 during 1985-1994). The large increase in Atlantic major hurricanes during the last 10 years is primarily a result of the multi-decadal increase in the Atlantic Ocean thermohaline circulation (THC) and not due to global temperature increase. Changes in salinity are believed to be the driving mechanism. These multi-decadal changes have also been termed the Atlantic
Multi-Decadal Oscillation (AMO). Even when the large increase in Atlantic major
hurricane activity is added to the non-Atlantic global total of major hurricanes, there is no significant global difference (232 vs. 256) in the numbers of major hurricanes between these two most recent 10-year periods.
COMPARISON OF PACIFIC CATEGORY 4-5 TROPICAL CYCLONE ACTIVITY
DURING THE LAST TWO 10-YEAR PERIODS
The most reliable comparison of Category 4-5 hurricanes that can likely be made is to compare the last ten years (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004) with the prior ten years (1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994) for the storm areas monitored by the US and Japan. The two North Pacific basins do not indicate that the number of hurricanes of Category 4-5 intensity have increased in the last 10 years when global surface temperature have risen (Table 3).
COMPARISON OF ATLANTIC HURRICANE ACTIVITY BETWEEN THE LAST
15-YEAR ACTIVE PERIOD (1990-2004) WITH AN EARLIER ACTIVE
15-YEAR PERIOD (1950-1964)
There have been past hurricane periods in the Atlantic which have had just as many major hurricanes and Category 4-5 hurricanes as in recent years. A comparison of the last 15 years of hurricane activity with an earlier 15-year period from 1950-64 shows no significant difference in major hurricanes or Category 4-5 hurricanes ( year period, however. This is a reflection of the availability of the satellite in the later period. It would not have been possible that a hurricane, particularly a major hurricane, escaped detection in the earlier period. But many weaker systems far out in the Atlantic undoubtedly went undetected before satellite observations.
SUMMARY
Despite what many in the atmospheric modeling and forecast communities may believe, there is no physical basis for assuming that global tropical cyclone intensity or frequency is necessarily related to global mean surface temperature changes of less than ±0. No credible observational evidence is available or likely will be available in the next few decades which will be able to directly associate global temperature change to changes in global Category 4-5 hurricane frequency and intensity.
shows the official average of the annual number of super typhoons in the West Pacific (equivalent to the number of category 3-4-5 or major hurricanes of the Atlantic). Note that between 1950-1972 and over the last 18 years (1987-2004), the number of super-typhoons has averaged about five per year while during the Atkinson-Holliday period of 1973-1986 it was less than half this number. Yet weaker storm frequency during the 1973-1986 period was about the same as in the earlier and later periods. If we disregard this anomalous 1973-1986 period and compare annual frequency of super-typhoon activity between 1950-1972 versus 1987-2004, we see little difference despite the recent global warming trend.
(
Category 3-4-5). There has been US-Japanese satellite coverage of the north Pacific during the last 20 years, and both satellite and aircraft reconnaissance data have been available in the Atlantic. The biggest rise in global surface air temperature occurred during the last 10 years. The NOAA-NCEP reanalysis of global mean temperature differences between the last two 10-year periods show that the last 10 years (1995-2004) of global surface temperature have been about 0.4 o C warmer than the earlier 10-year period of 1985-1994. If there was an influence of global warming on major hurricane activity, one would expect to see this increase represented by greater numbers of global major hurricanes during the last 10 years in comparison with the earlier 10-year period.
5 o C. As the ocean surface warms, so does the global upper air temperature to maintain conditionally unstable lapse-rates and global rainfall rates at their required values. Seasonal and monthly variations of SST within individual storm basins show only very low correlations with monthly, seasonal, and yearly variations of hurricane activity. These correlations are typically of the order of about 0.3, explaining only about 10 percent of the variance. Other factors such as tropospheric vertical wind shear, surface pressure, low level vorticity, mid-level moisture, etc. play more dominant roles in explaining hurricane variability on shorter time scales. Although there has been a general global warming over the last 30 years and particularly over the last 10 years, the SST increases in the individual tropical cyclone basins have been smaller (about half) and, according to the observations, have not brought about any significant increases in global major tropical cyclones except for the Atlantic which as discussed, has multidecadal oscillations driven primarily by changes in salinity.
Table 1of the Webster et al. paper indicates that there were 32 Indian Ocean and South Pacific Category 4-5 tropical cyclones in 1975-89 and 79 (247 percent more) during the 15-year period of 1990-2004. Such large increases are not reasonable given our lack of confidence in the Category 4-5 measurement techniques and the fact that the frequencies of the weaker cyclones in these basins did not show much difference. This paper also presents data which shows that there has been no general increase in the number of global hurricanes and tropical storms over the last 35 years during which global sea-surface temperatures have been rising. I concur with this measurement. It agrees with the recent research by my colleague, Phil Klotzbach, who has made similar tabulations.
Table 1 .
1Comparison of the annual average of super-typhoon activity in three multi-decadal periods in the western North Pacific. The middle period
intensity scheme. Reported maximum wind values were too low.Years
Annual Average
Number of
Super-Typhoons
Basin July-Sept
SST ( o C)
10-25 o N; 120-160 o E
1950-1972
5.3
28.93
1973-1986 (AH)
2.3
28.92
1987-2004
4.9
29.22
Who would believe that the annual super typhoon activity of the 14 year period
1973-86 (years AH technique was applied) would be only 44 percent of the
annual super typhoon activity of the prior 23-year period or the current 18-year
period? This period of suppressed super-typhoon frequency during 1973-86
closely corresponded with the first 15-year period of Webster et al.'s 1975-89
Table 2
2shows the number of measured major hurricanes (Cat. 3-4-5) around the
globe (excluding the Atlantic). Note that there has been no apparent difference
in reported major (Cat. 3-4-5) hurricanes between these two 10-year periods
despite the globe being about 0.4 o C warmer in the recent period.
Table 2 .
2Comparison of observed major (Cat. 3-4-5) tropical cyclones in all
global basins (except the Atlantic) in the two most recent 10-year periods of
1985-94 and 1995-2004.
1985-1994
(10 Years)
1995-2004
(10 Years)
North & South
Indian Ocean
45
50
South Pacific &
Australia
44
41
NW Pacific
88
87
Northeast Pacific
41
40
GLOBE TOTAL
(excluding Atlantic)
218
218
Table 3 .
3Comparison of the number of Category 4-5 hurricanes in the North
Pacific during the last two 10-year periods.
1985-1994
(10 Years)
1995-2004
(10 Years)
NE PACIFIC
31
30
NW PACIFIC
70
65
TOTAL
101
95
Table 4 )
4even though the global surface temperatures
Table 4 .
4Comparison of Atlantic tropical cyclones of various intensities between1950-1964 and the recent 15 year period of 1990-2004. Cat.
4-5
Cat.
3
Net
IH
Net
H
Cat.
1-2
TS
NS
July-August SST
10-25 o N; 30-70 o W
1950-64
(15 yrs)
24
23
47
98
51
50
148
25.69
1990-04
(15 yrs)
25
18
43
100
57
78
178
26.11
1990-04
minus
1950-64
+1
-5
-4
+2
+6
+28
+30
+0.42
Percent
Increase
+4% -22% -9% +2% +12% +56% +18%
---
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| sample_1484 | 0.9998 | arxiv | |
Vaschenko V M
Ye A Loza *State Ecological Academy, Kyiv, Ukraine, E-mail: **State Ecological Academy, Kyiv, Ukraine, E-mail:ozonetemperaturecorrelationscattering indexabsorption indexbias error
Influence of the stratosphere temperature on ozonosphere optical characteristics and instrumental problems of total ozone content remote measurements In this paper we investigate stratosphere temperature impact on remote ozone satellite and ground-based optical observations. High correlation between stratospheric temperature and instrumentally determined total ozone content requires taking into account temperature dependency of ozone absorption and scattering indexes and of other atmosphere characteristics for inverse ozone observations problem solution. The assumption that the majority of observed ozone anomalies and trends are caused by atmosphere temperature change is made.
Introduction
Remote passive investigations of the Earth atmosphere state and content are based on spectrometric analysis of scattered in the atmosphere solar radiation. Its parameters depend on spectral scattering coefficients of atmospheric components -oxygen, nitrogen, small atmospheric components including ozone and aerosol.
Optical radiation scattering characteristics by atmospheric components depend on many factors, e.g. their concentration, external pressure, atmosphere temperature [1], external electric and magnetic fields [2], solar constant variations [3], etc. Moreover there 1 are effects connected to fractal fluctuations in the atmosphere [4] and overlapping of absorption, radiation and scattering spectra of the atmospheric components.
Remote atmosphere spectrometry considers these and other phenomenon by atmospheric models created for regional scale with some degree of account for seasonal variations. The accuracy of experimental results obtained by such models application is satisfactory for latitudes up to 70 o due to a specific quantity of contact (chemical) experimental data on small atmospheric components concentration. However, the accuracy of ozone observations may reduce due to anomalous atmospheric phenomenon or insufficient atmosphere experimental investigations in high latitudes.
Therefore, taking into account ecology, climate and socio-political importance of the Earth ozone layer, this paper considers interconnection between temperature variations and anomalies and trends of instrumentally determined total ozone content (ITOC). The conclusions and suggestions for other probable phenomenon are made.
Problem formulation
It is known that molecular absorption spectral band form, in particular its full width at half maximum and maximum height, depend on external conditions -and first of all on temperature. The spectral band broadening may be inhomogeneous (first of all caused by Doppler effects which strongly depends on gas molecules velocity distribution, i.e. on temperature) and homogeneous (mainly due to impact broadening that depends on temperature and pressure). These two broadening types are always observed together in nature and the spectral band form is described by Voigt profile [5,6]. Spectral bands of molecular absorption may have very complex form due to overlapping of different oscillatory and rotational energy levels and produce a sophisticated optics and thermodynamics problem.
Moreover, apart from classical effects we should also consider non-linear interaction cross-section increase with temperature increase and absorption cross-section temperature hysteresis phenomenon, first of all due to hysteresis changes in chemical-andphysical atmosphere content due to temperature change [7]. 2 Ozone observations are also influenced by temperature change of other atmosphere components optical properties due to the same temperature effects in other molecular and atomic gases and ions. Moreover temperature changes in atmosphere aerosol are much harder to predict, e. g. due to possible phase changes [7] and chemical compound change due to temperature-dependent reactions with external environment.
The natural temperature range in the Earth atmosphere is greater than 100 degreesfrom +50 o C at the equator to -70 o C at the poles. This leads to significant ozone scattering coefficients change and therefore to non-linear increase in ITOC bias errors. The registered temperature records for the last century are -89.2 o C ("Vostok" station, Antarctic, 1983) and +57.8 o C (Libyan desert, Libya, 1922). At height of ozone maximum (20-30 km ) the stratospheric temperature is less than near-surface by 45-75 degrees and the pressure drops from 1000 to 20-100 mBar.
Ozone absorption and scattering coefficients temperature change
Many authors stress the importance of knowing the experimental temperature dependency for ozone scattering and absorption effective cross-sections for accurate determination of atmosphere transparency in visible and UV spectrum ranges [8][9][10][11].
Changes in ozone absorption coefficients in visible range at temperature change by 80 degrees are estimated up to 40% at edges of the absorption band [12] and up to 10% at its maximum [13]. Considering the fact that absorption coefficients used in atmospheric models differ from the last experimental results [14] there is an high demand for detailed laboratory investigations of ozone optical properties dependency on temperature and pressure and also for synchronous atmosphere ozone and temperature observations and for effective theoretical algorithm of these data interpretation.
Theoretical calculations [1] show that atmosphere transparency and, respectively, absorption and scattering coefficients are directly-proportional to both temperature and pressure at near-ground atmosphere layer. Especially these changes are essential in UV range, where ITOC determination error may reach 15% at temperature change by 40 degrees and about 6% at pressure change by 40 mBar [1]. 3 For latitudes above 70 o due to climate conditions influence (and first of all the stratosphere temperature) an unaccounted earlier bias error appears that according to ground-based [15] and satellite [16] experimental investigations may be estimated 10% at minimum. It may be avoided only by parallel atmosphere temperature measurements. It is well-known that Dobson spectrometer and others standard devices for ozone concentration measurements give significantly underestimated values of ITOC in case atmosphere temperature reduction at the height of ozone maximum [17].
Using this dependency a method based on ozone absorption spectral band wings intensity measurements synchronous to total ozone content measurements by spectral band maximum was proposed [18][19][20].
Temporal anomalies and trends of instrumentally determined total ozone content
Such ITOC temperature dependency leads to correlation of long-term ITOC reduction trend [21] with temperature reduction on decades scale [22][23][24]. For the height of ozone maximum a high positive correlation of ITOC and temperature is observed for quasi-two years and half-year ITOC oscillations according to spectrometry [25][26][27] and LIDAR data [28]. Short-period correlation of ITOC and temperature is also observed at 13-27 days scale [29-31]. Similar phenomenon were also observed for other gases [32].
At heights 30-80 km anti-correlation of ITOC and temperature is found, while for other heights -a high positive correlation with no time delay is observed [25-27, 33-36].
ITOC and temperature dynamics is described by equal fractal dependencies [4].
For some experiments the ITOC and near-ground temperature correlation reaches 0.9 [37,38]. However such dependency may not be considered reliable because near-ground temperature is not linearly connected to the stratospheric temperature.
Therefore a large quantity of investigations show that at all timescales from days to decades a high correlation between ITOC and stratosphere temperature is observed pointing at their close interconnection. Here ozone integral spectral scattering and absorption coefficients variation with temperature change may be misinterpreted as total 4 ozone content change. This is also true for remote optical investigations of other small atmospheric components.
Spatial anomalies of instrumentally determined total ozone content
The results of 14-years atmosphere observation by TOMS (Total Ozone Mapping Spectrometer) and MSU (Microwave Sounding Unit) at 150-50 mBar height showed stable high temporal-spatial correlation between stratospheric temperature and ITOC both for local phenomenon and for global trends [39,40]. The same dependency was found for sudden stratosphere heating in Arctic in 2002, revealed by space Fourier-spectrometer MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) [41]. The same effect was also revealed by other ground-based and satellite optical measurements [42]. From 30 November to 1 December 1999 a "mini-ozone hole" was observed over Europe with its maximum coinciding with temperature minimum in the tropopause [44].
The same localized manifestation of ITOC and temperature coupling was observed in October 1987 and November 1999 in polar regions [45].
Investigation of ozone anomalies over Europe during winter 1991-1992 revealed correlation between temperature and instrumentally determined ozone partial pressure in the atmosphere [46]. The same phenomenon was observed for the edge of the Polar stratospheric vortex and the South oscillation [47]. Synchronous observation at McMurdo station at Antarctic Peninsula also show high positive correlation between ITOC and temperature [48].
Localization of low stratosphere temperature over Antarctic is explained in [49].
Therefore we may make a conclusion that the reduction in ozone layer absorption ability in polar regions during polar winter may be caused not by real atmospheric ozone quantity change, but by stratosphere temperature influence on ozone molecules and other atmospheric components scattering and absorption coefficients. 5 The phenomenon of ITOC dependency on temperature and other atmospheric components characteristics will manifest for all the optical methods based on measurement of optical radiation absorption or scattering by ozone. Due to temperature change all the methods including UV-spectrometry and LIDAR investigations will correlate with one another but despite this will have a high uncontrolled bias error.
Time-delayed temperature phenomenon in ozone layer
We should also stress that ITOC and temperature correlation is non-linear [50].
Moreover, there are inert temperature phenomenon. days at different heights [53][54][55]. Also 27-days variations in spatial distribution of ITOC are found to be connected to Sol rotation [56].
Atmosphere dynamics and atmosphere aerosol impact
During sand storms in deserts it was found that ITOC correlates with atmosphere aerosol state [57]. Based on in-year synchronous ITOC and temperature variations investigation their connection to atmosphere aerosol state was found [58,59]. There is an suggestion that temperature and aerosol state change together with solar activity variations played the most important role in reduction of ITOC in 1979ITOC in -1993. 6 A reliable interconnection of ITOC and wind intensity was found [62,63], which was associated by some authors with parallel stratosphere cooling [64]. Atmosphere dynamics influence on ITOC was also observed [65][66][67][68][69].
Conclusions
1. The temperature of the lower stratosphere significantly influences instrumentally determined total ozone content due to ozone absorption and scattering coefficients temperature dependency. Contemporary ozone measurement methods do not consider temperature impact during total ozone content determination leading to bias errors at least 15-20%, especially at polar regions. Therefore careful experimental investigations of ozone scattering and absorption coefficients temperature dependency determination is required to include it in theoretic models.
2. High positive correlation between instrumentally determined total ozone content and stratosphere temperature is observed both in time and in space. The correlation coefficients of instrumentally determined total ozone content and stratosphere temperature are found to be 0.6 to 0.9 in different papers. This means that bias error of instrumentally determined total ozone content may be over 90%.
3. Anomalous or seasonal stratosphere temperature reduction leads to phenomenon of instrumentally determined total ozone content reduction. As a result, the phenomenon of "ozone holes" may be explained by optical-and-temperature phenomenon due to change of ozone absorption and scattering coefficients and not ozone molecules quantity change. This is especially important for Antarctic and Arctic where Sol zenith angles are large and stratosphere temperature is very low in winter. 4. Measured by remote methods instrumental values of total ozone content may also change due to atmosphere dynamics and temperature or seasonal change in properties of other atmospheric components, first of all -aerosol. 5. In order to avoid bias error and to understand real physical-and-chemical nature of ozone holes and planetary waves measurement complexes for synchronous investigation of total ozone content, aerosol characteristics and temperature must be 7 developed. Also theoretical apparatus of ozone models should be improved to accommodate these phenomenon.
Moreover, in different regions the value of the correlation is constant. It changes depending on geographic location of the observation site [43].
The ozone layer state significantly influences the atmosphere temperature -the more ozone absorption coefficients and ozone content are the more energy it absorbs changing the atmosphere temperature. Moreover the time-delayed phenomenon are connected to temperature dependency of ozone chemical reactions [22]. Also ozone isotope content changes depending on stratosphere temperature [51, 52]. On short time intervals under solar UV-radiation flux change at low latitudes according to the data of SBUV (Solar Backscattered Ultraviolet Instrument) and SAMS (Stratospheric and Mesospheric Sounder) installed at Nimbus 7 satellite a correlation of ITOC and solar flux variation was found to be 0.3 to 0.6 with phase shifts from 3 to 13
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| sample_1516 | 0.9595 | arxiv | |
SPAIN ON FIRE: A NOVEL WILDFIRE RISK ASSESSMENT MODEL BASED ON IMAGE SATELLITE PROCESSING AND ATMOSPHERIC INFORMATION
Helena Liz-López helena.liz@alumnos.upm.es
Computer Systems Department
Computer Systems Department
Universidad Politécnica de Madrid
Spain
Javier Huertas-Tato javier.huertas.tato@upm.es
Signal Theory and Communications Department
Universidad Politécnica de Madrid
Spain
Jorge Pérez-Aracil jorge.perezaracil@uah.es
Computer Systems Department
Universidad de Alcalá
spain
Carlos Casanova-Mateo
LATUV, Remote Sensing Laboratory
Universidad Politécnica de Madrid
Spain
Julia Sanz-Justo
Computer Systems Department
Universidad de Valladolid
spain
David Camacho david.camacho@upm.es
Universidad Politécnica de Madrid
Spain
SPAIN ON FIRE: A NOVEL WILDFIRE RISK ASSESSMENT MODEL BASED ON IMAGE SATELLITE PROCESSING AND ATMOSPHERIC INFORMATION
Wildfire risk assessmentAutoencoderRegression modelDeep LearningFusionatmospheric variablesFew-shot Learning
Each year, wildfires destroy larger areas of Spain, threatening numerous ecosystems. Humans cause 90% of them (negligence or provoked) and the behaviour of individuals is unpredictable. However, atmospheric and environmental variables affect the spread of wildfires, and they can be analysed by using deep learning. In order to mitigate the damage of these events we proposed the novel Wildfire Assessment Model (WAM). Our aim is to anticipate the economic and ecological impact of a wildfire, assisting managers resource allocation and decision making for dangerous regions in Spain, Castilla y León and Andalucía. The WAM uses a residual-style convolutional network architecture to perform regression over atmospheric variables and the greenness index, computing necessary resources, the control and extinction time, and the expected burnt surface area. It is first pre-trained with self-supervision over 100,000 examples of unlabelled data with a masked patch prediction objective and fine-tuned using 311 samples of wildfires. The pretraining allows the model to understand situations, outclassing baselines with a 1,4%, 3,7% and 9% improvement estimating human, heavy and aerial resources; 21% and 10,2% in expected extinction and control time; and 18,8% in expected burnt area. Using the WAM we provide an example assessment map of Castilla y León, visualizing the expected resources over an entire region.
Introduction
Forests cover 30% of terrestrial ecosystems, representing a total of 4.06 billion hectares [33] and are home to 80% of amphibians, 75% of birds and 68% of mammals worldwide [59]. At the environmental level, in addition to affecting biodiversity (animal and plant), forests are also an important factor in soil transformation, vegetation succession, soil degradation, and air quality, among others [48]. Wildfires threaten to disturb these ecosystems with increasing frequency and damage, a worrying byproduct of climate change [51,28] among many other factors. Fires can also directly affect humans destroying buildings, burning crops, causing the death of animals, or directly have an effect on the health of the population due to the direct action (burns) or indirect action (smoke inhalation) of fire [52].
In recent years the Copernicus Sentinel-3 mission recorded 16000 wildfires throughout the world in August 2018 and 79000 in the same period of 2019, which is a large increase in a single year [17]. In Spain, between January and August, the burnt area in 2022 was 247.667 hectares, an area almost five times larger compared to the previous year, 51.571 hectares. In addition, the number of large fires has increased from 16 fires in 2021 to 51 between January and August 2022. Thus, the highest figure since 2012, when 34 large fires occurred, had already been reached 1 . Some European countries show an increasing number of wildfires also in the burnt area, as stated by European Forestry Fire Information System (EFFIS). For example, Romania, Italy and France have increased the number of fires and burnt area, showing double the increase in 2022 compared to the annual average between 2006 and 2021 2 . The growing in severity over the years is concerning. Quality tools are needed to help control and manage resources in order to minimize the damage they cause.
Fire causes that can be aggregated into two groups: natural or anthropogenic. The latter can be divided into two types: accidental, due to human negligence; or provoked, whether caused by arsonists or pyromaniacs [53]. In most cases the cause of wildfires is unknown, but if the origin is known human causes account for more than 90% of the total number of wildfires. This makes fire prediction very difficult, since human behaviour is still unpredictable [55,35,46]. For this reason, an accurate fire prediction model can be considered unfeasible as it would have to rely on individual human behaviour, i.e., when a person is going to commit a reckless act that triggers a fire or when a person is going to decide to start a fire. However, the severity of a fire is tightly related to the existing environmental and vegetation state conditions before its occurrence. Therefore, severity could be estimated observing these conditions [10,5].
Atmospheric and environmental variables that influence fire intensity are usually georeferenced variables with a latitude and longitude. Their similarity to images makes this modality analyzable with Computer Vision (CV) techniques such as Convolutional Neural Networks (CNN). These architectures have outstanding ability to identify patterns in data, which enhances the performance of earlier systems based on machine learning models. Due to their strong performance in a variety of tasks, such as computer vision or natural language processing, this advantage has made them a benchmark in deep learning (DL) [32].
However, most state-of-the-art articles use machine learning techniques, and the few that use DL do not explore options such as CNN. One of the possible reasons for not exploring this type of technique is the lack of data, since most datasets contain a small number of samples. For this reason, we have decided to explore the option of creating a pretrained autoencoder (AE) that is capable of learning the patterns and understanding the atmospheric and environmental variables used. Later, we transfer the encoder to a regression task to predict the variables related to fire management. The article can be divided into five main modules, as shown in Figure 1.
The main contribution of this manuscript is the creation of a regression model based on Deep Learning techniques for wildfire management, called Wildfire Assessment Model (WAM), pretrained with atmospheric and environmental variables of the area and finetuned with a very small data set, 445 samples. However, this is not the only contribution presented in this manuscript:
• The approach used to create the input data is novel and provides more information than traditional approaches. • WAM model creates a Deep Learning baseline for comparisons for future work in the field.
• A new AE model that uses categories instead of the original sample, extracting information on how the meteorological and environmental variables work.
This manuscript has been structured as follows: Section 2 summarizes the most relevant work in the state of the art, with a special focus on fire severity and burnt area prediction problems; Section 3, describes in detail the atmospheric and environmental variables used, as well as the labels that are intended to be predicted; Section 4, describes the proposed methodology for this problem, how we have prepared the samples that are the input to our models, the encoder model and the regression model, the baselines against which we compare ourselves and the final visualization; Section 5 presents the experimental results, and Section 6 presents the main conclusions and possible lines of future work.
Related work
Since the 1990s, artificial intelligence has been applied to the science and management of wildfires [26], as these techniques can contribute to fire detection and management [6]. The features used in this field, such as atmospheric, vegetation, or topological variables, can be analysed using DL techniques. These techniques can extract information from samples faster and more efficiently than humans for specific tasks [14], and their effectiveness can be observed in other problems related to ecology [18,50,13,57] and the environment [49,60,40].
Within the field of wildfire management, we can find different types of tasks before, during and after the event. At the level of fire prevention, we can find articles on lightning prediction to try to prevent fires at those points [41] or to predict which areas have favourable fire conditions [56]. During the active period of wildfires, these techniques can be used to predict which area will burn based on the evolution [24], the spread and growth of the fire [47]. Finally, machine learning techniques can be applied to post-fire management, such as managing area regeneration [20], the socioeconomic effects of the incident [15] or the long-term effects on the substrate, such as erosion [8], and how air quality and particulate matter will evolve [66,36].
Wildfire prediction systems
As we have introduced above, one of the most explored lines of research in this field is the prediction of wildfires. These systems try to predict whether a fire will be caused by a series of atmospheric, topological, vegetation, and human conditions in a given area. Campos-Vargas and Vargas-Sanabria [9] attempts to predict the probability of fires in tropical dry forests in an area of Costa Rica (Guanacaste Conservation Area) between 1997 and 2020 using a generalized least squares model (GLS), using different variables: slope, accessibility, fire line density and burnt area. Xu et al. [61] studied the influence of climate warming on the frequency of wildfires in Changsha (China) between 2011 and 2017, for which they created a dataset consisting of 20622 fire incidents, using atmospheric variables: wind, precipitation, and daily maximum and minimum temperature. However, the previous variables have been combined and finally three variables have been used: every day's fire frequency, daily maximum temperature, and daily minimum temperature. In this article, they used three different models: random forest, SVM, and polynomial, to compare the performance of the different models, they used the MSE metric and R 2 , which showed that the best model was the random forest followed by the polynomial regression model, both using the minimum daily temperature variable. Although the results are promising, the variables used in this study are too limited. Janiec and Gadal [27] studied the risk of fire among six different classes, i.e. a multiclass problem in Yakutia (Russia) between 2001 and 2018. They used different environmental, vegetation, topographic and human variables and conducted two studies, the first at the level of the whole region (Yakutia) and the other of a more specific area (Nyurbinsky), for each of which two different models, random forest, and maximum entropy, each of which performed better in one region, Yakutia and Nyurbinsky, respectively. Another example of fire prediction is Milanović et al. [37], that analyse the probability of fires in eastern Serbia between 2001 and 2018, divided in five different categories (very low, low, moderate, high, and very high), although unlike other articles, they do not specify the number of samples used, each sample is made up of a total of 17 variables that we can classify into 4 different groups: vegetation, anthropogenic, topographic, and climatic. The aim of the article is to predict the risk of fire with two different models, random forest and logistic regression, and finally to show the probabilities in a map format. Kang et al. [30] show a system to predict the probability of fires in southern Korea between 2014 and 2019. To do so, they classified fires into four risk classes using different meteorological, geographic and fuel data. To analyse these data, they used an ensemble composed of two catboost models where the input was different, the first model used all variables while the second one only used the atmospheric variables. Michael et al. [36] have developed a fire probability mapping system for Greece during 2007, dividing fires into five different categories. The machine learning techniques used were logistic regression, random forest, and XGBoost. Regarding the variables used for this problem they did not rely only on static climatic and topological variables of the study area, but also included dynamic vegetation variables such as NVDI. The best performing model for this problem was XGBoost. Pham et al. [45] attempt to predict fire risk in Vietnam's e Pu Mat National Park, using a total of 57 wildfire samples, having each one of them nine variables (basically anthropological, vegetation, meteorological and topological). To analyse these data, they used different algorithms, Bayes Network, Naive Bayes, decision tree, and Multivariate Logistic Regression and tried to generate a map from the predicted classes (divided into three different classes). The best performing model was the Bayes network with an AUC = 0.96, followed by the decision tree with an AUC = 0.94.
We can observe how many authors use machine learning techniques such as random forest or Logistic Regression among others to predict wildfires. This is striking considering the great progress of Deep Learning and the fact that the variables used are usually geo-referenced, which also allows them to be analysed with computer vision techniques such as convolutional neural networks. However, we can find some examples that use deep learning. For example, Choi and Jun [11] analyse the risk of fires in Korea between 2011 and 2017. The dataset consists of 201.082 samples composed of 107 different variables that cause and prevent wildfires. To improve current prediction systems, the article uses three different systems: logistic regression, artificial neural networks, and fire risk indexing, which are combined to calculate the final fire risk assessment. Mohajane et al. [38] developed five different ensemble-based models to predict wildfire risk: random forest, support vector machine, multilayer perceptron, which is a neural network, classification and regression tree, and logistic regression. The study area was in the north of Morocco between 2005 and 2015, of which they have a total of 510 wildfire samples, containing a total of 10 variables (topographic, socioeconomic and meteorological).
Regarding most recent works, it can be seen that Deep Learning techniques are barely used in forest fire studies. This could be explained because of the limited number of samples used in the different works analysed; for that reason we have decided to explore the use of these techniques in a problem of wildfire risk assessment overcoming the limitation set by the number of samples. Another limitation is that the authors try to predict whether a fire will occur or not at a specific point or region, which is extremely difficult since in many cases only meteorological and topological variables are taken into account, which would allow only the prediction of natural fires. Even if anthropological variables are taken into account, such as distance to nearest towns or the existence of routes such as roads, it does not come close to reality, since as mentioned in Section 1 there are two main reasons for human causes: accidental and provoked, which can be caused by arsonists and pyromaniacs, and human behaviour is impossible to predict. For all these reasons, we decided against creating a wildfire prediction system, due to the number of variables involved and the difficulty of predicting human behaviour.
Use of convolutional neural networks in active fire detection
Other works are focused on the rapid detection of active fires, where we can observe a greater presence of neural networks, in particular convolutional neural networks. Muhammad et al. [39] have developed a system for the detection of active fires in forests, houses, and vehicles, for which they have created a dataset with 68,457 samples and were processed by a convolutional network composed of five convolutional layers and three dense layers, reaching an accuracy greater than 0.94. Park et al. [44] combines multiple AI frameworks, including a CNN, a deep neural network, and adaptive fuzzy logic for fire detection. The aim of the system is early detection of active fires in order to be able to carry out a rapid response and minimise damage; the system is focused on finding a solution to the transmission of information, which is the main bottleneck of these systems. Zhang et al. [64] show another example of early detection of active fires in images. For this purpose, they divided each image into 16x16 patches and tried to detect on which patches flames appeared. For this, they use a dataset composed of 25 videos, including a total of 21 positive and 4 negative sequences. They use two different architectures, the first one a standard CNN composed of three convolutional layers and two dense layers; and the second architecture, based on the previous one, which is trained with local patches that do not contain global information of the sample. Although these models are interesting and use similar techniques to ours, they are only useful when the fires are active, while our objective is to anticipate them, in order to manage resources efficiently and minimise the damage caused by the fire. These models have two main limitations. Firstly, they require security cameras to detect fires, which limits their application. These systems are suitable for urban areas or nearby areas, however, they are unfeasible in forested areas, as it would be difficult to monitor the entire forest area. Secondly, these systems are designed to detect signs of active fires, such as flames or smoke, which allows a quick reaction to such an event but not prevention or pre-fire management, as is our objective in this work.
Machine learning for wildfire management
Wildfire management can be carried out in different ways, either during the event or before it. One of the options to try to minimise the damage caused by these events is to predict how the fire will spread. For example, Zohdi [65] shows a system to predict the evolution of active fires based on the trajectories of hot particles, wind, updraughts and the topology of the surrounding combustible material. The authors created a simulation combined with machine learning algorithms to try to predict the dispersion of the fire and the possible generation of new ignition sites. The results obtained by the system are plotted in three dimensions to show in which direction the fire will spread. Julian and Kochenderfer [29] develop a deep reinforcement learning system using different decentralized controllers that accommodate the high dimensionality and uncertainty inherent in wildfires. For these, they tried two different approaches: the first by controlling aircraft decisions individually, and the second allow the aircraft to collaborate between them on a map and keep track of visited locations. To do this, they developed a stochastic system to simulate fire conditions and see how the fire will progress over time. The architecture presented consists of two different networks, one to process the images based on a typical convolutional neural network and another network composed of dense layers for the continuous inputs. Both outputs are merged and the final result is given by the input of 3 dense layers. McCarthy et al. [34] developed a system to predict the evolution of active wildfires, predicting the direction and area that will burn over time. The main problem with this approach, as they explain, is that they are difficult to predict due to the complexity of the problem. Consequently, they proposed a convolutional neural network based on the U-net and used geostationary multispectral images and environmental variables such as vegetation and terrain data. The results are displayed on a map, where the space that the fire will occupy every half hour is marked with different coloured lines. Hodges and Lattimer [24] created a series of samples from atmospheric variables, where each channel represents a different variable for the study area, corresponding to satellite measurements. They used 13 different variables related to vegetation, meteorology, topography and other variables, such as the initial burn map or the fuel model. They used the convolutional inverse graphics networks (DCIGN) model to predict the burn map, which is composed of two convolutional blocks followed by a reshape layer (flatten layer), a dense layer and finally a combination of a reshape layer and a convolutional layer that will generate the burn map, 6 and 24 hours after the beginning of the wildfire. Other works try to predict the final size of the affected area between different classes at the time a fire starts. For example, Coffield et al. [12] tries to predict the final size of the fire between 3 different classes based on meteorological, topographical and vegetation variables. They applied different machine learning algorithms, such as decision tree, random forest, k-nearest neighbours, gradient boosting, and multilayer perceptron. The problem with the latter article is that once the fire starts, the specialized crews can already see how big the fire is going to be.
Some articles tried to predict how susceptible a particular area will be to wildfires. This approach, unlike the previous, allows to better manage resources, try to prevent and minimise the damage caused by fires. Boulanger et al. [7] develops a consensus model based on five different machine learning models: generalized linear model, random forest, gradient-boosted, regression trees, and multivariate adaptive regression splines to project future burning rates in boreal Canada. The data used to design this system were taken between 1980 and 2000 and only fires where the number of hectares burnt was greater than 200 were taken into account. In total, 12228 samples were acquired using a series of climatic, vegetation, land cover, and topographic variables. Future climate projections were obtained from three climate models and three scenarios of anthropogenic climate forcing for three 30-year periods. Pais et al. [42] have developed a system to predict how susceptible an area is to fires based on topology vegetation variables between 2013 and 2015. They combined the information from all these variables to generate an image that can be analysed using a convolutional neural network, composed of three convolutional blocks of 1, 2 and 3 convolutional layers each and a dense layer. The system returns the ignition probability of each image and a GradCAM-based visualization that allows a better understanding of how the CNN has arrived at the final result. On the other hand, Zhang et al. [63] generate a global map of the probability of ignition, i.e. how susceptible each point is to fire using vegetation and environmental variables, such as wind, maximum and minimum temperature, humidity or soil moisture, among others. To generate the global fire susceptibility maps they tested four different techniques, two convolutional neural networks, and two MLP models. The first CNN uses two-dimensional convolutional layers and the second one uses one-dimensional convolutional layers; the same happens with the MLP models; the first one uses two-dimensional images flattened with a flatten layer as input, and the second one uses a one-dimensional array as input. As we can see, several authors generate maps from the results obtained by the different systems; this allows us to visualise the probability or risk of the fire, the susceptibility of the area to these events, the burnt area, and the spread of active or in a future wildfire. For example, Al-Fugara et al. [2] have developed a map where the wildfire susceptibility of each pixel in the study area can be seen. To do this, they have created a system of six classes that represent different degrees of susceptibility (very low, low, moderate, high, and very high); additionally, it is observed that most wildfires have occurred in areas with high susceptibility. Other authors, as Zhang et al. [63] generate maps on which measure the probability of ignition with a colour scale.
As with the work shown in Section 2.1, most fire management systems use machine learning algorithms without exploring other options such as deep learning, which has worked very well on other problems. Other work focuses on measuring the susceptibility of a fire to occur, which is another way of trying to predict fires, which as we have already explained is very complex as human behaviour is involved. The models that are really focused on management are those that try to predict the evolution of fires, these works try to predict the area that will burn throughout the wildfires, i.e. they focus on a single label, whereas we have tried to predict six labels related to fire management, including the resources needed and the time needed to control and extinguish fires.
In our work, we have tried to overcome several of the limitations present in the state of the art. First, as in most previous studies, we have an extremely small labelled dataset (597 wildfire data records), so we decided to apply few-shot learning techniques by creating an autoencoder that was able to learn the patterns of the different features of the samples and applying this knowledge to a regression task to predict the resources that would be needed in case of a wildfire. Finally, to facilitate its use by the final users, we have generated prediction maps that shows the resources needed in each area.
Data collection
The objective of this paper, as explained in Section 1, is to develop a regression model (WAM) capable of predicting the resources, the time needed to control and extinguish wildfires, and the area that will burn during the event, to help manage resources and reduce economic and environmental losses.
For the purpose of this work, we have used three different sources of information: 1) wildfire information, this information will be used to create the labels, including information on the locations where fires have occurred, including the resources needed to extinguish them, the time it took to control and extinguish the fire and the total area burned; 2) atmospheric variables, related to fire spread such as 10 metre U wind component or total column ozone; 3) greenness index, an indicator of vegetation health is another variable closely related to forest fire management. The last two will be combined using early fusion techniques to create the samples of the different fires (variable X) and the information on fire management will be the labels of these samples.
Wildfires in Spain
In this work, we used a dataset composed of 597 wildfire data records taken from two Spanish autonomous regions: Castilla y León (446) and Andalucía (151), see Figure 2. Each wildfire data record contains the coordinates, date, and relevant information about the wildfire. The coordinates of Castilla y León are latitudes between 40 and 43.3 and longitudes between -7.2 and -1.8; and the coordinates of Andalucía are latitudes between 35.5 and 38.5 and longitudes between -7.6 and 0. We can see that both regions are very close to each other, but there are significant differences; although they are two autonomous regions in Spain, they have totally different weather. Regarding the annual temperature, there are differences of more than 5 degrees between the both regions, the temperature of Castilla y León is colder. The annual rain, Andalucía has a greater diversity of environments, as it has arid areas (east of Andalucía) and more damp areas (west), while Castilla y León is more homogeneous, with a lower average, except in mountainous areas. Finally, with regard to radiation and insolation, there are also differences between the two, in Andalucía is higher than Castilla y León. Therefore, we can see that the conditions in both regions are very different and that wildfires management must be adapted to them. In Castilla y León the wildfires tend to be concentrated in two sub-regions, Zamora and León, and in others, such as Valladolid, Soria or Palencia, the number of wildfires is insignificant, which means that the fires are concentrated in the west. In Andalucía, wildfires are more distributed throughout the autonomous region, Figure 3b, with fewer events in the centre. Huelva, Málaga, Jaén and Almería are the most affected areas (number of events and burnt area). Although note that forest fires are more spread in Andalucía than in Castilla y León.
As mentioned above, each wildfire data record contains relevant information on fire management, such as extinction time or burnt area. This information is what we will use in our article as labels, each one is explained below. Regarding the Andaluca region, Figure 3b, can be seen some apparent unbalances between the burnt area and the time and resources needed to its extinction, as in the case of the subregion of Almera. On the other hand, in the case of Cordoba, Sevilla, and Cadiz subregions, we see an apparent lower burnt area compared to the number of fires. Another significant difference is that although both regions, Andalucía and Castilla y León, show a similar burnt area, the time and resources needed to extinguish wildfires are higher in Castilla y León. This could be related not only to the topography but also to the previous history of the burnt area (temperature, moisture, vegetation dryness, etc.).
Atmospheric variables
As mentioned above, the second source of information we have used is a set of atmospheric variables related to the spread of forest fires. As these data sources are geo-referenced, i.e. they can be arranged in two-dimensional matrices, as if they were images. These variables use a decimal coordinate system, and the distance between the measured latitudes is 111 km. These data were measured daily in our study period, depending on the variables, they were measured every hour or at different times of the day (always at the same times). These variables are explained as follows [23]:
• 10 metre U wind component: is the horizontal speed of air moving toward the east at a height of 10 metres above the Earth's surface. This variable is positive if the wind comes from the west [4]. • 10 metre V wind component: it is the vertical speed of air moving north at a height of 10 metres above the Earth's surface. 10 metre V wind component is positive if the wind comes from the south [4]. • 2 metre dewpoint temperature (K, kelvin): is the temperature that would have to be cooled for saturation to occur at 2 metres above the Earth's surface. It is a measure that combines humidity, temperature, and pressure. This parameter is calculated as an interpolation between the lowest level of the model and the Earth's surface, considering the atmospheric conditions [21]. • Surface net solar radiation(J/m 2 ): is the low-wave solar radiation incident on the Earth's surface, direct and indirect, less the reflected radiation. It is the radiation that crosses a horizontal plane to the Sun's direction [3]. • Surface net thermal radiation (J/m 2 ):is the radiation emitted by the atmosphere, clouds, and the Earth's surface.
It is the difference between downward and upward thermal radiation at the Earth's surface. The downward thermal radiation is the radiation reaching the surface emitted by clouds and the atmosphere; and the upward radiation corresponds to the radiation emitted by the surface and the downward radiation reflected by the surface [25]. • Surface solar radiation downwards (J/m 2 ): describes the amount of shortwave solar radiation that reaches the earth's surface on a horizontal plane. It represents the radiation incident on the Earth's surface, i.e. that which is not reflected by clouds, suspended particles, etc. [62]. • Surface thermal radiation downwards (J/m 2 ): is a type of thermal radiation that describes the thermal radiation reaching the earth's surface emitted by the atmosphere and clouds [25]. • Total column ozone ( kg/m 2 ): is the total ozone along a column from the surface to the top of the atmosphere.
It provides information on the densities in the atmosphere [54].
Greenness index
The last source of information used in this article is the greenness index (GI) or Green Leaf Index, which shows the relationship between the reflectance in the green channel compared to the other two visible light channels, red and blue [19]. Like the atmospheric variables they are geo-referenced and can be processed as images. The GI measurements were three times per month instead of daily, on the 1st, 11th and 21st day. The coordinate system used in this case is UTM (Universal Transverse Mercator) and the distance between two contiguous latitudes is 25 km compared to 111 km for the atmospheric variables.
Greenness index = 2Green − Blue − Red 2Green + Blue + Red(1)
Data preparation
Once we have defined the different data sources that we are going to use, we have to apply early fusion techniques that allow us to take advantage of all the available information. All these variables are georeferenced with X and Y coordinates for each value, a two-dimensional matrix where the columns correspond with the longitudes and the rows to the latitudes. However, they present differences: the coordinate systems and spatial/temporal resolution; therefore to apply early fusion of modalities, we need to preprocess the relevant information. For instance, the greenness index uses the UTM (Universal Transverse Mercator) system, while the atmospheric variables use the decimal coordinate system. For homogeneity, the GI variable is converted to decimal. Another difference between the information sources is the resolution, the atmospheric variables have a distance between the latitude values of 111 km while the GI variable has a distance of 25 km. However, we need the resolution of all variables to be the same to be able to combine both information sources, so we decided to change the resolution of atmospheric variables, to match the number of columns and rows match between the two variables and early fusion techniques can be applied. The last difference between them is the temporal resolution. Atmospheric variables are recorded on a daily basis and GI is recorded three times per month (from the 1st to the 10th, 11th to the 21st and 21st to the end of the month). Therefore, we decided to divide the variables into two different groups as follows:
• Daily: these variables are 10 metre U wind component and 10 metre V wind component. They are measured daily at 12:00 or 18:00, depending on the variable. If both measurements are available, we choose the first one, but if we do not have a measurement at 12:00, the one at 18:00 is taken. The value measured on the day of the fire was used for these variables because they are directly related to the occurrence of wildfires, as used in the Fire Weather Index [58].
• Trend: this category includes the greenness index, the dewpoint temperature of 2 m, evaporation, net surface solar radiation, net surface thermal radiation, downward surface thermal radiation, and total ozone of columns. The greenness index was not modified. For atmospheric variables the time-series discrete difference was calculated between the dates of measurement of the greenness index. The reasons for using the trend of these variables are the following.
-2 metre dewpoint temperature and evaporation: are metrics of water stress, so the trend measure will allow us to know if the area is losing water vapour or increasing water stress, which would favour the spread of the fire. -Surface net solar radiation and surface net thermal radiation : measures the radiation emitted by the Earth's surface. If these variables increase, it means that the surface is getting warmer. -Surface thermal radiation downwards: is a measure of the thermal radiation that reaches the earth's surface. If this variable increases, it means that the daily temperature tends to increase, which increases evaporation and favours the spread of the fire. -Total columns ozone: this gas is in the atmosphere and absorbs solar radiation and prevents the temperature from rising. If the amount of ozone decreases over time, this means that more solar radiation reaches the surface and will tend to increase the temperature.
To obtain all the matrices explained above, we take the wildfire central and extract the neighbouring data. Each set of fire coordinates results in a 128x128 matrix for each variable. We overlapped the different matrices generated at the end samples with dimensions 128x128x9. The labels are a list of six values, corresponding to the wildfire data records. Finally, the data were normalised, for the samples the z-score normalisation was used in all subsets (labelled and unlabelled samples) and for the labels the min-max normalisation was used.
Data
As explained in section 3.4, the number of wildfire data records is limited, which means that the set of available labelled samples is limited, especially for Deep Learning, so we decided to create also two unlabelled subsets and two labelled corresponding to the two autonomous regions for which we have wildfire data records.
• Unlabelled subsets: that corresponds with the subsets for which we do not have labels.
-Self-supervised data: We have generated a set of 100,000 samples taken at random coordinates and times within the parameters of our study in Castilla y León to train the encoder model, as it would be impossible to train the model with the available labelled data. -Map data: this system predicts the different labels for a specific point, which is not sufficiently explanatory to apply it in real cases, so we have created a set of unlabelled samples covering the entire map of the autonomous region of Castilla y León to create a visualisation that shows the predictions for a specific day, which means that we will generate one visualisation per label. To create the prediction maps, in the case of Castilla y León, we have generated a total of 2,970,000 individual samples superimposed on each other to obtain predictions for each location on the map.
• Labelled sets: that corresponds to the subsets for which we have recorded the labels, as we have explained above, it corresponds to the measurements collected in both autonomous regions.
-Castilla y León: set of 445 labelled samples from the autonomous region; we use this set to test the autoencoder, to fine-tune and test the WAM model representing, respectively, 70 and 30% of the samples. -Andalucía: set of 151 labelled samples from Andalucía, we use it to test the WAM model. This set of samples allows us to test the generalisability of our system when we change the study area.
Methodology
We can summarise the proposed methodology in Figure 4, which is composed of four modules. The first one is the data preprocessing step, where we prepare the images and the labels for the different models. In the second one, we build the AutoEncoder, train it with the random dataset and test it with the dataset of Castilla y León. Then, we used the trained encoder to develop the regression model to estimate the wildfire cost variables. Using the regression model, we develop a map for each variable, where each pixel value corresponds to a prediction.
Autoencoder pretraining
We developed an autoencoder for meteorological understanding. We approach this problem with a self-supervised masked image modeling (MIM) objective. We divide the 128x128 matrix into a grid of 8x8 patches where each patch is masked with a 0.5 probability (Figure 5 second column). Using the unmasked matrix patches ( Figure 5 third column) the system tries to predict the average of the masked values for each masked patch ( Figure 5 last column). In most papers such as [22,16,43,31] the autoencoders attempt to reconstruct the original image directly. In our case, the autoencoder tries to learn to recognise the patterns and trends in the different channels (atmospheric variables), we do not consider a full reconstruction useful enough to warrant the added modelling complexity. For this reason, we assigned discrete categorical labels to the mean values of the patches.
To select the adequate number of bins used in the experiments, we decided to run preliminary experiments with different values of bins: 4, 8, 16, 32 and 64 categories. We also explored for each experiment different values of learning rates (5e-5, 1e-4, 2e-4, 5e-4, 1e-3) in order to select the combination with the best performance on this task.
After preliminary experiments we settled on the following hyper-parameters for WAM pretraining as summarized in Table 1 Encoder architecture As we explained before, the encoder maps the features from the input into a latent representation. In this paper, we consider two different encoder architectures, with the purpose of developing an encoder that can better understand the patterns and trends of the variables.
• Sequential architecture: is composed of three different convolutional blocks, see Figure 6. Each has a convolutional layer with 128, 256, and 512, respectively, in the different convolutional blocks, with a kernel size of (3,3) and we apply the "same" padding method to adjust the size of the input to our requirement; the second is BatchNormalization layer followed by the activation function, which is ReLu; and finally there is a MaxPooling2D layer with a pool size of (2,2). Except for the convolutional layer, which has different values depending on the block, the rest have the same values in all convolutional blocks. • Residual architecture: In contrast to the previous architecture, this one presents skip connections or shortcuts to jump over some layers, see Figure 7. These connections allow for deeper networks with less vanishing gradient issues. Our architecture is composed of three different convolutional blocks, as the previous one. Figure 6: Visual representation of architecture 1, the different convolutional blocks can be seen in grey colour.
Each block has four convolutional layers with the same number of neurons (128, 256 and 512, respectively) with a batch normalization layer and a Gelu activation layer; at the end of each convolutional block there is a Max pooling layer. The convolutional layer has a kernel size of (3,3) with padding. In each convolutional block, the activation layer receives the output of the previous layer and the output of the last activation one, but there are no connections between the different convolutional blocks. Decoder architecture The decoder reconstructs the original image using the latent representation, i.e. filling in the masked patches. In other words, the decoder has to return the categorical values of the patches. Its architecture is composed of only two layers; the first one is a dense layer whose number of neurons is equal to the number of channels of the image, in our case 9, multiplied by the number of categories that the patches can take, 64, so the total number of neurons of the dense layer is 576, then there is a reshape layer which is in charge of changing the dimensions of the output; the desired dimension is (number of patches, number of patches, number of channels, categories). This allows the system to return the image with the same dimensions as the input.
The Wildfire Assessment (WAM) model
We assume that wildfires are inevitable and unpredictable but their spread is determined by natural causes and mitigated by human action. As such we build a model that can estimate the damage that a wildfire could provoke if it began on a given date; allowing for human experts to estimate required action. The labels to be used are the area that would burn in the fire, the time it would take to control and extinguish the wildfire, and the human, vehicle, and aerial resources needed to extinguish it. The number of samples is very small for deep learning techniques so we use a transfer learning approach, using the pre-trained weights from the previous task to fine-tune a regression model.
The latent representation is flattened and then perturbed by a Dropout with a rate of 70%, which is passed to a dense layer with 512 neurons and GELU activation. Finally, the classification layer of the model consists of a dense layer with six neurons with linear activation. The model was trained for a maximum of 6, 000 epochs using the Adam optimiser with a learning rate of 1e − 5. The metric and the loss function used to control the evolution of the model were the mean absolute error (MAE) and the mean squared error (MSE), respectively, from which MAE was selected as a checkpoint to store the model weights. To train the regression model we used the dataset from Castilla y León, composed by 446 samples; and we used the dataset from Andalucía to test the generalization of the pre-training model to other areas with different environmental conditions.
Baselines
In this paper, as we have explained in Section 4.4, we have used a private dataset that has not been published yet, which makes it impossible to compare it with other papers that work with our dataset. Furthermore, we decided to treat the atmospheric variables as two-dimensional matrices, where the central point coincides with the geographical position of the fire, but also took into account the area around the point, which is a novel approach in the field. The articles found in the field use classical machine learning to solve their tasks; whether they predict susceptibility, the area that will burn in case of wildfires, among others. To offer a fair comparison with state of the art techniques, the selected techniques were extracted from reviews of the literature of work in this field [26,1,6]: Decision trees, GBoost, Random forests, Support vector regression, and XGBoost.
Using the same arrays for the deep learning model we extract the mean, standard deviation and the centre point generating an array of 27 values for each sample. The matrices are generated from the original samples which, as mentioned above, had z-score normalization applied to them and were analysed using the techniques described above.
On the other hand, as in the Deep Learning models, Min-Max normalization is applied to the labels, so to measure the real performance of the results obtained with the regression models, the predictions were first denormalized and the MAE was measured with the real labels and the denormalized predictions.
Visualization
The last step of the methodology of this manuscript is the visualization of a map of the autonomous region for each unit of time and label (burnt area, control time, extinction time, human resources, vehicle resources, and aerial resources). For each pixel of the map, a sample was generated with input dimensions explained in Section 3.4, a total of 2,970,000 samples are prepared to generate the map, a frame remains on the outside of the map that cannot be generated due to the input size requirement. The 6 predictions were extracted from each of the samples and structured in a two-dimensional matrix to reconstruct the maps, one per each label.
Results
This section describes the results obtained with the proposed methodology and assesses its performance on the dataset explained in section 3, for the autonomous regions of Castilla y León and Andalucía between 2001 and 2012. The results can be divided into four different sections: firstly we evaluate the autoencoder performance, where we first perform a test to choose the training parameters, and secondly we compare the results obtained for the two proposed architectures, using the Sparse Categorical Accuracy metric; secondly we evaluate the performance of the proposed regression model and compare it with the most used techniques for similar state-of-the-art problems, using the Mean Square Error (MAE) metric. The third section corresponds to the prediction map, and the last one corresponds to the known limitations.
Performance of Autoencoder models
As mentioned above, before training the final models we did an initial hyper-parameter search before pre-training. Our objective with this search is not to maximize accuracy, instead we search for the hardest objective the model can still solve with fair accuracy. As explained in section 3, we combined different numbers of categories into which we divided the pixel values and different learning rate values. The results can be seen in Table 2. As a limited number of epochs are used models with lower number of bins achieve better accuracy, however it is observed that all models are able to learn patterns and fill the hidden patches. Given the results obtained for the combination of learning rate = 1e-4 and 64 bins, which achieved an accuracy of 0.6, we chose these parameters to train the models.
After the learning rate and number of classes are selected, the following experiments we will use a larger number of epochs and a larger batch size. This model was chosen because the high number of bins allows the model to learn fine-grained patterns and trends of the different atmospheric variables resulting in a better intermediate representation of the input data. In addition, the model trained with a learning rate of 1e-4 is the best performing model. Once we select the training parameters, we train the proposed architectures: sequential and residual ones. Table 3 shows the results obtained for the labelled training dataset, as it was trained and validated with the unlabelled random dataset. We can observe how the residual architecture results obtained better results, 0.861, compared to the sequential one, which achieved results of 0.773. Figure 8 confirms these results, as we can see that the residual one successfully reconstructs an image from the latent representation. Although there are differences between the results of both architectures, we decided to create regression models with both encoders to test their performance. The results obtained, Figure 8 and Table 3, show that the autoencoder models are able to understand the patterns and trends of different variables of the atmospheric variables and greenness index. It can be seen that the residual architecture obtains better results than the sequential architecture. The differences between the two architectures are the number of convolutional layers in each block and the use of skip connection or shortcuts. The residual architecture has more trainable parameters and the skip connections help avoid vanishing gradient issues, therefore this behaviour is within expectations.
WAM model
We analyze the performance of the different regression models proposed, table 5. We use the two encoders generated in the previous step and tested with and without fine-tuning. To check if these models work correctly, we compare them with five different baselines. Other deep learning techniques are not available at the time of writing, thus we choose the most common state-of-the-art techniques to compare with. Firstly, we observe that the worst performing model is Support Vector Regression, which presents the highest MAE values in all classes except aerial resources and control time; the second worst baseline is the decision tree, which presents the worst results in control time and aerial resources. The best performing baselines are GBoost and random forest, which improve the results of the models with frozen encoder for the human and heavy resource classes. All baselines predictions are better than the average of the training values.
We also compare our techniques to the baselines. We observe that the sequential architecture sometimes fails to achieve better performance than the baselines while in the other three classes (burnt surface, control time, and extinguishing time) they behave similarly to the fine-tuned encoder. On the other hand we observe that fine-tuning the entire encoder to the task achieves on average the best performance. Finally, if we compare the results obtained by the regression models generated with the encoder from sequential and residual architectures with fine-tune encoder, we can see that residual architecture works better, presenting the lowest MAE for three classes, burnt area, control time, and aerial resources; that is, it is the model with the best results of the nine models presented in table 5.
The results obtained in this section show how deep learning techniques can outperform classical machine learning models, which are used in the state of the art in the field of fire management. Furthermore, we can see how few-shot learning techniques achieve very good results in fire management with a limited number of samples. Our fine-tuned residual encoder has shown to achieve better to the rest of the models and baselines shown, although there is still a great margin for improvement, the results are promising. Figure 9: Forest map of Castilla y León. Dark green: Tree cover; Green: Sparse tree cover; light green: low tree cover; and greygreen: herbaceousshrub cover. This map is an adaptation of the forest map provided by Ministerio para la Transición Ecológica y el Reto Demográfico (Spain) 3 As we explain in Section 4, in addition to testing our model in the test set, to analyse its operation and performance, we have created a prediction map for a specific date, with three test samples. With these visualizations we want to analyse the risk assessment throughout the autonomous region when a fire occurs. As shown in figure 10, we have created a map for each of the labels, showing the resources that would be needed in case of fire.
Visualization
In all maps we can see that the areas close to the black spots, which correspond to the wildfires that occurred on a specific date, are the ones that would need more resources. If we compare these results with forest and wildfire maps, Figures 2 and 9, respectively, firstly, we can see that there are three wildfires in the west of the autonomous region, and also the areas with the highest values for the six labels are close to these points. In addition, these areas coincide in many areas with the highest vegetation cover. The evaluation of such visualizations is not straightforward, as we do not have a ground truth to compare with, but we can check if the marked areas match with the expected ones, i.e. if they are close to the fires.
We do not want to know exactly where a fire is, but we can give indications of how damaging a fire could be to an area. High hazard areas are high hazard areas because they have conditions that are prone to fire spread, which is an indicator that there is a greater likelihood of a fire occurring in that area.
Known limitations
As we explained before in Section 3, we used the Andalucía dataset to check the generalization of the model without fine-tuning with samples from the new area with different environmental conditions. For this purpose, we use the regression model that obtained the best performance in the Castilla y León dataset, the fine-tuned residual architecture encoder. Like in the previous section, we compare our model with five different baselines and the average. First of all, we can observe that the baselines results are similar in both experiments, except for the last label, aerial resources, where all baselines perform worse than the average baseline. Second, it is notable that the support vector regression and XGBoost models obtain the same results for both datasets. The rest of the models for the other five labels achieve better results than the average one. About our model only two labels have a lower MAE than average one: control and extinction time. The other variables have a higher MAE than average ones, burnt area, human, heavy and aerial resources. It is important to note that there are some other factors, such as: distance between the water sources and the fire location, type of plane or the orography, that may have an influence on the resource prediction.
The model we have used to test the new samples from Andalucía was fine-tuned with a set of 446 samples from Castilla y León, a limited region with different meteorological features and vegetation than Andalucía, so the model is not able to correctly predict the resources that would be needed in case of fires, except for the control and extinction time classes. The model has been trained by means of the atmospheric variables in a region surrounding Castilla y León region. Thus, different regions are affected by changes in the meteorological conditions. The model may need to be adjusted if it is to be applied to other areas, i.e. pretraining with a small sample set of the area of interest. Another factor that could also affect its generalization is that the encoder was trained with a set of random samples from Castilla y León.
Conclusions and future work
This paper proposes the WAM model architecture for the prediction of wildfire resource using atmospheric variables and the greenness index. Due to the limited number of labelled samples, we trained an autoencoder with unlabelled samples to learn the trends or patterns of the variables of a geographical area and apply the knowledge to a regression task that predicts the resources needed, the control and extinguishing time, and the area that would burn in case of a fire. Finally, we tested its ability to generalise to other areas with different meteorological conditions, using a dataset from Andalucía. The application in a specific location is limited, for this reason we create a prediction map for each label, showing the necessary resources in each location of the autonomous region of Castilla y León for a specific date.
The results are promising and the methodology is novel in the field of wildfires, as most published papers use machine learning algorithms without exploring other Deep Learning options or techniques. Firstly, the residual autoencoder architecture presents higher performance than the sequential one, because the skip connection provides an alternative path for the gradient with backpropagation and allows deeper layers to learn from the information of initial layers. However, it can be observed that better results are achieved by using the residual autoencoder architecture if the encoder is retrained in the regression task. Possibly the addition of new samples allows the regression model to pick up patterns that the autoencoder was not able to learn originally.
The model we propose is trained in a very specific region, an autonomous region of Spain, Castilla y León, so we analyse its generalization to other areas with different meteorological conditions, in our case Andalucía, another autonomous region of the same country. The results show that our model is able to correctly predict two of the labels, control and extinguishing time, but not the rest of the labels, i.e. WAM model is not able to adapt to other regions without retraining.
As we have explained above, the WAM model obtained better results when the encoder was retrained in the regression task, although the samples belonged to the same autonomous region. As the original model was pre-trained on a specific region it is not able to generalise to other areas with different meteorological conditions.
We have identified clear weaknesses of the model that can be sorted in several ways. First, the generalization capabilities fall short due to the low amount and specialization of pretraining data. This can be solved by widening the scope of the semi-supervised dataset (for example, cover the entire peninsula) and sampling more data points from the selected region. To support the increase in the dataset, a proportional enhancement of the model would be required; while maintaining the training methodology, a more powerful architecture could be applied, such as transformers or ConvNeXT. Another way to improve the performance of the proposed system is including more variables, some are included in many state-of-the-art works, such as distance to the nearest population, substrate use or orography and other variables closely related to wildfires management such as fuel models. Finally, as we can see from the published works in the area of wildfire management, this is an underexplored domain with numerous possibilities.
Figure 1 :
1Visual representation of WAM methodology steps.
1 .
1Burnt area (metres): total area affected by wildfire. 2. Control time (min): time required to enter the control phase, that is when the fire conditions have changed enough to prevent its propagation. 3. Extinction time (min): time until the fire is extinguished, that is, when there are no active hotspots and the technicians verify that there is no possibility of reignite. 4. Human resources (units): number of people involved in extinguishing the fire. 5. Aerial resources (units): number of aerial vehicles involved in the extinguishing of the fire.
Figure 2 :
2Map of Spain showing the locations of all wildfires recorded between 2001 and 2012. Wildfires in Castilla y León are highlighted in blue and those in Andalucía in red.
Figure 3 :
3Visual representation of labels grouped both by province and autonomous region.
6 .
6Heavy resources (units): number of heavy vehicles involved in the extinguishing of the fire.
Figure 4 :
4Visual representation of the proposed methodology for wildfire management. 1) Data generation, from the different data sources, the different subsets (labelled and unlabelled) were generated; 2) Autoencoder, training and validation of the autoencoder that learns the patterns of different atmospheric variables and greenness index; 3) Regression task, development of the WAM model for the prediction of resources needed in fire management; 4) Visualization, creation of daily prediction maps showing the resources needed if a fire were to break out at a particular point in the study area.
Figure 5 :
5Example of the preprocessing showing four channels of a sample, where the first column represents the atmospheric variables; the second column represents the mask for that channel; the third represents masked image and finally the fourth sample represents the label for the autoencoder.
Figure 7 :
7Visual representation of architecture 2, the different convolutional blocks can be seen in grey colour and the skip connections are represented by arrows.
Figure 8 :
8Examples of results from the two AutoEncoder for different samples of the labelled training set. The first and third columns correspond to the AutoEncoder labels, the second and fourth columns are the predictions of the two proposed architectures, sequential and residual architectures.
Figure 10 :
10Prediction maps, a visualization of burnt area, control and extinction time and needed resources.
Table 1 :
1Summary of parameters used in pretrain: optimization and training methodology.Optimization
Optimizer Adam
Learning rate 1e-4
Loss function Sparse Categorical Cross Entropy
Metric Sparse Categorical Accuracy
Training methodology
Maximum epochs 2000
Checkpoint monitor Sparse Categorical Accuracy
Batch size 64
Image size 128 x 128
# bins 64
Patch size 16x16
conv2D (128)
BatchNormaliztion
ReLu
MaxPooling2D
conv2D (256)
BatchNormaliztion
ReLu
MaxPooling2D
conv2D (512)
BatchNormaliztion
ReLu
MaxPooling2D
X
Table 2 :
2Accuracy of each parameters combination in the AE training.Number of bins
Learning rate 4
8
16
32
64
Table 3 :
3Results of the two AutoEncoder architectures evaluated with the labelled training set.Accuracy
Sequential architecture 0.773
Residual architecture 0.861
Table 4 :
4Results of the four regression models generated, frozen encoder and fine-tune encoder from both architectures, compared with the average and five models from the state of the art. Best result in bold.Average
baseline
Decission
Tree
GBoost
Random
Forest
Support
Vector
Regression
XGBoost
Frozen
encoder
Fine-tune
encoder
Improvement
(%)
Sequential
architecture
Residual
architecture
Sequential
architecture
Residual
architecture
Burnt
Area (m)
406,189
434,473
333,814
287,051
747,340
302,683
280,800
255,800
278,200
233,100
18,8%
Control Time
(min)
1846,537 1875,236 1274,760 1416,345 1660,959
1295,846 1218,000
1212,000
1192,000
1114,000
21%
Extintion Time
(min)
3255,813 2566,528 2630,425 2538,686 2797,823
2654,167 2234,000
2338,000
2230,000
2280,000
10,2%
Human
resources (units)
87,582
66,289
54,785
53,373
82,152
57,140
73,700
51,100
73,100
52,600
1,4%
Heavy
resources (units)
6,047
5,056
4,139
4,011
6,450
4,528
5,918
3,672
5,930
3,863
3,7%
Aerial
resources (units)
5,197
4,309
3,283
3,169
3,626
3,318
3,684
2,988
3,744
2,883
9%
Tree cover
Sparse tree cover
Low tree cover
Herbaceous/shrub
cover
Table 5 :
5Results of residual architecture with fine-tune encoder and baselines for Andalucía dataset. Control Time (min) 1747.570 1713.208 1276.427 1371.579 1660.959 1295.846 950.0 Extintion Time (min) 3067.964 2798.904 2559.446 2523.677 2797.823Average
baseline
Decision
Tree
GBoost
Random
Forest
Support
Vector
Regression XGBoost WAM
Burnt area (m) 393.209
391.556
320.148
293.271
747.340
302.683
751.5
2654.167 2268.0
Human resources (units) 83.971
63.671
56.237
53.931
82.152
57.140
206.6
Heavy resources (units) 5.996
5.247
4.189
4.061
6.450
4.528
14.414
Aerial resources (units) 4.993
6.107
5.817
5.665
6.103
5.918
11.01
https://www.epdata.es/datos/incendios-forestales-datos-estadisticas-cifras/267 2 https://effis.jrc.ec.europa.eu/apps/effis.statistics/estimates
https://www.miteco.gob.es/es/
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| sample_1537 | 0.5063 | arxiv | |
Global warming in the pipeline
James E Hansen
Climate Science, Awareness and Solutions
Columbia University Earth Institute
New YorkNYUSA
Makiko Sato
Climate Science, Awareness and Solutions
Columbia University Earth Institute
New YorkNYUSA
Leon Simons
The Club of Rome Netherlands, 's-Hertogenbosch
The Netherlands
Larissa S Nazarenko
NASA Goddard Institute for Space Studies
New YorkNYUSA
Center for Climate Systems Research
Columbia University Earth Institute
New YorkNYUSA
Isabelle Sangha
Climate Science, Awareness and Solutions
Columbia University Earth Institute
New YorkNYUSA
Karina Von Schuckmann
Mercator Ocean International
Ramonville St.-Agne
France
Norman G Loeb
NASA Langley Research Center
HamptonVAUSA
Matthew B Osman
Department of Geosciences
University of Arizona
TucsonAZUSA
Qinjian Jin
Department of Geography and Atmospheric Science
University of Kansas
LawrenceKSUSA
Pushker Kharecha
Climate Science, Awareness and Solutions
Columbia University Earth Institute
New YorkNYUSA
George Tselioudis
NASA Goddard Institute for Space Studies
New YorkNYUSA
Eunbi Jeong
CSAS KOREA
GoyangGyeonggi-doSouth Korea
Andrew Lacis
NASA Goddard Institute for Space Studies
New YorkNYUSA
Reto Ruedy
NASA Goddard Institute for Space Studies
New YorkNYUSA
Business Integra, Inc
New YorkNYUSA
Gary Russell
NASA Goddard Institute for Space Studies
New YorkNYUSA
Junji Cao
Institute of Atmospheric Physics
Chinese Academy of Sciences
BeijingChina
Jing Li
Department of Atmospheric and Oceanic Sciences
School of Physics
Peking University
BeijingChina
James E Hansen
Global warming in the pipeline
1 *Correspondence:
Improved knowledge of glacial-to-interglacial global temperature change implies that fastfeedback equilibrium climate sensitivity (ECS) is 1.2 ± 0.3°C (2σ) per W/m 2 . Consistent analysis of temperature over the full Cenozoic era -including "slow" feedbacks by ice sheets and trace gasessupports this ECS and implies that CO2 was about 300 ppm in the Pliocene and 400 ppm at transition to a nearly ice-free planet, thus exposing unrealistic lethargy of ice sheet models. Equilibrium global warming including slow feedbacks for today's human-made greenhouse gas (GHG) climate forcing (4.1 W/m 2 ) is 10°C, reduced to 8°C by today's aerosols. Decline of aerosol emissions since 2010 should increase the 1970-2010 global warming rate of 0.18°C per decade to a post-2010 rate of at least 0.27°C per decade. Under the current geopolitical approach to GHG emissions, global warming will likely pierce the 1.5°C ceiling in the 2020s and 2°C before 2050. Impacts on people and nature will accelerate as global warming pumps up hydrologic extremes. The enormity of consequences demands a return to Holocene-level global temperature. Required actions include: 1) a global increasing price on GHG emissions, 2) East-West cooperation in a way that accommodates developing world needs, and 3) intervention with Earth's radiation imbalance to phase down today's massive human-made "geo-transformation" of Earth's climate. These changes will not happen with the current geopolitical approach, but current political crises present an opportunity for reset, especially if young people can grasp their situation.This section gives a brief overview of the history of ECS estimates since the Charney report and uses glacial-to-interglacial climate change to infer an improved estimate of ECS. We discuss how ECS and the more general Earth system sensitivity (ESS) depend upon the climate state.Charney defined ECS as the eventual global temperature change caused by doubled CO2 if ice sheets, vegetation and long-lived GHGs are fixed (except the specified CO2 doubling). Other quantities affecting Earth's energy balanceclouds, aerosols, water vapor, snow cover and sea icechange rapidly in response to climate change. Thus, Charney's ECS is also called the "fast feedback" climate sensitivity. Feedbacks interact in many ways, so their changes are calculated in global climate models (GCMs) that simulate such interactions. Charney implicitly assumed that change of the ice sheets on Greenland and Antarctica -which we categorize as a "slow feedback"was not important on time scales of most public interest.ECS defined by Charney is a gedanken concept that helps us study the effect of human-made and natural climate forcings. If knowledge of ECS were based only on models, it would be difficult to narrow the range of estimated climate sensitivityor have confidence in any rangebecause we do not know how well feedbacks are modeled or if the models include all significant realworld feedbacks. Cloud and aerosol interactions are complex, e.g., and even small cloud changes can have a large effect. Thus, data on Earth's paleoclimate history are essential, allowing us to compare different climate states, knowing that all feedbacks operated.Climate sensitivity estimated at the 1982 Ewing SymposiumClimate sensitivity was addressed in our paper 7 for the Ewing Symposium monograph using the feedback framework implied by E.E. David and employed by electrical engineers. 17 The climate forcing caused by 2×CO2the imposed perturbation of Earth's energy balanceis ~ 4 W/m 2 . If there were no climate feedbacks and Earth radiated energy to space as a perfect black surface, Earth's temperature would need to increase ~ 1.2°C to increase radiation to space 4 W/m 2 and restore energy balance. However, feedbacks occur in the real world and in GCMs. In our GCM the equilibrium response to 2×CO2 was 4°C warming of Earth's surface. Thus, the fraction of equilibrium warming due directly to the CO2 change was 0.3 (1.2°C/4°C) and the feedback "gain," g, was 0.7 (2.8°C/4°C). Algebraically, ECS and feedback gain are related by ECS = 1.2°C/(1-g).(1)We evaluated contributions of individual feedback processes to g by inserting changes of water vapor, clouds, and surface albedo (reflectivity, literally whiteness, due to sea ice and snow changes) from the 2×CO2 GCM simulation one-by-one into a one-dimensional radiativeconvective model, 18 finding gwv = 0.4, gcl = 0.2, gsa = 0.1, where gwv, gcl, and gsa are the water vapor, cloud and surface albedo gains. The 0.2 cloud gain was about equally from a small increase in cloud top height and a small decrease in cloud cover. These feedbacks all seemed reasonable, but how could we verify their magnitudes or the net ECS due to all feedbacks?We recognized the potential of emerging paleoclimate data. Early data from polar ice cores revealed that atmospheric CO2 was much less during glacial periods and the CLIMAP project 19 5 used proxy data to reconstruct global surface conditions during the Last Glacial Maximum (LGM), which peaked about 20,000 years ago. A powerful constraint was the fact that Earth had to be in energy balance averaged over the several millennia of the LGM. However, when we employed CLIMAP boundary conditions including sea surface temperatures (SSTs), Earth was out of energy balance, radiating 2.1 W/m 2 to space., i.e., Earth was trying to cool off with an enormous energy imbalance, equivalent to half of 2×CO2 forcing.Something was wrong with either assumed LGM conditions or our climate model. We tried CLIMAP's maximal land icethis only reduced the energy imbalance from 2.1 to 1.6 W/m 2 . Moreover, we had taken LGM CO2 as 200 ppm and did not know that CH4 and N2O were less in the LGM than in the present interglacial period; accurate GHGs and CLIMAP SSTs produce a planetary energy imbalance close to 3 W/m 2 . As for our model, most feedbacks were set by CLIMAP. Sea ice is set by CLIMAP. Water vapor depends on surface temperature, which is set by CLIMAP SSTs. Cloud feedback is uncertain, but ECS smaller than 2.4°C for 2×CO2 would require a negative cloud gain. gcl ~ 0.2 from our GCM increases ECS from 2.4°C to 4°C (eq. 1) and accounts for almost the entire difference of sensitivities of our model (4°C for 2×CO2) and the Manabe and Stouffer model 20 (2°C for 2×CO2) that had fixed cloud cover and cloud height. Manabe suggested 21 that our higher ECS was due to a too-large sea ice and snow feedback, but we noted 7 that sea ice in our control run was less than observed, so we likely understated sea ice feedback. Amplifying feedback due to high clouds increasing in height with warming is expected and is found in observations, large-eddy simulations and GCMs. 22 Sherwood et al.23conclude that negative low-cloud feedback is "neither credibly suggested by any model, nor by physical principles, nor by observations." Despite a wide spread among models, GCMs today show an amplifying cloud feedback due to increases in cloud height and decreases in cloud amount, despite increases in cloud albedo. 24 These cloud changes are found in all observed cloud regimes and locations, implying robust thermodynamic control. 25
2
BACKGROUND INFORMATION AND STRUCTURE OF PAPER
It has been known since the 1800s that infrared-absorbing (greenhouse) gases (GHGs) warm Earth's surface and that the abundance of GHGs changes naturally as well as from human actions. 1,2 Roger Revelle wrote in 1965 that we are conducting a "vast geophysical experiment" by burning fossil fuels that accumulated in Earth's crust over hundreds of millions of years. 3 Carbon dioxide (CO2) in the air is now increasing and already has reached levels that have not existed for millions of years, with consequences that have yet to be determined. Jule Charney led a study in 1979 by the United States National Academy of Sciences that concluded that doubling of atmospheric CO2 was likely to cause global warming of 3 ± 1.5°C. 4 Charney added: "However, we believe it is quite possible that the capacity of the intermediate waters of the ocean to absorb heat could delay the estimated warming by several decades." After U.S. President Jimmy Carter signed the 1980 Energy Security Act, which included a focus on unconventional fossil fuels such as coal gasification and rock fracturing ("fracking") to extract shale oil and tight gas, the U.S. Congress asked the National Academy of Sciences again to assess potential climate effects. Their massive Changing Climate report had a measured tone on energy policyamounting to a call for research. 5 Was not enough known to caution lawmakers against taxpayer subsidy of the most carbon-intensive fossil fuels? Perhaps the equanimity was due in part to a major error: the report assumed that the delay of global warming caused by the ocean's thermal inertia is 15 years, independent of climate sensitivity. With that assumption, they concluded that climate sensitivity for 2×CO2 is near or below the low end of Charney's 1.5-4.5°C range. If climate sensitivity was low and the lag between emissions and climate response was only 15 years, climate change would not be nearly the threat that it is.
Simultaneous with preparation of Changing Climate, climate sensitivity was addressed at a Ewing Symposium at the Lamont Doherty Geophysical Observatory of Columbia University on 25-27 October 1982, with papers published in January 1984 as a monograph of the American Geophysical Union. 6 Paleoclimate data and global climate modeling together led to an inference that climate sensitivity is in the range 2.5-5°C for 2×CO2 and that climate response time to a forcing is of the order of a century, not 15 years. 7 Thus, the concept that a large amount of additional human-made warming is already "in the pipeline" was introduced. E.E. David, Jr., President of Exxon Research and Engineering, in his keynote talk at the symposium insightfully noted 8 : "The critical problem is that the environmental impacts of the CO2 buildup may be so long delayed. A look at the theory of feedback systems shows that where there is such a long delay, the system breaks down, unless there is anticipation built into the loop." Thus, the danger caused by climate's delayed response and the need for anticipatory action to alter the course of fossil fuel development was apparent to scientists and the fossil fuel industry 40 years ago. 9 Yet industry chose to long deny the need to change energy course, 10 and now, while governments and financial interests connive, most industry adopts a "greenwash" approach that threatens to lock in perilous consequences for humanity. Scientists will share responsibility, if we allow governments to rely on goals for future global GHG levels, as if targets had meaning in the absence of policies required to achieve them. 3 The Intergovernmental Panel on Climate Change (IPCC) was established in 1988 to provide scientific assessments on the state of knowledge about climate change 11 and almost all nations agreed to the 1992 United Nations Framework Convention on Climate Change 12 with the objective to avert "dangerous anthropogenic interference with the climate system." The current IPCC Working Group 1 report 13 provides a best estimate of 3°C for equilibrium global climate sensitivity to 2×CO2 and describes shutdown of the overturning ocean circulations and large sea level rise on the century time scale as "high impact, low probability" even under extreme GHG growth scenarios. This contrasts with "high impact, high probability" assessments reached in a paper 14 hereafter abbreviated Ice Meltthat several of us published in 2016. Recently, our paper's first author (JEH) described a long-time effort to understand the effect of ocean mixing and aerosols on observed and projected climate change, which led to a conclusion that most climate models are unrealistically insensitive to freshwater injected by melting ice and that ice sheet models are unrealistically lethargic in the face of rapid, large climate change. 15 Eelco Rohling, editor of Oxford Open Climate Change, invited a perspective article on these issues. Our principal motivation in this paper is concern that IPCC has underestimated climate sensitivity and understated the threat of large sea level rise and shutdown of ocean overturning circulations, but these issues, because of their complexity, must be addressed in two steps. Our present paper addresses climate sensitivity and warming in the pipeline, concluding that these exceed IPCC's best estimates. Response of ocean circulation and ice sheet dynamics to global warming-already outlined in the Ice Melt paperwill be addressed further in a later paper. 16 The structure of our present paper is as follows. Section 2 (Climate Sensitivity) makes a fresh evaluation of Charney's equilibrium climate sensitivity (ECS) based on improved paleoclimate data and introduces Earth system sensitivity (ESS), which includes the feedbacks that Charney held fixed. Section 3 (Climate Response Time) explores the fast-feedback response time of Earth's temperature and energy imbalance to an imposed forcing, concluding that cloud feedbacks buffer heat uptake by the ocean, thus increasing warming in the pipeline and making Earth's energy imbalance an underestimate of the forcing reduction required to stabilize climate. Section 4 (Cenozoic Era) analyzes temperature change of the past 66 million years, tightens evaluation of climate sensitivity, and assesses the history of CO2, thus providing insights about climate change. Section 5 (Aerosols) addresses the absence of aerosol forcing data via inferences from paleo data and modern global temperature change, and we point out potential information in "the great inadvertent aerosol experiment" provided by recent restrictions on fuels in international shipping. Section 6 (Summary) discusses policy implications of high climate sensitivity and the delayed response of the climate system. Reduction of greenhouse gas emissions as rapidly as practical has highest priority, but that policy alone is now inadequate and must be complemented by additional actions to affect Earth's energy balance. The world is still early in this "vast geophysical experiment"as far as consequences are concernedbut time has run short for the "anticipation" that E.E. David recommended.
CLIMAP SSTs were a more likely cause of the planetary energy imbalance. Co-author D. Peteet used pollen data to infer LGM tropical and subtropical cooling 2-3°C greater than in a GCM forced by CLIMAP SSTs. D. Rind and Peteet found that montane LGM snowlines in the tropics descended 1 km in the LGM, inconsistent with climate constrained by CLIMAP SSTs. CLIMAP assumed that tiny shelled marine species migrate to stay in a temperature zone they inhabit today. But what if these species partly adapt over millennia to changing temperature? Based on the work of Rind and Peteet, later published, 26 we suspected but could not prove that CLIMAP SSTs were too warm.
Based on GCM simulations for 2×CO2, on our feedback analysis for the LGM, and on observed global warming in the past century, we estimated that ECS was in the range 2.5-5°C for 2×CO2. If CLIMAP SSTs were accurate, ECS was near the low end of that range. In contrast, our analysis implied that ECS for 2×CO2 was in the upper half of the 2.5-5°C range, but our analysis depended in part on our GCM, which had sensitivity 4°C for 2×CO2. To resolve the matter, a paleo thermometer independent of biologic adaptation was needed. Several decades later, such a paleo thermometer and advanced analysis techniques exist. We will use recent studies to infer our present best estimates for ECS and ESS. First, however, we will comment on other estimates of climate sensitivity and clarify the definition of climate forcings that we employ.
IPCC and independent climate sensitivity estimates
Reviews of climate sensitivity are available, e.g., Rohling et al., 27 which focuses on the physics of the climate system, and Sherwood et al., 23 which adds emphasis on probabilistic combination of multiple uncertainties. Progress in narrowing the uncertainty in climate sensitivity was slow in the first five IPCC assessment reports. The fifth assessment report 28 (AR5) in 2014 concluded onlywith 66% probabilitythat ECS was in the range 1.5-4.5°C, the same as Charney's report 35 years earlier. The broad spectrum of information on climate changeespecially constraints imposed by paleoclimate dataat last affected AR6, 13 which concluded with 66% probability that ECS is 2.5-4°C, with 3°C as their best estimate (AR6 Fig. TS.6).
Sherwood et al. 23 combine three lines of evidence: climate feedback studies, historical climate change, and paleoclimate data, inferring S = 2.6-3.9°C with 66% probability for 2×CO2, where S is an "effective sensitivity" relevant to a 150-year time scale. They find ECS only slightly larger: 2.6-4.1°C with 66% probability. Climate feedback studies, inherently, cannot yield a sharp definition of ECS, as we showed in the cloud feedback discussion above. Earth's climate system includes amplifying feedbacks that push the gain, g, closer to unity than zero, thus making ECS sensitive to uncertainty in any feedback; the resulting sensitivity of ECS to g prohibits precise evaluation from feedback analysis. Similarly, historical climate change cannot define ECS well because the aerosol climate forcing is unmeasured. Also, forced and unforced ocean dynamics give rise to a pattern effect: 29 the geographic pattern of transient and equilibrium temperature changes differ, which affects ECS inferred from transient climate change. These difficulties help explain how Sherwood et al. 23 could estimate ECS as only 6% larger than S, an implausible result in view of the ocean's great thermal inertia. An intercomparison of GCMs run for millennial time scales, LongRunMIP, 30 includes 14 simulations of 9 GCMs with runs of 5,000 years (or close enough for extrapolation to 5,000 years). Their global warmings at 5,000 years range from 30% to 80% larger than their 150-year responses.
Our approach is to compare glacial and interglacial equilibrium climate states. The change of atmospheric and surface forcings can be defined accurately, thus leading to a sharp evaluation of ECS for cases in which equilibrium response is assured. With this knowledge in hand, additional information can be extracted from historical and paleo climate changes.
Climate forcing definitions
Attention to climate forcing definitions is essential for quantitative analysis of climate change. However, readers uninterested in radiative forcings may skip this section with little penalty.
We describe our climate forcing definition and compare our forcings with those of IPCC. Our total GHG forcing matches that of IPCC within a few percent, but this close fit hides larger differences in individual forcings that deserve attention.
Equilibrium global surface temperature change is related to ECS by
ΔTS ~ F × ECS = F × λ,(2)
where λ is a widely used abbreviation of ECS, ΔTS is the global mean equilibrium surface temperature change in response to climate forcing F, which is measured in W/m 2 averaged over the entire planetary surface. There are alternative ways to define F, as discussed in Chapter 8 31 of AR5 and in a paper 32 hereafter called Efficacy. Objectives are to find a definition of F such that different forcing mechanisms of the same magnitude yield a similar global temperature change, but also a definition that can be computed easily and reliably. The first four IPCC reports used adjusted forcing, Fa, which is Earth's energy imbalance after stratospheric temperature adjusts to presence of the forcing agent. Fa usually yields a consistent response among different forcing agents, but there are exceptions such as black carbon aerosols; Fa exaggerates their impact. Also, Fa is awkward to compute and depends on definition of the tropopause, which varies among models. Fs, the fixed SST forcing (including fixed sea ice), is more robust than Fa as a predictor of climate response, 32,33 but a GCM is required to compute Fs. In Efficacy, Fs is defined as
Fs = Fo + δTo/λ (3)
where Fo is Earth's energy imbalance after atmosphere and land surface adjust to the presence of the forcing agent with SST fixed. Fo is not a full measure of the strength of a forcing, because a portion (δTo) of the equilibrium warming is already present as Fo is computed. A GCM run of about 100 years is needed to accurately define Fo because of unforced atmospheric variability. That GCM run also defines δTo, the global mean surface air temperature change caused by the forcing with SST fixed. λ is the model's ECS in °C per W/m 2 . δTo/λ is the portion of the total forcing (Fs) that is "used up" in causing the δTo warming; radiative flux to space increases by δTo/λ due to warming of the land surface and global air. The term δTo/λ is usually, but not always, less than 10% of Fo. Thus, it is better not to neglect δTo/λ. IPCC AR5 and AR6 define effective radiative forcing as ERF = Fo. Omission of δTo/λ was intentional 31 and is not an issue if the practice is followed consistently. However, when the forcing is used to calculate global surface temperature response, the forcing to use is Fs, not Fo. It would be useful if both Fo and δTo were reported for all climate models.
A further refinement of climate forcing is suggested in Efficacy: effective forcing (Fe) defined by a long GCM run with calculated ocean temperature. The resulting global surface temperature change, relative to that for equal CO2 forcing, defines the forcing's efficacy. Effective forcings, Fe, were found to be within a few percent of Fs for most forcing agents, i.e., the results confirm that Fs is a robust forcing. This support is for Fs, not for Fo = ERF, which is systematically smaller than Fs. The Goddard Institute for Space Studies (GISS) GCM 34,35 used for CMIP6 36 studies, which we label the GISS (2020) model, 37 has higher resolution (2°×2.5° and 40 atmospheric layers) and other changes that yield a moister upper troposphere and lower stratosphere, relative to the GISS model used in Efficacy. GHG forcings reported for the GISS (2020) model 34,35 are smaller than in prior GISS models, a change attributed 35 Our GHG effective forcing, Fe, was obtained in two steps. Adjusted forcings, Fa, were calculated for each gas for a large range of gas amount with a global-mean radiative-convective model that incorporated the GISS GCM radiation code, which uses the correlated k-distribution method 38 and high spectral resolution laboratory data. 39 The Fa are converted to effective forcings (Fe) via efficacy factors (Ea; 42 The climate forcing from our formulae is slightly larger than IPCC AR6 forcings (Fig. 1 43 relative to the mean of the last 10 ky and Dome C CO2 amount from Luthi et al. 44 (kyBP is kiloyears before present).
Glacial-to-interglacial climate oscillations
In this section we describe how ice core data help us assess ECS for climate states from glacial conditions to interglacial periods such as the Holocene, the interglacial period of the past 12,000 years. We discuss climate sensitivity in warmer climates in Section 4 (Cenozoic Era).
Air bubbles in Antarctic ice corestrapped as snow piled up and compressed into icepreserve a record of long-lived GHGs for at least 800,000 years. Isotopic composition of the ice provides a measure of temperature in and near Antarctica. 43 Changes of temperature and CO2 are highly correlated (Fig. 2). This does not mean that CO2 is the primal cause of the climate oscillations.
Hays et al. 45 showed that small changes of Earth's orbit and the tilt of Earth's spin axis are pacemakers of the ice ages. Orbital changes alter the seasonal and geographical distribution of insolation, which affects ice sheet size and GHG amount. Long-term climate is sensitive because ice sheets and GHGs act as amplifying feedbacks: 46 as Earth warms, ice sheets shrink, expose a darker surface, and absorb more sunlight; also, as Earth warms, the ocean and continents release GHGs to the air. These amplifying feedbacks work in the opposite sense as Earth cools. Orbital forcings oscillate slowly over tens and hundreds of thousands of years. 47 The picture of how Earth orbital changes drive millennial climate change was painted in the 1920s by Milutin Milankovitch, who built on 19 th century hypotheses of James Croll and Joseph Adhémar. Paleoclimate changes of ice sheets and GHGs are sometimes described as slow feedbacks, 48 but their slow change is paced by the Earth orbital forcing; their slow change does not mean that these feedbacks cannot operate more rapidly in response to a rapid climate forcing.
We evaluate ECS by comparing stable climate states before and after a glacial-to-interglacial climate transition. GHG amounts are known from ice cores and ice sheet sizes are known from geologic data. This empirical ECS applies to the range of global temperature covered by ice cores, which we will conclude is about -7°C to +1°C relative to the Holocene. The Holocene is an unusual interglacial. Maximum melt rate was at 13.2 kyBP, as expected, 49 and GHG amounts began to decline after peaking early in the Holocene, as in most interglacials. However, several ky later, CO2 and CH4 increased, raising a question of whether humans were affecting GHGs. Ruddiman 50 suggests that deforestation began to affect CO2 6500 years ago and rice irrigation began to affect CH4 5,000 years ago. Those possibilities complicate use of LGM-Holocene warming to estimate ECS. However, sea level, and thus the size of the ice sheets, had stabilized by 7,000 years ago (Section 5.1). Thus, the millennium centered on 7 kyBP provides a good period to compare with the LGM. Comparison of the Eemian interglacial ( Fig. 2) with the prior glacial maximum (PGM) has potential for independent assessment. 43 ) and multi-ice core GHG amounts (Schilt et al.). 51 Green bars (1)(2)(3)(4)(5)(18)(19)(20)(21)(120)(121)(122)(123)(124)(125)(126)(137)(138)(139)(140)(141)(142)(143)(144) are periods of calculations.
LGM-Holocene and PGM-Eemian evaluation of ECS
In this section we evaluate ECS by comparing neighboring glacial and interglacial periods when Earth was in energy balance within less than 0.1 W/m 2 averaged over a millennium. Larger imbalance would cause temperature or sea level change that did not occur. 52 Thus, we can assess ECS from knowledge of atmospheric and surface forcings that maintained these climates.
Recent advanced analysis techniques allow improved estimate of paleo temperatures. Tierney et al. 53 exclude micro biology fossils whose potential to adapt makes them dubious thermometers. Instead, they use a large collection of geochemical (isotope) proxies for SST in an analysis constrained by climate change patterns defined by GCMs. They find cooling of 6.1°C (95% confidence: 5.7-6.5°C) for the interval 23-19 kyBP. A similarly constrained global analysis by Osman et al. 54 finds LGM cooling at 21-18 kyBP of 7.0 ± 1°C (95% confidence). 55 Tierney (priv. comm.) attributes the difference between the two studies to the broader time interval of the former study, and suggests that peak LGM cooling was near 7°C.
Seltzer et al. 56 use the temperature-dependent solubility of dissolved noble gases in ancient groundwater to show that land areas between 45°S and 35°N cooled 5.8 ± 0.6°C in the LGM. This cooling is consistent with 1 km lowering of alpine snowlines found by Rind and Peteet. 26 Land response to a forcing exceeds ocean response, but polar amplification makes the global response as large as the low latitude land response in GCM simulations with fixed ice sheets (SM Fig. S3). When ice sheet growth is added, cooling amplification at mid and high latitudes is greater, 7 making 5.8°C cooling of low latitude land consistent with global cooling of ~7°C.
LGM CO2, CH4 and N2O amounts are known accurately with the exception of N2O in the PGM when N2O reactions with dust in the ice core corrupt the data. We take PGM N2O as the mean of the smallest reported PGM amount and the LGM amount; potential error in the N2O forcing is ~0.01 W/m 2 . We calculate CO2, CH4, and N2O forcings using Eq. (4) and formulae for each gas in Supp. Material for the periods shown by green bars in Fig. 3. The Eemian period avoids early CO2 and temperature spikes, assuring that Earth was in energy balance. Between the LGM (19-21 kyBP) and Holocene (6.5-7.5 kyBP), GHG forcing increased 2.25 W/m 2 with 77% from CO2. Between the PGM and Eemian, GHG forcing increased 2.30 W/m 2 with 79% from CO2.
Glacial-interglacial aerosol changes are not included as a forcing. Natural aerosol changes, like clouds, are fast feedbacks. Indeed, aerosols and clouds form a continuum and distinction is arbitrary as humidity approaches 100 percent. There are many aerosol types, including VOCs (volatile organic compounds) produced by trees, sea salt produced by wind and waves, black and organic carbon produced by forest and grass fires, dust produced by wind and drought, and marine biologic dimethyl sulfide and its secondary aerosol products, all varying geographically and in response to climate change. We do not know, or need to know, natural aerosol properties in prior eras because their changes are feedbacks included in the climate response. However, human-made aerosols are a climate forcing (an imposed perturbation of Earth's energy balance). Humans may have begun to affect gases and aerosols by the mid-Holocene (Section 5), but we minimize that issue by using the 6.5-7.5 kyBP window to evaluate climate sensitivity.
Earth's surface change is the other forcing needed to evaluate ECS: (1) change of surface albedo (reflectivity) and topography by ice sheets, (2) vegetation change, e.g., boreal forests replaced by brighter tundra, and (3) continental shelves exposed by lower sea level. Forcing by all three can be evaluated at once with a GCM. Accuracy requires realistic clouds, which shield the surface. Clouds are the most uncertain feedback. 57 Evaluation is ideal for CMIP 58 PGM-Eemian global warming provides a second assessment of ECS, one that avoids concern about human influence. PGM-Eemian GHG forcing is 2.3 W/m 2 . We estimate surface albedo forcing as 0.3 W/m 2 less than in the LGM because sea level was about 10 m higher during the PGM. 66 North American and Eurasian ice sheet sizes differed between the LGM and PGM, 67 but division of mass between them has little effect on the net forcing ( Fig. S4 65 ). Thus, our central estimate of PGM-Eemian forcing is 5.5 W/m 2 . Eemian temperature reached about +1°C warmer than the Holocene, 68 based on Eemian SSTs of +0.5 ± 0.3°C relative to 1870-1889, 69 or +0.65 ± 0.3°C SST and +1°C global (land plus ocean) relative to 1880-1920. However, the PGM was probably warmer than the LGM; it was warmer at Dome C ( Fig.2), but cooler at Dronning Maud Land. 70 Based on deep ocean temperatures (Section 4), we estimate PGM-Eemian warming as 0.5°C greater than LGM-Holocene warming, i.e., 7.5°C. The resulting ECS is 7.5/5.5 = 1.36°C per W/m 2 . Although PGM temperature lacks quantification comparable to that of Seltzer et al. 56 and Tierney et al. 53 for the LGM, the PGM-Eemian warming provides support for the high ECS inferred from LGM-Holocene warming.
We conclude that ECS for climate in the Holocene-LGM range is 1.2°C ± 0.3°C per W/m 2 , where the uncertainty is the 95% confidence range. The uncertainty estimate is inherently subjective, as it depends mainly on the ice age surface albedo forcing. The GHG forcing and glacial-interglacial temperature change are well-defined, but the efficacy of ice age surface forcing varies among GCMs. This variability is likely related to cloud shielding of surface albedo, which reaffirms the need for a focus on precise cloud observations and modeling.
State dependence of climate sensitivity
ECS based on glacial-interglacial climate is an average for global temperatures -7°C to +1°C relative to the Holocene and in general differs for other climate states because water vapor, aerosol-cloud and sea ice feedbacks depend on the initial climate. However, ECS is rather flat between today's climate and warmer climate, based on a study 71 covering a range of 15 CO2 doublings using an efficient GCM developed by Gary Russell. 72 Toward colder climate, icesnow albedo feedback increases nonlinearly, reaching snowball Earth conditionswith snow and ice on land reaching sea level in the tropicswhen CO2 declines to a quarter to an eighth of its 1950 abundance (Fig. 7 of the study). 71 Snowball Earth occurred several times in Earth's history, most recently about 600 million years ago 73 when the Sun was 6% dimmer 74 than today, a forcing of about -12 W/m 2 . Toward warmer climate, the water vapor feedback increases as the tropopause rises, 75 the tropopause cold trap disappearing at 32×CO2 (Fig. 7). 71 However, for the range of ECS of practical interestsay from half preindustrial CO2 to 4×CO2state dependence of ECS is small compared to state dependence of ESS.
Earth system sensitivity (ESS) includes amplifying feedbacks of GHGs and ice sheets. When we consider CO2 change as a known forcing, other GHGs provide a feedback that is smaller than the ice sheet feedback, but not negligible. Ice core data on GHG amounts show that non-CO2 GHGs including O3 and stratospheric H2O produced by changing CH4provide about 20% of the total GHG forcing, not only on average for the full glacial-interglacial change, but as a function of global temperature right up to +1°C global temperature relative to the Holocene (Fig. S5).
Atmospheric chemistry modeling suggests that non-CO2 GHG amplification of CO2 forcing by about a quarter continues into warmer climate states. 76 Thus, for climate change in the Cenozoic era, we approximate non-CO2 GHG forcing by increasing the CO2 forcing by one-quarter.
Ice sheet feedback, in contrast to non-CO2 GHG feedback, is highly nonlinear. Preindustrial climate was at most a few halvings of CO2 from runaway snowball Earth and LGM climate was even closer to that climate state. The ice sheet feedback is reduced as Earth heads toward warmer climate today because already two-thirds of LGM ice has been lost. Yet remaining ice on Antarctica and Greenland constitutes a powerful feedback, which humanity is about to bring into play. We can illuminate that feedback and the climate path Earth is now on by examining data on the Cenozoic erawhich includes CO2 levels comparable to today's amountbut first we must consider climate response times.
13
CLIMATE RESPONSE TIMES
In this section we define response functions for global temperature and Earth's energy imbalance that help explain the physics of climate change. Response functions help reveal the role of cloud feedbacks in amplifying climate sensitivity and the fact that cloud feedbacks buffer the rate at which the ocean can take up heat.
Climate response time was surprisingly long in our climate simulations 7 Slow climate response accentuates need for the "anticipation" that E.E. David, Jr. spoke about. If ECS is 4°C (1°C per W/m 2 ), more warming is in the pipeline than widely assumed. GHG forcing today already exceeds 4 W/m 2 . Aerosols reduce the net forcing to about 3 W/m 2 , based on IPCC estimates (Section 5), but warming still in the pipeline for 3 W/m 2 forcing is 1.8°C, exceeding warming realized to date (1.2°C). Slow feedbacks increase the equilibrium response even further (Section 6). Large warmings can be avoided via a reasoned policy response, but definition of effective policies will be aided by an understanding of climate response times.
Temperature response function
In the Bjerknes lecture 79 at the 2008 American Geophysical Union meeting, JEH argued that the ocean in many 80 GCMs had excessive mixing, and he suggested that GCM groups all report the response function of their modelsthe global temperature change versus time in response to instant CO2 doubling with the model run long enough to approach equilibrium. The response function characterizes a climate model and enables a rapid estimate of the global mean surface temperature change in response to any climate forcing scenario:
TG(t) = ʃ [dTG(t)/dt] dt = ʃ λ × R(t) [dFe/dt] dt.(5)
TG is the Green's function estimate of global temperature at time t, λ (°C per W/m 2 ) the model's equilibrium sensitivity, R the dimensionless temperature response function (% of equilibrium response), and dFe the forcing change per unit time, dt. Integration over time begins when Earth is in near energy balance, e.g., in preindustrial time. The response function yields an accurate estimate of global temperature change for a forcing that does not cause reorganization of ocean circulation. Accuracy of this approximation for temperature for one climate model is shown in Chart 15 in the Bjerknes presentation and wider applicability has been demonstrated. 82 We study ocean mixing effects by comparing two GCMs: GISS (2014) 83 and GISS (2020), 35 both models 84 described by Kelley et al. (2020). 34 Ocean mixing is improved in GISS (2020) by use of a high-order advection scheme, 85 finer upper-ocean vertical resolution (40 layers), updated mesoscale eddy parameterization, and correction of errors in the ocean modeling code. 34 The GISS (2020) model has improved variability, including the Madden-Julian Oscillation (MJO), El Nino Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO), but the spectrum of ENSO-like variability is unrealistic and its amplitude is excessive, as shown by the magnitude of oscillations in Fig. 4a. Ocean mixing in GISS (2020) may still be excessive in the North Atlantic, where the model's simulated penetration of CFCs is greater than observed. 86 Despite reduced ocean mixing, the GISS (2020) model surface temperature response is no faster than in the GISS (2014) model ( Fig. 4b): it takes 100 years to reach within 1/e of the equilibrium response. Slow response is partly explained by the larger ECS of the GISS (2020) model, which is 3.5°C versus 2.7°C for the GISS (2014) model, but something more is going on in the newer model, as exposed by the response function of Earth's energy imbalance.
Earth's energy imbalance (EEI)
When a forcing perturbs Earth's energy balance, the imbalance drives warming or cooling to restore balance. Observed EEI is now about +1 W/m 2 (more energy coming in than going out) averaged over several years. 87 High accuracy of EEI is obtained by tracking ocean warmingthe primary repository for excess energyand adding heat stored in warming continents and heat used in net melting of ice. 87 Heat storage in air adds an almost negligible amount. Radiation balance measured from Earth-orbiting satellites cannot by itself define the absolute imbalance, but, when calibrated with the in situ data, satellite Earth radiation budget observations provide invaluable EEI data on finer temporal and spatial scales than the in situ data. 88 After a step-function forcing is imposed, EEI and global surface temperature must each approach a new equilibrium, but EEI does so more rapidly, especially for the GISS (2020) model (Fig. 5). EEI in GISS (2020) needs only a decade to reach within 1/e of full response (Fig. 5b), but global surface temperature requires a century (Fig. 4b). Rapid decline of EEIto half the forcing in 5 years (Fig. 5a)has practical implications. First, EEI defines the rate heat is pumped into the ocean, so if EEI is reduced, ocean warming is slowed. Second, rapid EEI decline implies that it is wrong to assume that global warming can be stopped by a reduction of climate forcing by the amount of EEI. Instead, the required reduction of forcing is larger than EEI. The difficulty in finding additional reduction in climate forcing of even a few tenths of a W/m 2 is substantial. 68 Calculations that help quantify this matter are discussed in Supporting Material.
What is the physics behind the fast response of EEI? The 2×CO2 forcing and initial EEI are both nominally 4 W/m 2 . In the GISS (2014) model, the decline of EEI averaged over the first year is 0.5 W/m 2 (Fig. 5a), a moderate decline that might be largely caused by warming continents and increased heat radiation to space. In contrast, EEI declines 1.3 W/m 2 in the GISS (2020) model (Fig. 5a). Such a huge, immediate decline of EEI implies existence of an ultrafast climate feedback. Climate feedbacks are the heart of climate change and warrant discussion.
Slow, fast and ultrafast feedbacks
Charney et al. 4 described climate feedbacks without discussing time scales. At the 1982 Ewing Symposium, water vapor, clouds and sea ice were described as "fast" feedbacks 7 presumed to change promptly in response to global temperature change, as opposed to "slow" feedbacks or specified boundary conditions such as ice sheet size, vegetation cover, and atmospheric CO2 amount, although it was noted that some specified boundary conditions, e.g., vegetation, in reality may be capable of relatively rapid change. 7 The immediate EEI response (Fig. 5a) implies a third feedback time scale: ultrafast. Ultrafast feedbacks are not a new concept. When CO2 is doubled, the added infrared opacity causes the stratosphere to cool. Instant EEI upon CO2 doubling is only Fi = +2.5 W/m 2 , but stratospheric cooling quickly increases EEI to +4 W/m 2 . 89 All models calculate a similar radiative effect, so it is useful to define an adjusted forcing, Fa, which is superior to Fi as a measure of climate forcing. In contrast, if cloud changethe likely cause of the present ultrafast changeis lumped into the adjusted forcing, each climate model has its own forcing, losing the merit of a common forcing.
Kamae et al. 90 review rapid cloud adjustment distinct from surface temperature-mediated change. Clouds respond to radiative forcing, e.g., via effects on cloud particle phase, cloud cover, cloud albedo and precipitation. 91 The GISS (2020) model alters glaciation in stratiform mixed-phase clouds, which increases supercooled water in stratus clouds, especially over the Southern Ocean [ Fig. 1 in the GCM description 34 ]. The portion of supercooled cloud water drops goes from too little in GISS (2014) to too much in GISS (2020). Neither model simulates well stratocumulus clouds, yet the models help expose real-world physics that affects climate sensitivity and climate response time. Several models in CMIP6 comparisons find high ECS. 91 For the sake of revealing the physics, it would be useful if the models defined their temperature and EEI response functions. Model runs of even a decade can define the important part of Figs. 4a and 5a. Many short (e.g., 2-year) 2×CO2 climate simulations with each run beginning at a different point in the model's control run, could define cloud changes to an arbitrary accuracy. If the EEI response is faster than the temperature response, it implies that the climate forcing reduction required to stabilize climate is greater than EEI, as discussed in Supporting Material. The need for better understanding of ultrafast feedbacks does not alter the high ECS inferred from paleoclimate data. The main role of GCMs in the paleoclimate analyses that we use to assess climate sensitivity is to define climate patterns, which allows more accurate assessment of global temperature change from limited paleo data samples. 53,54,56
CENOZOIC ERA
In this section, we use data from ocean sediment cores to explore causes of climate change in the past 66 million years. High ECS implies that only moderate CO2 change is needed to account for Earth's long-term climate change.
Cenozoic climate allows us to investigate a key thesis of our perspective article: the danger that models are less sensitive than the real world to a climate forcing such as CO2 change. We refer to GCMs, in general, and ice sheet modeling, in particular. Present assessments of Cenozoic CO2 may be affected by a coupled GCM/ice sheet model finding that transition between unglaciated and glaciated Antarctica occurs at 700-840 ppm CO2. 92 In addition, GCMs have a long-standing difficulty in producing Pliocene warmth 93 especially in the Arctic, without large, probably unrealistic, GHG forcing. Our conclusion in Section 2 that (fast feedback) ECS is high, 1.2°C ± 0.3°C per W/m 2 , and our inference in Section 3 that amplifying cloud feedbacks cause the ECS increase from 0.6°C to 1.2°C per W/m 2 , suggest that GCMs must simulate clouds well to reproduce Cenozoic climate change. While we cannot develop cloud modeling here, we can examine the effect of high ECS on interpretation of Cenozoic climate change.
Atmospheric CO2 is a control knob 94 on Earth's temperature. CO2 on glacial-interglacial time scales is largely a feedback spurred by weak astronomical forcing, but Fig. 2 shows the tight control that CO2 maintains on those time scales. We obtain a more complete picture of CO2 as a forcing and feedback with aid of consistent calculations over the entire Cenozoic era. Specifically, we use our derived ECS and a proxy (oxygen isotope) measure of deep ocean temperature to infer a history of Earth's surface temperature and atmospheric CO2 throughout the Cenozoic era. Progress has been made in proxy measurement of CO2 via carbon isotopes in alkenones and boron isotopes in planktic foraminifera, 95 yet there is still a wide scatter among the results and fossil plant stomata tend to suggest smaller CO2 amounts. 96 Proxy measures of CO2 and indirect constraints on CO2 based on oxygen isotopes need to work in concert because of shortcomings in understanding of the physics of both the oxygen isotope temperature proxy 97 and CO2 proxies. 95 Merits of the oxygen isotope approach include high temporal resolution and precision. We aim to show that deep ocean temperature change provides a useful measure of surface temperature change and that the oxygen isotope proxy provides a check on CO2 proxies, as well as better understanding of Cenozoic climate change.
Deep ocean temperature and sea level from δ 18 O
Glacial-interglacial CO2 oscillations ( Fig. 2) involve exchange of carbon among surface carbon reservoirs: the ocean, atmosphere, soil and biosphere. Total CO2 in the reservoirs also can vary, mainly on longer time scales, as carbon is exchanged with the solid Earth. CO2 then becomes a primary agent of long-term climate change, leaving orbital effects as "noise" on larger climate swings. Oxygen isotopic composition of benthic (deep ocean dwelling) foraminifera shells provides a starting point for analysis of Cenozoic temperature. Fig. 6 includes the recent highresolution record of Westerhold et al. 98 and data of Zachos et al. 47
The latter two equations are based on LGM δ 18 O values δ 18 OLGM Z = 4.9 and δ 18 OLGM W = 5.3. Holocene and LGM deep ocean temperatures are specified as 1°C 102 and -1°C. 100 Coefficients in the equations are calculated as shown by the equation (11) example.
Tdo Z (°C) = 5 -2.55 (δ 18 O -1.75) (1.75 < δ 18 O < 3.32),(10)Tdo Z (°C) = 1 -2 (δ 18 O -3.32)/(4.9 -3.32) = 1 -1.27 (δ 18 O -3.32) (3.32 < δ 18 O),(11)Tdo W (°C) = 6 -2.10 (δ 18 O -1.5) (1.5 < δ 18 O < 3.88),(12)Tdo W (°C) = 1 -1.41 (δ 18 O -3.88) (3.88 < δ 18 O),(13)
In Supporting Material, we graph Zachos and Westerhold δ 18 O, SL and Tdo for the full Cenozoic, the Pleistocene, and past 800 thousand years (sea level is compared to data of Rohling et al. 103 ).
Cenozoic TS
In this section we use Tdo to estimate Cenozoic surface temperature (TS). Tdo is closely tied to sea surface temperature (SST) at high latitudes where deepwater forms. For climate warmer than the Holocene, we assume that TS change is equal to Tdo change, as an initial approximation. Thus,
TS ⁓ Tdo -TdoH + 14°C = Tdo + 13°C, (δ 18 O < δ 18 OH)(14)
where we take Holocene mean TS as 14°C and TdoH as 1°C. For colder climate, Tdo changes more slowly than TS as Tdo approaches the freezing point. We use linear interpolation between the Holocene and the LGM and knowledge that the LGM was ~7°C cooler than the Holocene:
TS = 14°C -7°C × (δ 18 O -δ 18 OH)/(δ 18 OLGM -δ 18 OH). (δ 18 O > δ 18 OH)(15)
EECO (Early Eocene Climatic Optimum) temperature is ~27°C for Westerhold and ~25°C for Zachos data (Fig. 7). The difference between the data sets likely is related to imprecision in conversion of Tdo to TS. We interpret the Westerhold . Antarctic Dome C data 43 (red) relative to last 1,000 years is multiplied by 0.6 to account for polar amplification (which is greater for land areas than for SST) and 14°C is added for absolute scale.
[ΔSST (latitude)/ΔSST (ocean mean)] is close to unity in the polar oceans (Fig. 8), but not up to the Antarctic coast where most AABW is formed. Polar amplification of SST change should reach Antarctica, allowing AABW to be a good approximation of global TS change, after global warming reaches a level with much reduced Antarctic sea ice. However, Cenozoic temperature inferred from AABW reflects this "slow start" from the Holocene level. In contrast, the efficacy of polar SST is near unity for today's climate in regions of deepwater formation in the Northern Hemispherethe Greenland and Nordic Seas. Thus, we take global temperature inferred from the Westerhold data set as a more realistic estimate of Cenozoic temperature change.
Why use Tdo to estimate TS, when proxies exist for TS? TS proxies have large uncertainties 97 and cannot match the rich detail of benthic δ 18 O. Studies that combine multiple proxies 104,105 yield maximum Eocene temperature similar to, or 1-2°C warmer than, our result at the EECO based on Westerhold data (Fig. 7). Differences are not large enough to alter conclusions of our paper.
Cenozoic CO2
We obtain the CO2 history required to yield the Cenozoic TS history from the relation
ΔF(t) = (TS(t) -14°C)/ECS,(17)
where ΔF(t) (0 at 7 kyBP) includes changing solar irradiance and amplification of CO2 forcing by non-CO2 GHGs and ice sheets. The GHG amplification factor is taken as 1.25 throughout the Cenozoic (Section 2.6). The amplification applies to solar forcing as well as CO2 forcing because it is caused by temperature change, not by CO2. Solar irradiance is increasing 10% per billion years; 74 thus solar forcing (240 W/m 2 today) increases 2.4 W/m 2 per 100 million years. Thus,
ΔF(t) = 1.25 × [ΔFCO2(t) + ΔFSol(t)] × AS. (δ 18 O > δ 18 OH)(18)
AS, surface albedo amplification, is smaller in moving from the Holocene to warmer climatewhen the main effect is shrinking of Antarctic icethan toward colder climate. For δ 18
ΔF(t) = 3.19 × [ΔFCO2(t) + ΔFSol(t)]. (δ 18 O > δ 18 OH)(20)
For climate warmer than the Holocene up to Oi-1, i.e., for δ 18 OOi-1 < δ 18 O < δ 18 OH,
ΔF(t) = 1.25×[ΔFCO2(t) + ΔFSOL(t) + FIceH × (δ 18 OH -δ 18 O)/(δ 18 OH -δ 18 OOi-1)].(21)
FIceH, the (Antarctic plus Greenland) ice sheet forcing between the Holocene and Oi-1, is estimated to be 2 W/m 2 (Fig. S4, Target CO2). For climate warmer than Oi-1
ΔF(t) = 1.25× [ΔFCO2 + ΔFSol(t) + ΔFIceH].(22)
All quantities are known except ΔFCO2(t), which is thus defined. Cenozoic CO2 (t) for specified ECS is obtained from TS(t) using the CO2 radiative forcing equation (Table 1, Supp. Material). We use the Westerhold TS history, which is more realistic for reasons given above. Resulting CO2 (Fig. 9) is about 1,000 ppm in the EECO, 400 ppm at Oi-1, and 300 ppm in the Pliocene for the most probable ECS (1.2°C per W/m 2 ). These values depend on ECS and assumption that non-CO2 gases provide 20% of the GHG forcing, but our lowest value for ECS (1°C per W/m 2 ) leaves Pliocene CO2 near 300 ppm, rising only to ~ 450 ppm at Oi-1 and ~ 1200 ppm at EECO.
Assumed Holocene CO2 amount is also a minor factor. We tested two cases: 260 and 278 ppm (Fig. 9). These were implemented as the CO2 values at 7 kyBP, but the Holocene-mean values were similara few ppm less than CO2 at 7 kyBP in both cases. The Holocene = 278 ppm case increases CO2 about 20 ppm between today and Oi-1, and about 50 ppm at the EECO. However, such a high value for Holocene CO2 causes the amplitude of inferred glacial-interglacial CO2 oscillations to be less than reality (Fig. 9), providing support for the Holocene 260 ppm level and for the interpretation that high late-Holocene CO2 was due to human influence.
Proxy measures of Cenozoic CO2 yield a notoriously large range. A recent review 95 constructs a CO2 history with early Cenozoic values ~800-1600 ppm and Loess-smoothed CO2 ~800 ppm at Oi-1 and 350-400 ppm in the Pliocene. These Oi-1 and Pliocene values are not plausible without overthrowing the concept that global temperature is a response to climate forcings. We conclude that actual CO2 was near the low end of the range of proxy measurements.
Interpretation of Cenozoic TS and CO2
In this section we consider Cenozoic TS and CO2 histories, which are rich in insights about climate change with implications for future climate.
In Target CO2 65 and elsewhere 106 we argue that the broad sweep of Cenozoic temperature is a result of plate tectonic (popularly "continental drift") effects on CO2. Solid Earth sources and sinks of CO2 are not balanced at any given time. CO2 is removed from surface reservoirs by: (1) chemical weathering of rocks with deposition of carbonates on the ocean floor, and (2) burial of organic matter. 107,108 CO2 returns via metamorphism and volcanic outgassing at locations where oceanic crust is subducted beneath moving continental plates. The interpretation in Target CO2 was that the main Cenozoic source of CO2 was associated with the Indian plate (Fig. 10 Fig. 6) before resuming high speed, 99 leaving an indelible signature in the Cenozoic δ 18 O history (Fig. 6) that supports our interpretation of the CO2 source. Since the continental collision, subduction and CO2 emissions continue at a diminishing rate as the India plate underthrusts the Asian continent and pushes up the Himalayan mountains. 114 We interpret the decline of CO2 over the past 50 million years as, at least in part, a decline of the metamorphic source from continued subduction of the Indian plate, but burial of organic matter and increased weathering due to exposure of fresh rock by Himalayan uplift 115 may contribute to CO2 drawdown. Quantitative understanding of these processes is limited, 116 e.g., weathering is both a source and sink of CO2. 117 This picture for the broad sweep of Cenozoic CO2 is consistent with current understanding of the long-term carbon cycle, 118 but relative contributions of metamorphism 116 and volcanism 119 are uncertain. Also, emissions from rift-induced Large Igneous Provinces (LIPs) 120,121 contribute to long-term change of atmospheric CO2, with two cases prominent in Fig. 6. The Columbia River Flood Basalt at ca. 17-15 MyBP was a principal cause of the Miocene Climatic Optimum, 122 but the processes are poorly understood. 123 A more dramatic event occurred as Greenland separated from Europe, causing a rift in the sea floor; flood basalt covered more than a million square kilometers with magma volume 6-7 million cubic kilometers 121the North Atlantic Igneous Province (NAIP). Flood basalt volcanism occurred during 60.5-54.5 MyBP, but at 56.1 ± 0.5 MyBP melt production increased by more than a factor of 10, continued at a high level for about a million years, and then subsided (Fig. 5 of Storey et al.). 124 The striking Paleocene-Eocene Thermal Maximum (PETM) δ 18 O spike (Fig. 6) occurs early in this million-year bump-up of δ 18 O. Svensen et al. 125 proposed that the PETM was initiated by the massive flood basalt into carbon-rich sedimentary strata. Gutjahr et al. 126 developed an isotope analysis, concluding that most of PETM carbon emissions were volcanic, with climate-driven carbon feedbacks playing a lesser role. Yet other evidence, 127 while consistent with volcanism as a trigger for the PETM, suggests that climate feedbackperhaps methane hydrate releasemay have caused more than half of the PETM warming. We discuss PETM warming and CO2 levels below, but first must quantify the mechanisms that drove Cenozoic climate change and consider where Earth's climate was headed before humanity intervened.
24 Fig. 11. Climate forcings and slow feedbacks relative to 7 kyBP from terms in equation (21) The sum of climate forcings (CO2 and solar irradiance) and slow feedbacks (ice sheets and non-CO2 GHGs) that maintained EECO warmth was 10.5 W/m 2 (Fig. 11) Most of the global warming for today's atmosphere is still in the pipeline, as will be discussed in Section 6.5.
Prospects for another Snowball Earth
We would be remiss if we did not comment on the precipitous decline of Earth's temperature over millions of years. Was Earth falling off the table into another Snowball Earth?
Global temperature plummeted in the past 50 million years, with growing, violent, oscillations (Figs. 6 and 7). Was Earth headed to a runaway albedo feedback? Glacial-interglacial average CO2 declined from about 300 ppm to 225 ppm in the past five million years in an accelerating decline (Fig. 9a). As CO2 fell to 180 ppm in recent glacial maxima, an ice sheet covered most of Canada and reached midlatitudes in the U.S. Continents in the current supercontinent cycle 109 are now dispersed, with movement slowing to 2-3 cm/year. Emissions from the last high-speed highimpact tectonic eventcollision of the Indian plate with Eurasiaare fizzling out. The most recent large igneous province (LIP) eventthe Columbia River Flood Basalt about 15 million years ago (Fig. 6) is no longer a factor, and there is no evidence of another impending LIP. Snowball conditions are possible, even though the Sun's brightness is increasing and is now almost 6% greater 74 than it was at the last snowball Earth, almost 600 million years ago. 73 Runaway snowball likely requires only 1-2 halvings 71 of CO2 from the LGM 180 ppm level, i.e., to 45-90 ppm. Although the weathering rate declines in colder climate, 129 weathering and burial
Paleocene Eocene Thermal Maximum (PETM)
The PETM event provides an invaluable benchmark for assessing the eventual impact of the human-made climate perturbation and the time scale for natural recovery of the climate system.
Westerhold data have 10°C deep ocean warming at the PETM (Fig. 12), which is greater than surface warming found in other proxy temperature data. A summary 130 of low latitude SST data has 3-4°C PETM warming. GCM-assisted data assimilation 131 We conclude that human-made climate forcing has reached the level that drove PETM climate change; today's 1.2°C global warming is but a fraction of the equilibrium response to gases now in the air. The greater warming in the pipeline and its impacts are not inevitable, as discussed in Section 6, because climate's delayed response allows preventative actions. Better understanding of the PETM will aid policy considerations, but we must bear in mind two major differences between the PETM and human-made climate change.
First, there were no large ice sheets on Earth in the PETM era. Today, ice sheets on Antarctica and Greenland make the Earth system sensitivity (ESS) greater than it was at the time of the PETM, as quantified above. Equilibrium response to today's human-made climate forcing includes deglaciation of Antarctica and Greenland, with sea level 60 m (about 200 feet) higher than today and the potential for chaotic climate change this century, as discussed in Section 6. The second major difference between the PETM and today is the rate of change of the climate forcing. Most of today's climate was introduced in a century, which seems to be 10 times or more faster than the PETM forcing growth. Although it is conceivable that a bolide impact 134 triggered the PETM, the issue is the time scale on which the climate forcingincreased GHGsoccurred. Despite uncertainty in the carbon source(s), data and modeling point to duration of a millennium or more for PETM emissions. 130,135 Better understanding of the PETM could inform us on the important topic of climate feedbacks. The Gutjahr et al. 126 inference that most of the PETM emissions were volcanic is persuasive, yet we know of no other case in which a large igneous province produced such large, temporallyisolated emissions. The double peak in deep ocean δ 18 O (and thus in inferred temperatures, cf. Fig. 12, where each square is a binning interval of 5,000 years), which also is found in terrestrial data, 136 needs to be understood. Perhaps the sea floor rift occurred in two events, or the rift was followed tens of thousands of years later by methane hydrate release as a feedback to the ocean warming; much of today's methane hydrate is in stratigraphic deposits hundreds of meters below the sea floor, where millennia may pass before a thermal wave from the surface reaches the deposits. 137 Another potential feedback contribution, from peat, seems almost unavoidable. Northern peatlands today contain more than 1000 Gt carbon, 138 much of which could be mobilized on millennial time scales at PETM warming levels. 139 Numerous hyperthermal events in the Cenozoic record testify to the importance of such feedbacks, because the events seem to be spurred by modest orbital forcings and include negative carbon isotope excursions. 140 Emissions from such feedbacks, including the terrestrial biosphere and permafrost, seem to be more chronic than catastrophic on the short-term, but if policies are not designed to terminate growth of these feedbacks (Section 6), it may become impossible to avoid climate catastrophe.
Policy discussion requires an understanding of the role of aerosols in climate change. Fig. 13. Observed global surface temperature (black line) and expected GHG warming with two choices for ECS. The blue area is the estimated aerosol cooling effect. The temperature peak in the World War II era is in part an artifact of inhomogeneous ocean data in that period. 68
AEROSOLS
The role of aerosols in climate change is uncertain because aerosol properties are not measured well enough to define their climate forcing. In this section we find ways to estimate the climate forcing via aerosol effects on Earth's temperature and Earth's energy imbalance.
Aerosol impact is suggested by the gap between observed global warming and expected warming due to GHGs based on ECS inferred from paleoclimate (Fig. 13). Expected warming is from Eq. 4 with the normalized response function of the GISS (2020) model. Our best estimate for ECS, 1.2°C per W/m 2 , yields a gap of 1.5°C between expected and actual warming in 2022. Aerosols are the likely cooling source. The other negative forcing discussed by IPCCsurface albedo changeis estimated by IPCC (Chapter 7, Table 7.8) to be -0.12 ± 0.1 W/m 2 , an order of magnitude smaller than aerosol forcing. 13 Thus, for clarity, we focus on GHGs and aerosols.
Absence of global warming over the 70-year period 1850-1920 ( Fig. SPM.1 of IPCC AR6 WG1 report 13 ) is a clue about aerosol forcing. GHG forcing increased 0.54 W/m 2 in 1850-1920, which causes an expected warming ~0.4°C by 1920 for ECS = 1°C per W/m 2 . Natural forcingssolar irradiance and volcanic aerosolsmight contribute to lack of warming, but no persuasive case has been made for the required downward trends of those forcings. Human-made aerosols are the likely offset of GHG warming. Such aerosol cooling is a Faustian bargain 106 because payment in enhanced global warming will come due once we can no longer tolerate the air pollution. Ambient air pollution causes millions of deaths per year, with particulates most responsible. 141
Evidence of aerosol forcing in the Holocene
In this section we infer evidence of human-made aerosols in the last half of the Holocene from the absence of global warming. Some proxy-based analyses ,142 report cooling in the last half of the Holocene, but a recent analysis 54 that uses GCMs to overcome spatial and temporal biases in proxy data finds rising global temperature in the first half of the Holocene followed by nearly constant temperature in the last 6,000 years until the last few centuries (Fig. 14). Antarctic, deep ocean, and tropical sea surface data all show stable temperature in the last 6,000 years ( Fig. S6 of reference 65 ). GHG forcing increased 0.5 W/m 2 during those 6,000 years (Fig. 15), yet Earth did not warm. Fast feedbacks alone should yield at least +0.5°C warming and 6,000 years is long enough for slow feedbacks to also contribute. How can we interpret the absence of warming?
Humanity's growing footprint deserves scrutiny. Ruddiman's suggestion that deforestation and agriculture began to affect CO2 6500 year ago and rice agriculture began to affect CH4 5,000 years ago has been criticized 50 mainly because of the size of proposed sources. Ruddiman sought sources sufficient to offset declines of CO2 and CH4 in prior interglacial periods, but such large sources are not needed to account for Holocene GHG levels. Paleoclimate GHG decreases are slow feedbacks that occur in concert with global cooling. However, if global cooling did not occur in the past 6,000 years, feedbacks did not occur. Earth orbital parameters 6,000 years ago kept the Southern Ocean warm, as needed to maintain strong overturning ocean circulation 144 and minimize carbon sequestration in the deep ocean. Maximum insolation at 60°S was in late- spring (mid-November); since then, maximum insolation at 60°S slowly advanced through the year, recently reaching mid-summer (mid-January, Fig. 26b of Ice Melt 14 ). Maximum insolation from late-spring through mid-summer is optimum to warm the Southern Ocean and promote early warm-season ice melt, which reduces surface albedo and magnifies regional warming. 48 GHG forcing of -0.2 W/m 2 in 10-6 kyBP (Fig. 15) was exceeded by forcing of +1 W/m 2 due to ice sheet shrinkage (Supp. Material in Target CO2 65 ) for a 40 m sea level rise (Fig. 16). Net 0.8 W/m 2 forcing produced expected 1°C global warming (Fig. 14). The mystery is the absence of warming in the past 6,000 years. Hansen et al. 48 suggested that aerosol cooling offset GHG warming. Growing population, agriculture and land clearance produced aerosols and CO2; wood was the main fuel for cooking and heating. Nonlinear aerosol forcing is largest in a pristine atmosphere, so it is unsurprising that aerosols tended to offset CO2 warming as civilization developed. Hemispheric differences could provide a check. GHG forcing is global, while aerosol forcing is mainly in the Northern Hemisphere. Global offset implies a net negative Northern Hemisphere forcing and positive Southern Hemisphere forcing. Thus, data and modeling studies (including orbital effects) of regional response are warranted but beyond the scope of this paper.
Industrial era aerosols
Scientific advances often face early resistance from other scientists. 146 Examples are the snowball Earth hypothesis 147 and the role of an asteroid impact in extinction of non-avian dinosaurs, 148 which initially were highly controversial but are now more widely accepted. Ruddiman's hypothesis, right or wrong, is still controversial. Thus, we minimize this issue by showing aerosol effects with and without preindustrial human-made aerosols.
Global aerosols are not monitored with detail needed to define aerosol climate forcing. 149,150 IPCC 13 estimates forcing (Fig. 17a) from assumed precursor emissions, a herculean task due to many aerosol types and complex cloud effects. Aerosol forcing uncertainty is comparable to its estimated value (Fig. 17a), which is constrained more by observed global temperature change than by aerosol measurements. 151 IPCC's best estimate of aerosol forcing (Fig. 107) and GHG history define the percent of GHG forcing offset by aerosol coolingthe dark blue area in Fig. 17b. However, if human-made aerosol forcing was -0.5 W/m 2 by 1750, offsetting +0.5 W/m 2 GHG forcing, this forcing should be included. Such aerosol forcinglargely via effects of land use and biomass fuels on cloudscontinues today. Thirty million people in the United States use wood for heating. 152 Such fuels are also common in Europe 153,154 and much of the world. Fig. 17b encapsulates two alternative views of aerosol history. IPCC aerosol forcing slowly becomes important relative to GHG forcing. In our view, civilization always produced aerosols as well as GHGs. As sea level stabilized, organized societies and population grew as coastal biologic productivity increased 155 and agriculture developed. Wood was the main fuel. Aerosols travel great distances, as shown by Asian aerosols in North America. 156 Humans contributed to both rising GHG and aerosol climate forcings in the past 6,000 years. One result is that humancaused aerosol climate forcing is at least 0.5 W/m 2 more than usually assumed. Thus, the Faustian payment that will eventually come due is also larger, as discussed in Section 6.
Ambiguity in aerosol climate forcing
In this section we discuss uncertainty in the aerosol forcing. We discuss why global warming in the past centuryoften used to infer climate sensitivityis ill-suited for that purpose.
Recent global warming does not yield a unique ECS because warming depends on three major unknowns with only two basic constraints. Unknowns are ECS, net climate forcing (aerosol forcing is unmeasured), and ocean mixing (many ocean models are too diffusive). Constraints are observed global temperature change and Earth's energy imbalance (EEI). 87 Knutti 157 and Hansen 79 suggest that many climate models compensate for excessive ocean mixing (which reduces surface warming) by using aerosol forcing less negative than the real world, thus achieving realistic surface warming. This issue is unresolved and complicated by the finding that cloud feedbacks can buffer ocean heat uptake (Section 3), affecting interpretation of EEI.
IPCC AR6 WG1 best estimate of aerosol forcing (Table AIII.3) 13 is near maximum (negative) value by 1975, then nearly constant until rising in the 21 st century to -1.09 W/m 2 in 2019 (Fig. 18). We use this IPCC aerosol forcing in climate simulations here. We also use an alternative aerosol scenario 158 that reaches -1.63 W/m 2 in 2010 relative to 1880 and -1.8 W/m 2 relative to 1850 (Fig. 18) based on modeling of Koch 159 that included changing technology factors defined by Novakov. 160 This alternative scenario 161 is comparable to the forcing in some current aerosol (Fig. 18). Human-made aerosol forcing relative to several millennia ago may be even more negative, by about -0.5 W/m 2 as discussed above, but the additional forcing was offset by increasing GHGs and thus those additional forcings are neglected, with climate assumed to be in approximate equilibrium in 1850.
Many combinations of climate sensitivity and aerosol forcing can fit observed global warming. The GISS (2014) model (ECS = 2.6°C) with IPCC AR6 aerosol forcing can match observed warming (Fig. 19) in the last half century (when human-made climate forcing overwhelmed natural forcings, unforced climate variability, and flaws in observations). However, agreement also can be achieved by climate models with high ECS. The GISS (2020) model (with ECS = 3.5°C) yields greater warming than observed if IPCC aerosol forcing is used, but less than observed for the alternative aerosol scenario (Fig. 19). This latter aerosol scenario achieves agreement with observed warming if ECS ~ 4°C (green curve in Fig. 19). 163 Agreement can be achieved with even higher ECS by use of a still more negative aerosol forcing. Fig. 19. Global temperature change TG due to aerosols + GHGs calculated with Green's function Eq (5) using GISS (2014) and GISS (2020) response functions (Fig. 4). Observed temperature is the NASA GISS analysis. 164,165 Base period: 1951-1980 for observations and model. The issue we raise is the magnitude of the aerosol forcing, with implications for future warming when particulate air pollution is likely to be reduced. We suggest that IPCC reports may have gravitated toward climate sensitivity near 3°C for 2×CO2 in part because of difficulty that models have in realistically simulating amplifying cloud feedbacks and a climate model tendency for excessive mixing of heat into the deep ocean. Our finding from paleoclimate analysis that ECS is 1.2°C ± 0.3°C per W/m 2 (4.8°C ± 1.2°C for 2×CO2) implies that the (unmeasured) aerosol forcing must be more negative than IPCC's best estimate. In turnbecause aerosolcloud interactions are the main source of uncertainty in aerosol forcingthis finding emphasizes the need to measure both global aerosol and cloud particle properties.
The case for monitoring global aerosol climate forcing will grow as recognition of the need to slow and reverse climate change emerges. Aerosol and cloud particle microphysics must be measured with precision adequate to define the forcing. 167,149 In the absence of such Keeling-like global monitoring, progress can be made via more limited satellite measurements of aerosol and cloud properties, field studies, and aerosol and cloud modeling. As described next, a wonderful opportunity to study aerosol and cloud physics is provided by a recent change in the IMO (International Maritime Organization) regulations on ship emissions.
The great inadvertent aerosol experiment
Sulfate aerosols are cloud condensation nuclei (CCN), so sulfate emissions by ships result in a larger number of smaller cloud particles, thus affecting cloud albedo and cloud lifetime. 168 Ships provide a large percentage of sulfates in the North Pacific and North Atlantic regions (Fig. 20). It has been suggested that cooling by these clouds is overestimated because of cloud liquid water adjustments, 169 Fig. 18) is not a measure of aerosol forcing uncertainty. The larger bar, from Chapter 7 172 of AR6, has negative forcing as great as -2 W/m 2 , but even that does not measure the full uncertainty. Changes of IMO emission regulations provide a great opportunity for insight into aerosol climate forcing. Sulfur content of fuels was limited to 1% in 2010 near the coasts of North America and in the North Sea, Baltic Sea and English Channel, and further restricted there to 0.1% in 2015. 173 In 2020 a limit of 0.5% was imposed worldwide. The 1% limit did not have a noticeable effect on ship-tracks, but a striking reduction of ship-tracks was found after the 2015 IMO regulations, especially in the regions near land where emissions were specifically limited. 174 Following the additional 2020 regulations, 175 global ship-tracks were reduced more than 50%. 176 Earth's albedo (reflectivity) measured by CERES (Clouds and Earth's Radiant Energy System) satellite-borne instruments 88 (Fig. 22), a region of relatively little ship traffic. This change is an order of magnitude larger than the estimate of potential detector degradation. 88 Climate models predict a reduction of cloud albedo in this region as a feedback effect driven by global warming. 181 Continued monitoring of absorbed energy can confirm the reality of the change, but without global monitoring of detailed physical properties of aerosols and clouds, 149 it will be difficult to apportion observed change among the candidate causes.
The North Pacific and North Atlantic regions of heavy ship traffic are ripe for more detailed study of cloud changes and their causes, although unforced cloud variability is large in such subglobal regions. North Pacific and North Atlantic regions both have increased absorption of solar radiation after 2015 (Fig. 22). The 2014-2017 maximum absorption in the North Pacific is likely enhanced by reduced cloud cover during the positive PDO, but the more recent high absorption is during the negative PDO phase. In the North Atlantic, the persistence of increased absorption for the past several years exceeds prior variability, but longer records plus aerosol and cloud microphysical data are needed for full interpretation.
SUMMARY
Richard Feynman needled fellow physicists about their reticence to challenge authority, 182 using the famous oil drop experiment in which Millikan derived the electron charge. Millikan's result was a bit off. Later researchers moved his result in small incrementsuncertainties and choices in experiments require judgmentand after years the community arrived at an accurate value. Their reticence to contradict Millikan was an embarrassment to the physics community, but it caused no harm to society. Scientific reticence, 183 in part, may be a consequence of the scientific method, which is fueled by objective skepticism. Another factor that contributes to irrational reticence among rational scientists is "delay discounting," a preference for immediate over delayed rewards. 184 The penalty for "crying wolf" is immediate, while the danger of being blamed for having "fiddled while Rome was burning" is distant. Also, one of us has noted 185 evidence that larding of papers and research proposals with caveats and uncertainties notably increases chances of obtaining research support. "Gradualism" that results from reticence seems to be comfortable and well-suited for maintaining long-term support.
Reticence and gradualism reach a new level with the Intergovernmental Panel on Climate
Change (IPCC). The prime example is IPCC's history in evaluating climate sensitivity, the most basic measure of climate change, as summarized in our present paper. IPCC reports must be approved by UN-assembled governments, but that constraint should not dictate reticence and gradualism. Climate science clearly reveals the threat of being too late. "Being too late" refers not only to assessment of the climate threat, but also to advice on the implications of the science for policy. Are not we as scientists complicit if we allow reticence and comfort to obfuscate our description of the climate situation and its implications? Does our trainingyears of graduate study and decades of experiencenot make us the best-equipped to advise the public on the climate situation and its implications for policy? As professionals with the deepest understanding of planetary change and as guardians of young people and their future, do we not have an obligation, analogous to the code of ethics of medical professionals, to render to the public our full and unencumbered diagnosis and its implications? That is our aim here.
Equilibrium climate sensitivity (ECS)
The 1979 Charney study 4 considered an idealized climate sensitivity in which ice sheets and non-CO2 GHGs are fixed. The Charney group estimated that the equilibrium response to 2×CO2, a forcing of 4 W/m 2 , was 3°C, thus an ECS of 0.75°C per W/m 2 , with one standard deviation uncertainty σ = 0.375°C. Charney's estimate stood as the canonical ECS for more than 40 years. The current IPCC report 13 concludes that 3°C for 2×CO2 is their best estimate for ECS.
We compare recent glacial and interglacial climates to infer ECS with a precision not possible with climate models alone. Uncertainty about Last Glacial Maximum (LGM) temperatures has been resolved independently with consistent results by Tierney et al. 53 and Seltzer et al. 56 The Tierney approach, using a collection of geochemical temperature indicators in a global analysis constrained by climate change patterns defined by a global climate model, is used by Osman et al. 54 to find peak LGM cooling 7.0 ± 1°C (2σ, 95% confidence) at 21-18 kyBP. We show that, accounting for polar amplification, these analyses are consistent with the 5.8 ± 0.6°C LGM cooling of land areas between 45°S and 35°N found by Seltzer et al. using the temperaturedependent solubility of dissolved noble gases in ancient groundwater. The forcing that maintained the 7°C LGM cooling was the sum of 2.25 ± 0.45 W/m 2 (2σ) from GHGs and 3.5 ± 1.0 W/m 2 (2σ) from the LGM surface albedo, thus 5.75 ± 1.1 W/m 2 (2σ). ECS implied by the LGM is thus 1.22 ± 0.29°C (2σ) per W/m 2 , which, at this final step, we round to 1.2 ± 0.3°C per W/m 2 . For transparency, we have combined uncertainties via simple RMS (root-mean-square). ECS as low as 3°C for 2×CO2 is excluded at the 3σ level, i.e., with 99.7% confidence.
More sophisticated mathematical analysis, which has merits but introduces opportunity for prior bias and obfuscation, is not essential; error assessment ultimately involves expert judgement. Instead, focus is needed on the largest source of error:
LGM surface albedo change, which is uncertain because of the effect of cloud shielding on the efficacy of the forcing. As cloud modeling is advancing rapidly, the topic is ripe for collaboration of CMIP 58 (Coupled Model Intercomparison Project) with PMIP 59 (Paleoclimate Modelling Intercomparison Project).
Simulations should include at once change of surface albedo and topography of ice sheets, vegetation change, and exposure of continental shelves due to lower sea level.
Knowledge of climate sensitivity can be advanced further via analysis of the wide climate range in the Cenozoic era (Section 6.3). However, interpretation of data and models, and especially projections of climate change, depend on understanding of climate response times.
Climate response times
We expected climate response timethe time for climate to approach a new equilibrium after imposition of a forcingto become faster as mixing of heat in ocean models improved. 79 That expectation was not met when we compared two generations of the GISS GCM. The GISS (2020) GCM is demonstrably improved 34,35 in its ocean simulation over the GISS (2014) GCM as a result of higher vertical and horizontal resolution, more realistic parameterization of sub-grid scale motions, and correction of errors in the ocean computer program. 34 Yet the time required for the model to achieve 63% of its equilibrium response remains about 100 years. There are two reasons for this, one that is obvious and one that is more interesting and informative.
The surface in the newer model warms as fast as in the older model, but it must achieve greater warming to reach 63% of equilibrium because its ECS is higher, which is the first reason that the response time stays long. The other reason is that Earth's energy imbalance (EEI) in the newer model decreases rapidly. EEI defines the rate that heat is pumped into the ocean, so a smaller EEI implies a longer time for the ocean to reach its new equilibrium temperature. Quick drop of EEIin the first year after introduction of the forcingimplies existence of ultrafast feedback in the GISS (2020) model. For want of an alternative with such a large effect on Earth's energy budget, we infer a rapid cloud feedback and we suggest (Section 3.3) a set of brief GCM runs that could define cloud changes and other diagnostic quantities to an arbitrary accuracy.
The Charney report 4 recognized that clouds were a main cause of a wide range in ECS estimates. Today, clouds still cast uncertainty on climate predictions. Several CMIP6 36 GCMs have ECS of ~ 4-6°C for 2×CO2 186,187 with the high sensitivity caused by cloud feedbacks. 91 As cloud modeling progresses, it will aid understanding if climate models report their 2×CO2 response functions for both temperature and EEI (Earth's energy imbalance).
Fast EEI responsefaster than global temperature responsehas a practical effect: observed EEI understates the reduction of climate forcing required to stabilize climate. Although the magnitude of this effect is uncertain (see Supporting Material), it makes the task of restoring a hospitable climate and saving coastal cities more challenging. On the other hand, long climate response time implies the potential for educated policies to affect the climate outcome before the most undesirable consequences occur.
The time required for climate to reach a new equilibrium is relevant to policy (Section 6.6), but there is another response time of practical importance. With climate in a state of disequilibrium, how much time do we have before we pass the point of no return, the point where major climate impacts are locked in, beyond our ability to control? That's a complex matter; it requires understanding of "slow" feedbacks, especially ice sheets. It also depends on how far out of equilibrium we are. Thus, we first consider the full Earth system sensitivity.
Earth system sensitivity (ESS)
The Cenozoic erathe past 66 million yearsprovides an opportunity to test understanding of Earth system sensitivity, including ice sheet feedback. Earth was so warm in the early Cenozoic that there were no large ice sheets, but after the Early Eocene Climatic Optimum (EECO) fifty million years before present (50 MyBP), global temperature declined until 34 MyBP, when an ice sheet, aided by the albedo feedback, rapidly glaciated Antarctica. Earth then stayed within a moderate temperature range until gradual cooling in the Pliocene epoch (from about 5.3 to 2.6 MyBP) led to periodic ice sheet formation in the Northern Hemisphere during the Pleistocene. The most recent interglacial periodthe Holocene epochbegan about 11.6 kyBP.
Atmospheric CO2 amount in the past 800,000 years, well-known from bubbles of air trapped in the Antarctic ice sheet (Fig. 2), confirms expectation that CO2 is the main control knob 94 on global temperature. We assume that this control existed at earlier times and infer the Cenozoic CO2 history required to produce an estimated Cenozoic surface temperature history (Fig. 23).
The temperature history is based on the oxygen isotope δ 18 O in shells of deep-ocean-dwelling foraminifera preserved in ocean sediment, 98 which is affected by ambient temperature at time of shell formation. Deep-ocean temperature reflects polar surface temperature where deepwater forms; we assume that polar ocean temperature change approximates global temperature change, as polar amplification of temperature change approximately offsets the fact that ocean surface temperature change understates global (land plus ocean) temperature change. Global temperature thus implied by δ 18 O peaks at 27°C (+13°C relative to the Holocene) at the EECO (Fig. 23a), similar to independent estimates. Extraction of CO2 from the temperature record requires the additional assumptions that the non-CO2 GHG feedback is consistently 20% of the CO2 forcing (Sec. 2.6) and thatas suggested by climate models 71 the net effect of fast feedbacks varies little for CO2 amounts between the Holocene level and two or three times that amount. The resulting CO2 history falls in the lower part of the wide range estimated from CO2 proxy data. 95 Our inferred CO2 history supports the dominant role of plate tectonics (continental drift) in causing CO2 change and thus climate change in the Cenozoic era. The two-step 99 that the Indian plate executed as it moved through the Tethys (now Indian) ocean left an indelible signature in atmospheric CO2 and global temperature. CO2 emissions from ocean crust subduction were greatest when the Indian plate was moving fastest (inset, Fig. 6) and peaked at its hard collision with the Eurasian plate at 50 MyBP. Diminishing metamorphic CO2 emissions continue as the Indian plate is subducted beneath the Eurasian plate, pushing up the Himalayan Mountains, but emissions are exceeded by carbon drawdown from weathering and burial of organic carbon. Fig. 24. Forcing required to yield Cenozoic temperature for today's solar irradiance, compared with human-made GHG forcing in 2022.
Plate tectonics thus dominate the broad sweep of Cenozoic CO2, but the record is also punctuated by igneous province events. Most notable are the North Atlantic Igneous Province (caused by a rift in the sea floor as Greenland pulled away from Europe), which triggered the Paleocene-Eocene Thermal Maximum event about 56 MyBP, and the Columbia River Flood Basalt about 15 MyBP (Fig. 6). These natural causes of CO2 and climate change are now exceeded by humanmade change of atmospheric composition, which is occurring so rapidly that climate change cannot keep up with the climate forcing. The equilibrium response for the present climate forcing provides useful information about the drive for further climate change, as there are limitations on what Earth's energy imbalance can tell us (Sec. 6.5).
Thus, one merit of analyzing the Cenozoic is the perspective it provides on present greenhouse gas (GHG) levels. The dashed line in Fig. 24 marks the "we are here" level of GHG climate forcing, which is 70% of the forcing that maintained the EECO global temperature of +13°C relative to the Holocene. GHG forcing today is far above the level needed to deglaciate Antarctica, if the forcing is left in place long enough. CO2 when Antarctica deglaciated was only about 400 ppm (Fig. 23b), revealing that today's ice sheet models are unrealistically lethargic (Sec. 6.6). In addition, we find that CO2 during the Pliocene was only about 300 ppm, supporting other indications 93 that today's climate models driven by realistic CO2 amounts cannot produce Pliocene warmth. 188 As discussed in Section 4.3, if we specified Holocene CO2 as 278 ppm rather than 260 ppm, the inferred Pliocene CO2 would increase about 20 ppm and CO2 at Antarctic deglaciation would increase about 50 ppm. This change would not qualitatively alter the discussion in this paragraph. However, we present evidence in Section 4.3 that 260 ppm is the correct natural level of Holocene CO2, the larger CO2 amount in late Holocene being an anthropogenic effect.
GHGs are not the only large human-made climate forcing. Understanding of ongoing climate change requires that we also include the effect of aerosols (fine airborne particles).
Aerosols
Aerosol climate forcing is larger than the recent (AR6) IPCC estimate. Aerosols probably provided a significant climate forcing prior to the industrial revolution. We know of no other persuasive explanation for the absence of significant global warming during the past 6000 years (Fig. 14), a period in which the GHG forcing increased 0.5 W/m 2 (Fig. 15). Climate models that do not incorporate a growing negative aerosol forcing yield significant warming in that period, 189 a warming that, in fact, did not occur. Negative aerosol forcing, increasing as civilization developed and population grew, is expected. As humans burned fuels at a growing ratewood and other biomass for millennia and fossil fuels in the industrial eraaerosols as well as GHGs were an abundant, growing, biproduct. The aerosol source from wood-burning has continued in modern times. 190 GHGs are long-lived and accumulate, so their forcing will dominate eventually, unless aerosol emissions grow higher and higherthe Faustian bargain. 106 We conclude that peak aerosol climate forcingin the first decade of this centuryhad a (negative) magnitude of at least 1.5-2 W/m 2 . We estimate that the GHG plus aerosol climate forcing during the period 1970-2010 grew +0.3 W/m 2 per decade (+0.45 from GHG, -0.15 from aerosols), which produced observed warming of 0.18°C per decade. With current policies, we expect climate forcing for a few decades post-2010 to increase 0.5-0.6 W/m 2 per decade and produce global warming at a rate of at least +0.27°C per decade. In that case, global warming should reach 1.5°C by the end of the 2020s and 2°C by 2050 (Fig. 25).
Such an acceleration is highly dangerous in a climate system that is far out of equilibrium and dominated by multiple amplifying feedbacks. The single best sentinel for climate, our best measure of where global temperature is headed in the next decade, is Earth's energy imbalance.
Earth's energy imbalance
Earth's energy imbalance (EEI) is the net gain (or loss) of energy by the planet, the difference between absorbed solar energy and emitted thermal (heat) radiation. As long as EEI is positive, Earth will continue to get hotter. EEI is hard to measure, a small difference between two large quantities (Earth absorbs and emits about 240 W/m 2 averaged over the entire planetary surface), but change of EEI can be well-measured from space. 88 Absolute calibration is from the change of heat in the heat reservoirs, mainly the global ocean, over a period of at least a decade, as required to reduce error due to the finite number of places that the ocean is sampled. 87 EEI varies year-toyear (Fig. 26), largely because global cloud amount varies with weather and ocean dynamics, but averaged over several years EEI helps inform us about what is needed to stabilize climate.
The data suggest that EEI has doubled since the first decade of this century (Fig. 26). This increase is the basis for our prediction of post-2010 acceleration of the global warming rate. The increase may be partly due to restrictions on maritime aerosol precursor emissions imposed in 2015 and 2020 (Section 5.6), but the growth rate of GHG climate forcing also increased in 2015 and since has remained at the higher level (Section 6.6).
The reduction of climate forcing required to reduce EEI to zero is greater than EEI. The added burden is a result of ultrafast cloud feedback (Section 3.3). Cloud feedbacks are only beginning to be simulated well, but climate sensitivity near 1.2°C per W/m 2 implies that the net cloud feedback is large, with clouds accounting for as much as half of equilibrium climate sensitivity.
Continuation of precise monitoring of EEI is essential as a sentinel for future climate change and for the purpose of assessing efforts to stabilize climate and avoid undesirable consequences. Global satellite monitoring of geographical and temporal changes of the imbalance and ocean in situ monitoring (especially in polar regions of rapid change) are both needed for the sake of understanding ongoing climate change. Discussions 191 between the first author (JEH) and field glaciologists 192 20 years ago revealed a frustration of the glaciologists with the conservative tone of IPCC's assessment of ice sheets and sea level. One of the glaciologists saidregarding a photo 193 of a moulin (a vertical shaft that carries meltwater to the base of the ice sheet) on Greenland -"the whole ice sheet is going down that damned hole!" Their concern was based on observed ice sheet changes and paleoclimate evidence of sea level rise by several meters in a century, which imply that ice sheet collapse is an exponential process. Thus, as an alternative to the IPCC approach that relies on ice sheet models coupled to atmosphere-ocean GCMs (global climate models), we made a study that avoided use of an ice sheet model, as described in the paper Ice Melt. 14 In the GCM simulation, a growing amount of freshwater was added to the ocean surface mixed layer around Greenland and Antarctica, with the flux in the early 21 st century based on estimates from in situ glaciological studies 194 and satellite observations of sea level trends near Antarctica. 195 Doubling times of 10 and 20 years were used for the growth of freshwater flux. One merit of the GCM used in Ice Melt was its reduced, more realistic, small-scale ocean mixing, with a result that Antarctic Bottom Water in the model was formed close to the Antarctic coast 14 as it is in the real world. Continued growth of GHG emissions and meltwater led to shutdown of the North Atlantic and Southern Ocean overturning circulations, amplified warming at the foot of the ice shelves that buttress the ice sheets, and other feedbacks consistent with "nonlinearly growing sea level rise, reaching several meters over a time scale of 50-150 years." This paper exposed urgency to understand the dynamical change, the climate chaos that would occur with ice sheet collapse, a situation that may have occurred during the Eemian period when it was about as warm as today, as discussed in the Ice Melt paper. That period has potential to help us understand how close we are to a point of no return and sea level rise of several meters.
Global warming and sea level rise in the pipeline
Ice Melt was blackballed from IPCC's AR6 report in a form of censorship, 15 as alternative views normally are acknowledged in science. Science grants ultimate authority to nature, not to a body of scientists. In the opinion of JEH, IPCC is comfortable with gradualism and does not want its authority challenged. Caution has merits, but with a climate system characterized by a delayed response and amplifying feedbacks, excessive reticence is a danger, especially for young people. Concern about locking in nonlinearly growing sea level rise is amplified in our present paper by the revelation that the equilibrium response to current atmospheric composition is a nearly icefree Antarctica. Portions of the ice sheets well above sea level may be recalcitrant to rapid change, but enough ice is in contact with the ocean to provide of the order of 25 m (80 feet) of sea level rise. The implication is that if we allow a few meters of sea level rise, that may lock in a much larger sea level rise. Happily, we will suggest that it is still feasible to stabilize sea level.
Policy implications
This section is the first author's perspective based on more than 20 years of experience on policy issues beginning with workshops that he organized at the East-West Center in Hawaii, meetings and workshops with energy experts, and trips to more than a dozen nations for consultations with government officials, energy experts, and environmentalists.
The world's present energy and climate path has good reason. Fossil fuels powered the industrial revolution and raised living standards in much of the world. Fossil fuels still provide most of the world's energy (Fig. 27a) and produce most CO2 emissions (Fig. 27b). Fossil fuel reserves and recoverable resources could provide most of the world's energy for the rest of this century. 198 Much of the world is still in early or middle stages of economic development. Energy is needed and fossil fuels are a convenient, affordable source of energy. One gallon (3.6 liters) of gasoline (petrol) provides the work equivalent of more than 400 hours labor by a healthy adult. These benefitsnot evil business executivesare the basic reason for continued emissions.
The United Nations employs targets for a global warming limit and for emission reductions as a tool to cajole progress in limiting climate change. IPCC has defined scenarios that help us judge progress toward meeting such targets. Among the RCP scenarios ( Fig. 28) in the IPCC AR5 report, the RCP2.6 scenario defines the rapid downward trend of greenhouse gas climate forcings needed to prevent global warming from exceeding 2°C relative to preindustrial climate. The gap between that scenario and reality continues to grow. In principle, the 0.03 W/m 2 gap in 2022 could be closed by extraction of CO2 from the air. However, the required negative emissions (CO2 extracted from the air and placed in permanent storage) must be larger than the desired atmospheric CO2 reduction by a factor of about 1.7. 68 Thus, the required CO2 extraction is 2.1 ppm, which is 7.6 GtC. Based on a pilot carbon capture plant built in Canada, Keith 199 estimates an extraction cost of $450-920 per tC, as clarified elsewhere. 200 Keith's cost range yields an extraction cost of $3.4-7.0 trillion. This is for excess emissions in 2022 only; it is an annual cost. Given the difficulty the UN faced in raising $0.1 trillion for climate purposes and the growing annual emissions gap (Fig. 27), this example shows both the need to reduce emissions as rapidly as practical and the fact that carbon capture cannot be viewed as the solution, although it may play a role in a portfolio of policies, if its cost is driven down.
Climate policy under the Framework Convention demonstrably fails to curb and reverse growth of GHGs (Figs. [27][28][29]. [The Covid pandemic dented emissions, but 2022 global emissions are at a record high level.] This is the "tragedy of the commons": as long as fossil fuel pollution can be dumped in the air free of charge, agreements such as the 1997 Kyoto Protocol 201 and 2015 Paris Agreement have little effect on global emissions. Energy is needed to raise living standards and fossil fuels are still the most convenient, affordable source of that energy. Thus, growth of emissions is occurring in emerging economies (Figs. 29 and 30a), while mature economies are still the larger source of the cumulative emissions (Fig. 30b) that drive climate change. 202,203 Thus, exhortations at UN meetings, imploring reduced emissions, have little global effect.
Meanwhile, climate science has exposed a crisis that the world is loath to appreciate. Nor has IPCC, the scientific body advising the world on climate, bluntly informed the world that it has no plan to address the threat posed to the future of today's young people and their children. Leaders are allowed to profess that greater ambitions for future emission reductions are what is needed. Yet the only IPCC scenarios that would phase down human-made climate change amount to "a miracle will occur." Scientific equations do not include a "miracle" term. The IPCC scenario that moves rapidly to negative global emissions has biomass-burning powerplants that capture and sequester CO2, a nature-ravaging proposition without scientific and engineering credibility and without a realistic chance of being deployed at scale and on time to address the climate threat.
A new plan is essential. The plan must cool the planet to preserve our coastlines. Even today's temperature would cause eventual multimeter sea level rise, and a majority of the world's large and historic cities are on coastlines. Cooling will also address other major problems caused by global warming. We should aim to return to a climate close to that in which civilization developed, in which the nature that we know and love thrived. As far as is known, it is still feasible to do that without passing through an irreversible disaster such as many-meter sea level rise. Given the situation that we have allowed to develop, three actions are now essential.
First, a rising global price on GHG emissions must underly energy and climate policies, with enforcement by border duties on products from countries that do not have an internal carbon fee or tax. Public buy-in and maximum effectiveness require that the collected funds be distributed to the public, an approach that helps address global wealth disparities. Economists in the U.S. overwhelmingly support carbon fee-and-dividend 204 ; college and high school students, who have much at stake, join in advocacy. 205 The science rationale for a rising carbon price with a level playing field for energy efficiency, renewable energies, nuclear power, and all innovations has long been understood, but not achieved. Instead, fossil fuels and renewable energy are heavily subsidized, including use of "renewable portfolio standards" that allow utilities to pass added costs to consumers. Thus, nuclear energy has been disadvantaged and excluded as a "clean development mechanism" under the Kyoto Protocol, based in part on myths about damage caused by nuclear energy that are not supported by scientific facts. 207 A rising carbon price is not a panaceamany other actions are neededbut it is the sine qua non. Without it, fossil fuels will continue to be used extensively.
Second, effective global cooperation is needed to achieve reduction of GHG climate forcing. High income countries, mainly in the West, are responsible for most of the cumulative fossil fuel CO2 emissions ( Fig. 29b and Fig. 30), which are the main drive for global warming, 202,203 even though the West is a small fraction of global population. De facto cooperation between the West and China drove down the price of renewable energy, but more cooperation is needed to develop emission-free technologies for the rest of the world, which will be the source of most future GHG emissions (Fig. 29a). A crucial need is carbon-free electricity, the essential, growing, clean-energy carrier. In the West, except for limited locations with large hydropower, the main source of clean electricity has been nuclear power, and nation's with emerging economies are eager to have modern nuclear power because of its small environmental footprint. Thus, China-U.S. cooperation in development of modern nuclear power was proposed, but then stymied by U.S. prohibition of technology transfer. 208 Competition is normal, but it can be managed if there is a will, reaping benefits of cooperation over confrontation. 209 Of late, priority has been given instead to economic and military hegemony, despite recognition of the climate threat, and without consultation with young people or seeming consideration of their aspirations. We must not foreclose the possibility of return to a more ecumenical perspective of our shared future. Scientists can improve global prospects by maintaining and expanding international cooperation. Awareness of the gathering climate storm will grow this decade, so we must increase scientific understanding worldwide as needed for climate restoration.
Third, we must take actions to reduce and reverse Earth's energy imbalance to keep global climate within a habitable range. Highest priority must be on phasing down emissions, but, due to past failure to reduce GHG emissions, it is now implausible to achieve the needed timely change of Earth's energy balance solely via GHG emission reductions. Phasedown of emissions cannot restore Earth's energy balance within less than several decades, which is too slow to prevent grievous escalation of climate impacts and probably too slow to avoid locking in loss of the West Antarctic ice sheet and sea level rise of several meters. Given that several years are needed to forge a political approach for climate restoration, as discussed below, intense investigation of potential actions should proceed now. This will not deter action on mitigation of emissions; on the contrary, it will spur such action and allow search for "a miracle." A promising approach to overcome humanity's harmful geo-transformation of Earth is temporary solar radiation management (SRM). Risks of such intervention must be defined, as well as risks of no intervention; thus, the U.S. National Academy of Sciences recommends research on SRM. 210 An example of SRM is injection of atmospheric aerosols at high southern latitudes, which global simulations suggest would cool the Southern Ocean at depth and limit melting of Antarctic ice shelves. 15, 211 The most innocuous aerosols may be salt or fine salty droplets extracted from the ocean and sprayed into the air by autonomous sailboats. 212 This approach has been discussed for potential use on a global scale, 213 but even use limited to Southern Hemisphere high latitudes will require extensive research and forethought to avoid unintended adverse effects. 214 The present decade is probably our last chance to develop the knowledge, technical capability, and political will for the actions needed to save global coastal regions from long-term inundation.
These three basic actions are feasible, but they are not happening. Did we scientists inform the public and policymakers well? Opportunities for progress often occur in conjunction with crises. Before describing today's crisis and opportunity, we should review prior cases. In 1992, it was the climate crisis per se, with the Framework Convention on Climate Change. William Clinton was elected President of the United States with his party in control of both houses of Congress. Clinton's most climate-consequential action was in his first State-of-the-Union address as he declared "We are eliminating programs that are no longer needed, such as nuclear power research and development." For 30 years since, renewable energy received unlimited subsidy via renewable portfolio standards, and renewable energies are now ready for prime time. However, nuclear power, the potential carbon-free complement to renewables for baseload electricity, was denied such support, so today most electricity worldwide is from fossil fuels. At the next global crisis, the financial crisis of 2008, Barack Obama was elected President of the United States, with his party in control of both houses of Congress. Obama pledged to address "a planet in peril" in his campaign, but with Congress poisedindeed, forcedto pass economic legislation, Obama did not attempt to include the most fundamental needed action: a price on carbon.
Today, the world faces a crisisextreme political polarization, especially in the United Statesthat threatens effective governance. Yet it is a great time to be a young person, because the crisis offers the opportunity to help shape the futureof the nation and the planet. The problem and solution are not hard to understand. After World War II, in leading the formation of the United Nations, the World Bank, the Marshall Plan, and the Universal Declaration of Human Rights, the United States reached a peak close to being the aspired "shining city on a hill." The "American dream" of economic opportunity seemed real to most people; anyone willing to work hard could afford college. Immigration policy welcomed the brightest; NASA in the 1960s invited scientists from European countries, Japan, China, India, Canadathose wanting to stay found immigration to be straightforward. But the power of special interests in Washington grew, government became insular and inefficient, and Congress refuses to police itself; first priority is reelection and maintenance of elite status, supported by special interests. Thousands of pages of giveaways to special interests lard every funding bill, including the climate bill titled "Inflation Reduction Act" -Orwellian double-speakevery dollar borrowed from young people via deficit spending. The public is fed up with the Washington swamp but hamstrung by rigid two-party elections focused on a polarized cultural war, while the elite is satisfied with a system that allows them to accumulate wealth without paying taxes.
A third party that takes no money from special interests is needed to save democracy, which is essential if the West is to be capable of helping preserve the planet and a bright future for coming generations. Young people showed their ability to drive an electionvia their support of Obama and later Bernie Sanderswithout taking any funding from special interests. Groundwork is being laid now to allow third party candidates in 2026 and 2028 elections in the United States. Ranked voting is being advocated in every state -to avoid the "spoiler" effect of a third party. It is asking a lot to expect young people to grasp the situation that they have been handedbut a lot is at stake for them. As they realize that they are being handed a planet in decline, the first reaction may be to stamp their feet and demand that governments do better, but the effect of that is limited and inadequate. Nor is it sufficient to parrot the big environmental organizations, which have become part of the problem, as they are largely supported by the fossil fuel industry and wealthy donors who are comfortable with the status quo. Instead, young people have the opportunity to provide the drive for a revolution that restores the ideals of democracy while developing the technical knowledge that is needed to navigate the stormy sea that their world is setting out upon.
Required timings are consistent. Several years are needed to alter the political system such that the will of the majority has an opportunity to be realized. Several years of continued climate change will elevate the priority of climate change and confirm the inadequacy of the present policy approach. Several years will permit improved understanding of the climate science and thus help to assess risks and benefits of alternative actions.
SUPPORTING MATERIAL
Fig. S1. Greenhouse gas (GHG) climate forcings for the five terms in Equation (4). The forcings incorporate efficacies, including effects of a 3-dimensional atmosphere and seasonal change, which alter the adjusted forcings calculated with a 1-dimensional radiative-convective model.
SM1. GHG forcing formulae and comparison with IPCC forcings
Formulae 215 (Table 1) for adjusted forcing, Fa, were numerical fits to 1-D calculations with the GISS GCM radiation code using the correlated k-distribution method. 38 Gas absorption data were from high spectral resolution laboratory data. 39 These Fa were converted to Fe via GCM calculations that include 3-D effects, as summarized in Eq. (4), where the coefficients are from Table 1 of Efficacy. 32 The factor 1.45 for CH4 includes the effect of CH4 change on stratospheric H2O and tropospheric O3. We assume that CH4 is responsible for 45% of the O3 change. 40 The remaining 55% of the O3 forcing is obtained by multiplying the IPCC AR6 O3 forcing (0.47 W/m 2 in 2019) by 0.55 and by 0.82, where the latter factor is the efficacy that converts Fa to Fe. The non-CH4 portion of the O3 forcing is thus 0.21 W/m 2 in 2019. The time-dependence of this portion of the O3 forcing is from 42 49 Fig. S2. Test of accuracy of 2-term approximation for forcing by the three gases.
SM2. Approximation for N2O forcing
CO2 and CH4 are well-preserved in ice cores. However, the N2O record is corrupted in some time intervals by chemical reactions with dust particles in the ice core. For such intervals we approximate the N2O forcing by increasing the sum of CO2 and CH4 forcings by 12%, i.e., we approximate the forcing for all three gases as 1.12×[F(CO2) + F(CH4)]. The accuracy of this approximation is checked in Fig. S2 via computations for the past 132 ky, when data are available for all three gases from the multi-core composite of Schilt et al. 51 nor Fig. S3. Climate forcings provided in current IPCC report 13 for GHGs plus aerosols and for all human-made forcings, i.e., excluding only volcano and solar forcings.
SM3. Comparison of GHG + Aerosol forcing with All Human-Made forcing
IPCC all human-made forcings include land-use effects and contrails, which have large relative uncertainties. The forcings in Fig. S3 are those provided by IPCC (cf. Annex III of the current IPCC physical sciences report). 13
SM4. Land warming vs. global warming: effect of polar amplification
Land areas usually have a larger response to a forcing as shown by the response in Fig. S4 of the GISS (2020) GCM to 2×CO2 forcing. The warming over land at latitudes 45S to 35N (2.62°C) after 150 years (mean for years 101-200 is 18% larger than the global mean warming. However, the equilibrium warming (3.52°C) of this low-latitude land is only 2% larger than global warming (3.44°C), as a result of the polar amplification of global warming. This result indicates thatfor a case in which ice sheets are held fixedthe measurement of Seltzer et al. of LGM cooling of 5.8°C for land area 45°S-35°N is representative (within 2%) of the equilibrium temperature change for a planet in which the ice sheets are held fixed, as polar amplification of temperature change offsets the fact that land response to a forcing exceeds ocean response. Moreover, in the LGM in the real world, ice sheets were not fixed. Polar amplification of temperature change in the LGM, compared to the Holocene, was substantially increased by the growth of ice sheets, as shown in Fig. 9 of Hansen et al. (1984). Thus, the LGM global cooling would be substantially greater than the 5.8°C cooling of land area 45°S-35°N.
The two main flaws in this assumption are partly offsetting. First, equilibrium SST change at high latitudes where deepwater forms is larger than global SST change because of polar amplification (Fig. S4). Second, SST change is smaller than global TS change because land temperature change exceeds SST change, although this difference is not as great for the equilibrium change of interest as it is for today's transient change (Fig. S4).
SM5. CH4 and N2O forcings as percent of CO2 forcing in Antarctic ice cores.
Based on the CO2, CH4 and N2O amounts in the multi-ice core GHG tabulation constructed by Schilt et al.) 51 for the past 140,000 years, we calculated the ratio of CH4 and N2O forcings to the CO2 forcing. The data cover a range of global temperature between the LGM minimum and the Eemian maximum.
SM6. δ 18 O data of Zachos and Westerhold and inferred sea level and Tdo
Zachos and Westerhold δ 18 O for the full Cenozoic, the Pleistocene, and past 800 thousand years are shown in Fig. S6, as well as the inferred sea level and Tdo (sea level is compared to data of Rohling et al. 103 ).
SM7. Global warming in the pipeline: Green's function calculations
Global warming in the pipeline (∆Tpl) after a CO2 doubling is the portion of the equilibrium response (Teq) that remains to occur at time t, i.e., ∆Tpl = Teq -T(t). If EEI were equivalent to a climate forcing, warming in the pipeline would be the product of EEI and climate sensitivity (°C per W/m 2 ), i.e., warming in the pipeline would be EEI ×ECS/4, where we have approximated the 2×CO2 forcing as 4 W/m 2 . Fig. S7 shows the 2×CO2 results for the GISS (2014) and GISS (2020) GCMs. EEI is not a good measure of the warming in the pipeline, especially for the newer GISS model. The warming in the pipeline for the GISS (2014) model is typically ~30% larger than implied by EEI and ~90% larger in the GISS (2020) model. If these results are realistic, they suggest that reduction of the human-made climate forcing by an amount equal to EEI will leave a planet that is still pumping heat into the ocean at a substantial rate.
Real-world climate forcing is added year-by-year with much of the GHG growth in recent years, which Fig. 4 suggests will limit the discrepancy between actual warming in the pipeline and that inferred from EEI. Thus, we also make Green's function calculations of global temperature and EEI for 1750-2019 for GHG plus IPCC aerosol forcings. Green's function calculations are useful, with a caveat noted below, for quantities for which the response is proportional to the forcing. We calculate TG (t) using Eq. (4) and EEIG (t) using
EEIG (t) = ʃ [1 -REEI(t)] × [dF(t)/dt] dt,(S1)
where REEI (Fig. 5b) is the EEI response function (% of equilibrium response) and dF is forcing change per unit time. Integrations begin in 1750, when we assume Earth was in energy balance.
The results (Fig. S8) show that the excess warming in the pipeline (excess over expectations based on EEI) is reduced to 15-20% for the GISS (2014) model, but it is still 70-80% for the GISS (2020) model. This topic thus seems to warrant further examination, but it is beyond the scope of our present paper. The first matter to investigate is the cause of the ultrafast response of EEI (Fig. 5 of the main paper), which could be done via the model diagnostics discussed in that section of our paper. If the large difference between the EEI response functions of the two GISS models is related to supercooled cloud water, Fig. 1 of Kelley et al. (2020) 34 suggests that the real-world effect may fall between that of the two models. If the higher climate sensitivity of the GISS (2020) model is related to this cloud water phase problem, more realistic treatment of the latter may yield a climate sensitivity between that of the 2014 and 2020 models.
If real world climate sensitivity for 2×CO2 is near 4°C or higher, as we have concluded, the total cloud feedback is likely to be even higher than that of the GISS (2020) model. We suggest that it would be useful to calculate response functions for other models, especially models with high climate sensitivity, to help analyze feedbacks and to allow inexpensive climate simulations for arbitrary forcing scenarios. One major caveat: we have used a single response function calculated for 2×CO2. Especially in view of cloud feedbacks, it seems likely that the response function for aerosol forcing is different from that for CO2 forcing, because most tropospheric aerosols exist well below the clouds. Much might be learned from calculating response functions for GHGs, tropospheric aerosols, stratospheric aerosols, and solar irradiance, for example.
Fig. 3 .
3Dome C temperature(Jouzel et al.
Fig. 4 .
4(a) Global mean surface temperature response to instant CO2 doubling and (b) normalized response function (percent of final change). Thick lines in Figs. 4 and 5 are smoothed 81 results.
Fig. 5 .
5(a) Earth's energy imbalance (EEI) for 2×CO2, and (b) EEI normalized response function.
Fig. 8 .
8Product of 0.706 (SST undershoot of global TS change) and polar amplification of SST change [ΔSST (latitude)/ΔSST (ocean mean)] for the global ocean (left) and Atlantic Ocean, based on equilibrium response (years 4001-4500) in 2×CO2 simulations of GISS (2020) model.
Fig. 9 .
9Cenozoic CO2 estimated from δ 18 O of Westerhold et al. (see text). Black lines are for ECS = 1.2°C per W/m 2 ; red and green curves (ECS = 1.0 and 1.4°C per W/m 2 ) are 1 My smoothed.Blue curves (last 800,000 years) are Antarctica ice core data.44
Fig. 10 .
10Continental configuration 56 MyBP.113 Continental shelves (light blue) were underwater as little water was locked in ice. The Indian plate was moving north at about 15 cm per year.
Fig. 12 .
12Temperature and CO2 implied by δ 18 O, if the data were indicative of the global mean. Realistic PETM global surface warming of 5.6°C yields peak PETM CO2 = 1270 ppm (see text). of organic matter continue, so decrease of atmospheric CO2 could have continued over millions of years, if the source of CO2 from metamorphism and vulcanism continued to decline.Thus, in the absence of human activity, Earth may have been headed for snowball Earth conditions within the next 10 or 20 million years. However, chance of future snowball Earth is now academic. Human-made GHG emissions remove that possibility on any time scale of practical interest. Instead, GHG emissions are now driving Earth toward much warmer climate.
Fig. 14 .
14Global mean surface temperature change over the past 24 ky, reproduced fromFig. 2of Osman et al.54 including Last Millennium reanalysis of Tardif et al.143
Fig. 15 .
15GHG climate forcing in past 20 ky with vertical scale expanded for the past 10 ky on the right. GHG amounts are from Schilt et al.51 and formulae for forcing are in Supporting Material.
Fig. 16 .
16Sea level since the last glacial period relative to present. Credit: Robert Rohde145
Fig. 17 .
17(a) Estimated greenhouse gas and aerosol forcings relative to 1750 values. (b) Aerosol forcing as percent of GHG forcing. Forcings for dark blue area are relative to 1750. Light blue area adds 0.5 W/m 2 forcing estimated for human-caused aerosols from fires, biofuels and land use.
Fig. 18 .
18Aerosol forcing relative to 1850 from IPCC AR6, an alternative aerosol scenario 158 and two aerosol model scenarios of Bauer et al. (2020). 162 models
Fig. 20 .
20Total sulfate (parts per trillion by volume) and percentage of total sulfate provided by shipping in simulations of Jin et al.166 prior to IMO regulations on sulfur content of fuels.
Fig. 21 .
21Global absorbed solar radiation relative to mean of the first 120 months of CERES data. CERES data available at http://ceres.larc.nasa.gov/order_data.php
over the 22-years March 2000 to March 2022 reveal a decrease of albedo and thus an increase of absorbed solar energy coinciding with the 2015 change of IMO emission regulations. Global absorbed solar energy is +1.05 W/m 2 in the period January 2015 through December 2022 relative to the mean for the first 10 years of data(Fig. 21). This increase is 5 times greater than the standard deviation (0.21 W/m 2 ) of annual absorbed solar energy in the first 10 years of data and 4.5 times greater than the standard deviation (0.23 W/m 2 ) of CERES data through December 2014. The increase of absorbed solar energy is notably larger than estimated potential CERES instrument drift, which is <0.085 W/m 2 per decade.88 Increased solar energy absorption occurred despite 2015-2020 being the declining phase of the ~11-year solar irradiance cycle.177 Nor can increased absorption be attributed to correlation of Earth's albedo (and absorbed solar energy) with the Pacific Decadal Oscillation (PDO): the PDO did shift to the positive phase in 2014-2017, but it returned to the negative phase in 2017-2022.178 Given the large magnitude of the solar energy increase, cloud changes are likely the main cause. Quantitative analysis 178 of contributions to the 20-year trend of absorbed solar energy show that clouds provide most of the change. Surface albedo decrease due to sea ice decline contributes to the 20-year trend in the Northern Hemisphere, but that sea ice decline occurred especially in 2007, with minimum sea ice cover reached in 2012; over the past decade as global and hemispheric albedos declined, sea ice had little trend.179 Potential causes of the cloud changes include: 1) reduced aerosol forcing, 2) cloud feedbacks to global warming, 3) natural variability.180 Absorbed solar energy was 0.78 W/m 2 greater in 2015-2022 than in the first Fig. 22. Absorbed solar radiation for indicated regions relative to first 120 months of CERES data. Southern Hemisphere 20-60°S is 89% ocean. North Atlantic is (20-60°N, 0-60°W) and North Pacific is (20-60°N, 120-220°W). Data source: http://ceres.larc.nasa.gov/order_data.php decade of CERES data at latitudes 20-60°S
Fig. 23 .
23(a) Cenozoic surface temperature estimated from deep ocean oxygen isotope data of Westerhold et al.98 and (b) implied CO2 history for ECS = 1.2°C per W/m 2 (black curve); red and green curves for ECS = 1.0 and 1.4°C per W/m 2 are 1 My smoothed.
Fig. 25 .
25Global temperature relative to 1880-1920. Edges of the predicted post-2010 accelerated warming rate (see text) are 0.36 and 0.27°C per decade.
Fig. 26 .
2612-month running-mean of Earth's energy imbalance, based on CERES satellite data for EEI change normalized to 0.71 W/m 2 mean for July 2005 -June 2015 based on in situ data.
Fig. 27 .
27Global energy consumption and CO2 emissions(Hefner at al. 196 and BP 197 ).
Fig. 28 .
28Annual growth of climate forcing by GHGs 41 including part of O3 forcing not included in CH4 forcing (Supp. Material). MPTG and OTG are Montreal Protocol and Other Trace Gases.
Fig. 29 .
29Fossil fuel CO2 emissions from mature and emerging economies. China is counted as an emerging economy. Data sources: Heffner et al. 196 for 1751-2017 and BP 197 for 2018-2020.
Fig. 30 .
30Fossil fuel CO2 emissions by nation or region as a fraction of global emissions. Data sources: Heffner et al. 196 for 1751-2017 and BP 197 for 2018-2020.
Fig. 31 .
31Cumulative per capita national fossil fuel emissions.206
Fig. S4 .
S4Surface temperature response to 2×CO2 of GISS (2020) GCM (Sections 3).
51 Fig. S5 .
51S5CH4 and N2O radiative forcings as a percent of the CO2 forcing in past 140 ky.
Fig. S6 .
S6Zachos and Westerhold δ 18 O and inferred sea level and Tdo for the full Cenozoic, the Pleistocene, and the past 800 thousand years. Sea level data are from Rohling et al.103
Fig. S7 .
S7Ratio of warming in the pipeline to EEI, (Teq -T)/EEI, for the first 300 years after instant doubling of CO2 for (a) GISS(2014) model and (b) GISS 2020 model.
Fig. S8 .
S8Ratio of warming in the pipeline to EEI, (Teq -TG)/EEIG, in response to GHG and IPCC aerosol forcing for the period 1750-2019 using the response functions for the GISS (2014) model (left) and (b) GISS (2020) model (right).
Table 1 of
1Efficacy) based on GCM simulations that include the 3-D distribution of each gas. The total GHG forcing isFig. 1. IPCC AR6 Annex III greenhouse gas forcing, 13 which employs Fa for O3 and Fo for other GHGs, compared with the effective forcing, Fe, from Eq. (4). See discussion in text.The CH4 coefficient (1.45) includes the effect of CH4 on O3 and stratospheric H2O, as well as the efficacy (1.10) of CH4 per se. We assume that CH4 is responsible for 45% of the O3 change.40 Forcing caused by the remaining 55% of the O3 change is based on IPCC AR6 O3 forcing (Fa = 0.47 W/m 2 in 2019); we multiply this AR6 O3 forcing by 0.55 × 0.82 = 0.45, where 0.82 is the efficacy of O3 forcing fromTable 1of Efficacy. Thus, the non-CH4 portion of the O3 forcing is 0.21 W/m 2 in 2019. MPTGs and OTGs are Montreal Protocol Trace Gases and Other Trace Gases.41 A list of these gases and a table of annual forcings since 1992 are available as well as the earlier data.Fe = Fa(CO2) + 1.45 Fa(CH4) + 1.04 Fa(N2O) + 1.32 Fa(MPTGs + OTGs) + 0.45 Fa(O3).
(4)
). In 2019, the final year of AR6 data, our GHG forcing is 4.00 W/m 2 ; the AR6 forcing is 3.84 W/m 2 . Our forcing should be larger, because IPCC forcings are Fo for all gases except O3, for which they provide Fa (AR6 section 7.3.2.5).Table 1in Efficacy allows accurate comparison: δTo for 2×CO2 for the GISS model used in Efficacy is 0.22°C, λ is 0.Tyndall and other greenhouse giants 1 is no longer imaginary. Humanity is now taking its first steps into the period of consequences. Earth's paleoclimate history helps us assess the potential outcomes.Fig. 2. Antarctic Dome C temperature for past 800 ky from Jouzel et al.67°C per W/m 2 , so δTo/λ = 0.33
W/m 2 . Thus, the conversion factor from Fo to Fe (or Fs) is 4.11/(4.11-0.33). The non-O3 portion
of AR6 2019 forcing (3.84 -0.47 = 3.37) W/m 2 increases to 3.664 W/m 2 . The O3 portion of the
AR6 2019 forcing (0.47 W/m 2 ) decreases to 0.385 W/m 2 because the efficacy of Fa(O3) is 0.82.
The AR6 GHG forcing in 2019 is thus ~ 4.05 W/m 2 , expressed as Fe ~ Fs, which is ~1% larger
than follows from our formulae. This precise agreement is not indicative of the true uncertainty
in the GHG forcing, which IPCC AR6 estimates as 10%, thus about 0.4 W/m 2 . We concur with
their error estimate and employ it in our ECS uncertainty analysis (Section 6.1).
We conclude that the GHG increase since 1750 already produces a climate forcing equivalent to
that of 2×CO2 (our formulae yield Fe ~ Fs = 4.08 W/m 2 for 2021 and 4.13 W/m 2 for 2022; IPCC
AR6 has Fs = 4.14 W/m 2 for 2021). The human-made 2×CO2 climate forcing imagined by
Charney,
model with ECS of 2°C, if the mixed layer provides the only heat capacity. However, while the mixed layer is warming, there is exchange of water with the deeper ocean, which slows the mixed layer warming. The longer response time with high ECS allows more of the ocean to come into play. If mixing into the deeper ocean is approximated as diffusive, surface temperature response time is proportional to the square of climate sensitivity.78 for the 1982 Ewing
Symposium. The e-folding time -the time for surface temperature to reach 63% of its
equilibrium response -was about a century. The only published atmosphere-ocean GCM -that
of Bryan and Manabe 77 -had a response time of 25 years, while several simplified climate
models referenced in our Ewing paper had even faster responses. The longer response time of
our climate model was largely a result of high climate sensitivity -our model had an ECS of 4°C
for 2×CO2 while the Bryan and Manabe model had an ECS of 2°C.
The physics is straightforward. If the delay were a result of a fixed source of thermal inertia, say
the ocean's well-mixed upper layer, response time would increase linearly with ECS because
most climate feedbacks come into play in response to temperature change driven by the forcing,
not in direct response to the forcing. Thus, a model with ECS of 4°C takes twice as long to reach
full response as a
that have been used for many studies in the past quarter century. When Earth has negligible ice sheets, δ18 O ( 18 O amount relative to a standard), provides an estimate of deep ocean temperature (right scale in Fig. 6) 47 Fig. 6. Global deep ocean δ 18 O. Black line: Westerhold et al. (2020) 98 data in 5 kyr bins until 34 MyBP and subsequently 2 kyr bins. Green line: Zachos et al. (2001) 47 data at 1 Myr resolution. Lower left: velocity 99 of Indian tectonic plate. PETM = Paleocene Eocene Thermal Maximum; EECO = Early Eocene Climatic Optimum; Oi-1 marks the transition to glaciated Antarctica; MCO = Miocene Climatic Optimum; NAIP = North Atlantic Igneous Province. This equation is used for the early Cenozoic, up to the large-scale glaciation of Antarctica at ~34 MyBP (Oi-1in Fig. 6). At larger δ 18 O (colder climate), lighter 16 O evaporates preferentially from the ocean and accumulates in ice sheets. In Zachos data, δ 18 O increases by 3 between Oi-1 and the LGM. Half of this δ 18 O change is due to the 6°C change of deep ocean temperature between Oi-1 (5°C) and the LGM (-1°C). 100 The other 1.5 of δ 18 O change is presumed to be due to the ~180 m sea level (SL) change between ice-free Earth and the LGM, with ~60 m from Antarctic ice and 120 m from Northern Hemisphere ice. Thus, as an approximation to extract both SL and Tdo from δ 18 O, Hansen et al. 71 assumed that SL rose linearly by 60 m as δ 18 O increased from 1.75 to 3.25 and linearly by 120 m as δ 18 O increased from 3.25 to 4.75.As with most proxy climate measures, δ 18 O is fraught with complexities that affect interpretation of recorded change.97,101 Complications in the Cenozoic record are revealed by differences between the Zachos (Z) and Westerhold (W) δ 18 O time series(Fig. 6), as we discuss below. Despite complications, the δ 18 O records carry an enormous amount of information about climate change, and a simple linear analysis provides a useful beginning. We modify prior equations71 because of differences between the Z and W data. For example, the mid-Holocene (6-8 kyBP) values of δ 18 O in the Z and W data sets are δ 18 OH Z = 3.32 and δ 18 OH W = 3.88. Thus, the sea level (SL) equations, relative to SL = 0 in the mid-Holocene, are:Tdo(°C) = -4 δ 18 O + 12.
(5)
SL Z (m) = 60 -38.2 (δ 18 O -1.75)
(δ 18 O < 3.32, maximum SL = +60 m),
(6)
SL W (m) = 60 -25.2 (δ 18 O -1.5)
(δ 18 O < 3.88, maximum SL = +60 m),
(7)
SL Z (m) = -120 (δ 18 O -3.32)/1.58 (δ 18 O > 3.32),
(8)
SL W (m) = -120 (δ 18 O -3.88)/1.42 (δ 18 O > 3.88).
data as putting greater weight on North Atlantic Deep Water (NADW); most Westerhold ocean sediment cores are from the Atlantic, with an anchor core from Walrus Ridge in the South Atlantic (Westerhold's Fig. S1 98 ). Zachos data are more globally distributed and reflect more Antarctic Bottom Water (AABW) conditions.Imprecision of NADW or AABW as a measure of TS change is due to the unknown spatial pattern of TS change. If temperature changed uniformly over the globe, we could obtain global TS change from temperature change at a single point, but uniform temperature change is far from reality. Our assumption that polar ocean SST change approximates global temperature change is based on expectation that global SST undershoot of global temperature change is largely offset by polar amplification of SST change, an expectation that can be tested with GCM simulations. Equilibrium global SST response of the GISS (2020) GCM to 2×CO2 forcing is 70.6% of the global (land plus ocean) response. The product of 0.706 and polar amplification of SST change 20 Fig. 7. Cenozoic temperature based on Zachos and Westerhold δ 18 O data (see text)
O > δ18 OH, we take AS as its average value over the period from the Holocene to the LGM: Thus, for climate colder than the Holocene,AS = (FIce + FGHG )/FGHG = (3.5 W/m 2 + 2.25 W/m 2 )/(2.25 W/m 2 ) = 2.55. (δ 18 O > δ 18 OH) (19)
Westerhold deep ocean sites exceeds global surface warming during the singular PETM event. Nunes and Norris 132 describe evidence that deep ocean circulation changed at the start of the PETM with a shift in location of deep-water formation that delivered relatively warmer waters to the deep sea, a circulation change that persisted for at least 40,000 years. The North Atlantic flood basalt itself may have contributed to warmth of the deep ocean.accounting for spatial patterns of
climate change yields PETM global surface warming 5.6°C (5.4-5.9°C, 95% confidence). We
conclude that warming at Thus, even though δ 18 O yields a good estimate of surface temperature for the broad sweep of the
Cenozoic, it does not give a valid estimate of TS and CO2 during the PETM. Instead, we use the
5.6°C global surface warming estimate of Tierney et al. 131 with the pre-PETM TS and CO2 from
our analysis (Fig. 12) to obtain peak PETM CO2. With the most likely ECS (1.2°C per W/m 2 ),
pre-PETM (56-56.4 MyBP) CO2 is 725 ppm; peak PETM CO2 is 1270 ppm if CO2 provides 80%
of the GHG forcing, thus less than a doubling of CO2. (In the unlikely case that CO2 caused
100% of the GHG forcing, required CO2 is 1450 ppm, exactly a doubling.) CO2 amounts for
ECS = 1.0 and 1.4°C per W/m 2 are 890 and 620 ppm in the pre-PETM and 1710 and 1020 ppm
at peak PETM, respectively. Again, in these extreme ECS cases, the CO2 forcing of the PETM is
moderately less than a CO2 doubling. Our 20% contribution by non-CO2 GHGs (amplification
factor 1.25, Section 2), is nominal; indeed, Hopcroft et al., e.g., estimate a 30% contribution
from non-CO2 GHGs, 133 thus an amplification factor 1.43. Hopcroft et al. particularly wanted to
account for Pliocene Arctic warmth, but the inability of climate models to produce Pliocene
warmth may be related more to the failure of most climate models to capture cloud and ice sheet
feedbacks.
Table AIII.3 in IPCC AR6. MPTGs and OTGs are Montreal Protocol Trace Gases and Other Trace Gases.41 An updated list of these gases and a table of their annual forcings since 1992 are available as are earlier data.
The response functions for global temperature and EEI, for both the 2014 and 2020 models, smoothed and unsmoothed, are available at http://www.columbia.edu/~mhs119/ResponseFunctionTables/ DATA AVAILABILITY "The data used to create the figures in this paper are available in the Zenodo repository, at https://dx.doi.org/[doi]."
ACKNOWLEDGMENTSWe thank Eelco Rohling for inviting JEH to describe our perspective on global climate response to human-made forcing. JEH began to write a review of past work, but a paper on the LGM by 55 Jessica Tierney et al.53and data on changing ship emissions provided by Leon Simons led to the need for new analyses and division of the paper into two parts. We thank Jessica also for helpful advice on other related research papers and Ed Dlugokencky of the NOAA Earth System Research Laboratory for continually updated GHG data. JEH designed the study and carried out the research with help of Makiko Sato and Isabelle Sangha; Larissa Nazarenko provided data from GISS models and helped with analysis; Leon Simons provided ship emission information and aided interpretations; Norman Loeb and Karina von Schuckmann provided EEI data and insight about implications; Matthew Osman provided paleoclimate data and an insightful review of the entire paper; Qinjian Jin provided simulations of atmospheric sulfate and interpretations; Eunbi Jiang reviewed multiple drafts and advised on presentation; all authors contributed to our research summarized in the paper and reviewed and commented on the manuscript.All authors declare that they have no conflicts of interest. Climate Science, Awareness and Solutions, which is directed by JEH and supports MS and PK is a 501(C3) non-profit supported
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Global temperature stabilization via controlled albedo enhancement of lowlevel maritime clouds. J Latham, P Rasch, C C Chen, https:/royalsocietypublishing.org/doi/full/10.1098/rsta.2008.0137Phil Trans R Soc A. 366Latham J, Rasch P, Chen CC et al. Global temperature stabilization via controlled albedo enhancement of low- level maritime clouds. Phil Trans R Soc A 2008;366:3969-87
Reflecting sunlight to reduce climate risk: priorities for research and international cooperation. S M Patrick, Council on Foreign Relations. Special Report. 93date last accessedPatrick SM, Council on Foreign Relations. Special Report No. 93, April 2022 Reflecting sunlight to reduce climate risk: priorities for research and international cooperation (4 December 2022, date last accessed)
Global warming in the twenty-first century: an alternative scenario. J Hansen, M Sato, R Ruedy, https:/www.pnas.org/doi/10.1073/pnas.170278997Proc Natl Acad Sci. 97Hansen J, Sato M, Ruedy R et al. Global warming in the twenty-first century: an alternative scenario. Proc Natl Acad Sci 2000;97:9875-80
| sample_1571 | 1 | arxiv | |
The overestimated potential of solar energy to mitigate climate change
16 Oct 2017
Marcos Paulo Belançon
Programa de Pós-graduação em Processos Químicos e Bioquímicos Universidade Tecnológica Federal do Paraná CEP
85503-390Pato Branco, ParanáBrasil
The overestimated potential of solar energy to mitigate climate change
16 Oct 201710.1038/nenergy.2017.140(Dated: 18 de Outubro de 2017)
Many aspects of solar energy and policies to tackle the energy transition have been neglected. Even though the earth is plenty of sun energy, our planet is not plenty of resources to transform that energy into electricity. This is a case between many others where an strongly optimistic bias is shadowing the white elephant in the room.
In the defense of Photovoltaics (PV) Creutzig et al published their view on "The underestimated potential of solar energy to mitigate climate change" [1]. They wrote, for example: "Direct solar energy has a technical potential of 1,500-50,000 EJ per year, exceeding the projected global primary energy demand of about 1,000 EJ per year in 2050".
We should pay attention to what exactlly means "technical"in such sentence. If technically available means achievable with today's technology, the statement is false. On the other hand, if it is interpreted with the belief that science will figure out a solution the statement may be true. In a previous work [2] we have presented a point of view where this optimism is a threat, which may be delaying the real discussion that we should made.
The sun provides virtually "limitless energy", and the most efficient devices we have to use this energy are solar water heaters; those devices may reach efficiencies as high as 70% at full sun. Thermal energy, however, is a "low quality" energy that can not be used to cover all of our needs. By this way, we aim to convert more sunlight into electricity.
The PV market is by far dominated by Silicon, a technology discovered half a century ago. It is true that Silicon PV is quite cheap today, however "symbolic human prices" measured in dollars may not reflect the "real natural prices". We are consuming 25 kg of Silver per MWp of Silicon PV built [3]. This means that with the today's production rate running around 100GW p we are consuming 2500 metric tons of Silver per year; that is 10% of global extraction of Silver.
This PV production can guarantee only 2500GW p of PV installed, because in 25 years from now we will be replacing the PV's that are new today. If we consider a capacity factor of about 20%, something like 500GW , or about 5% of mankind's primary energy is all the solar electricity we are going to have in 2040 if we do not expand the production. Even though many optimists will say that this is exactly what is going to happen, one may point that it is not so clear that the industry will reduce even more the Silver consumption; the learning curve of Silicon PV industry is already mature, and there is not much space for improve production efficiencies and reduce prices. Other technologies such as thin film PV's rely on Cadmium, Tellurium, Indium and Selenium, all of those will limit * marcosbelancon@utfpr.edu.br the production rate of thin films far below the Silicon PV's level.
One may see in the news that many companies in Japan, Europe and North America are declaring insolvency and/or loosing stock value due cheaper China PV's. There are even some doubt about if the Chinese companies are really making money; the hyphothesis that the demand is lower than the supply of PV's can be perfectly sustained for now.
I do like solar energy, but we don't have scientifical evidence to sustain that our civilization lifestyle will be saved by Photovoltaics. Many are concerned about efficiencies of solar cells, but we do not have a problem with that. An average brazilian house may produce its own electricity with about 15m 2 of commercial Silicon PV; on the other hand, if we want the same amount of energy from biomass, for example, a hundred times more area should be necessary. Our technologies are already far more efficient than photosynthesis.
One may ask, then, why Brazil has so much biomass and little PV's? The Brazilian geography makes possible that huge areas of land can be used for Sugar Cane production; Brazil's land used to produce sugar cane reached 90.000km 2 this year, which is about the size of Portugal. Brazil's primary energy is 41% renewable [4], and it is oftenly interpreted that Brazil achieve this because of its great hydroeletric power. However, Sugar Cane produces 16.7% of the primary energy while hydro produces 11%. All biomass combined produces twice more energy than hydro, and with Sugar Cane an efficient liquid fuel is obtained. Ethanol and electricity from Sugar Cane in Brazil accounts for 580 T W h [4] of primary energy; electricity from PVs in Germany in 2016 accounted for only 38 T W h [5]. The secrets of Brazil energy mix are 1) location, not far from equator, 2) half of the world population density, 3) almost no coal resources available and 4) consumption per capita equals to the world average.
Many will also point out that governments should tax fossil fuels, meanwhile the United States have choosen the opposite direction during the Obama administration. They reduced the direct emission of Green House Gases (GHG) by replacing Coal by Shale Gas to generate electricity [6]. Shale oil and Canadian oil sands provided a way to avoid middle east fossil fuels; by this way an "energy war" between OPEC and North America pushed oil prices down. Those policies have made gas electricity so cheap in US that some nuclear plants were shutdown this year, what in turn will reduce the effectiveness of Shale gas in reduce GHG emissions further. And Shale has already give signals that if we stop drilling new wells the output may go down pretty fast [7]. The optimism bias of those standing for PV's are analogous to that of Obama's view. Both are looking to a small scale of the challenge and forgetting many aspects when claiming how effective Shale or PV's may be to solve our energy dilemma.
There are no alternative to fossil fuels able to reach the world scale because we can not produce sugar cane everywhere, neither produce as much PV's as we would like to. Many other questions such as storage are important but it does not come first than our capability to produce the PV's. By one way or another, the age of rapid growth in energy supply seems to be going to an end, because the energy return on energy invested is decreasing [8]. We are moving towards low quality and environmentally costly fossil fuels at the same pace we try to build a renewable energy infrastructure that relies on complex technologies that demand increasing extraction rate of finite scarse minerals.
If we let apart the faith that science will continuosly improve technologies and innovate making our civilization run as a "perpetual motion machine", one may state that the second law of thermodynamics guarantees that natural resources, such as oil or silver, will become less abundant and more costly to extract. By this way, in the short term some companies and countries will go bankrupty due the low prices, as we have seen, and next the cost of fossil fuels, PV's and every energy based on scarse resources will become more expensive.
The belief in endless growth of consumption that have been central in our civilization makes our behavior be very similar to that of a microbial culture. It is true that overpopulation puts pressure in our ecosystem, however, it is also true that during the last century our consumption per person has grown faster than the population. The energy transition is a great goal for our civilization, but it may be useless if we do not rethink our civilization itself.
. F Creutzig, P Agoston, J C Goldschmidt, G Luderer, G Nemet, R C Pietzcker, 10.1038/nenergy.2017.140F. Creutzig, P. Agoston, J. C. Goldschmidt, G. Luderer, G. Nemet, and R. C. Pietzcker, (2017), 10.1038/nenergy.2017.140.
. M P Belançon, arXiv:1710.01064M. P. Belançon, (2017), arXiv:1710.01064.
. R O Connell, C Alexander, R Atrachan, B Alway, S Nambiath, J Wiebe, L Wong, E Rannestad, S Li, D Aranda, N Scott-Gray, The World Silver Survey. R. O. Connell, C. Alexander, R. Atrachan, B. Alway, S. Nambiath, J. Wiebe, L. Wong, E. Rannes- tad, S. Li, D. Aranda, and N. Scott-Gray, "The World Silver Survey 2017," (2017).
Balanço Energético Nacional. Epe, EPE, "Balanço Energético Nacional," (2017).
. Ise Fraunhofer, Energy-Charts. Fraunhofer ISE, "Energy-Charts," (2017).
. B Obama, 10.1126/science.aam6284Science. 355126B. Obama, Science 355, 126 (2017).
More Rigs Don't Mean More. C Buurma, N S Malik, U.S. GasC. Buurma and N. S. Malik, "More Rigs Don't Mean More U.S. Gas," (2017).
. T G Taylor, J A Tainter, 10.1111/ajes.12162American Journal of Economics and Sociology. 751005T. G. Taylor and J. A. Tainter, American Journal of Economics and Sociology 75, 1005 (2016).
| sample_1586 | 0.9726 | arxiv | |
Impact of Climate Simulation Resolutions on Future Energy System Reliability Assessment: A Texas Case Study
Xiangtian Zheng
Department of Electrical and Computer Engineering
Texas A&M University
77843College StationTXUSA
Le Xie
Department of Electrical and Computer Engineering
Texas A&M University
77843College StationTXUSA
Texas A&M Energy Institute
77843College StationTXUSA
Kiyeob Lee
Department of Electrical and Computer Engineering
Texas A&M University
77843College StationTXUSA
Dan Fu
Department of Oceangraphy
Texas A&M University
77843College StationTXUSA
Jiahan Wu
Department of Electrical and Computer Engineering
Texas A&M University
77843College StationTXUSA
Ping Chang
Department of Oceangraphy
Texas A&M University
77843College StationTXUSA
Impact of Climate Simulation Resolutions on Future Energy System Reliability Assessment: A Texas Case Study
IENERGY
20231 † Corresponding authorIndex Terms-High-resolution climate modelpower system reliabilityresource adequacy
The reliability of energy systems is strongly influenced by the prevailing climate conditions. With the increasing prevalence of renewable energy sources, the interdependence between energy and climate systems has become even stronger. This study examines the impact of different spatial resolutions in climate modeling on energy grid reliability assessment, with the Texas interconnection between 2033 and 2043 serving as a pilot case study. Our preliminary findings indicate that while low-resolution climate simulations can provide a rough estimate of system reliability, high-resolution simulations can provide more informative assessment of lowadequacy extreme events. Furthermore, both high and low-resolution assessments suggest the need to prepare for severe blackout events in winter due to extremely low temperatures.Index Terms-High-resolution climate model, power system reliability, resource adequacy 1 The data, model and codes for all analyses in this paper are publicly available at the GitHub repository https://github.com/tamu-engineering-research/ ClimateResolutionPowerReliability. arXiv:2305.04929v1 [physics.ao-ph] 5 May 2023
I. INTRODUCTION
Climate change has emerged as one of the most pressing global challenges, and the energy sector is a key player in enabling decarbonization. However, climate change also poses significant challenges to the energy sector, such as ensuring the availability of energy resources [1], accommodating the expansion of electricity demand [2], and enhacing the resilience of power networks [3]. To address these challenges and ensure a sustainable and resilient energy future, it is crucial to develop a reliable and rigorous approach to model and assess the impacts of climate change on power systems.
Recent studies in the field of climate-energy research have analyzed the impact of climate change on energy grids in multiple aspects. Researchers have quantified the increase in future electricity demand [4] and the expansion of wind generation [5]. Meanwhile [6] shows clear trends of capacity and load throughout the globe but uncertainty on the regional scale. Studies have also investigated the influences on grid reliability and resilience at different scales. [7] shows the drop of power grid reliability due to both low impact variations and extreme events, [8] shows that the reliability of electricity supply with varying renewable mix and energy storage has regional geophysical constraints. while [9] shows that the British grid with high renewable penetration grids may suffer operational inadequacy due to single-year planning. Furthermore, [10] shows a relatively high vulnerability of urban areas due to the compound effects of urban density and climate change.
These studies rely heavily on reliable climate projections. However, constructing reliable statistical prediction models based solely on historical weather data is challenging due to the limited availability of reliable observational records, particularly weather extremes, such as hurricanes. Therefore, climate simulations play a critical role in accurately projecting future climate conditions and assessing their impacts. Recent advances in climate modeling have led to significant improvements, such as increased spatial resolution [11], improved representation of physical processes [12], and machine learning and AI based technologies [13], [14]. In particular, the recent unprecedented set of high-resolution climate simulations [11] is capable of explicitly representing some of small-scale regional processes and yields more realistic weather extreme statistics that are not adequately simulated by the standard low-resolution climate models used by the latest assessment report of the Intergovernmental Panel on Climate Change (IPCC) [15]. As such, these high-resolution climate simulations are particularly valuable for assessing the impacts of climate change on regional energy system reliability that requires high-resolution climate information.
While high-resolution climate simulations show promise for improving power system adequacy assessment, there are several key research gaps that must be addressed to fully unlock its potential for the energy sector. One major challenge is the need for more comprehensive and consistent methodologies to integrate climate simulation data into power system planning, from long-term capacity and transmission expansion to shortterm demand forecasting and dispatch strategies. In addition, more accurate and detailed climate information is required to improve the accuracy of modeling and simulation efforts, particularly at the local and regional level, where extreme events can play a vital role.
In this paper, leveraging an ongoing collaborative effort in climate and energy system modeling, we conduct a pilot study on the impact of different resolutions of climate simulations on energy grid reliability assessment. 1 We find that while low-resolution climate simulation can aid in a crude system reliability assessment, high-resolution climate simulation can reveal a higher frequency of extreme events. Additionally, both high and low-resolution assessments suggest the need to prepare for severe blackout events in winter due to extremely low temperatures.
It should be noted that for this preliminary study, we have made the assumption that the future Texas grid's capacity and load are independent of the projected climate change. Furthermore, our power grid simulations are solely driven by projected future climate data as input rather than interactive simulations that consider the potential impacts of the energy sector on climate change. Besides, we only use one single simulation of high (0.25 degree or 25 km) and low-resolution (1 degree or 100 km) model under Representative Concentration Pathway (RCP) 8.5 forcing for this preliminary study. 2 Therefore, future studies with ensembles of simulations are needed to validate the statistical robustness of the conclusions.
The rest of the paper is structured as follows. Section II introduces the definition of resource adequacy, which is used as a criterion for evaluating system reliability. Section IV shows the impact of different resolutions of climate data on grid reliability, the sensitivity of grid reliability to climate conditions, and discusses the potential of climate energy research and future research directions. Section V summarizes the findings of the study and draws conclusions on the impact of climate simulation resolution on grid reliability assessment.
II. FORMULATION OF RESOURCE ADEQUACY
In this study, we use the reserve margin, one of the resource adequacy indicators, as the reliability criterion, which equals the difference between the total concurrent load and the total operational capacity. To investigate the impact of climate simulation resolution on grid reliability, we perform reliability assessment in a bottom-up way as defined in Eq. 1.
M ymdh =P g ymdh − P l ymdh ,(1a)P l ymdh = nz i=1 P l zymdh ,(1b)P g ymdh = ns i=1P s iymdh + nw i=1P w iymdh + ns i=1P t iymdh , (1c)
where M ymdh is the reserve margin at hour h on day d in month m of year y,P g ymdh is the total operational generation capacity, P l ymdh is the total load demand. In addition,P l iymdh represents the zonal load demand, whileP w iymdh ,P s iymdh , and P t iymdh are the operational generation capacity of individual wind, solar, and traditional (thermal and hydro) plants, respectively.
In this study, we focus on evaluating the resource adequacy of the Texas interconnection between 2033 and 2043. To achieve accurate long-term assessments of operational generation capacity and load demand, we consider not only climate factors, but also capacity and load expansion factors, as well as planned generation outages in the Texas interconnection. As a result, we require models to simulate generation capacity and load demand that can account for climate conditions, as well as models for long-term capacity expansion, load expansion, and planned generation outages.
III. METHODOLOGY
This section describes the development of a future Texas grid that encompasses precise spatial data on the location and capacity of generations and loads, along with the planning of generation outages. The constructed grid can be utilized to evaluate the system reliability using different resolutions of climate simulation data as input. The overview of the entire process is shown in Fig. 1.
A. Data Collection and Processing
1) Climate Simulation Data
Global climate simulations were conducted using the Community Earth System Model (CESM) version 1.3, with a 6hour temporal resolution, in both high-resolution (0.25 degree or 25 km) and low-resolution (1 degree or 100 km) configurations. As discussed in [11], high-resolution climate simulations yield significant improvement in simulating not only regional climate mean states, but also weather extreme events. To assess the impact of climate model resolution on energy system reliability, we conduct a pilot case study from 2033 to 2043 in the Texas region, utilizing atmosphere temperature, relative humidity, and dew point at 2-meter height, wind speed at 100meter and direct and net solar radiation flux at surface obtained from the climate model output stored on a data server [16] to derive energy grid reliability.
2) Data for Generation Capacity Models
We obtain the layout and size information of individual operable generation units in the real Texas grid from the Energy Information Administration (EIA) [17]. These data contain geographical location, technology, fuel type, turbine model, nameplate power factor, and nameplate capacity over seasons.
3) Data for Load Models
We obtain the layout and size information of individual loads from a 2,000-bus synthetic Texas grid [18] due to the lack of real high-resolution load data. This information includes longitude, latitude, and active power. In addition, we calculate the share of individual loads in their respective load zones based on their active power and total power in the load zones to obtain a more detailed understanding of the distribution of loads in the region.
Furthermore, since we will use a regression model for load modeling, it is necessary to have historical weather and load data for training and validation purposes. To this end, we collect historical weather data at 203 Automated Surface Observing System (ASOS) sites throughout Texas from [19], as well as zonal load data from the Electric Reliability Council of Texas (ERCOT) [20]. The historical weather data contains temperature, dew point, relative humidity, and wind speed, which we average and interpolate to unify into hourly data. The zonal load data provides hourly electricity consumption at the zonal level in the real Texas grid. Fig. 1: Schematic of resource adequacy assessment based on climate data using models of generation capacity, load, planned outage, and expansion.
4) Data for Load Expansion Models
As we do not utilize bottom-up econometric approaches for long-term load expansion between 2033 and 2043 in this study, we use the long-term load forecast between 2023 and 2032 collected from ERCOT [21]. The long-term load forecast data comprises monthly peak total load projections in the Texas interconnection from 2023 to 2032, which are generated from econometric models incorporating various factors such as the number of premises in different customer classes, weather variables, and calendar variables.
5) Data for Planned Outage Models
In order to examine the pattern of planned outages for various types of generation, we obtain historical data on planned generation capacity outages from ERCOT [20]. This data provides hourly planned capacity outages of intermittent (wind and solar) and non-intermittent (thermal and hydro) resources, respectively.
B. Power Grid Modeling and Simulation
1) Models of Operational Generation Capacity
We utilize physical models to estimate the operable generation capacity of each type of generation unit over the years, considering the model projected climate conditions. To obtain the climate data for a particular generation plant, we select the sample with climate data that is geographically closest in terms of Euclidean distance.
We model the operational capacity of wind farms as a function of the wind speed as defined bȳ
P w iymdh = 1 − η w iymdh * φ w i * P w iy * C i (V ymdh ) ,(2)
where η w iymdh is the planned generation outage rate, φ w i is the nameplate power factor,P iy is the nameplate capacity in year y, C i is the wind-speed-power curve dependent on the brand and turbine type, and V iymdh is the real-time local wind speed.
We model the operational capacity of solar photovoltaic (PV) farms as a function of net solar flux as defined bȳ
P s iymdh = 1 − η s iymdh * φ s i * P s iy * S iymdh ,(3a)S iymdh = S iymdh / max m,d,h S iymdh ,(3b)
where η s iymdh is the planned generation outage rate, φ s i is the nameplate power factor,P s iy is the nameplate capacity in year y, S iymdh is the real-time local net solar flux, and S max iy is the maximum net solar flux in year y.
We model the operational capacity of traditional hydro and thermal plants, including natural gas, nuclear, coal, and biomass, as a season-dependent function as defined in
P t iymdh = 1 − η t iymdh * φ t i * P t iy * β m ,(4)
where η t iymdh is the planned generation outage rate, φ t i is the nameplate power factor, andP t iy is the nameplate capacity in year y. Additionally, β m is a month-dependent factor that ranges from 0 to 1, indicating the varying efficiency in different seasons, and remains constant throughout the months within the same season.
2) Zonal Load Model
We utilize regression models to estimate the load demand of each load zone over the years, considering the climate conditions. Similarly, to obtain the climate data for a particular load, we select the sample with climate data that is geographically closest in terms of Euclidean distance. We model zonal loads as functions of time, temperature, dew point, relative humidity, and wind speed as defined in
P l zymdh = f z X zymdh P l,max zy − P l,min zy + P l,max zy , (5a) X zymdh = i∈z α zi X iymdh ,(5b)X iymdh = [T iymdh , D iymdh , H iymdh , V iymdh , m, d, h], (5c)
where P l zymdh is the real-time zonal load demand, f z is the normalized zonal load model, P l,max zy and P l,min zy are the maximum and minimum load demand in zone z in year y,X zymdh is the average environmental condition in zone z, α zi means the share of load i in zone z that follows i∈z α i = 1, and T iymdh , D iymdh , H iymdh , and V iymdh are local temperature, dew point, relative humidity, and wind speed at load i, respectively, Specifically, we employ a neural network to implement the normalized zonal load model f z for each zone. In the training process, we collect the historical zonal load data as P l zymdh , calculateX zymdh based on historical weather data, and train the model by optimizing on the objective function
min θ y,m,d,h P l zymdh − f z X zymdh ; θ ,(6)
where θ is the trainable parameters of the neural network. Table I displays the performance of all zonal load regression models, which indicates the accuracy of load prediction.
3) Planned Generation Unit Outage Model
To estimate the operable capacity, we consider the planned outages of generation units. Our approach assumes that the planned outage capacity of a specific generation type is proportional to its total installed capacity. Therefore, it is essential to determine the planned outage rate, which represents the ratio of the planned outage capacity to the total installed capacity of the same generation type. We estimate the planned outage rate using the hourly planned outage capacity reported by ERCOT in 2019 and the installed capacity data from EIA in 2019.
The distribution of planned outage rates for intermittent renewable and non-intermittent traditional generation units is shown in Fig. 2-a. It is observed that non-intermittent units, mainly thermal and hydro generation, have planned outages during the spring and winter of each year for maintenance purposes. On the other hand, intermittent units have relatively low rates of planned outages with a more uniform distribution.
4) Expansion Model
In this subsection, we will present models for capacity and load expansion that can be applied to calculate the nameplate capacityP x iy in Eq. 2-4 and the maximum P l,max zy and minimum load demand P l,min zy in Eq. 5. We employ polynomial regression models to forecast the installed generation capacity for each generation type from 2023 to 2043, using the EIA's installed capacity data from 2014 to 2022. For thermal, hydro, and wind generation, we utilize first-order polynomial models (linear regression), while for solar generation, we use a second-order polynomial regression model (quadratic regression). This is primarily due to the clear superlinear increasing trend observed in the historical installed capacity of solar generation within the Texas interconnection. Fig. 2 We employ regression models to estimate the trend in power demand between 2033 and 2043, using the ERCOT long-term load forecast report [21] that predicts monthly peak loads between 2023 and 2032. We notice a trend of continuous increase with a decreasing rate of growth, and that the maximum and minimum monthly peak loads show differentiable growth rates. To account for these characteristics, we employ logistic growth regression models for regression and prediction on maximum and minimum monthly peak loads, using the equation y = c/ (1 + a * exp (−bt)), where a, b, c are the coefficients to learn, t represents the year, and y denotes the maximum or minimum monthly peak load. We estimate the minimum and maximum load demand (P l,max zy and P l,min zy ) by using the predicted maximum monthly peak loads for the former, and by estimating the latter through the growth rate of the predicted minimum monthly peak loads and historical minimum load data from 2019. Fig. 2-c depicts the trend in maximum and minimum loads. It is worth emphasizing that the minimum and maximum loads for future years are used for scaling purposes and should be interpreted as the anticipated minimum and maximum load under the same weather conditions as in the past, rather than as the precise minimum and maximum loads based on future climate projections. It is observed that the growth rate of the maximum load is 13% between 2023 and 2043, whereas that of the minimum load is 24%. Specifically, the maximum peak load will increase from 82,308 MW in 2023 to 91,755 MW in 2033, and eventually reach 93,054 MW in 2043, while the minimum load will increase from 33,517 MW in 2023 to 40,838 MW in 2033, and eventually reach 41,668 MW in 2043.
IV. RESULTS
A. Resource Adequacy Assessment
We utilize the proposed models for load demand and operational generation capacity to estimate the resource adequacy from 2033 to 2043, using data from single high and lowresolution climate simulations, respectively. For the sake of clarity, we will refer to the reliability assessment based on the high-resolution (low-resolution) climate simulation data as the high (low) resolution reliability assessment in the rest of this section.
Since analyzing climate-induced extreme events is a crucial objective of long-term reliability assessment, we initially prioritize the top 1% of events with the lowest adequacy in each year between 2033 and 2043. Fig. 3 illustrates the linear trend of their average resource adequacy, with both high and low-resolution reliability assessments indicating a clear decreasing trend over the years. Additionally, the highresolution assessment consistently displays lower adequacy than the low-resolution assessment.
B. Statistics of Extreme Events
To achieve a better understanding of potential climateinduced extreme events, we classify low-adequacy extreme events into three types based on the threshold of the Energy Emergency Alert (EEA) state, which is triggered when the reserve in the Texas interconnection falls below 2,300 MW. These event types are: (1) blackout events, which happen when the resource adequacy falls below 0, (2) emergency events, which occur when the resource adequacy ranges from 0 to 2,300 MW, and (3) warning events, which take place when the resource adequacy ranges from 2,300 to 4,600 MW.
It is evident from Fig. 4-a that high-resolution reliability assessment can detect more emergency events between 2033 to 2043, but there is no significant difference in the number of blackout and warning events detected. To be precise, the highresolution assessment identifies a total of 60 extreme events, while the low-resolution assessment identifies 48. Notably, the seasonal distribution of the counts of events shown in Fig.4 c. d.
Emergency events at summer nights Average at summer nights shows that the grid experiences more frequent events during the summer months, which aligns with empirical observations. Furthermore, the high-resolution assessment detects a greater number of extreme events in all three categories. Specifically, the high-resolution assessment shows a significantly higher number of emergency events during the summer months. Please see more detailed statistics of extreme events in Appendix A.
As there are notable disparities between the summer emergency events detected by high and low-resolution assessments, we investigate the causes of these events. Surprisingly, all of these events occur during the night period from 6 p.m. to 12 a.m. While the low-resolution assessment identifies emergency events caused by consistently high load and low wind capacity compared to the average during summer nights (Fig. 5-b and d), the high-resolution assessment reveals more emergency events with two types of causes (Fig. 5-a and c), including (1) high load and low wind capacity and (2) average or belowaverage load with extremely low wind capacity. This suggests that high-resolution climate simulation provides a wider range of weather conditions that can lead to extreme events with low adequacy.
To summarize, while low-resolution climate simulation can aid in a first-order long-term system reliability assessment of the Texas interconnection between 2033 and 2043, highresolution climate simulation is more effective in providing informative assessments, especially for emergency events that occur during the night in summer with low wind speeds. : Simulated climate conditions during two worst blackout events detected by high and low-resolution reliability assessments. a1, a2, a3 show the high-resolution simulated temperature, wind speed, and the corresponding estimated generation mix and adequacy during 0 to 6 a.m. on February 5 th , 2036. b1, b2, b3 show the low-resolution simulated temperature, wind speed, and the corresponding estimated generation mix and adequacy during 0 to 6 a.m. on January 10 th , 2042.
C. Blackout Events in Winter
Despite blackout events being more frequent during the summer, their severity during winter is even greater than that of summer, as measured by the average resource adequacy. In this context, we present the worst blackout events identified by high and low-resolution reliability assessments for further discussion. Specifically, the worst blackout event detected by the high-resolution assessment occurs during the early morning hours of February 5 th , 2036, with a power shortage of 4,462 MW, while the worst event detected by the lowresolution assessment occurs during the early morning hours of January 10 th , 2042, with a power shortage of 6,967 MW. It is important to note that the timing information presented in the data is for illustrative purposes only, as climate simulations cannot provide precise timing information for any single extreme event. Moreover, the relative severity between the two blackout events should not be taken as a conclusion as well, as it is based on observations from single simulations. Please see the detailed explanation in Appendix B. Fig. 6 shows comparison of high and low-resolution simulated climate conditions during the two identified worst blackout events. The common cause of both events is the compound effects of the high load demand due to extremely low temperatures (Figs. 6-a1 and b1), low wind generation power resulting from low wind speeds (Figs. 6-a2 and b2), and lack of solar generation power during early morning hours, as shown in Figs. 6-a3 and b3.
Despite determining the severity of the worst blackout event through a single round of simulation may be not meaningful because of the small sample size (Appendix B), there may still be important policy implications that can be derived from both scenarios. First, the grid will continue to face challenges in meeting demand during low-temperature extremes, even with over 200,000 MW of installed renewable generation. This highlights the importance of developing complementary technologies to address the intermittency of renewables, such as large-scale demand response programs and long-term energy storage. Second, our model does not account for the possibility of generation facility malfunction during extreme climate events, such as the extremely low temperatures experienced in Texas in February 2021. This can greatly exacerbate grid reliability issues. Therefore, implementing weatherization measures for all generation units is crucial to enhance grid reliability against extreme weather, as such events will not be isolated incidents in the future.
D. Discussion
In this study, the extendable framework that can incorporate granular climate data allows higher resolution modules of operation and long-term planning. For instance, future studies can customize high-resolution modeling of emerging technologies for better assessment, such as granular layout and sizing information of massive roof-top solar PV panels, long-term energy storage, large flexible loads, and fast growing electric vehicles (EVs). By leveraging state-of-the-art climate models and accounting for the inherent uncertainties, researchers and policymakers can more effectively assess the potential impacts of climate change on energy grid reliability and develop suitable adaptation and mitigation strategies to ensure a resilient and sustainable energy future. Despite the high spatial resolution of climate data and the extendability of the assessment framework, it is crucial to acknowledge that this study has several significant areas that require improvement in future research.
Regarding climate simulation output, it would be advantageous to have hourly data with a large ensemble size to capture more statistically reliable information. This pilot study incorporating high-resolution climate modeling with the power system model could be further optimized by increasing the output frequency from every 6 hours to every hour. In solar-dominated grids, such as the California interconnection, resource scarcity can be a challenge during sunset hours, while in wind-dominated grids, wind speeds can vary significantly within an hour. By obtaining hourly climate simulation outputs, we can gain a better understanding of the variability of renewable resources and accurately assess their impact on the power grid, aiding in informed decisions regarding optimal siting and sizing. Furthermore, a single realization of climate simulation as we used in this pilot study cannot adequately assess the statistical robustness and uncertainties of future climate, and a large ensemble of high-resolution climate simulations is desirable for future studies. With large ensemble simulations, we can obtain more robust statistics about extreme events, allowing us to examine in more details the impact of different model resolutions.
Regarding power system modeling, this study has several simplifications that need improvement in future research. First, for long-term load modeling, we have not taken into account emerging technologies such as rooftop solar PV panels and EVs, which can significantly alter the future energy consumption pattern. Second, we have not used an econometric model to predict the development of demographics and sectors that can change the distribution of load demand across Texas. Third, we have not used geophysical models to assess local renewable potential to guide the deployment and retirement of traditional and renewable generation plants. Additionally, we have not used binary outage states or derates for each individual power plant, which needs further refinement. Finally, we have not incorporated unit commitment and economic dispatch to represent the impact of temporal correlated decision-making and the limitation of system topology, such as congestion.
V. CONCLUSION
The presented framework in this pilot study provides a preliminary long-term reliability assessment for the Texas interconnection from 2033 to 2043, utilizing both high and low-resolution climate simulation data. Our findings reveal that high-resolution climate data can more accurately identify emergency events, particularly those that occur during summer nights. Furthermore, the analysis shows that both high and low-resolution assessments detect the worst blackout event in winter. Future studies with large ensemble simulations are needed to validate the statistical robustness of the conclusions. There are several areas for future research, such as the need for hourly climate simulation outputs, integration of emerging technologies and demographics, and the incorporation of renewable potential and unit commitment in power system modeling. Fig. 7 shows the counts of different types of events from 2033 to 2043 by high and low-resolution reliability assessment. Interestingly, there is no consistent overestimation or underestimation in the relative relationship between the yearly counts of events determined by the low-resolution climate data and those determined by the high-resolution climate data. This is primarily due to the fact that the difference between high and low-resolution climate modeling cannot be solely attributed to differences in granularity that can be approximated by interpolation. Instead, there may be qualitative differences between the two approaches. In other words, the low-resolution climate simulation may show extreme weather during certain periods that are not present in the high-resolution simulation, and vice versa.
APPENDIX A STATISTICS OF EXTREME EVENTS OVER YEARS
APPENDIX B DIFFERENCES BETWEEN HIGH AND LOW-RESOLUTION
CLIMATE SIMULATIONS
It is important to emphasize that the difference between low and high-resolution climate simulations at the same period is not merely a matter of increased granularity that can be approximated by interpolation, but rather a fundamental qualitative difference. This is demonstrated in Fig. 8, which compares the simulated temperatures during the worst blackout events in winter using both high and low-resolution assessments. The climate simulation process essentially involves simulating stochastic partial differential equations with slightly perturbed initial states. Therefore, different rounds of simulations, even with the same resolution configuration, may result in completely different outcomes in each period. Hence, analyzing a single event by a single round of simulation is not appropriate. To obtain useful and reliable information, it is essential to analyze the statistics of certain variables over a sufficiently long time horizon. Additionally, it is critical to increase the number of simulations in the ensemble to obtain statistically robust conclusions. High resolution temperature Low resolution temperature High resolution temperature Low resolution temperature Fig. 8: Comparison of simulated temperatures during the worst blackout event detected by high-resolution reliability assessment, which occurs during 0 to 6 a.m. on February 5 th , 2036, as well as the worst blackout event detected by low-resolution reliability assessment, which occurs during 0 to 6 a.m. on January 10 th , 2042. a1, a2 show the simulated contrasting temperatures in the worst event detected by high-resolution reliability assessment during the first blackout event. b1, b2 show the simulated contrasting temperatures in the worst event detected by low-resolution reliability assessment during the second blackout event.
Fig. 3 :Fig. 4 :
34The linear trends of the average adequacy for the top 1% of events with the lowest adequacy, as determined by both high and low-resolution assessments. Counts of blackout, emergency, and warning events between 2033 and 2043 based on high (HR) and low (LR) resolution reliability assessment. a. Total count of each type of events from 2033 to 2043. b. Total count of each type of events in each season from 2033 to 2043.
Fig. 5 :
5Comparison of load power and wind capacity between summer emergency events and corresponding summer night averages in simulated data. a, b show show the comparison of load power between emergency events and summer night average for high and low-resolution assessments, respectively. c, d show the comparison of wind capacity between emergency events and summer night average for high and low-resolution assessments, respectively.
Fig. 6
6Fig. 6: Simulated climate conditions during two worst blackout events detected by high and low-resolution reliability assessments. a1, a2, a3 show the high-resolution simulated temperature, wind speed, and the corresponding estimated generation mix and adequacy during 0 to 6 a.m. on February 5 th , 2036. b1, b2, b3 show the low-resolution simulated temperature, wind speed, and the corresponding estimated generation mix and adequacy during 0 to 6 a.m. on January 10 th , 2042.
Fig. 7 :
7Counts of blackout, emergency, and warning events for each year between 2033 and 2043 based on high (HR) and low (LR) resolution reliability assessment.
.m. -6 a.m. on February 5 th , 2036 0 a.m. -6 a.m. on January 10 th , 2042 Temperature (°C)
TABLE I :
IPerformance of zonal load regression models Neural network configuration contains two hidden layers of 100 neurons with ReLU as activation functions.Fig. 2: Planned generation outage rate, predicted generation capacity, and predicted load demand. a. Planned generation outage rates of intermittent and non-intermittent generation resources. b. Predicted generation capacity of thermal, hydro, wind, and solar generation. c. Predicted maximum and minimum loads.Metric
COAST
EAST
FWEST NORTH NCENT SOUTH SCENT WEST
R 2
0.97
0.97
0.96
0.97
0.97
0.97
0.97
0.97
MAE (GW)
0.34
0.05
0.04
0.02
0.48
0.11
0.22
0.03
MSE (GW 2 )
0.21
3.8e-3
3.2e-3
9.1e-4
0.41
0.02
0.09
1.8e-3
* 01/01 03/01
05/01
07/01
09/01
11/01
01/01
Day of year
5
10
15
20
25
30
Planned outage rate (%)
Planned outage rate of
intermittent resources
Planned outage rate of
traditional resources
2014
2020
2026
2032
2038
Year
0
25000
50000
75000
100000
125000
150000
175000
200000
Generation capacity (MW)
Wind capacity (historical)
Solar capacity (historical)
Hydro capacity (historical)
Thermal capacity (historical)
Wind capacity (predicted)
Solar capacity (predicted)
Hydro capacity (predicted)
Thermal capacity (predicted)
a.
b.
c.
2023
2027
2031
2035
2039
2043
Year
40000
50000
60000
70000
80000
90000
Load demand (MW)
Maximum load by ERCOT
Maximum load by our study
Minimum load by ERCOT
Minimum load by our study
2044
-b illustrates the trends in generation capacity for different sources. Specifically, the thermal generation capacity is expected to gradually decrease from 101,286 MW in 2022 to 94,397 MW in 2033, and eventually reach 87,983 MW in 2043. On the other hand, the hydro generation capacity is predicted to increase slowly from 723 MW in 2022 to 784 MW in 2033, and eventually reach 848 MW in 2043. The solar generation capacity is expected to experience a massive increase from 4,880 MW in 2022 to 79,795 MW in 2033, and eventually reach 196,368 MW in 2043. Finally, the wind generation capacity is expected to steadily increase from 30,059 MW in 2022 to 66,209 MW in 2033, and eventually reach 93,522 MW in 2043.
RCP 8.5 represents a "very high baseline emission scenario" in which greenhouse gas concentrations are projected to continue to rise throughout the 21 st century, which is generally taken as the basis for worst-case climate change scenarios.
ACKNOWLEDGMENTThis research is partly supported by NSF grant AGS-2231237. Portions of this research were conducted with the advanced computing resources provided by the Texas Advanced Computing Center at University of Texas, Austin and Texas A&M High Performance Research Computing.
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| sample_1626 | 1 | arxiv | |
Consequences of catastrophic disturbances on 1 population persistence and adaptations Corresponding author: 14
Simone Vincenzi simon.vincenz@gmail.com
Dipartimento di Scienze Ambientali
Università degli Studi di Parma
5 Viale G. P. Usberti 33/AI-43100ParmaItaly
Michele Bellingeri
Dipartimento di Scienze Ambientali
Università degli Studi di Parma
5 Viale G. P. Usberti 33/AI-43100ParmaItaly
Simone Vincenzi
Dipartimento di Scienze Ambientali 16 Università degli Studi di Parma
Consequences of catastrophic disturbances on 1 population persistence and adaptations Corresponding author: 14
1 6 7 8 9 10 11 12 13 17 Viale G.P. Usberti 33/A 18 I-43125 Parma 19 Tel.: +39 0521 905696 20 Fax.: +39 0521 906611 21 22 23 24 2Catastrophic disturbancePopulation dynamicsMonte Carlo 44 simulationsMutationSelection pressure 45 3
25The intensification and increased frequency of weather extremes is emerging as one 26 of the most important aspects of climate change. We use Monte Carlo simulation to 27 understand and predict the consequences of variations in trends (i.e., directional 28 change) and stochasticity (i.e., increase in variance) of climate variables and 29 consequent selection pressure by using simple models of population dynamics. 30 Higher variance of climate variables increases the probability of weather extremes 31 and consequent catastrophic disturbances. Parameters of the model are selection 32 pressure, mutation, directional and stochastic variation of the environment. We 33 follow the population dynamics and the distribution of a trait that describes the 34 adaptation of the individual to the optimum phenotype defined by the 35 environmental conditions 36The survival chances of a population depend quite strongly on the selection 37 pressure and decrease with increasing variance of the climate variable. In general, 38 the system is able to track the directional component of the optimum phenotype. 39Intermediate levels of mutation generally increase the probability of tracking the 40 changing optimum and thus decrease the risk of extinction of a population. With 41 high mutation, the higher probability of maladaptation decreases the survival 42 chances of the populations, even with high variability of the optimum phenotype. 43
Introduction
directions and at new intensities, and the degree to which species respond 6
Model of population dynamics 110
We consider a population that consists of hermaphrodite individuals living in a 111 spatially-extended habitat modeled as a vector of length K, where K is the carrying 112 capacity of the system (i.e., maximum number of individuals supported). This 113 means that only one individual can occupy each element j =1…K of the vector, and 114 introduces density-dependent population regulation through a ceiling effect, as 115 described below. We assume that individuals cannot move, therefore an individual 116 occupies the same element during the simulation. 117
The populations has discrete generations (i.e., reproduction is discrete in time) and 118 is composed of N(t) individuals. Generations are overlapping, meaning that parents 119 do not die after reproducing. Each individual is characterized by a single 120 quantitative trait φ with value ranging from 0 to 1. The population lives in a habitat 121 characterized by an optimum phenotype Θ(t) that exhibits temporal change. This is 122 assumed to result from variations in a climate variable, such as rainfall or 123 temperature, selecting for a phenotype. The degree of maladaptation between the 124 optimum phenotype Θ(t) and a single trait φi defines the fitness of an individual.
125
The time step is one year. 126
In general, the temporal change of the optimum phenotype may be either 127 directional, stochastic or a combination of both. A simple model for this is a 128 optimum phenotype Θ(t) that moves at a constant rate β µ per year, fluctuating 129 randomly about its expected value µ(t). We thus introduce a directional and 7 stochastic temporal change of the optimum phenotype (Fig.1a). Θ(t) is randomly 131 drawn at each time step from a normal distribution Ν (µ(t),sd(t)), where µ(t) = µ0 + 132 β µ t and sd(t) = sd0 + βsdt. The probability p of an individual i with fitness f(i) survive to next year is: 147
p(i)= exp(-(s * f(i)) 2 ) (2) 148
where s is the selection pressure. With increasing s the habitat is more demanding 149 (for a given fitness f the probability of survival decreases). Since no individual can 150 be perfectly adapted to the moving optimum phenotype Θ, we did not account for a 151 decrease in survival probability with age (in case of constant Θ over simulation 8 time, accounting for it would be necessary to avoid the presence of individuals 153 living forever). 154
Offspring inherit the trait φ from its parents p1 and p2 as follows:
155 φ 0 = 0.5 (φp 1 + φp2) + Mε (3) 156
where φ 0 is the trait value of the offspring, φp 1 and φp2 are the trait values of the 157 parents, M represents mutation-segregation-recombination [22] and ε is random 158 number drawn from a uniform distribution bounded between (-1,1). We will refer to 159 M as simply mutation. 160
The Monte Carlo simulation at a time t during the simulation proceeds as follows: 161 1) We draw the optimum phenotype Θ(t) from Ν (µ(t),sd(t)). produce randomly from 1 to 4 offspring (we chose 4 as the maximum to allow for a quick rebound of population size after a strong reduction and repeat the procedure up to j= K. 177 6) As we assume that the optimum phenotype Θ(t) defines the whole time-step, 178 we applied steps (2) and (3) to offspring. Following an example provided 179 above, a heat wave affects the survival of both adults and offspring. This 180 further intensifies the selective consequences of the optimum phenotype. 181
Offspring are placed randomly on the empty elements of the vector to avoid 182 spatial autocorrelation. When all the empty elements have been occupied, the 183 remaining offspring die (density-dependence through a ceiling effect). 184
Offspring at year t become adults at year t+1 and are able to reproduce. 185
Our simulation model has the following control parameters: carrying capacity of the 186 environment K, mutation M, selection pressure s and the parameters which govern 187 directional and stochastic variations of the optimum phenotype, that is µ0, β µ , sd0
260
There is a range of the selection pressure values within all scenarios of variability in 261 which populations have some probability to persist (Fig. 3). Outside this range, 262 broadly for s higher than 2.8, the probability of extinction increases in all scenarios. 263
If selection is too strong, then the distance between the average phenotype and the 264 optimum is small at any time during simulation, but the decrease in population size 265 induced by selection may be too high for population persistence. If the selection is 266 weaker, fewer individuals die from ill-adaptation and the population can persist 267 with a greater diversity in trait φ. all scenarios of variability (Fig. 1). An increase in selection pressure tends to 296 decrease time of extinction in all scenarios of variability. 297
In general, the system is able to track the directional component of the optimum 298 (Fig. 5). The mean value of trait φ at the end of simulation time does not depend on 299 selection, therefore even for very small selective pressure and in presence of sufficient mutation M, the mean value of trait φ follows the directional component 301 of Θ (Fig. 6). With no mutation or very low mutation, there is little potential for 302 adaptive shifts and thus the mean value of φ is largely determined by the optimum 303 phenotypes in the first few years (Fig. 6). For βsd = 0.0005 and βsd = 0.0010 the mean 304 value of trait φ in the population increases, and thus tracks the changes in µ(t), also 305 for very high mutation. In contrast, for βsd = 0.0015 and βsd = 0.0020 the mean value 306 of trait φ increases with increasing mutation, but with very high mutation the mean 307 value of trait φ tends to be lower than in scenarios with lower variability. Since in an 308 substantial fraction of replicates with high mutation the population went extinct 309 ( Fig. 3), we cannot exclude that for only a particular sequence of Θ near the end of
of climate variables, extreme weather events causing catastrophic 134 disturbances (i.e., very large deviations of a system's behavior from the habitual 135 one) in a sequence of independently and identically distributed random variables 136 are either the maximal values in a time window or they are defined by overcoming 137 a predefined threshold (threshold crossing) [20]. In our model, values of Θ(t) 138 outside (0,1) represent an extreme event causing a catastrophic disturbance to which 139 the vast majority of individuals cannot be adapted, thus causing a population 140 collapse (i.e., strong reductions in population size). This may be interpreted as a 141 catastrophic flood following an exceptional rainfall or a heat wave caused by high 142 temperatures. 143 Our model is similar in spirit to the one used by Droz and Pekalsky [21]. The fitness 144 of an individual i with trait value φi is
162 2 )
2We compute the fitness of individuals by applying Eq (1) and calculate their 163 survival probability by applying Eq (2). 164 3) We define the survival of individuals with Bernoulli trials. 165 4) We compute the total number of individuals alive N(t) and check the 166 distribution of trait φ in the population. A population is considered extinct if 167 at any time during the simulation there are less than ten individuals left. 168 5) We pick the first individual alive starting from j = 1. When the individual j is 169 alive, we check if the (j+1) individual is alive. If yes, the parents j and (j+1) 170
188 and βsd. To simplify the interpretation of results, we set some of the parameters. For 189 each replicate: K = 2000, µ0 = 0.5, β µ = 0.001 and sd0 = 0.1. Simulations were 190 performed for combinations of s (from 2.5 to 3.5), M (from 0 to 0.2) and βsd taking 191 values 0.0005, 0.0010, 0.0015, 0.0020 (scenarios of increasing variability of Θ over 192 simulation time, Fig. 1b). 193 population size of 500 individuals (one fourth of carrying capacity) because we 196 wanted to explore the space of parameters allowing for extinctions in the first years 197 of simulation. 198 We use different quantities to characterize the behavior of the simulated 199 populations. At the level of single replicates, we recordeddependent value of the trait φ, and in particular the mean value of 205 φ (ranging from 0 to 1) at the end of simulation time, only when the 206 population did not go extinct. 207 We did not focus on the number of individuals at the end of simulation time (100 208 years) since it was largely determined by the succession of Θ near the end of 209 simulations (Fig. 2). 210 For an ensemble of realizations (100 replicates for a fixed set of parameters)population extinction, computed as the number of replicates in 213 which the population went below ten individuals during simulation time. replicates of the mean value of trait at the end of simulation 217 time, for the replicates in which the populations did not go extinct. 218 3. Results and discussion 219 In Fig. 1b we show the probability of catastrophes with the different scenarios of 220 variability of Θ. The probability of a catastrophe, that is of optimum phenotype 221 Θ(t) outside (0,1), reaches a maximum of 0.12 at the end of simulation time (t = 100) 222 for the most variable scenario (βsd = 0.0020). With the parameters we chose, there is 223 a higher probability of extreme events in the same direction as directional change 224 (more values of Θ > 1 than < 0 are expected), although the probability of both events 225 increases over the simulation time (Fig. 1a). In other words, with increasing 226 temperatures there is a higher probability of heat waves than of cold waves and 227 with increasing rainfall (and thus increasing flows) there is an higher probability of 228 floods than of droughts. 229 The consequences of different values of βsd for the probability of extreme events is 230 clear after the first 40-50 years of simulation while little difference among scenarios 231 in the probability of extreme events can be noted before that time. In Fig. 2 we 232 report examples of replicates for the four scenarios of variability. For all replicates 233 we set s = 3 and M = 0.1 (thus intermediate values for both parameters). With 234 higher values of βsd the population shows repeated collapses. Selection tries to bring the average trait close to the instantaneous optimum, while mutation introduces 236 diversity and broadens the distribution of the trait. There is a clear shift in all 237 replicates of the mean value of trait φ toward 0.6 over simulation time -which is the 238 value taken by µ when t = 100 -even in high variability scenarios. The only 239 exception is the scenario with the highest variability, in which at t = 100 there is a 240 mean value of trait φ in the proximity of 0.5. In the specific example provided, a few 241 years of Θ below 0.6 "push back" the trait φ toward lower values than those selected 242 for by the directional component of Θ. 243 As noted by Siepielski et al. [25], the "temporal landscape" of selection across taxa 244 shows that the strength and the direction of selection often vary through time, even 245 in absence of climate change. Especially with strong selection pressure and high 246 variability of the optimum Θ, alternating selection over time might cancel out 247 periods of directional selection such that effective selective (quasi) neutrality of trait 248 variation is maintained over time. However, after a single extreme event or a 249 succession of them, this balancing effect does not occur, leading to directional 250 changes in trait frequency within the population. Apart from the contribution of 251 directional change, the distribution of trait φ is "pulled" toward higher values over 252 simulation time, since there is a higher probability of extreme events in the same 253 direction as directional change (as previously discussed). 254 In Fig. 3 we present a phase diagram of equal probability of extinction in the 255 mutation-selection plane for each scenario of variability of Θ . The survival chances 256 of a population depend quite strongly on the selection pressure and decrease 257 substantially with increasing βsd for the same selection-
268 For
268βsd = 0.0020 populations can survive only with intermediate levels of mutation 269 and very low selection pressure, while extinction is the inevitable outcome for all 270 other selection-mutation combinations (Fig. 3). The adaptive value of intermediate 271 levels of mutation is clear also for βsd = 0.0005 and for βsd = 0.0010, while for βsd = 272 0.0015 the only clear pattern is along a selection gradient. It appears from Fig. 3 that 273 increasing mutation amplitude is adaptive up to intermediate values, while higher 274 mutation values are not adaptive (they increase the probability of population 275 extinction). 276 Contrary to our results, Bena et al. [14] found that mutation is unfavorable to the 277 survival of a population in a constant environment, since it increases the probability of a mismatch of offspring phenotype to the environment optimum, even though 279 the parents might be well-adapted. Therefore, any level of mutation will result in 280 the production of non-optimal trait in a constant environment (given an adapted 281 population), but it will increase the probability of tracking a moving optimum and 282 thus increase the survival chances of a population. According to our results, even in 283 presence of high variability of the optimum phenotype Θ, high mutation increases 284 the probability of losing adaptations in the next generation and thus decreases the 285 probability of population persistence. When mutation is low, the population cannot 286 track the variations of Θ. In conclusion, for both mutation extremes (high or low 287 mutation) there is an increase in the probability of maladaptation, albeit for 288 different reasons, and consequent risk of extinction. 289 The influence of selection, mutation and βsd on the average time to extinction is 290 reported in Fig. 4. For βsd = 0.0005, for the few populations going extinct with 291 intermediate mutations, this happens only in the first years of simulation after an 292 unfavorable succession of alternate Θ (direction of selection varying through time). 293 With intermediate selection pressure, populations go extinct mostly at the end of 294 simulation time, when an increase of occurrence of extreme values is expected for 295
310simulation time (resulting in mean value of trait close to 0.5) the populations were 311 able to persist, thus preventing more general insights.312 4. Conclusions 313 Extreme events occur in all systems with complex dynamics, but the details of the 314 creation of these large fluctuations are still rarely understood, and therefore their 315 prediction, including that of their consequences on natural populations, remains a 316 challenge. However, many significant impacts of climatic change are likely to come 317 about from shifts in the intensity and frequency of extreme weather events and the 318 prediction of their effects on population dynamics and evolution of traits in natural 319 populations call for wide and intense scientific investigations. These events may 320 result in rapid mortality of individuals and extinction of populations or species [26, 321 33]. Variations in disturbance timing, predictability, frequency and severity make 323 difficult to predict sign and strength of selection [10]. In some cases, catastrophic 324 events may be so swift or severe that there is little possibility for adaptive 325 responses, with population extinction being the inevitable result. However, given 326 sufficient evolutionary potential (i.e., genetic variation within a populations), 327 models suggest that species can survive the effects of extreme events [34]. However, 328 if variability of the optimum phenotype is too high, a relevant potential for 329 extinction exists even when populations might possess genetic variation for 330 adaptation. 331 Despite simplifying the life-cycle of a natural population, the model we have 332 presented here provides a useful starting point for the investigation of the potential 333 of the populations to adapt (and survive) to an increase in the variability of 334 environmental conditions. The simulations showed that the probability of survival 335 of populations is dramatically affected by slight increases of the variance of the 336 optimum phenotype. Although not universal across scenarios of variability, 337 intermediate mutation seem to be adaptive, while increasing selection pressure 338 consistently decreases the probability of population persistence. 339 Intergovernmental Panel on Climate Change, 2007. 347 [3] A. Jentsch, J. Kreyling, C. Beierkuhnlein, A new generation of climate change 348 experiments: events, not trends, Front. Ecol. Environ. 5 (2007) 315-324. 349 [4] M. Smith, The ecological role of climate extremes: current understanding and 350 future prospects, J. Ecol. 3 (2011) 651-655. 351 [5] P. S. White, M.D. MacKenzie, R.T Busing, Natural disturbance and gap phase 352 dynamic in southern Appalachian spruce-fir forests, Can. J. For. Res. 15(1985C. A. Stockwell, A. P. Hendry, M. T. Kinnison, Contemporary evolution meets 357 conservation biology, Trends Ecol. Evol. 18 (2003) 94-101. 358 [8] T.R. Karl, R.W. Knight, N. Plummer, Trends in high-frequency climate 359 variability in the 20th century, Nature 377 (2005) 217] A. Pękalski, M. Ausloos, Risk of population extinction from periodic and abrupt 370 changes of environment, Physica A 11 (2008) 2526-2534. 371 [14] I. Bena, M. Droz, J. Szwabinski, A. Pekalski, Complex population dynamics as a 372 competition between multiple time-scale phenomena, Phys. Rev. E 76 (2007) 011908. 373 [15] R.D. Holt, R. Gomulkiewicz, Conservation implications of niche conservatism 374 and evolution in heterogeneous environments, in: R. Ferriere, U. Dieckmann, ] V. Grimm, E. Revilla, U. Berger, F. Jeltsch, W.M. Mooij, S.F. Railsback, H-H. 391 Thulke et al., Pattern-oriented modeling of agent-based complex systems: Lessons 392 from Ecology, Science 310 (2005) 987-991. 393 [24] P. A. Stephens, W. J. Sutherland, R. P. Freckleton, What is the Allee effect?] A.M. Siepielski, J.D. Di Battista, S.M. Carlson, It's about time: the temporal 396 dynamics of phenotypic selection in the wild, Ecol. Lett. 12 (2009) 1261-76. 397 [26] C. Bigler, O. Ulrich Bräker, H. Bugmann, M. Dobbertin, A. Rigling, Drought as 398 an inciting mortality factor in Scots pine stands of the Valais, Switzerland, Figure Captions
422 Fig. 1 - 431 Fig. 2 -
42214312Weather extremes. (a) Expected increase in the probability of occurrence of 423 extreme weather events with climate change (gray areas) for an hypothetical climate 424 variabile (e.g., rainfall, temperature), as defined in our model. Solid line represent 425 current scenario (µ = 0.5, sd = 0.1) while dotted line represent a future scenario at 426 the end of simulation time (dotted line, µ = 0.6, sd = 0.25). Jentsch et al. [3] and 427 Smith [4] provided similar representations. (b) Expected probability of optimum 428 phenotype Θ(t) outside (0,1) for different changes in variability during simulation 429 time. Solid line -βsd = 0.0005; short-dashed line -βsd = 0.0010; long-dashed line -βsd 430 = 0.0015; dashed-dotted line -βsd = 0.0020. Examples of simulations. Examples of simulation for the four scenarios of 432 variability with selection pressure s = 3 and mutation M = 0.1. The optimum 433 phenotype Θ(t) is randomly drawn at each time step from a normal distribution Ν 434 (µ(t),sd(t)), where µ(t) = µ0 + β µ t and sd(t) = sd0 + βsdt. The histograms represent the 435 distribution of trait φ at t = 1, 20, 40, 60, 80, 100. The vertical dashed line is set at 0.5. 436 The mean value of trait of the population tracks the directional change (µ = 0.6 at t = 437 100) in all the examples of simulation except for βsd = 0.0020 at t = 100. The 438 fluctuations in population size tend to increase with increasing βsd, parallel to 439 increase in fluctuations of optimum phenotype Θ(t).
440 Fig. 3 -Fig. 4 -Fig. 5 - 456 Fig. 6 -
4403454566Phase diagram for extinction probability. Phase diagram of equal probability of 441 extinction in the mutation-selection plane for the four scenarios of variability of 442 Phase diagram for mean time to extinction. Phase diagram of equal mean time to 447 extinction in the mutation-selection plane for the four scenarios of variability Phase diagram for mean value of trait. Phase diagram of equal mean across 450 replicates of the mean value of trait φ at the end of simulation time in the mutation-451 selection plane for the four scenarios of variability of Θ (βsd = 0.0005, 0.0010, 0.0015, 452 0.0020). The mean was computed only for the populations which persisted up to the 453 end of simulation time. The white region in the phase diagram for βsd = 0.0020 454 indentifies mutation-selection combinations for which populations had no chances 455 to persist up to end of simulation time (see Fig. 3). Distribution of trait for increasing mutation. Examples of the distribution of 457 trait φ for increasing mutation M at the end of simulation time. All simulations 458 performed with s = 3 and βsd = 0.0010.
M
= 0.05 M = 0.10 M = 0.15 M = 0.20
number of offspring produced by following a pattern-oriented procedure[23]
caused by an extreme event). If no, the individual j does not reproduce. This
introduces the Allee effect[24], that is a positive density-dependent effect at
low densities through higher mating opportunities. Then, we proceed to (j+2)
φ drawn from a uniform distribution bounded between (0,1)(Fig.2). We chose a
,28, 29, 30] and changes in community structure and ecosystem function [31, 32,
biotic invasions, Mol. Ecol. 1 (2008) 361-372.
[2] IPCC. Contribution of Working Group I to the Fourth Assessment Report of the
Nature 427 (2004) 332-336.
[10] M.G. Turner, Disturbance and landscape dynamics in a changing world.
Ecosystems 9 (2006) 330-343.
Acknowledgements 340The authors thank Luca Bolzoni and Kate Richerson for discussion and comments 341 which greatly increased the quality of the manuscript. 342
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Episodic death 405 across species of desert shrubs. M N Miriti, S Rodriguez-Buritica, S J Wright, H F Howe, Ecology. 88M.N. Miriti, S. Rodriguez-Buritica, S.J. Wright, H.F. Howe, Episodic death 405 across species of desert shrubs, Ecology 88 (2007) 32-36.
Drought induces lagged tree 407 mortality in a subalpine forest in the Rocky Mountains. C Bigler, D G Gavin, C Gunning, T T Veblen, Oikos. 116C. Bigler, D. G. Gavin, C. Gunning, T. T. Veblen, Drought induces lagged tree 407 mortality in a subalpine forest in the Rocky Mountains, Oikos 116 (2007) 1983-1994.
Impact of an extreme climatic event on community 409 assembly. K M Thibault, J H Brown, PNAS. 105K. M. Thibault, J. H. Brown, Impact of an extreme climatic event on community 409 assembly, PNAS 105 (200) 3410-3415.
Long-term oscillations in grassland 411 productivity induced by drought. N M Haddad, D Tilman, J M Knops, Ecol. Lett. 5N.M. Haddad, D. Tilman, J.M.H Knops, Long-term oscillations in grassland 411 productivity induced by drought, Ecol. Lett. 5 (2002) 110-120.
Europe-wide reduction in primary productivity caused by the 413 heat and drought in 2003. Ph, Ciais, Nature. 437Ph. Ciais et al., Europe-wide reduction in primary productivity caused by the 413 heat and drought in 2003, Nature 437 (2005) 529-533.
| sample_1644 | 0.7883 | arxiv | |
Scientists' Warning on Technology
Bill Tomlinson
Department of Informatics
University of California
92697Irvine, IrvineCAUSA
School of Information Management
Victoria University of Wellington -Te Herenga Waka
WellingtonNew Zealand
Andrew W Torrance
School of Law
University of Kansas
66045LawrenceKSUSA
Sloan School of Management
Massachusetts Institute of Technology
02142CambridgeMAUSA
William J Ripple
Department of Forest Ecosystems and Society
Oregon State University
97331CorvallisORUSA
Scientists' Warning on Technology
1 * Corresponding author.
In the past several years, scientists have issued a series of warnings about the threats of climatechange and other forms of environmental disruption. Here, we provide a scientists' warning on how technology affects these issues. Technology simultaneously provides substantial benefits for humanity, and also profound costs. Current technological systems are exacerbating climate change and the wholesale conversion of the Earth's ecosystems. Adopting new technologies, such as clean energy technologies and artificial intelligence, may be necessary for addressing these crises. Such transformation is not without risks, but it may help set human civilizations on a path to a sustainable future.second warning, 2 updating the information provided by the 1992 notice; this document has been signed by more than 15,000 scholars across many different scientific fields. Since that time, scholars around the world have begun to publish a series of "Scientists' Warning" articles, detailing perspectives from their particular disciplines to document the array of environmental issues currently threatening the Earth. To date, 39 articles have been published, and more than 50 more are currently in preparation. Collectively, these articles seek to offer a broad understanding of ways that humanity is undermining the foundation of its own existence.Two key articles in the Scientists' Warning series-"Scientists' Warning on Population" 3 and "Scientists' Warning on Affluence" 4 -index into a set of concerns that rose to prominence several decades ago as part of the so-called I=PAT equation. 5,6 This equation describes environmental impact (I) as being a function of population (P), affluence (A), and technology (T). While technology is equally salient to these discussions as population and affluence, to date, there has not been an article providing a scientists' warning on technology. This article seeks to fill that gap.In this article, we have adapted the definition of technology originally suggested by Stanford scientist Brian Arthur 7 , and define technology as "a quantifiable and duplicatable means to fulfill a human purpose." Technologies are typically developed by human civilizations to solve problems and produce benefits for people (e.g., the Haber-Bosch process to produce fertilizer for enhanced agricultural productivity, steam engines to manufacture and distribute consumer goods, automobiles to support largescale mobility, etc.). However, those very technologies create problems of their own (often called costs or externalities 8 in economics and related fields), via a variety of social and environmental impacts (water pollution, social inequality, climate change, etc.). This dual nature of technology-that of both solving and creating problems-provides the underpinnings for the core argument of this article.Here, we focus on two domains of technological innovation as exemplars of the range of forms technology can take: clean energy technologies 9,10 and artificial intelligence (AI). 11,12 The benefits of clean energy technologies, such as electrification, regarding climate change and other environmental issues are well-established. 9,10 The benefits of AI in these domains are promising but still emerging. 11,12 achieve long-term societal goals. Nevertheless, even though new technologies will come with new harms, the harms of current technologies (e.g., climate change) are so severe that it is imperative to pursue new technologies that can supplant the old. Humanity should not allow the potential for future harm to prevent itself from pursuing critical technological change.And finally, we warn that, although technology will almost certainly be a central part of a large-scale human response to environmental degradation, technology alone will not be enough; we need "deep economic, political, and cultural adjustments",15and new narratives that help people acclimate to new ways of life. There are efforts afoot to develop technologies that can support such efforts to develop and spread new narratives; 17 we encourage technological innovations that help envision sustainable futures and help people learn how to bring them into existence.Technologies represent crucial tools that, along with economic, political, and cultural shifts, can help humanity address the looming issues threatening life on Earth. This article seeks to provide a theoretical framework for thinking about the various benefits and harms that arise from current and future technological systems, and how to integrate them with civilization-scale transitions to sustainability.
Introduction
In 1992
, the Union of Concerned Scientists issued a warning to humanity, writing: "great change in our stewardship of the [E]arth and the life on it is required, if vast human misery is to be avoided and our global home on this planet is not to be irretrievably mutilated", 1 In 2017, a team of scientists published a While both of these technologies have great potential, they also entail various risks, from electronic waste and (temporary) job displacement for electrification technologies 9 to runaway energy use and existential threats from potential future superintelligences for AI. 13 While technology has played a key role in both bringing about many of the global challenges humanity currently faces, and may also play a key role in mitigating them, we warn against placing too much faith in technology to solve such issues singlehandedly. 14 As a 2012 National Academies report titled Computing Research for Sustainability states: "Despite the profound technical challenges involved, sustainability is not, at its root, a technical problem, nor will merely technical solutions be sufficient.
Instead, deep economic, political, and cultural adjustments will ultimately be required, along with a major, long-term commitment in each sphere to deploy the requisite technical solutions at scale.
Nevertheless, technological advances and enablers have a clear role in supporting such change." 15 In that spirit, we offer three warnings relating to technology.
First, we warn that some current technologies are creating great harm through climate change and habitat loss, and that these technologies should be phased out as soon as possible. Accordingly, we encourage rapid and comprehensive decarbonization 10 and other technological shifts 11 to reduce the harms brought about by current technologies. This phase-out may be enabled by broad-scale adoption of electrification technologies, an embracing of the possibility of allowing AI to help coordinate and augment our abilities to address the global sustainability challenges facing humanity, and research and development on other technologies that may support these efforts. In addition, we also discuss the possibility of undesign 16 , the act of intentionally extracting technology from a given context. Second, we warn that future technologies are likely to produce harms of their own, only some of which we can predict in advance; while we encourage pursuing these new technologies with vigor as substitutions for current harmful technologies, we also encourage vigilance about the potential for future harm. Initiatives to pursue innovation should be intertwined with important threads of research about harm prevention. This article provides an array of perspectives emerging in technological fields about how to integrate rapid technological transformation with appropriate reduction of harmful externalities to technological improvement, but also proposed that material consumption and human population all combined with technology to degrade the environment. 5 To help clarify the terms of the debate, Ehrlich and Holdren adapted a simple mathematical formula that Commoner 6 had included in a footnote (p. 211-212) to yield an equation that attempted to illustrate the relationships among what they termed population, affluence, and technology. This equation 5 is as follows: I = P * A * T For Ehrlich and Holdren, I represented impact on the environment, P the human population, A affluence (that is, wealth per person), and T technology (that is, impact on the environment per wealth per person). These three variables were carefully defined so that, when multiplied, P, A, and T would cancel out of the equation, leading to the identity I = I; conversely, P, A, and T may themselves be decomposed to highlight additional subfactors as long as all factors may still cancel out to yield I = I. Another useful characteristic of the I=PAT equation stemmed from the fact that the relationship among P, A, and T was multiplicative; consequently, a rise or fall in any of these variables had the potential to change I. For I to rise, PAT would have to increase, and, for I to decline, PAT would have to decrease. For example, if, during one year, population rose by 2% and affluence rose by 4%, T would have to decrease by 6%-in other words, the impact on the environment per unit of wealth per person would have to decline-simply to prevent I from growing.
Until recently, human population had grown robustly for hundreds of years. Worldwide population grew by about 2% in 1970 22 (the date the I=PAT equation was conceived), while, in the same period, the world economy (a measure of affluence) grew by about 8% per capita. 22,23 Though complicated to measure, it is unlikely that the annual rate of technological improvement, as measured by the T factor, has ever approached 10% since the Industrial Revolution. Simply put, the P and A factors have routinely outrun improvements in technology that reduced impact. Nevertheless, since 1970, growth in both population and affluence have slowed substantially. These changes, combined with the invention of powerful new technologies discussed below, offer the possibility that T may soon more than counterbalance the effects of P and A, driving I in a desirable direction: downwards.
How might this occur? The technological improvements discussed later in this article-most prominently, clean energy technologies and artificial intelligence-offer a pathway to dramatic reductions in carbon emissions and in other environmental harms, and the possibility of staggering transformations across a wide swath of human activity. These changes may be sufficient to cause humanity to enter an age in which the T factor in I=PAT grows at a rate large enough to withstand (continued but slowing) growth in both P and A.
The Dual Nature of Technology
Technology is usually created to fix some sort of problem. As anthropologist Joseph Tainter has written: "Over the past 12,000 years, we have responded to challenges with strategies that cost more labor, time, money, and energy, and that go against our aversion to such costs. We have done this because most of the time complexity works. It is a basic problem-solving tool. Confronted with problems, we often respond by developing more complex technologies, establishing new institutions, adding more specialists or bureaucratic levels to an institution, increasing organization or regulation, or gathering and processing 7 And, as new technologies become available, they often substitute for existing ways of living (see Fig. 1, showing the substitution of cars for horses in the US in the 1900s). [29][30][31][32] Technologies are often framed as force multipliers for human activities (e.g., in military, 33 healthcare, 34 and many other domains). The sustainability domain is no exception, with technological innovations working alongside existing human efforts to preserve the environment and improve long-term wellbeing. 15 Particular technologies, however, have been and continue to be accountable for creating profound societal costs as well. Technological innovations have supported human efforts at hunting and agriculture for thousands of years, at the cost of the overexploitation of many animal species 35 and deforestation 36 around the world. Digital technologies have enabled human communication and connection, but have perpetuated biases that are harmful to millions of people. 37 An array of technologies have contributed to pervasive health risks for billions of people 38 (even though the broader arc of technology appears to bend toward greater health, as evidenced by the trend toward increased human lifespan 25 ). And contemporary technologies, en masse, are contributing greatly to climate change, biodiversity loss, and many other environmental issues. 39 The potential for harm has sometimes served to curve innovation in human societies. For example, in Medieval Europe, numerous laws prohibited specific types of innovation. For example, in 14th Century France, "[t]o ensure that no one gained an advantage over anyone else, commercial law prohibited innovation in tools or techniques…" 40 Similarly, a social movement, named the "Luddites", arose during the Industrial Revolution in the United Kingdom. 41 Though the aims of the movement were somewhat complex, the Luddites challenged innovations, such as the Spinning Jenny, that allowed one person to do the work of several. The English romantic poet Lord Byron himself made passionate speeches in the British Parliament, hoping to convince the government to ban such technological advances as harmful to laborers. 42 While the benefits of technology often serve those creating the technology or funding its development, the costs are often accrued by people other than the creators, by non-human species, or via diffuse effects across long periods of time and/or space. These costs are sometimes referred to as "negative externalities" by economists. For example, the invention of the internal combustion engine allowed humans to travel and transport products rapidly over long distances, but drove demand for fossil fuels whose mining caused habitat destruction, and whose combustion emitted damaging pollutants like sulfur dioxide, nitrogen oxides, lead, particulate matter, carbon monoxide, and carbon dioxide. 43 The acronym NIMBY, meaning "Not In My Back Yard", reflects a sentiment that many people prefer not to have infrastructures (e.g., roads, train tracks) or harmful byproducts (e.g. nuclear waste) located or stored in areas near where they live. 44 The concept of "sacrifice zones," 45 Technological innovations are often energy intensive. 24 Modern technology has a particularly close relationship with one particular energy source-fossil fuel-that is both vastly powerful and vastly impactful in terms of pollutants such as carbon dioxide. 48 Looking backwards in time, technologies powered by fossil fuels, such as the steam engine, enabled the industrial revolution and its attendant vast increase in human living standards, but also facilitated social stratification through wealth accumulation and health effects, such as respiratory illnesses, across all social strata. 49 Currently, internal combustion engines enable mass mobility and global supply chains, through cars, trucks, ships, and trains; however, they are heavily implicated in a dramatic rise in CO2 concentrations in the atmosphere and accompanying climate change. 39 Many other fossil-fuel-powered technologies have spread rapidly through the industrialized world over the last century as well (see Fig. 2). 29 Climate change is one of the most urgent and important environmental threats currently facing Earth. Climate change is causing sea level rise, threatening to displace hundreds of millions 50 or even billions 51 of people, and altering myriad habitats for organisms worldwide. Climate change is impacting growing seasons and precipitation patterns, 52 which could undermine major elements of humanity's food infrastructure and food security. 53 And climate change is creating extreme weather events, which create profound harm for both humans and nonhumans. 54,55 Carbon emissions are also a major factor in ocean acidification. 56 While there are important efforts afoot to decarbonize many aspects of human civilizations, 9,10 carbon emissions from human technologies and activities are still rising, 57 and the effects of such emissions are likely to persist for many decades after any emissions slow-down, or even outright decrease, that may occur. 58
Figure 2: In the past century, fossil-fuel-intensive technologies have become ubiquitous in the US. 29
Fossil-fuel-powered technologies have also enabled the large-scale conversion of the Earth's ecosystems for use for agriculture and other human purposes. But many of these transformations have come at the cost of the forced migration of indigenous populations, 59 the disruption of non-human populations that resided there long before human occupation, 60 and the compromising or complete destruction of existing ecosystem services. 61 This conversion of ecosystems is a key factor in biodiversity loss and deforestation. 36 Many thousands of species are being threatened by anthropogenic environmental effects, potentially leading to what some scientists are calling the Sixth Great Extinction. 62 Biodiversity loss is also implicated in the spread of diseases such as Ebola. 63 In fact, biodiversity loss and climate change appear to affect one another substantially. Humans are transforming the Earth, incidentally creating great harm to the other species with whom we share the planet, to other humans in the future, and in many cases to other humans currently alive.
Technology Is Implicated in Environmental Harm
While a previous Scientists' Warning article has placed affluence in the key role causing such environmental transformations, 4 technology is nevertheless heavily implicated in these issues. Most of the harm arises from externalities of technologies; for example, fossil fuel companies do not seek to cause climate change via their emission of greenhouse gasses, but have traditionally not borne the costs of that harm due to unwillingness to sacrifice profits. 64 However, some forms of environmental harm are the express purpose of particular social or technological interventions; for example, the eradication of "pests" and "vermin" is typically very much intentional, as evidenced by the Australian policy that contributed greatly to the extinction of the thylacine. 65 Technological innovators may view themselves as neutral participants in the economy, but they are nevertheless complicit in the harms they propagate. We need to transform our cultures, politics, and societies to address these issues. And we need to transform how technologies amplify the impacts of our actions. In the remainder of this article, we use this conceptual basis to look forward toward technological approaches, and new forms of technology, that may help address these issues, and the effects and externalities that they will entail.
Toward Technological Change
An array of approaches to technology and technological change that have been discussed, many of which have relevance to the transition to a sustainable future. Table 1 provides a framework for understanding these approaches, structured around whether they are primarily concerned with present or future technological systems, and whether they focus on the benefits or costs of those systems. In the following subsections, we group these approaches into several high-level categories, that seek to a) reduce current harms, b) enable future benefits, c) reduce future harms, and d) enable new narratives that point toward sustainable futures.
Focus on Costs
Reducing Current Harms
A critical goal in addressing climate change is to reduce the use of currently harmful technologies, such as gasoline-powered internal combustion engines and coal-powered electricity plants. While the harm from these technologies are typically diffuse and pervasive rather than acute and local, there is nevertheless a strong scientific consensus that these technologies are heavily implicated in profound, long-term harm via pollution and global climate change. 39 The need for these changes are well established; we refer the reader to energy innovator Saul Griffith's excellent summary of the need to set aside these existing technologies. 9 We would also like to point to existing work on enabling transition pathways to allow human societies to abandon old technologies that are known to be harmful. 16,72,73 How exactly to disengage with the reduction in existing, widely-used technologies is a topic of some debate. Some activists propose that protests and divestment from fossil fuels are the best path forward. 74 "Fossil fuel divestment stigmatizes the fossil fuel industry for its culpability in the climate crisis and frames climate change as a moral crisis." 75 Others, such as Saul Griffith mentioned above, take a more conciliatory view: "Climate activists can fight the fossil fuel companies until the end of our lives, or Americans can come together, thank these companies for a century of service, and engage with them in the fight for our future." Regardless of the exact approach, the reduction, mitigation, or even elimination of technological systems with vast harmful externalities is critical to the future thriving of humanity and other species.
We see two main pathways for reducing, mitigating, or eliminating fossil-fuel-based technology. The first pathway involves technological substitution. The replacing of one technological system by another has been a common method for addressing the shortcomings of one technology when another is available. 66 For example, there are promising efforts afoot to substitute fossil-fuel-based systems with electrification and other clean energy technologies. 9 We discuss the benefits and costs of these technologies in a later subsection, and note that much of the electricity used in "clean" technologies, such as electric cars, still currently originates from burning fossil fuels.
The second pathway involves undesign. Undesign involves the "intentional negation of technology," 16 and "articulating the value of absence," 72 that is using the tools of design to offer alternative courses of action that do not entail continued use of a technology. Undesign seeks to reduce the usage of a particular type of technology, and as such, could be a useful approach for reducing fossilfuel-based technologies in some contexts. Nevertheless, undesign is difficult in contexts where people have come to rely strongly on particular goods and services; in such contexts, people may need to be guided to new cultural narratives in which those goods and services are less central. We discuss the need for new narratives below as well.
Both substitution and undesign need to push against resistance to change, which tends to focus on the benefits of the current systems (e.g., "the fact that we value the groups to which we belong, and therefore changing our attitudes or behavior is tantamount to leaving the comfortable embrace of a social reality of which we are a part" 71 ), regardless of their harms (especially their long-term, diffuse, or physically or temporally distal harms).
Whether via substitution or undesign, research into how to disconnect, or diminish the impact of, many different processes in industrial civilizations from their underlying fossil fuel technological infrastructures is of paramount importance.
Enabling Future Benefits
To enable the reduction or phasing out of fossil fuels, it is also critical to continue researching, developing, deploying, and evaluating novel forms of technology that may take its place. The adoption of new technologies may usher in an array of benefits. We use two main classes of technology as elucidating instances of the benefits that may arise from the deployment of new technologies: clean energy technologies and artificial intelligence.
Clean energy technologies include electrification technologies-from solar panels to electric transportation systems to heat pumps in every home. While electrification may not be able to address every aspect of decarbonization (e.g., long-distance aviation is difficult to achieve without energy-dense liquid fuels 10 ), large-scale electrification is a key component of "net zero" emissions energy systems. 10 Large-scale electrification will entail substantial changes to industrial infrastructures such as the energy grid; however, it should not require severe austerity or profound alterations in most people's lived experiences. 9 These technologies can allow humans in industrial civilizations to maintain similar standards of living as they do with fossil-fuel powered systems, but less expensively in the long run, and with far lower environmental impacts. 9 The second class of technology we discuss here is AI. AI does not impinge on near-term carbon emissions as dramatically and immediately as clean energy does, but it also shows great promise across longer time horizons. AI is already being used to enable land use reform via the planning of wildlife corridors, 76 to monitor methane emissions, 77 and to optimize supply chains. 78 Beyond those domains, AI has the potential to guide humanity to new ways of living that are currently beyond our abilities to conceive, develop, and deploy. AI is currently far less energy-intensive than humans at tasks such as writing and illustration that were previously almost exclusively the domain of human creativity, 79 which could have far-reaching implications for future visions of human civilizations. Similarly, AI is becoming quite competent at writing computer code (see Fig. 3), which could help manage the complexities of 8 billion plus people cohabiting on Earth. While AI is likely to make many human jobs obsolete, it may also enable the coordination of human systems far more effectively than humans have traditionally done. 80 (It is also likely to create entirely new classes of jobs. 81 ) It may open entirely new ways of undertaking other tasks, potentially transforming domains from individual wellbeing 82 to international diplomacy. 83 While current AI systems are not without their challenges (e.g., they are often wrong 84 ), there are efforts afoot to connect different types of AI systems together (e.g., large language models with knowledge graphs 85 ) to overcome the limitations of each genre.
Two technological approaches are relevant here: a "technology within limits" perspective, 68 As technology seeks to serve such long-term goals, we encourage technological innovators to engage with their work using a "limits" perspective. (A limits perspective may be juxtaposed with "technological evangelism," 70 a term often used for an approach primarily focused on the benefits of technology; while evangelism is sometimes seen as being uninterrogated and "hype" focused, it may be a useful approach as well, for example, in overcoming resistance to change.) 86 VSD 67 offers a framework for thinking about the benefits (and also the harms) of future technological systems. VSD integrates with the substitution approach discussed earlier, as VSD seeks to foster the development of technological changes that are aligned with human values, both in terms of the new systems that will be adopted, and the old systems that will be supplanted.
Despite the great potential for these technologies across many domains, we nevertheless caution against unbridled techno-utopianism. Technological development is famous for failing to deliver on "quick fixes" and other promises of change. 14 While the pressing demands of environmental crises encourage a vigorous pursuit of technological change, we now want to turn to the challenges implicated in these potential future technologies, and encourage vigilance against likely future problems that they may pose.
Reducing Future Harms
While broad adoption of clean energy technologies has powerful benefits, given the need to address climate change, such technologies are likely to create or exacerbate some environmental and social problems in the future, such as human rights abuses associated with cobalt mining, 87 proliferation of electronic waste, 88 and short-term job displacement (although it is likely to create even more jobs on a longer time horizon). 9 There are almost certainly other challenges, decades in the future, that will not become apparent until electrification has become as pervasive as fossil fuel-based energy systems now are. While it is critical in the present to electrify as rapidly as possible to maintain high standards of living while phasing out fossil fuels, it nevertheless remains relevant with electrification, as with all human technologies, to remain vigilant about future harms that may arise from this new energy system.
The long-term risks of the proliferation of AI are perhaps more broadly concerning. One possible future harm involves the runaway use of energy. Regardless of how much clean energy we may be able to derive from broad-scale electrification, future AI may be able to use it in the quest for ever more highly optimized human processes, ever finer personalization of content, and other human goals. Current AI models require energy on par with several car lifespans to train them; 13,89 regardless of how large future energy resources may be, future AIs will almost certainly be able to increase its energy uses until it is operating in a context of limits. 68 (We note that, at present, the carbon emissions of AI engaging in many tasks is still far less than the emissions produced by humans doing the equivalent work. 79 ) A second concern involves the problem of autonomous AIs becoming independent and powerful enough that they pose a real danger to humanity. This concern is sometimes explored under the moniker of the "alignment problem". 90,91 The alignment problem involves understanding how to align the goals of a very powerful AI with the goals of its creators, or of humanity more broadly. 90,91 Science fiction has been rife with instances of dangerous AI superintelligences, from The Terminator to The Matrix; nevertheless, concern with the alignment problem is now entering more traditional scientific discourse as AI becomes more powerful. 90,91 In addition to these existential concerns, AI could propagate an array of other harms, from perpetuating biases, 37 to overoptimizing systems in violation of human values, 92 to empowering crime. 93 While we identify here an array of potential future harms from both electrification and AI, we believe that these harms are substantially less problematic than these technologies' potential benefits from addressing the pressing environmental crises that humanity is currently facing.
To address the externalities that may arise from both of these forms of technology, technologists must engage with design processes that grapple with those issues from the outset, rather than seeing them as a secondary concern. Design processes that take many stakeholders into account, including nonhuman species and ecosystems, 94 have a greater chance of doing so effectively. 95 One approach to addressing the harms of future technologies is a "benign technology" perspective. 69 This perspective also arose out of computing; we present an adapted version here, expanded to encompass all technology:
We propose one possibility: benign [technology], a general design framework for building [technological] systems that are less likely to produce harmful impacts to the ecosystem (and thus to human society) and are less likely to become trapped by Sevareid's Law (that "the chief source of problems is solutions"). (Adapted from Raghavan. 69 )
The benign technology principle involves exerting effort to identify and address externalities.
"[W]hen we do build things, we should engage in a critical, reflective dialog about how and why these things are built." 72 VSD 67 , discussed earlier, also addresses the prospect that preventing harm from future technologies should be central to the process of technological innovation.
We encourage technologists to engage with both the benefits and the harms of the technologies they are creating as well as of those they are supplanting.
Enabling New Narratives
Finally, researchers should seek to create and study technologies that teach and inspire people to consider new narratives that could underpin how our civilizations interact with the ecosystems in which they are embedded. While some efforts at enacting change may allow for human lives in the industrialized world to continue largely unchanged, 9 there are also important calls for new cultural narratives that do not involve the many forms of environmental harm that are closely intertwined with modern market economies. As environmental journalist George Monbiot has written, "[w]e have to come together to tell a new, kinder story explaining who we are, and how we should live." 96 Technology can help articulate such new stories, and teach them to potentially billions of people.
The question of what narratives are needed relates to the two exemplar technology domains we have discussed above. Clean energy technologies are likely to integrate with existing lifestyles in the industrialized world sufficiently that they may not entail substantial shifts in how we live our lives.
However, to realize the potential of AI, we may need to undertake substantive shifts in lifestyle. We will need to develop new cultural narratives that align with sustainable futures. 97 Hopefully, these shifts will be in the direction of higher quality of life. "The only way you can change a story is to offer a new one.
And you can do so only by producing a better story." 97 An approach called design fiction (defined as "the deliberate use of diegetic prototypes to suspend disbelief about change" 98 ) can be used to help envision new futures. Design fiction has been used to envision sustainable futures in particular. 99 This approach to the design of technology can help people think in a "different conceptual space" 98 , and thereby get past the confines of present technologies and present cultural norms and expectations to conceptualize the transition to sustainability.
We issue a global appeal for technology developers and researchers to develop new technologies, and for artists, designers, and storytellers to develop new narratives, that help civilizations integrate these technologies in ways that improve human lives, the lives of non-human species, and the prospects for the future of life on Earth. Many people feel that technology will save us. But it will only save us if we develop cultural norms that allow it to do so. " [O]nly widespread changes in norms can give humanity a chance of attaining a sustainable and reasonably conflict-free society." 100
Scientists' Warnings
This article is a warning, but it is a warning in three parts. The first part warns that current technologies are causing profound environmental and social harm. It is critical to phase out these technologies as soon as possible.
The second part warns that, as human civilizations deploy new technologies in the process of phasing out current technologies, it is important to remain vigilant for potential future harm, and attempt to reduce that harm as much as possible. Nevertheless, despite their potential to cause various forms of harm, we strongly believe that the potential for future technologies, and in particular clean energy and AI technologies, to enable human civilizations to address the current, dire environmental problems such as climate change and biodiversity loss are well worth the future technological risks these systems may engender. We offer this warning because there is a real risk that human civilizations will fail to transform their energy systems, infrastructures, cultures, politics, and societies fast enough to avert the potentially catastrophic impacts of environmental disruption and societal collapse. Therefore, this warning is here to warn humanity not to fear these changes, and not to fail to make these changes, but instead to embrace the possible futures that these technologies may enable.
The final part of the warning is that, while technology is very powerful, and has been instrumental in shaping many aspects of the world humans have made over the past several thousand years, technology alone will likely be insufficient to enable a transition to a sustainable future. Sustainable futures will require profound shifts in culture, politics, and society more broadly. 15 We hope that the myriad technological fields will support these transitions as effectively as possible, rather than becoming entrenched in business as usual. Sustainable futures can hopefully support the long-term wellbeing of humanity and many other species, and technology can hopefully help bring these futures into existence.
We propose that the following is an admirable goal for this effort: the indefinite continuation and ongoing well-being of the human species and other currently existing species. This goal is unachievable, since various individuals and species are inherently in conflict, via food webs, competition for habitat, etc. Nevertheless, we see it as a target at which to aim our efforts. And we anticipate that technological change will be integral to working toward that goal.
Figure 1 :
1This chart shows the substitution of cars for horses that occurred in the US in the 1900s. Many technologies of the 1800s---carriages, carts, plows, etc.---were often horse powered, and thus the number of horses serves as a proxy for the prevalence of such technologies.
too, reflects the phenomenon of people in power sacrificing the wellbeing of regions and communities distal to themselves by causing or allowing pollution and other harmful materials to accumulate there. Nevertheless, many current human cultures embrace, and are characterized by, technological innovation. For example, the vast majority of countries in the world are members of technologypromoting treaties such as the Paris Convention on the Protection of Industrial Property, the Patent Cooperation Treaty, and the World Trade Organization Trade-Related Aspects of Intellectual Property agreement. 46,47
and the value sensitive design (VSD)67 framework. While the "limits" perspective was developed within the computing field, we see it as being relevant to technology more broadly. We present here a modified version of two of the key insights presented byNardi et al. in their foundational article on the topic: We [propose] that [technology fields] transition toward '[technology] within limits,' exploring ways that new forms of [technology] may support well-being for both humans and non-human species while enabling human civilizations to live within global ecological and material limits. [Technology] underlies virtually all the infrastructure of global society, and will therefore be critical in shaping a society that meaningfully adapts to global limits. (Adapted from Nardi et al. 68 )
Figure 3 :
3This figure shows output from the ChatGPT AI system running GPT-4 creating a simple simulation of a clean energy-based power grid.
Table 1 :
1A matrix showing various approaches to technological change, grouped based on whether they focus on present technology vs. future technology, and whether they focus on the costs or benefits of those technologies.
AcknowledgmentsThis material is based upon work supported by the US National Science Foundation under Grant No. DUE-2121572.Competing InterestsThe authors declare no competing interests.
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Author Contributions. Author Contributions
conceived the project. B.T. led the writing of the manuscript and creation of the figures. B T , A , B.T. and A.T. conceived the project. B.T. led the writing of the manuscript and creation of the figures.
wrote the I=PAT section and contributed content and revisions throughout the manuscript and figures. W.R. contributed content and revisions throughout the manuscript and figures. All authors reviewed and confirmed the final manuscript. A T , A.T. wrote the I=PAT section and contributed content and revisions throughout the manuscript and figures. W.R. contributed content and revisions throughout the manuscript and figures. All authors reviewed and confirmed the final manuscript.
| sample_1655 | 0.9827 | arxiv | |
Accelerating Exploration of Marine Cloud Brightening Impacts on Tipping Points Using an AI Implementation of Fluctuation-Dissipation Theorem
Haruki Hirasawa
University of Victoria
VictoriaBCCanada
Sookyung Kim sookim@parc.com
Palo Alto Research Center
Palo AltoCA, US
Peetak Mitra
Palo Alto Research Center
Palo AltoCA, US
Excarta, Palo AltoCA, US
Subhashis Hazarika
Palo Alto Research Center
Palo AltoCA, US
Salva Ruhling-Cachay
Palo Alto Research Center
Palo AltoCA, US
University of California San Diego
San DiegoCA, US
Dipti Hingmire
University of Victoria
VictoriaBCCanada
Kalai Ramea
Palo Alto Research Center
Palo AltoCA, US
Hansi Singh
University of Victoria
VictoriaBCCanada
Philip J Rasch
University of Washington
SeattleWA, US
Accelerating Exploration of Marine Cloud Brightening Impacts on Tipping Points Using an AI Implementation of Fluctuation-Dissipation Theorem
Marine cloud brightening (MCB) is a proposed climate intervention technology to partially offset greenhouse gas warming and possibly avoid crossing climate tipping points. The impacts of MCB on regional climate are typically estimated using computationally expensive Earth System Model (ESM) simulations, preventing a thorough assessment of the large possibility space of potential MCB interventions. Here, we describe an AI model, named AiBEDO, that can be used to rapidly projects climate responses to forcings via a novel application of the Fluctuation-Dissipation Theorem (FDT). AiBEDO is a Multilayer Perceptron (MLP) model that uses maps monthly-mean radiation anomalies to surface climate anomalies at a range of time lags. By leveraging a large existing dataset of ESM simulations containing internal climate noise, we use AiBEDO to construct an FDT operator that successfully projects climate responses to MCB forcing, when evaluated against ESM simulations. We propose that AiBEDO-FDT can be used to optimize MCB forcing patterns to reduce tipping point risks while minimizing negative side effects in other parts of the climate.
Introduction Marine Cloud Brightening
Tipping points in the climate system are critical components of the climate response to anthropogenic warming, as they have the potential to undergo rapid, self-perpetuating, and possibly irreversible changes (McKay et al. 2022). Should warming approach or cross a threshold that activates such a tipping point, the damage caused by crossing the threshold may be sufficiently severe that a climate intervention ought to be undertaken to prevent it. One such class of interventions are solar radiation modification (SRM) methods which slightly modify the climate's energy budget by scattering away a portion of incoming sunlight (also called solar radiation) to counter some of the effects of greenhouse warming.
Here, we consider one such SRM technique, Marine Cloud Brightening (MCB), in which sea salt aerosols would be injected into marine boundary layer clouds to increase Copyright © 2022, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. their albedo (Latham et al. 2012). If MCB were to be deployed with the aim of limiting tipping point risk, it is crucial that we carefully assess if MCB does indeed reduce these risks and rule out MCB scenarios that might cause unintended climate changes or exacerbate tipping points (Diamond et al. 2022). Due to the short atmospheric lifetime of tropospheric aerosol particles, MCB interventions would be highly localized. This presents both a substantial challenge and a potential opportunity, as the possibility space of MCB interventions is vast, both in terms of strength and spatial pattern. Thus, a thorough assessment of the feasibility of MCB interventions must consider a wide range of potential scenarios. On the other hand, it may be possible to find specific patterns of MCB intervention that achieve desirable climate effects while minimizing negative side effects.
Typically, the effect of MCB is evaluated using simulations in Earth System Models (ESMs), which are comprehensive, dynamic models of the coupled atmosphere-oceanland-ice system (Rasch, Latham, and Chen 2009;Jones, Haywood, and Boucher 2009;Stjern et al. 2018). However, ESM simulations are computationally expensive, requiring tens of thousands of core-hours to obtain sufficient sample sizes to assess the impact of a given intervention scenario. Thus, they are impractical as tools to explore a wide range of possible MCB intervention patterns. To accelerate this exploration, we have developed AiBEDO, an AI model that emulates the relationship between atmospheric radiative flux anomalies and resulting surface climate changes. By using AiBEDO to project the climate impact of cloud radiative flux anomalies, we can rapidly evaluate the impact of MCBlike perturbations on the climate.
Fluctuation-Dissipation Theorem
As there are few MCB forcing simulations that have been conducted in the most recent generation of Coupled Model Intercomparison phase 6 (CMIP6) ESMs, we cannot train on an existing repository of ESM responses to MCB forcing. Thus, the design philosophy of AiBEDO borrows from the Fluctuation-Dissipation Theorem (FDT), a theorem emerging from statistical mechanics that posits that the response of a dynamical system to a perturbation can be inferred from the time-lagged correlation statistics of natural inter-nal fluctuations in the system (Kubo 1966;Leith 1975). Because the climate is such a dynamical system, FDT has been used to estimate the linear response of the climate to a range of forcings: CO 2 doubling and solar radiation perturbations (Cionni, Visconti, and Sassi 2004) and regional ocean heat convergence anomalies (Liu et al. 2018), among others. If the statistics of the dynamical system are Gaussian, the FDT operator L can be computed by convolving the covariance matrix between the predictor variables x and predictand variables y, C y, x (τ ), and the autocovariance matrix of x, C x, x (0), over time lags τ . The climatological mean response δ y = y − y (angle brackets indicating the climatological mean) to a constant forcing δ f is then computed as
δ y = L −1 δ f = ∞ 0 C y, x (τ )C −1 x, x (0)dτ δ f(1)
As FDT is limited to the linear component of the climate response, we seek to use an AI model with the intention of capturing both linear and non-linear components of the response and loosening some of the conditions required by classical FDT (namely that the probability density function of the relevant climate statistics must be Gaussian or quasi-Gaussian; see Cionni, Visconti, and Sassi 2004;Majda, Abramov, and Gershgorin 2010).
Here, we define an AiBEDO operator A τ ( x i (t)), which maps the statistical relationship from a given input x i (t) field to an output y i (t + τ ) field after some time lag τ ,
A τ ( x i (t)) : x i (t) → y i (t + τ ) .
(2) with i indexing the different initial conditions sampled from internal climate noise. Due to uncertainties in the initial condition x i (from monthly averaging and discrete sampling of the fields) and the chaotic dynamics of the system, there is no unique mapping from a given input x i (t) to a later output y i (t + τ ). Rather, AiBEDO projects the mean of the distribution of possible y i (t + τ ) trajectories after τ months given the initial conditions x i (t). We denote this mean using an overline, and the output of AiBEDO as y i (t + τ ). If we consider a case where x i (t) is perturbed by a infinitesimally small one-month forcing δf , the mean evolution becomes A τ ( x i + δf ) = y i (t + τ ). Linearizing the response, we approximate the effect of the forcing as
δ y i (t + τ ) = y i (t + τ ) − y i (t + τ ) = A τ ( x i (t) + δf ) − A τ ( x i (t))(3)
We assume that the time-mean climate response is equivalent to the mean response across many different initial conditions x i (ergodicity). Thus, we can compute the climate mean lag-τ response to a time varying forcing δ f (t) by averaging over N samples of internal variability x i . Following FDT, we then integrate the average lag-τ responses from τ = 0 to some upper limit τ = T max , where the response to a perturbation approximately converges to noise (we choose 48 months), to obtain the climate mean response:
δ y(t) = Tmax τ =0 1 N N i=0 A τ ( x i + δ f (t − τ )) − A τ ( x i )(4)
This allows us to replace the linear response function of classic FDT with a non-linear AiBEDO response function. Note, we assume there are no non-linearities between the AiBEDO responses at different lags (i.e., that the effect of δ f (t) is not affected by the changes induced by δ f (t − 1), δ f (t − 2), etc).
In this study, we discuss the model architecture and training data used to construct this novel AI-based approach to FDT, evaluate the performance of AiBEDO when emulating climate noise, and present a comparison of the AiBEDO response to MCB-like perturbations to the responses in the fully-coupled ESM. Finally, we propose strategies for estimating uncertainties in the AiBEDO response and exploring the possibility space of MCB intervention scenarios using AiBEDO. By assessing a wide range of MCB scenarios on a scale not possible with ESM experimentation, we aim to determine optimal scenarios to avoid crossing potential tipping points and rule out scenarios with undesirable impacts on tipping points.
Methods
Model Architecture
Here, we describe the generation of the AiBEDO operator A τ to map input radiative flux anomalies at time t (input:
x i (t) ∈ R d×cin ) to corresponding output surface climate variable anomalies after a time lag τ (output: y i (t + τ ) ∈ R d×cout ). To tackle this, we formulate the problem as a pixel-wise regression problem, learning a mapping from input fields to output fields, A τ : R d×cin → R d×cout , where d is the dimension of the data, and c in and c out are input and output channels, respectively, that are comprised of climate variables (listed in Table 1). To train the model A τ , we minimize L mse , the pixel-wise mean squared loss between the estimated climate response output y and the ground-truth climate response y, averaged over all dimensions of output:
L mse = 1 c out d y t+l − y t+l 2 2 ,(5)
Spherical Sampling The ESM data we use here is originally on a regular latitude-longitude grid, which is difficult to utilize for training purposes due to the large differences in grid areas between points near the equator versus those at the poles. Specifically, it is challenging to accurately depict the Earth's rotational symmetry through the use of twodimensional meshes, leading to inaccurate representations of significant climate patterns in ML models that assume a two-dimensional format of data. For this reason, we utilize a geodesy-aware spherical sampling that converts the 2D latitude longitude grid to a spherical icosahedral mesh. Icosahedral grids are specified at the lowest resolution by defining twenty equilateral triangles to form a convex polygon, called an icosahedron. The vertices of the icosahedron are equally spaced points on the sphere that circumscribes it. The resolution of the mesh can be increased by dividing each edge of the icosahedron in half and projecting each new point onto the circumscribed sphere. By resampling in this manner, we are able to iteratively increase the resolution on the sphere. Here, we perform bilinear interpolation (non-conservative) from 2-D climate data to a level-5 icosahedral grid which whose vertices define a 1-D vector of length 10242 (i.e, d =10242) with a nominal resolution of ∼220 km.
Machine Learning method In this work, we utilize a Multi-Layer Perceptron (MLP) model. MLP models have proven to be effective for spatio-temporal modeling of ESM data (Park, Yoo, and Nadiga 2019;Wang et al. 2014). MLP is a representative structure of Deep Neural Networks (DNNs) in which an input and an output layer are inter-connected with multiple hidden layers. Each node in a given layer is fully connected with all nodes in the previous layer. The connection between any two nodes represents a weighted value that passes through the connection signal between them. A non-linear activation function is used in each node to represent non-linear correlation in the connection between nodes. The operation between consecutive layers is defined as multiplication between nodes in previous layer and corresponding weight parameters, and applying activation function.
Here, we use MLP with 4-hidden layers and 1024 nodes in each layer with layer normalization (Ba, Kiros, and Hinton 2016). We use Gaussian error linear units (Gelu) activation in each layer (Hendrycks and Gimpel 2016). We combine MLP with the spherical sampling approach to create an S-MLP architecture to generate A τ . A schematic of our S-MLP model architecture is shown in Figure 1.
Training data
Because the signal-to-noise ratio in short-term climate fluctuations is small, FDT requires a large amount of training data. We use a subset of the Community Earth System Model 2 Large Ensemble (CESM2-LE) as a source of internal climate variations (Rodgers et al. 2021) (Table 2), specifically the 50 ensemble members in which historical simulations are forced with smoothed biomass burning emissions between 1997 and 2014. Each of these 50 ensemble members is forced identically, but is initialized with different initial conditions, meaning that individual members differ only in the chaotic fluctuations internal to the climate system. As such, the CESM2-LE is one of the largest data sets of single-ESM CMIP6-generation simulations for training and testing our model, as it provides a total of nearly 100,000 months of data.
We use a set of six input variables and three output variables. These variables are listed in Table 1. The data are preprocessed by subtracting the ensemble mean of the LE at each grid point, month, and year of the historical time series. This removes both the seasonal cycle and long term secular trends in the data, leaving only monthly fluctuations internal to the system. We then bilinearly remap the data from the original 2D latitude-longitude ESM grid to the spherical icosahedral grid for use by the AI model using Climate Data Operators (cdo; Schulzweida 2022).
Validation dataset
To validate AiBEDO's ability to plausibly model the climate response to MCB-like perturbations, we compare the AiBEDO response to responses from a novel set of fully dynamic, coupled CESM2 simulations (Hirasawa et al. 2023). These simulations are summarized in Table 2. MCB forcing is imposed by increasing in-cloud liquid cloud droplet number concentrations to 600cm −3 within three selected regions in the northeast Pacific, southeast Pacific, and southeast Atlantic, together and separately in SSP2-4.5 simulations (Shared Socioeconomic Pathway 2 -4.5Wm −2 forcing). The effect of MCB is then calculated by taking the difference between the perturbed simulations and the baseline SSP2-4.5 simulations. In addition to the coupled CESM2 simulations, we have conducted "fixed-sea surface temperature" (fixed SST) simulations, wherein the MCB-like forcing is imposed in the model with SSTs held to climatological values. These are used to calculate the effective radiative forcing (ERF) due to the MCB forcing (Forster et al. 2016). AiBEDO is perturbed (δ f ) with the annual mean cres, crel, cresSurf, crelSurf, netTOAcs, and netSurfcs anomaly fields from the year-2000 MCB Perturbed minus year-2000 Control simulations. Thus, we can compare AiBEDO and CESM2 responses to the same MCB ERF. Note that it is crucial that δ f is computed using fixed SST simulations, as radiation anomalies computed this way do not include radiative feedbacks, which are considered to be part of the response rather than the forcing. In principle, the effects of these feedbacks are encoded in the mappings AiBEDO has learned. Thus, AiBEDO responses using radiation perturbations computed from coupled CESM2 simulations avoids "double counting" the effect of the radiative feedbacks.
In order to calculate the response to the radiative perturbations, we first run AiBEDO on 480 randomly sampled months of preprocessed CESM2 internal variability radiation anomalies to obtain a control ensemble of AiBEDO outputs. Then, we run AiBEDO on the same 480-month sample, but with the MCB radiation perturbations added to the variability, giving us a perturbed ensemble of AiBEDO outputs. The impact of the MCB perturbations is estimated as the difference between the control and perturbed AiBEDO outputs. This is repeated for the different time lags. This methodology ensures that the input anomaly fields in the simulations are not too different from the model training data set. Running AiBEDO with the regional radiation perturbations results in artifacts, as the near-zero anomalies outside the per-
Model training and inference
The decoupled weight decay regularization optimization method, AdamW (Loshchilov and Hutter 2017) was utilized to train our model in an iterative manner. The learning rate was initially set to 2 × 10 −4 and exponentially decayed at a rate of 1 × 10 −6 per epoch. We trained the model for 15 epochs with a batch size of 10. Our S-MLP models have ∼ 108M trainable parameters, and it takes around 1 minute per single epoch for training. The model inference takes an average of 0.5 seconds per data point to generate a prediction.
Results
Emulation of Climate Noise
We validate the baseline performance of AiBEDO for emulating the connection between input radiative fluxes to the output surface climate variables (i.e. equation 2) for a sample of preprocessed CESM2 data in Fig. 2 a-f from the CESM2's CMIP6 contribution, data that is not included in the training dataset but uses the same ESM and boundary conditions. This is done by first running AiBEDO with a set of preprocessed input variables from CESM2, then computing the root mean squared error (RMSE) of the resulting AiBEDO output time series with the corresponding lagged CESM2 output time series at each grid point. We find that the RMSE is generally highest in regions where internal variability is also high, such as high tas (Fig. 2a) and ps (Fig. 2e) RMSE at high latitudes and high pr (Fig. 2c) RMSE in the tropics. We then compute the ratio of the RMSE and the CESM2 standard deviation in time: smaller values identify regions where AiBEDO performs best relative to the internal climate noise. This ratio indicates that for all three output variables (Fig. 2b,d,f), AiBEDO performs substantially better in the tropics and subtropics and over oceans, with the tropical Pacific in particular being well represented (this may be a result of the high variance explained by the El Nino-Southern Oscillation). The ratio is slightly under 1 for much of the mid and high latitudes and over land, especially for pr, which may be a consequence of the removal of the seasonal cycle and less direct radiation-surface climate connections in these regions, as they are strongly controlled by synoptic variability. There are a few regions where AiBEDO has a greater than 1 ratio, notably for pr in the dry regions of the subtropical south Pacific and Atlantic 2d. This again may be a consequence of missing seasonal in- , and e,f show surface pressure (ps). Panels h,g show the normalized RMSE (h) and correlations (g) computed along the spatial dimension in solid lines for the three output variables from different AiBEDO lag models. Dashed lines show the normalized RMSE and correlation computed assuming that the anomaly at month 0 remains the same over time (i.e. the persistence null hypothesis). RMSE here is normalized by the climatological spatial standard deviation of the output variable anomalies.
formation, as the rainfall in the region is linked to seasonal shifts in the intertropical convergence zone. Fig. 2 g,h shows the spatial RMSE (normalized by the standard deviation) and correlation scores for different versions of AiBEDO trained at different lags respectively. As lag increases, the predictive skill of the model decreases as expected. Notably, we find that the model outperforms persistence consistently across time lags, indicating AiBEDO has learned a considerable amount of information beyond the simple memory of 0-month temperature anomalies. We see that AiBEDO performs better than background climate noise even at relatively long time 36-month time lags with best performance for precipitation, followed by temperature and surface pressure. Because the normalized RMSE becomes approximately one after 24 months and the correlation drops to zero at 48-months for all three variables, we select 48 months as the upper limit for the time lag integration.
Response to MCB perturbations
To validate that AiBEDO can plausibly project climate responses to MCB-like perturbations, we compare the CESM2 coupled model responses to those from the lag-integrated AiBEDO responses (i.e. equation 4) for radiative flux anomalies computed from fixed-SST MCB simulations. Here, we use a preliminary version of AiBEDO with lags τ = 1, 2, 3, 4, 5, 6, 12, 24, 36, and 48 months. To compute the lag integral we use Simpson's rule integration to interpolate between the unevenly spaced lags. Fig. 3 shows the CESM2 and AiBEDO responses for the three output variables. We find that AiBEDO is able to reproduce the pattern of climate response to MCB, with correlation scores of 0.83 for tas, 0.72 for pr, and 0.8 for ps. However, there are substantial discrepancies in the magnitude of the responses, with AiBEDO generally projecting larger anomalies than CESM2. This is reflected in the relatively high RMSE when comparing the fields. This magnitude discrepancy may be a result of the missing lags in the integration, which will be filled in future versions of the model. Nevertheless, AiBEDO successfully identifies key remote teleconnected responses to the MCB forcing, specifically the La Niña-like tas signal in the Pacific, with strong cooling in the tropical Pacific and warming in the midlatitudes east of Asia and Australia, as well as cooling over low-latitude land regions. One notable discrepancy is that northern Eurasia warms in AiBEDO, while there is a weak cooling tas signal in CESM2. This may be in part due to the low signal to noise of the response in this region. AiBEDO also reproduces key pr changes: it projects drying in northeast Brazil, central Africa, and southern North America and Europe and wetting in the Sahel, south and southeast Asia, Australia, and central America. Using these responses, we can estimate the tendency of MCB impacts to affect key regional tipping points. For example, Amazon and Sahel pr changes indicate increased risk of Amazon dieback and Sahel greening, respectively (Zemp et al. 2017;McKay et al. 2022). The general cooling of the tropical ocean suggests a reduced risk of coral dieoff tipping points. However, owing to the lower performance of AiBEDO at high latitudes, we may struggle to evaluate key crysopheric tipping points, such as Eurasian and North American permafrost loss.
We also assess the impact of MCB forcing in the individual NEP, SEP, and SEA regions compared to CESM2 simulations with equivalent regional forcing (Fig. 4). We find that AiBEDO performance is weaker when considering these regional perturbations than when all three regions are perturbed together. In particular, AiBEDO's performance when projecting the NEP forcing response declines from a global spatial correlation of 0.79 for ALL to 0.39 for NEP. AiBEDO correlations scores are better for SEA at 0.48 and best for SEP at 0.75. The weak NEP correlation is due to AiBEDO's too-strong La Niña-like response in the Pacific, possibly indicating that the model over-learns from the El Niño-Southern Oscillation at the expense of other modes of variability. Nevertheless, AiBEDO correctly attributes climate responses to the different forcing regions in several key regions. For example, it correctly identifies that SEP forcing causes La Niña-like cooling and increases in South Asian, West Africa, and Australian rainfall; and finds that SEA forcing causes tropical Pacific warming and Amazon drying (not shown). In all four cases, AiBEDO performs better in the tropics relative to higher latitudes and better over oceans (Fig. 4b) than over land (Fig. 4c). This aligns with the regions where AiBEDO emulation skill is the highest (Fig. 2b), indicating that the ability of the model to correctly project climate responses to MCB forcing is closely related to its ability to emulate internal variability.
Discussion
In this study, we present a novel framework for rapidly projecting climate responses to forcing by replacing the linear response function in FDT with a non-linear AI model, which we name AiBEDO. AiBEDO is a MLP model with spherical sampling that maps the relationship between monthlymean radiative flux anomalies and surface climate variable anomalies. The model successfully emulates the connection between variations in radiative fluxes and surface climate variables out to lags of several months. We verify AiBEDO's projections for the case of MCB by comparison to fully coupled CESM2 MCB responses and find that our model is able to skillfully project the pattern of surface temperature, precipitation, and surface pressure response to MCB. We argue the model has sufficient skill to to be useful in estimating the effects of MCB interventions on regional climate indices related to key tipping points, particularly at low latitudes and over oceans. For example, AiBEDO projections reproduce rainfall decreases in the southeast Amazon and increases in the Sahel found in reference CESM2 MCB simulations, indicative of increased risks to tipping points associated with Amazon dieback and Sahel greening.
To the authors' knowledge, this is the first application of Fluctuation-Dissipation theory to climate data using AI methods. We use a generalization of linear FDT with which we can use a non-linear model to generate mean climate responses to radiative flux anomalies. Notably we use a large single-ESM ensemble of climate model data, which is crucial for AiBEDO to successfully learn the mapping between climate variables, particularly as the time lag increases. Thus, large ensembles like the CESM2-LE are vital resources for training models like AiBEDO. This produces a novel AI model that can plausibly project the impact of MCB on climate, opening the possibility of exploring forcing scenarios on a vastly larger scale than is possible with ESMs.
We note that while we have selected radiative flux variables as inputs and surface climate variables as outputs here, in principle AI-FDT can be applied to any set of inputs and outputs for which there is sufficient signal-tonoise for a model to learn. Thus, AI models of this kind have the potential to serve as tools with which large existing datasets can be leveraged to generate first look estimates prior to undertaking computationally expensive new ESM simulations, as an AiBEDO projection can be generated in O(10 1 ) processor-seconds while just one of the coupled CESM2 MCB simulations we performed here required O(10 9 ) processor-seconds.
Future Work
To provide practical information about climate responses to forcing, we must estimate the uncertainty in the projec-tions. Here we only consider the uncertainty due to internal variability in the input data when running AiBEDO, but we must also consider uncertainty due to the underlying training dataset. In particular, because ESMs are only an approximation of the real world, different ESMs exhibit different internal fluctuations. In the case of climate modeling, multi-ESM ensembles, made possible by the Coupled Model Intercomparison Project (CMIP), can be used to quantify this model uncertainty. Thus, we plan to develop an analogous ensemble of AiBEDO models trained on internal fluctuations from different ESMs. Because of the large data requirements of training AiBEDO, we must use single-model initial condition Large Ensembles, of which there exist several from CMIP5 and CMIP6 ESMs (Deser et al. 2020), such as the MPI-ESM1.1 Grand Ensemble (Maher et al. 2019) and the CanESM2 Large Ensemble (Kushner et al. 2018).
Furthermore, though we have verified AiBEDO performance in the response to MCB here (which is largely a shortwave cloud perturbation), AiBEDO includes longwave and clearsky input variables. Thus, AiBEDO may be able to project responses to greenhouse gas and anthropogenic sulphate forcings (both tropospheric pollution and stratospheric injections). We therefore plan to apply AiBEDO to these forcings as well by perturbing the model with ERFs computed from fixed SST simulations with these emissions (Forster et al. 2016).
Using the rapid generation of projections enabled by AiBEDO, we will also develop a method for optimizing MCB forcing patterns to achieve regional climate targets, drawing from the robust existing body of AI-based optimization methods. This will allows us to explore an array of possible MCB scenarios to find which ones may produce desirable regional outcomes. For example, which MCB forcing pattern might achieve the greatest global mean cooling while minimizing drying in the Amazon? Or which patterns minimize polar amplification? This exploration will accelerate the generation of policy-relevant MCB forcing scenarios and allow estimates of the scenario uncertainty in MCB intervention impacts, which is arguably the largest uncertainty in SRM generally (MacMartin et al. 2022).
Figure 1 :
1Schematic view of the Spherical Multi-Layer Perceptron (S-MLP) model used in this study.
Figure 2 :
2One-month lag AiBEDO compared to CESM2 LE data (a-f). Panels a,c,e show the root mean squared error (RMSE) computed in the time dimension at each icosahedral spherical grid point calculate across 480 months. Panels b,d,f show the ratio of RMSE to the standard deviation of the preprocessed data. Panels a,b show surface temperature (tas), c,d show precipitation(pr)
Figure 3 :
3Annual mean temperature (top row -a,b), precipitation (middle row -c,d), and surface pressure (bottom row -e,f) anomalies due to a constant MCB-like forcing for CESM2 (left column) and AiBEDO (right column). Note that the color scale is larger in the AiBEDO figures. Spatial correlation scores and RMSE between the CESM2 and AiBEDO are displayed in the figure labels on the left side.
Figure 4 :
4Correlation scores between CESM2 and AiBEDO tas responses to MCB forcing for both land and ocean (a), just ocean (b), and just land (c) in different latitude bands for all MCB regions (ALL), Northeast Pacific (NEP), southeast Pacific (SEP), and Southeast Atlantic (SEA).
Net surface clear-sky radiative flux plus all-sky surface heat flux inputVariable
Description
Role in AiBEDO
cres
Net TOA shortwave cloud radiative effect
input
crel
Net TOA longwave cloud radiative effect
input
cresSurf
Net Surface shortwave cloud radiative effect
input
crelSurf
Net Surface longwave cloud radiative effect
input
netTOAcs
Net TOA clear-sky radiative flux
input
netSurfcs lsMask
Land fraction
input
ps
Surface pressure
output
tas
Surface air temperature
output
pr
Precipitation
output
Table 1: Name, description, and use by AiBEDO of variables derived from CESM2 LE historical smoothed biomass burning
monthly mean data. Thus, c in = 7 channels and c out = 3 channels. All radiative and heat fluxes at the surface and top of
atmosphere (TOA) are positive down.
Experiment
Role
Forcing
Time span
N
Historical LE
training, testing, validation
historical
1850 -2015
50
Y2000 Control
perturbation
Year 2000 Fixed SST
1 -20
N/A
Y2000 MCB Perturbed
perturbation
Year 2000 Fixed SST +
MCB in NEP, SEP, and SEA
1 -10
N/A
SSP2-4.5 LE
response validation
SSP2-4.5
2015 -2100
17
SSP2-4.5 + ALL MCB
response validation
SSP2-4.5 +
MCB in NEP, SEP, and SEA
2015 -2065
3
SSP2-4.5 + NEP
response validation
SSP2-4.5 + MCB in NEP
2015 -2065
3
SSP2-4.5 + SEP
response validation
SSP2-4.5 + MCB in SEP
2015 -2065
3
SSP2-4.5 + SEA
response validation
SSP2-4.5 + MCB in SEA
2015 -2065
3
Table 2 :
2CESM2 simulations used to train and verify AiBEDO. NEP, SEP, SEA denote regions where 600cm −3 CDNC MCB forcing is imposed, where NEP -Northeast Pacific (0 to 30N; 150W to 110W), SEP -Southeast Pacific (30S to 0; 110W to 70W), SEA -Southeast Atlantic (0 to 30N; 25W to 15E). Note the fixed SST simulations use constant climatological conditions, so we do not note specific years for these simulations.turbation regions are entirely unlike any fields the model is
trained on.
AcknowledgementsWe thank Linda Hedges of Silver Lining and Brian Dobbins of the National Center for Atmospheric Research for their assistance with AWS and CESM2 computing. The development of AIBEDO is funded under the DARPA AIassisted Climate Tipping-point Modeling (ACTM) program under award DARPA-PA-21-04-02. AiBEDO training and CESM2 simulations were performed using Amazon Web Services (AWS) computing resources thanks to a generous computing grant from Amazon. We thank the CESM2 Large Ensemble Community Project and supercomputing resources provided by the IBS Center for Climate Physics in South Korea. Documentation of this project can be found at https://aibedo.readthedocs.io/en/latest/index.html.
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| sample_1674 | 0.9998 | arxiv | |
Life cycle costing analysis of deep energy retrofits of a mid-rise building to understand the impact of energy conservation measures
Haonan Zhang
School of Engineering
Faculty of Applied Science
The University of British Coulmbia
V1V1V7KelownaBCCanada
Life cycle costing analysis of deep energy retrofits of a mid-rise building to understand the impact of energy conservation measures
Building energy retrofits have been identified as key to realizing climate mitigation goals in Canada. This study aims to provide a roadmap for existing mid-rise building retrofits in order to understand the required capital investment, energy savings, energy cost savings, and carbon footprint for mid-rise residential buildings in Canada. This study employed EnergyPlus to examine the energy performance of 11 energy retrofit measures for a typical multi-unit residential building (MURB) in Metro Vancouver, British Columbia, Canada. The author employed the energy simulation software (EnergyPlus) to evaluate the pre-and post-retrofit operational energy performance of the selected MURB. Two base building models powered by natural gas (NG-building) and electricity (E-building) were created by SketchUP. The energy simulation results were combined with cost and emission impact data to evaluate the economic and environmental performance of the selected energy retrofit measures. The results indicated that the NG-building can produce significant GHG emission reductions (from 27.64 tCO2e to 3.77 tCO2e) by implementing these energy retrofit measures. In terms of energy savings, solar PV, ASHP, water heater HP, and HRV enhancement have great energy saving potential compared to other energy retrofit measures. In addition, temperature setback, lighting, and airtightness enhancement present the best economic performance from a life cycle perspective. However, windows, ASHP, and solar PV, are not economical choices because of higher life cycle costs. While ASHP can increase life cycle costs for the NG-building, with the financial incentives provided by the governments, ASHP could be the best choice to reduce GHG emissions when stakeholders make decisions on implementing energy retrofits.
Introduction
Extensive use of fossil fuels and associated greenhouse gas (GHG) emissions have been identified as catalysts for climate change and associated environmental impacts [1]. In response to the increasing concern about climate change impacts due to anthropogenic activities, the government of Canada has established an ambitious emission reduction target, promising to reduce carbon emissions by 80% by 2050 compared to the 2005 level [2]. It is suggested that stationary combustion, transportation, and fugitive sources constitute 82% of the GHG emissions of the country [3]. Thus, Canada aims to reduce energy use in multiple sectors in order to reduce associated GHG emissions [2].
In recent years, the building sector has garnered greater attention for its need to reduce GHG emissions in Canada. According to national GHG inventory, Canadian buildings are responsible for 12% of the total national GHG emissions. Moreover, the residential building sector accounts for 11% of national energy use in 2017 [2]. Recognizing the importance of reducing energy use and emissions associated with the building sector, governments have introduced policies, standards, and design guidelines to improve building energy performance. For example, the British Columbia Energy STEP Code (BCESC) has been launched to put British Columbia (BC) on a path to meet the provincial target to make all new buildings "net-zero energy ready" by 2032 [4]. However, policy initiatives that promote energy efficiency of aging buildings are lacking. Poor energy performance of aging buildings is responsible for a significant portion of the increasing GHG emissions associated with the building sector [9].
In Canada, over 50% of residential buildings are more than 30 years old, and over 20% are older than 50 years or more [5]. Old buildings mostly use non-renewable energy sources. Moreover, the systems and materials have often deteriorated with the age of the old buildings [8], [9]. Therefore, these old buildings consume more resources leading to higher environmental impacts and emission footprints [5]. As the replacement rate of old buildings by new construction is only 1.0-3.0% per annum [8], the environmental impacts associated with the old building stock need to be reduced through retrofitting in order to achieve the emission reduction targets of Canada [9,10]. Previous studies have shown that building energy retrofits have significant energy and GHG emissions saving potential [11]. Furthermore, retrofits can also deliver other benefits, such as cost savings and enhanced thermal comfort [12,13]. Therefore, devising energy performance enhancement and retrofit strategies for Canadian buildings is a timely discussion.
While municipalities have developed many plans to achieve resiliency and emissions reduction targets, retrofitting existing buildings for net zero or near net zero emissions remains one of the most challenging parts of reaching the climate action targets due to the diverse portfolio, early adopter disadvantage, and economic barriers. Multi-unit residential buildings (MURBs) represent a large and growing share of the building stock in cities across Canada.
In British Columbia, the City of Richmond intends to undertake a deep energy building retrofit of a mid-rise building to identify and verify the potential impacts of a series of energy conservation measures (ECMs) on energy consumption and GHG emission savings. This study aims to provide a roadmap for existing mid-rise building retrofits in order to understand the required capital investment, approximate energy savings, corresponding energy cost savings, and carbon footprint for a mid-rise residential building deep energy retrofit.
Energy retrofit interventions
In general, building retrofit interventions can be classified under three categories, including demand side solutions, supply side solutions, and transformation of energy consumption patterns (i.e. human factors) [12]. Demand side solutions include strategies to reduce building heating and cooling load and other end-uses with energy retrofits and upgrades. Upgrades in building envelop insulation, air tightness, window insulation, heating ventilation and air-conditioning (HVAC) systems, hot-water unit, and appliances are some common focus areas in demand-side management [15,16]. Supply side solutions consist of renewable energy solutions such as solar photovoltaics (PV) and wind energy, which are recognized as alternative energy systems to generate electricity for buildings [17]. Supply side solutions have received much scrutiny in recent years with the increasing pressures to reduce the environmental impacts associated with energy use [15,16]. Transformation of energy consumption patterns is applying advanced control techniques or providing householders with building operation strategies to facilitate energy efficiency through behavior change [18]. This section discusses possible retrofit options, including the improvement of building envelope components, HVAC systems, and occupant behaviors and lighting systems, and renewable energy systems.
Upgrades in building envelope
In existing buildings, heat losses or gains through building envelopes affect the energy use and the indoor condition, and produce a significant amount of energy depletion. Therefore, retrofitting the external walls and roofs has a considerable impact on reducing building energy consumptions. This kind of retrofit measures should improve the thermal performance of buildings [19]. Common upgrades in building envelope components include wall insulation, roof insulation, and windows [20].
Upgrades in HVAC systems
Previous research shows that the most substantial energy saving potential can be achieved by improving the building HVAC systems [19]. Existing old buildings usually have less-efficient HVAC systems, especially those systems powered natural gas. In the recent years, the development of heat pump have presented great energy saving potential for existing old buildings. In addition, HVAC control has an important impact on energy management [21]. HVAC control aims to optimize operation systems and avoid excessive cycling of system components and the conflicts between them. Adjustments in HVAC control strategies are essential to reduce building energy consumptions [12].
Occupant behaviours and lighting systems
Multi-unit residential building (MURB) occupants without electrical sub-metering tend to use more electricity than those who are sub-metered [12]. The cost of electricity is often hidden in fixed costs, while the actual electricity cost per suite varies according to fluctuations in energy use. Individual sub-metering ensures occupants are aware of their energy consumption. In order to manage energy costs, occupants have the option to reduce their in-suite appliance use and lighting. Light-Emitting Diode (LED) lighting have presented greater energy saving potential compared to conventional lights [10].
Renewable energy systems
In addition to demand side retrofit measures, supply-side retrofit measures, such as building integrated solar PV systems, are becoming popular in Canada. Solar PV can generate and store electricity during daytime and this electricity is used when demanded. Majority of the installed solar PV panels are equipped with an inverter to convert DC to AC and allow the household to utilize the produced electricity [22]. In addition, solar PV can be connected to the electricity grid. If the supplied electricity to the grid is more than the used electricity, the credits will carry over to the next utility bill [23].
Building energy modeling
This research selected a typical mid-rise MURB located in the City of Richmond, British Columbia, Canada as a case study. The author employed the energy simulation software (EnergyPlus) to evaluate the pre-and post-retrofit operational energy performance of the selected MURB. EnergyPlus (developed by Lawrence Berkeley National Laboratory) is the most popular energy simulation and design tool for buildings across the world. It employs long-term monthly weather data in a bin-based method to analyze energy performance for a given building.
Base building definition
The selected building is a three-floor muti-unit residential building. The building floor plan is shown in Figure 1.
Renewable energy:
Solar PV: Solar PV can be installed on roof top to generate and store electricity during daytime and this electricity is used when demanded.
Occupant behaviors and others:
Heating temperature setpoint setback: This measure is a low/no cost measure that leads to saving a great deal of energy at hours that space temperature does not necessarily require to be at design temperature. While the set point temperature on occupied hours remains unchanged at 22, with this measure the setback temperatures for heating are adjusted to 18 °C .
Lighting: Conventional lighting are replaced with LED lights.
Appliances: Appliances are replaced with electric appliances (15% higher energy efficiency)
Energy modeling process
Typical MURBs in BC can be categorized into two clusters according to their energy sources: electricity-powered buildings and natural gas-powered buildings. To represent the majority of existing MURBs in BC and develop a comprehensive retrofit plan, the author developed two building energy models according to the energy sources.
The authors employed Google SketchUP with OpenStudio as an add-in to create the physical base building model, as shown in Figure 2. Then, the building model was imported to EnergyPlus to evaluate the energy performance of different retrofit measures.
Figure 2. Physical base building model in SketchUP
After importing the physical building model to EnergyPlus, the author must input more information associated with building envelope materials, HVAC systems, lighting, electric equipment. The building characteristics are shown in Table 1. The developed building energy models are shown in Figure 3 and Figure 4. In order to evaluate the effectiveness of different retrofit measures, comparing the post-retrofit performance against the original performance of a given building is necessary. Thus, after creating the base building models, the author must input the selected energy retrofit measures in the base building energy models and evaluate the postretrofit building energy performance. The pre-and post-retrofit energy performance is discussed in Section 5. The upfront cost of a retrofit project is an essential consideration for building owners. Homeowners are inclined to choose cheaper equipment or material to reduce the upfront cost, according to a retrofit survey conducted in Canada [24]. However, purchasing equipment or material with low market prices without considering the operational performance might raise the LCC. The LCC accounts for all cost elements associated with a retrofitting project. Depending on the conditions, a retrofit package with a higher upfront cost may produce better LCC performance due to higher cost savings [25].
Life cycle cost analysis (LCCA) is generally regarded as a pecuniary evaluation method for an existing asset or a potential investment. LCCA accounts for immediate and long-term expenses. LCC is the "cost of an asset or its parts throughout its lifecycle while meeting the performance requirements". In the building and construction sector, ISO 15686-5 was issued for the financial evaluation of "Buildings and con-structed assets". In this study, the considered LCC includes the upfront cost, the operational cost, and the disposal cost.
Upfront cost
Upfront cost is a combination of cost of equipment and installation. In this study, RSMeans Building Construction Costs database and literature were referred to identify the capital costs of the identified retrofits. For a given retrofit scenario, upfront costs (UC) associated with envelop and energy system upgrades can be calculated by the following equation.
.2 Carbon tax
The energy cost rates of this building were ¢15 and ¢3.2 per kWh of electricity and natural gas respectively. An additional cost that needs to be considered atop the energy costs is Carbon tax costs. While the current carbon tax cost in Canada is $50 per ton of CO2e, based on the government's announcement, it is expected to increase by $15 per year, reaching $170 per ton in 2030. Although there could be a stop in carbon tax increase in 2030 at $170/ton, it is also reasonable to assume that the price of carbon will continue to increase. To date there is no official announcement for the carbon tax changes after 2030. However, some news are spread around increases to $300 by 2050. In this study, linear increase of carbon tax after 2030 until it reaches $300 by 2050 was assumed.
Operational cost
Operational cost of a retrofit has three main components including operational energy cost, maintenance costs, and replacement costs. Reliable maintenance cost data figures associated with different retrofits were not found in the literature. On the other hand, the maintenance costs of residential energy system components are significantly lower compared to operational energy costs associated with the energy system due to energy use. Therefore, only energy cost savings were considered under the operational costs. The energy cost savings and replacement costs were calculated in comparison to the base (existing condition) building using building energy simulations. Energy simulation results can be used to determine the annual operational cost savings of a given retrofit strategy.
Energy simulation results
This section presents the per-and post-retrofit energy performance of the case study building.
Performance of the base building models
Performance of the selected energy retrofit measures
The section presents the energy performance of the selected energy retrofit measures. Figure 6 depicts the annual energy reductions of individual retrofit measures for the two buildings. NGbuildings present much more cost saving potential compared to E-buildings. Solar PV presents the greatest energy saving potential (around 410 GJ), followed by ASHP (320 GJ). Windows and water HP have similar energy performance, with the energy reduction of around 170 GJ. In terms of upgrades in envelope insulation, wall insulation enhancement can save more energy use compared to roof insulation. Appliances and lighting enhancement show the least energy saving potential among the selected energy retrofit measures.
Figure 6. Annual energy reductions of individual retrofit measures
As shown in Figure 7, E-buildings present much more cost saving potential compared to NGbuildings. Similar to energy saving potential, the installation of solar PV is the most cost-effective energy retrofit measure, showing the energy cost saving of around 10K CAD. In addition, ASHP presents significant annual energy cost saving potential for NG-buildings (6.18K CAD). However, the energy cost saving for NG-building is not significant. This because the space heating energy source switches from natural gas to electricity, and the electricity price is higher than natural gas price. Annual energy cost saving (K CAD) E-Building NG-Building Figure 8 shows the annual emission reductions of the selected energy retrofit measures. NGbuildings have greater emission reduction potential compared to E-buildings due to a higher emission factor of natural gas. The installation of ASHP in NG-buildings can significantly reduce GHG emissions (21.60 tCO2e), followed by HRV (8.79 tCO2e), and windows (8.55 tCO2e). Upgrades in wall insulation and temperature setback can approximately reduce GHG emissions by 5 t CO2e for NG-buildings. Other energy retrofit measures are not significant for emission reductions.
Figure 8. Annual GHG emissions of individual retrofit measures
The following figures present the cumulative effect of annual energy consumptions, energy cost, and GHG emissions for the studied buildings. The energy consumptions can be decreased from around 2200 GJ to 1200 GJ, reduced by 44%. In terms of energy costs, the cost saving potential of E-buildings is greater than that of NG-buildings, with the former decreasing by 35K CAD and the latter decreasing by 27K CAD. However, NG-buildings can produce much more GHG emission reductions compared to E-buildings. The annual GHG emissions of NG-buildings can be decreased from 27.64 tCO2e to 3.77 tCO2e by implementing these retrofit measures. Thus, governments and stakeholders should pay more attention to NG-building to achieve the target of emission reductions. Figure 11. Cumulative effect of energy consumption for NG-Building Figure 13. Cumulative effect of energy cost for E-Building Figure 14. Cumulative effect of energy cost for NG-Building
Life cycle costing results
This section discusses the life cycle costing results for each of the studied energy retrofit measures. For E-buildings, Figure 18 indicates that the life cycle costs of upgrades in temperature setback is negative, which means that the operational energy cost savings of these retrofit measures are higher than the upfront costs of these measures. Among these retrofit measures, temperature setback presents the greatest cost saving potential, followed by lighting, and airtightness enhancement. On the other hand, upgrades in windows, ASHP, and solar PV are not economical. The life cycle costs of the retrofit measures for NG-buildings are shown in Figure 19. Temperature setback and lighting enhancement are the most cost-effective energy retrofits measures. In addition, airtightness, wall insulation, roof insulation are also economical retrofit measures. However, the replacement of windows can significantly increase life cycle costs (around 270 KCAD). Furthermore, ASHP and solar PV are not economical energy retrofit measures, which can increase life cycle costs of 220K CAD and 120K CAD, respectively. Life cycle cost Figure 19. Life cycle cost of individual retrofit measures for NG-Building
Conclusion
Energy retrofits play an essential role in reduce building energy consumptions and associated GHG emissions. This study employed EnergyPlus to examine the energy performance of 11 energy retrofit measures for typical multi-unit residential buildings located in the City of Richmond, British Columbia, Canada. The energy simulation results were combined with cost and emission impact data to calculate economic and environmental performance of the buildings. The results indicated that NG-buildings can produce significant GHG emission reductions (from 27.64 tCO2e to 3.77 tCO2e) by implementing these energy retrofit measures. In terms of energy savings, solar PV, ASHP, water heater HP, and HRV enhancement have great energy saving potential compared to other energy retrofit measures. In addition, temperature setback, lighting, and airtightness enhancement present the best economic performance from a life cycle perspective. However, windows, ASHP, and solar PV, are not economical choices because of higher life cycle costs. While ASHP can increase life cycle costs for NG-buildings, with the financial incentives provided by the governments, ASHP could be the best choice to reduce GHG emissions when stakeholders make decisions on implementing energy retrofits. Life cycle cost
Figure 1 .
1The floor plan of the case study building 3.2 Considered energy retrofit measures 3.2.1 Envelope Add roof insulation: R16. These base cases along with a series of roof insulation retrofits ranging from 2-inches (R-8) to a maximum of 4-inches (R-16) Add wall insulation: R16. These base cases along with a series of roof insulation retrofits ranging from 2-inches (R-8) to a maximum of 4-inches (R-16) Windows improvement: Triple pane, U value: 1.044 w/m2 K, SHGC: 0.615 Air tightness improvement: Air Source Heat Pump (ASHO): coefficient of performance: COP~2.75 Water heating: Water Heater Heat Pump (Water HP): COP~3.0 Heating recovery ventilator (HRV): sensible eff. 0.65
Figure 3 .
3Electricity-heated building energy model
Figure 4 .
4Natural gas-heated building energy model 4 Life cycle costing
The unit capital cost of the ℎ building envelope material • , = The area of the ℎ building envelope component • , = The capital cost of the ℎ energy systems 4
Figure 5 .
5The annual carbon tax cost savings (CAD) • = The annual electricity consumption of the base building model (GJ) • = The annual natural gas consumption of the base building model (GJ) • = The annual electricity consumption of the retrofitted building model (GJ) • = The annual natural gas consumption of the retrofitted building model (GJ) • = The local grid electricity emission factor (tCO2e/GJ) • = The local grid natural gas price (tCO2e /GJ) • = The carbon tax (CAD/tCO2e) Carbon tax cost
The annual operational cost savings (CAD) • = The local grid electricity price (CAD/kWh) • = The local grid natural gas price (CAD/GJ) The net present value (NPV) of the operational cost savings was considered in LCC calculations to account for time value of money. The NPV of the operational cost savings can be calculated using the following equation.
The net present value of operational cost savings • = The discounted rate (%) • = The project lifetime The total life cycle cost of a retrofit measure can be determined by the following equation.
Figure 7 .
7Annual energy cost savings of individual retrofit measures
Figure 9 .Figure 10 .
910Cumulative effect of energy consumption for E-Building Cumulative effect of energy consumption for E-Building (%)
Figure 12 .
12Cumulative effect of energy consumption for NG-Building (%)
Figure 13 .
13Cumulative effect of energy cost for E-Building (%)
Figure 14 .
14Cumulative effect of energy cost for NG-Building (%)
Figure 18 .
18Life cycle cost of individual retrofit measures for E-Building
Table 1 .
1Base building model Fan coil unit, Water cooled chiller, Boilers and chillers; Heating system seasonal NG CoP: 0.8, E CoP: 1.0, Domestic hot water Electricity, Dedicated hot water boiler, Delivery temperature: 60°C, CoP: 0.85 Stucco, Wire mesh on building paper, 9.5 Plywood, 38*89 Studs, R-14 batt insulation, 12 DrywallBuilding characteristics
Specifications Data
HVAC
System
Thermostat
Heating: 22°C , Cooling: 26°C
Air
infiltration
0.001314 m3
/s-m2
Exterior Wall
Floor RSI
RSI=0.66 Carpet, plywood, joist, drywall
Roof RSI
Ceiling
under Attic
Roofing, 38*235 Joists, R-28 batt insulation, 16
Drywall
Windows and
WWR%
U -value
3.57 W/m2 K
SHGC
Double glazed aluminum frame -0.760
Lighting
density
8.5250 W/m2
Plug load
8.0729 W/m2
Table 2 .
2Annual energy, cost and emission impact of the base building modelsParameter
E-building
NG-building
Total energy consumption (GJ)
2125.11
2212.47
Energy cost (CAD)
56.08K
52.20K
GHG emission (tCO2e)
6.79
27.64
Annual energy cost of NG-BuildingFigure 15. Cumulative effect of GHG emission for E-Building Figure 15. Cumulative effect of GHG emission for E-Building (%) Annual GHG emission of E-Building Figure 16. Cumulative effect of GHG emission for NG-Building Figure 17. Cumulative effect of GHG emission for NG-Building (%)Annual GHG emission of NG-Building70.79 70.15 69.85 69.30 68.96 67.22 66.80 66.64 64.29
57.58 56.76
43.49
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
Energy
cost
(K
CAD)
100%
61%
99%
99% 98%
97%
95%
94%
94%
91%
81%
80%
61%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Base
model
Lighting
Electric
appliances
Temperature
Setback
Airtightness
Windows
Wall
insulation
Roof
insulation
ASHP
Water
HP
HRV
Solar
PV
End
Cost
Changes
6.79 6.74 6.71 6.55 6.47 6.11 6.00 5.96 5.57
4.99 4.92
3.77
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
GHG
smission
(t
CO2)
100%
56%
99%
99% 97%
95%
90%
88%
88%
82%
74%
72%
56%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Base
model
Lighting
Electric
appliances
Temperature
Setback
Airtightness
Windows
Wall
insulation
Roof
insulation
ASHP
Water
HP
HRV
Solar
PV
End
Emission
Changes
27.64 27.61 27.58
24.08
22.19
15.05
12.72 11.88
5.57 4.99 4.92 3.77
0.00
5.00
10.00
15.00
20.00
25.00
30.00
GHG
emission
(t
CO2)
100%
14%
100% 100% 87%
80%
54%
46%
43%
20%
18%
18%
14%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Base
model
Lighting
Electric
appliances
Temperature
Setback
Airtightness
Windows
Wall
insulation
Roof
insulation
ASHP
Water
HP
HRV
Solar
PV
End
Emission
Changes
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| sample_1739 | 0.961 | arxiv | |
Multimodal Wildland Fire Smoke Detection
Siddhant Baldota
University of California
San Diego
Anantha Shreyas
University of California
San Diego
Jaspreet Kaur Ramaprasad
University of California
San Diego
Shane Bhamra
University of California
San Diego
Ravi Luna
University of California
San Diego
Eugene Ramachandra
University of California
San Diego
Harrison Zen
University of California
San Diego
Daniel Kim
University of California
San Diego
Ismael Crawl
University of California
San Diego
Ilkay Perez
University of California
San Diego
Garrison W Altintas
University of California
San Diego
Mai H Cottrell
University of California
San Diego
Nguyen
University of California
San Diego
Multimodal Wildland Fire Smoke Detection
Research has shown that climate change creates warmer temperatures and drier conditions, leading to longer wildfire seasons and increased wildfire risks in the United States. These factors have in turn led to increases in the frequency, extent, and severity of wildfires in recent years. Given the danger posed by wildland fires to people, property, wildlife, and the environment, there is an urgency to provide tools for effective wildfire management. Early detection of wildfires is essential to minimizing potentially catastrophic destruction. In this paper, we present our work on integrating multiple data sources in SmokeyNet, a deep learning model using spatio-temporal information to detect smoke from wildland fires. Camera image data is integrated with weather sensor measurements and processed by SmokeyNet to create a multimodal wildland fire smoke detection system. We present our results comparing performance in terms of both accuracy and time-to-detection for multimodal data vs. a single data source. With a time-to-detection of only a few minutes, SmokeyNet can serve as an automated early notification system, providing a useful tool in the fight against destructive wildfires.
Introduction
Research has shown that climate change creates warmer temperatures and drier conditions, leading to longer wildfire seasons and increased wildfire risks in many areas in the United States [1] [2]. These factors have in turn led to increases in the frequency, extent, and severity of wildfires [3]] [4] According to the National Centers for Environmental Information (NCEI) [5], which keeps track of weather and climate events with significant economic impacts, there have been 20 wildfire events exceeding $1 billion in damages in the United States from 1980 to 2022, and 16 of those have occurred since 2000 [3]. In the western United States, climate change has doubled the forest fire area from 1984 to 2015 [6].
Given the danger posed by wildland fires to people, property, wildlife, and the environment, there is an urgency to provide tools for effective wildfire management. Early detection of wildfires is essential to minimizing potentially catastrophic destruction. Currently, wildfires are detected by humans: scouts trained to be on the lookout for wildfires, residents in an area, or passersby. We propose here a system for automated wildfire smoke detection to provide early notification of wildfires.
In previous work [7], we introduced FIgLib (Fire Ignition Library), a dataset of labeled wildfire smoke images from fixed-view cameras, and SmokeyNet, a novel deep learning architecture using spatio-temporal information from camera imagery to detect smoke from wildland fires. Here, we extend that work by investigating the use of multiple data sources to improve performance in terms of both accuracy and time-to-detection. Specifically, we integrate weather sensor measurements with camera imagery to create a multimodal wildland fire smoke detection system.
Data
The work presented in this paper makes use of two different types of data: camera imagery and weather sensor measurements.
FIgLib Data
Camera imagery comes from the Fire Ignition images Library (FIgLib) dataset [8]. The FIgLib dataset consists of sequences of wildfire images captured from fixed cameras at HPWREN sites [9]. Each fire contains 80 minutes of MP4 high resolution video feed, with 40 minutes prior to the beginning of the fire and 40 minutes after the beginning of the fire, providing negative and positive samples of fire images, respectively. After removing out-of-distribution sequences (e.g., night fires), sequences with missing and/or mislabeled annotations, and sequences without matching weather data, a subset of 255 fires remained. This subset was partitioned into 131 fires for training (51.4%), 63 fires for validation (24.7%), and 61 fires for testing (23.9%).
Weather Data
Weather data in the HPWREN[10] [9], SDG&E [11], SC-Edison [12] networks is fetched from weather stations using the Synoptic's Mesonet API [13]. Synoptic is a service that helps in storing and serving weather data. The weather data has 23 attributes, out of which we selected the ones that have under 5% missing data for the FIgLib time frame of 03 June 2016 to 12 July 2021. These filtered attributes are: air temperature, relative humidity, wind speed, wind gust, wind direction, and dew point temperature. Wind speed and wind direction can be expressed as the radius and angle in a polar coordinate system [14], which are then used to obtain cartesian co-ordinates [15] − → u and − → v . This is done in aggregating the weather data.
Methods
This section presents methods used for data preparation and model building.
Data Preparation
The FIgLib data and the weather data have to be pre-processed before being fed into the model. This subsection discusses the procedures that we followed.
FIgLib Data The images of the FIgLIb dataset that we use are resized and cropped to speed up training and to remove clouds (which may cause false positives) into images of size 1040 × 1856 pixels, as this can be then split into 224 × 224 sized tiles. These images are then subjected to random data augmentations and also normalized. Refer to [7] for details on how these images are processed.
Weather Data For each image in the chosen FIgLib data, we need to get the corresponding weather at the scene captured by the camera. This is done by fetching weather data from the three closest weather stations in the direction that the camera is facing, followed by normalization and aggregation. Also, there is a weather data point available every ten minutes, whereas the images are spaced one minute apart. So we employ linear interpolation to resolve the difference in temporal resolution.
Models
SmokeyNet The baseline model for multimodal wildland fire smoke detection, SmokeyNet, depicted in Figure 1, is a spatiotemporal gridded model consisting of three different networks: a convolutional neural network (CNN) [16], a long short-term memory model (LSTM) [17], and a vision transformer (ViT) [18]. The input to SmokeyNet is a tiled wildfire image and its previous frame from a wildfire image sequence to account for temporal context. A pre-trained CNN, namely ResNet34 [19], extracts feature embeddings from each raw image tile for the two frames independently. These embeddings are passed through an LSTM which assigns temporal context to each tile by combining the temporal information from the current and previous frame. These temporally combined tiles are passed through a ViT, which encodes spatial context over the tiles to generate the image prediction. The outputs of the ViT are spatiotemporal tile embeddings, and a classification (CLS) token that encapsulates the complete image information. [18]. This token is passed through a sequence of linear layers and a sigmoid activation to generate a single image prediction for the current image. Tile loss is computed using binary cross entropy for the CNN, LSTM, and ViT separately. Additionally, image loss is computed for the ViT. Figure 2 shows the high level architecture for the multimodal SmokeyNet model. For each FIgLib image passed through the model, the corresponding weather vector is also added to the model at two places: The weather vector is concatenated to the embedding from the CNN and to the embedding from the LSTM. The resulting vector is then passed through a hidden layer. The output from this hidden layer is propagated forward to the next component of SmokeyNet. The concatenation of the weather vector to the CNN embedding increases the dimensions of the weights from the CNN output to the LSTM. These extra connections are initialized with random weights. This is similarly done with the weights from the LSTM output to the ViT. Finally, when the output of the hidden layer is sent through the vision transformer, the final model outputs are tile and image probabilities.
Multimodal SmokeyNet
The training procedure for the model happens in two stages. First, the vanilla SmokeyNet model, as described in [7], is trained for 25 epochs with only camera image data. Using transfer learning, the multimodal model (Figure 2) is initialized with the best weights based on validation loss from the trained vanilla SmokeyNet model. The model is then further trained with integrated camera image and weather data, as described in further detail in Section 4. Training is performed using aggregated CNN tile loss, LSTM tile loss, and ViT tile loss and image loss, as shown in 1, similar to the vanilla model as described in [7]. Adding Weather Data Using the transfer learning approach and integrated camera image and weather data as described in Section 3.2 we train the multimodal SmokeyNet model shown in Figure 2 for 25 epochs with early stopping. Additionally, to verify that the addition of the weather data is adding some useful information to the model, we also run experiments by passing random weather tensors of the same size, drawn from a normal distribution.
Experiments
For all experiments, we use the best values for the hyperparameters as mentioned in [7], i.e, a learning rate of 1e-3, weight decay of 1e-3, image resizing of 90%, no dropout, image binary cross entropy loss with positive weight of 5, and a batch size of 2. To give more weighting to the weather data, we use a replication factor of ten, which means that the weather vector of size eight is replicated 8 × 10 and then concatenated to the CNN/LSTM embedding. From these results, we observe that both F1 and time-to-detection improved with the multimodal version of SmokeyNet over the baseline version with just camera imagery. Averaged over eight runs, F1 improved slightly. And the time-to-detection metric improved by approximately 1 minute, or 22%. Additionally, the standard deviation for both F1 and time-to-detection also decreased. Thus, the multimodal SmokeyNet model not only improves the time-to-detection and F1 on average, but also offers more stability in these metrics across fire sequences.
Results & Discussion
Our results demonstrate that SmokeyNet can effectively process multiple data sources for wildland fire smoke detection, boosting detection performance in terms of both F1 and time-to-detection over the baseline with a single data source. With a time-to-detection within a few minutes, SmokeyNet can be used as an automated early notification system, providing a useful tool in the fight against destructive wildfires.
For future work, we will analyze our results to gain insights into scenarios in which adding weather data improves performance. We will also investigate approaches to make use of unlabeled data to further improve detection performance. Additionally, we will explore methods to optimize the model's compute and memory resource requirements. Ultimately, our goal is to embed SmokeyNet into edge devices to enable insight at the point of decision for effective real-time wildland fire smoke detection.
Figure 1 :
1The SmokeyNet architecture takes two frames of the tiled image sequence as input and combines a CNN, LSTM, and ViT. The yellow blocks denote "tile heads" used for intermediate supervision while the blue block denotes the "image head" used for the final image prediction.
Figure 2 :
2The Multimodal SmokeyNet architecture integrates weather sensor measurements with camera images to perform wildfire smoke detection.
As mentioned in Section 2, we use a train / validation / test split of 131 / 63 / 61 fires (or 10,302 / 4,894 / 4,799 images) for all our experiments. The six weather attributes along with the − → u and − → v components as described in Section 2.2 constitute the vector, resulting in a weather vector of length eight. First, we run experiments on the vanilla SmokeyNet model to establish a baseline, and then train the multimodal SmokeyNet model with the integrated weather data. SmokeyNet Baseline As described previously, we need a baseline with which to compare the multimodal SmokeyNet model. For the baseline model, we take the original trained SmokeyNet model and train it for an additional 25 epochs.
Table 1
1provides a summary of the experiments. For each experiment, we report the accuracy, precision, recall, F1 score, and time-to-detection (TTD). For each row in the table, the reported scores are the average and standard deviation over eight runs.Table 1: Mean and standard deviation (SD) of Time-to-Detection (TTD), Accuracy, F1, Precision, and Recall metrics on the test set over eight runs. SmokeyNet is the baseline model without weather data. SmokeyNet with Random Weather uses the multimodal SmokeyNet architecture but with random numbers for the weather vector. SmokeyNet with Weather is multimodal SmokeyNet with actual weather data.Model
TTD (minutes)
Accuracy
F1
Precision
Recall
Mean
SD
Mean SD Mean SD Mean SD Mean SD
SmokeyNet
4.70
0.90
80.12 1.47 77.52 2.39 90.43 1.66 68.00 4.42
SmokeyNet with
Random Weather
4.88
0.96
79.50 0.77 76.90 1.31 89.40 1.51 67.53 2.63
SmokeyNet with
Weather
3.66
0.77
79.97 1.18 78.18 1.68 87.07 2.16 71.07 3.54
AcknowledgementsWe would like to thank the Meteorology Team at SDG&E for their valuable feedback and support. This work was supported in part by funding from SDG&E, and NSF award numbers 1730158, 2100237, 2120019 for Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI).
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| sample_1783 | 0.9819 | arxiv | |
IDENTIFICACION Y REGISTRO CATASTRAL DE CUERPOS DE AGUA MEDIANTE TECNICAS DE PROCESAMIENTO DIGITAL DE IMÁGENES EN LANDSAT-5 Universidad Nacional de Ingeniería
Kevin H Rojas
Ing. Electrónica
Ing. Física
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Laura <krojasl@uni Pe>
Ing. Electrónica
Ing. Física
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Christian B Cárdenas Álvarez
Ing. Electrónica
Ing. Física
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
DrGuillermo L Kemper Vásquez <guillermo.kemper@gmail.com>
Ing. Electrónica
Ing. Física
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Ing Ernesto Fonseca Salazar
Ing. Electrónica
Ing. Física
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
Universidad Nacional de Ingeniería
IDENTIFICACION Y REGISTRO CATASTRAL DE CUERPOS DE AGUA MEDIANTE TECNICAS DE PROCESAMIENTO DIGITAL DE IMÁGENES EN LANDSAT-5 Universidad Nacional de Ingeniería
Asesores:Palabras Clave: LandSat5Registro CatastralCuencas HidrográficasProcesamiento de Imágenes Satelitales Keywords: LandSatLand RegistryWatershedsSatellite Image Processing
Resumen:Los efectos del cambio climático mundial sobre los glaciares peruanos han dado origen a varios procesos de desglaciación en los últimos años. El efecto inmediato es la alteración en el tamaño de las lagunas y ríos. Las instituciones estatales que monitorean los recursos hidrológicos actualmente solo tienen estudios recientes sobre menos del 10% del total, los efectos del cambio climático y la falta de información actualizada acrecentaran los problemas social-económicos relacionados a los recursos hidrológicos en el Perú. El objetivo de este trabajo es desarrollar un aplicativo de software para automatizar el Registro Catastral de Cuerpos de Agua en el Perú, haciendo uso de técnicas de procesamiento digital de imágenes, el cual brindara herramientas para la detección, registro, análisis temporal y visualización de los cuerpos de agua. Las imágenes utilizadas son provenientes del satélite LandSat5, las cuales pasan por un pre-procesamiento de calibración y corrección propias del satélite, los resultados de la detección, se agrupan en un fichero que contiene los vectores de localización y las imágenes de los cuerpos de agua segmentados.Abstract:The effects of global climate change on Peruvian glaciers have brought about several processes of deglaciation during the last few years. The immediate effect is the change of size of lakes and rivers. Public institutions that monitor water resources currently have only recent studies which make up less than 10% of the total. The effects of climate change and the lack of updated information intensify social-economic problems related to water resources in Peru. The objective of this research is to develop a software application to automate the Cadastral Registry of Water Bodies in Peru, using techniques of digital image processing, which would provide tools for detection, record, temporal analysis and visualization of water bodies. The images used are from the satellite Landsat5, which undergo a pre-processing of calibration and correction of the satellite. Detection results are archived into a file that contains location vectors and images of the segmentated bodies of water.
INTRODUCCIÓN
La gestión de la información es hoy en día la herramienta más valiosa para afrontar los problemas ambientales, las autoridades distritales, regionales y nacionales administradores de los recursos hídricos, necesitan obtener información del comportamiento volumétrico de los recursos hídricos, esto para tener la certeza de tomar la mejor decisión en cuanto distribución, concesión de los recursos sin que afecte al medio ecológico y social.
Debido a los cambios visibles en los volúmenes de nevados que se han originado en la última década (e.g.
Nevado del Huascarán, Ancash), ha originado entre muchos otros efectos, el incremento del área de las lagunas y en algunos casos ha dado origen a la creación de lagunas y bofedales estacionales, el monitoreo de estos cambios se realiza solo en un 10% por las instituciones estatales, la Fig.1 Este concepto designa al objeto más pequeño que se puede distinguir en la imagen. Está determinada por el tamaño del píxel, medido en metros sobre el terreno.
Resolución Espectral:
Indica el número y anchura de bandas espectrales identificables por el satélite, en general se refiere al número, ancho y espaciamiento de las longitudes de onda a lo largo del espectro electromagnético que el sensor remoto es capaz de identificar.
Resolución Radiométrica:
Se presenta como la capacidad para detectar las variaciones de radiancia espectral, el número máximo de niveles digitales de la imagen suele identificarse como la resolución radiométrica del satélite y esta se indica por el número de niveles de gris captados por el sensor.
Resolucion Temporal:
Es la frecuencia de paso del satélite por un mismo punto de la superficie terrestre. Es decir cada cuanto tiempo pasa el satélite por la misma zona de la Tierra. Información de la Carpeta:
Contiene el ID de la imagen LandSat, la fecha y hora de la toma de la imagen y el software usado para su pre procesamiento.
Producto Metadata:
Contiene el nivel de preprocesamiento usado en la corrección de la imagen, el formato de salida de la imagen, el nombre del sensor, la ubicación por en coordenadas sexagesimales y UTM de las esquinas que conforman la imagen y los nombres de los archivos que acompañan a la metadata en la carpeta.
Atributos de la Imagen:
Contiene la cobertura de nubes en el momento de la toma, la calidad de la imagen, el ángulo azimutal y solar del sensor y valores de error calculados en el preprocesamiento de la imagen.
Radiancias:
Valores de Radiancias para cada una de las 7 bandas que conforman la imagen satelital.
Valores máximos y mínimos de ND por banda:
Contiene los máximos y mínimos de los Niveles Digitales por cada banda.
Parámetros de la Proyección sobre el plano:
Contiene los parámetros que caracterizan a la imagen en una proyección, estos son el mapa de proyección, el datum, el elipsoide modelo, la zona UTM y la orientación.
C.) Índices de Vegetación y Agua
La selección de los índices conlleva el análisis previo de cada uno de ellos. El presente trabajo utiliza los índices resultantes de la observación que mejor desempeño muestran, siendo también los que menos costo computacional conllevan.
Los índices de vegetación NDVI se muestra en la expresión (1).
VIS NIR
VIS NIR (1)
Las ecuaciones (2)
dmax / ) Lmin Lmax ( * min ND L L (4)
Donde "dmax" toma el valor de 255 según el MTL.
D.2) Calculo de la Reflectancia Aparente:
Las variables a usarse para el cálculo de la reflectancia se encuentran el archivo de metadatos de la imagen. En este paso usaremos:
Angulo de elevación solar (e).
Angulo cenital solar (z=90º -e).
Día del año juliano (dda).
Distancia tierra-sol en unidades astronómicas (d).
Valor medio de la irradiancia solar total en cada banda espectral (E).
La fórmula de cálculo de la reflectancia a partir de la Radiancia está dada por la ecuación (7) ya obtenida en el paso anterior. Un cálculo previo es la obtención de la distancia tierra-sol en el momento de toma, esto es posible mediante la siguiente expresión:
) cos( ) ( t t z E L L d a (7)
Los valores típicos para "t1", "t2" según el trabajo desarrollado por Chávez serian (0.70, 0.78, 0.85 y 0.91) y "cos (z)" respectivamente. En la ecuación 4, la variable "La" es el valor de reflectancia de un pixel cuyo valor teórico de reflectancia es cero. La morfología es el estudio de la forma y estructura de los objetos, su estudio es basado en las operaciones de teoría de conjuntos, teoría de retículos, topología y funciones aleatorias. El objetivo de estas operaciones es simplificar y conservar las principales características de forma de las regiones. Las operaciones morfológicas usadas por el software son la dilatación y erosión. Estas son descritas a continuación.
Dilatación: La dilatación se describe como un crecimiento de pixeles, es decir, se marca con 1 la parte del fondo de la imagen que toque un pixel que forma parte de la región. Esto permite que aumente un pixel alrededor de la circunferencia de cada región y así poder incrementar dimensiones, lo cual ayuda a rellenar hoyos dentro de la región.
〈 〉 Figura 7. Ejemplo de la operación morfológica Dilatar.
Erosión: La erosión de A por B se puede entender como el lugar geométrico de los puntos alcanzados por el centro de B cuando B se mueve dentro de A. Un ejemplo se muestra en la Fig.8.
〈 〉
La aplicaciones de operadores morfológicos en el software, es para la obtención de características de la imagen como el área y el perímetro, para ello es necesaria la aplicación sucesiva de la dilatación y erosión con el fin de obtener los bordes de la imagen segmentada. El diagrama de bloques se explica mejor en la sección de Desarrollo de Software. La Interfaz Gráfica de Usuario (GUI) es divido en zonas, cada una de estas zonas es conectado con las demás por medio de botones y eventos que llaman a resultados calculados por otras zonas de la interfaz, esto sugiere un procedimiento en procesar, segmentar y registrar, la Fig.12 muestra el esquema de la GUI. La descripción del procedimiento general para la interfaz es mostrado en la La obtención de los bordes de la laguna segmentada es realizada con la aplicación de operadores morfológicos sobre la imagen. En la Fig. 15 Las imágenes satelitales es una fuente de información abundante de los recursos naturales; los gobiernos y autoridades deben extender su uso y aplicación en el monitoreo, estudio y administración de recursos.
Es posible realizar un monitoreo remoto a resolución media de las cuencas hidrográficas para las instituciones estatales utilizando imágenes satelitales libres.
RECOMENDACIONES
El procedimiento de calibrado de una imagen, requiere de una corrección geométrica, en un futuro proyecto se adicionara las correcciones al software, con la finalidad de disminuir el error en los resultados obtenidos.
REFERENCIAS BIBLIOGRÁFICAS
Fabián Reuter, "Plataformas Orbitales y Sensores". Series
Didácticas N° 34, Cátedra de Teledetección y Cartografía.
Universidad Nacional de Santiago del Estero.
Emilio Chuvieco y Stijn Hantson, "Plan Nacional de
: near infrared, SWIR: short wavelength infrared y VISV es Visual Verde. es calcular las Radiancias Espectrales de la imagen Satelital, las variables involucradas en el cálculo están disponibles en el archivo de metadatos de la imagen satelital, en laFig. 6se muestran estos para un LandSat5.La ecuación que permite transformar los ND a valores de radiancia ( L ) se puede expresar como:
Figura 8 .Figura 11 .
811Ejemplo un proceso de reducción de la información de una imagen digital a dos valores: 0 (negro) y 255(blanco).Esta técnica consiste en comparar cada pixel de la imagencon un determinado umbral (valor límite que determina si un pixel será de color blanco o negro). Los valores de la imagen que sean mayores que el umbral toman un valor 255 (blanco), el resto de pixeles toman valor 0(negro). En la Figura siguiente muestra un ejemplo de binarizar una imagen digital. Figura 9. Imagen Digital binarizada con un umbral de 95. E.3) Representación en Falso Color. La visualización en falso color implica hacer una combinación de 3 bandas similar a la que se hizo en color verdadero RGB, sin embargo en este caso se combinan bandas que no necesariamente pertenecen al espectro visible con el fin de visualizar características resaltantes de la combinación de las bandas. Un ejemplo para visualizar en falso color es colocar la banda 5 como n=3, banda 4 como n=2 y banda 3 como n=1. El resultado es mostrado en la Fig. 10. Figura 10. Representación de bandas en falso color (Descripción Grafica del Procedimiento Usado en la interfaz de usuario.
F . )
.Desarrollo de Software.
FigF. 2 )F. 3 )F. 4 )
234de pasos para la obtención de información de las lagunas empieza por la adquisición de las imágenes de una base de datos ya creada en un fichero del computador, esta base de datos es obtenida desde el servidor Glovis USGS. Un ejemplo de la base de datos de imágenes es mostrado en laFig.13. La región de interés(ROI) está conformada por 3 paquetes de imágenes LandSat5; la Interfaz Gráfica de Usuario(GUI) muestra la opción de elección de una imagen que es parte de la ROI, una vez seleccionada se importan automáticamente todas las características del archivo Metadata y los mapa de bits de las 7 bandas espectrales de la imagen seleccionada. Corrección Calculo de los índices de Agua.La GUI tiene una lista de índices, el usuario realizara una selección del índice, con el cual se ejecutara la segmentación de lagunas. El cálculo de los índices es a bFigura 13. Conjunto de Imágenes LandSat5, clasificadas por fecha y lugar de adquisición.llevado a cabo usando las 6 bandas corregidas en el paso anterior. LaFig. 14los índices calculados para una región. Figura 14. Índices de NDWI (a), MNDWI (b) y NDVI(c) calculados sobre la laguna Chinchaycocha en Junín. Selección de Muestra a Procesar y Obtención de Características de la Imagen. Figura 15. Obtención de bordes de la laguna con operadores morfológicos. La selección de un punto de referencia dado por el usuario, inicia una secuencia interna de procesamiento de una zona cuyo centro es el punto de referencia dado por el usuario, el resultado son los parámetros a utilizar para la binarización de la imagen, el proceso se basa en el estudio del histograma de la zona seleccionada. Al finalizar la binarizacion se tiene solo la laguna más cercana al punto
muestra las lagunas en estudio por vertiente hidrográfica.OBJETIVOSEl presente trabajo propuesto tiene como finalidad la creación de un aplicativo de software para la detección, medición y análisis de cuerpos de agua a nivel de cuenca, el cual proporcione herramientas específicas a las entidades estatales, regionales y nacionales con el fin que puedan desarrollar un monitoreo permanente sobre una cuenca.Esta región es la Cuenca del Rio Santa, ubicada entre los departamentos Ancash y La Libertad con una extensión de más de 12 mil kilómetros cuadrados.Figura1 Laguna Según Vertientes, Fuente: Sistema Estadístico
Nacional Perú Compendio Estadístico. INRENA
El desarrollo de sensores satelitales de gama alta, ha
generado que los estudios sobre la tierra y sus recursos
naturales se acrecienten, así como también disminuya el
tiempo de levantamiento de datos de vastas áreas.
El precio de venta de imágenes satelitales de gran
resolución y de software dedicado al Sistema de
Información Geográfica (GIS), es la principal barrera para
realizar estudios de monitoreo a nivel Nacional en las
entidades estatales. Sin embargo hoy en día se cuenta con
imágenes de media resolución espacial, disponibles por el
Servicio de Geológico de los U.S (USGS), también los
entornos de programación han evolucionado, haciéndose
más gráficos y sencillos al trabajar con imágenes.
El Programa Espacial LandSat hace posible la descarga de
imágenes satelitales desde el servidor Glovis USGS, en él
se encuentran imágenes desde el año 1999 hasta la
actualidad. Este trabajo hace uso de Imágenes Satelitales
de mediana resolución distribuidas desde el servidor Glovis
USGS, que sirven para realizar estudios de los cuerpos de
agua de tamaño medio.
Disminuir el tiempo de adquisición de información
catastral de cuencas hidrográficas, solucionando así, un
problema de las autoridades administradoras de recursos
hídricos en las cuencas del país.
Englobar los conocimientos de Procesamiento de
Imágenes, Sistemas Geográficos de Información y
programación, orientándolos a solucionar a un problema
real de una institución.
DESCRIPCIÓN DEL PROYECTO
La implementación de los objetivos del proyecto se lleva a
cabo en 5 pasos, los cuales se describen en esta sección.
A. Creación de Base de Datos
B. Estudio del Satélite
C. Estudio de los índices
D. Pre procesamiento
E. Procesamiento
F. Desarrollo de Software
A.) Creación de una Base de Datos de Imágenes LandSat5
de la Cuenca a tratar.
Las imágenes del programa satelital LandSat5 están a
disposición en sitios webs como www.usgs.gov y
www.glcf.umd.edu, la adquisición es creando un usuario y
es posible descargar imágenes desde los años 1999 hasta la
2012, con imágenes captadas por el sensor sobre el Perú
de cada16 días.
El presente trabajo realiza el estudio sobre una región de
interés para la Autoridad Nacional del Agua (ANA)
institución nacional administradora de recursos hídricos.
El área de interés es cubierto con tres imágenes LandSat5,
estas son obtenidas desde el servidor Glovis USGS, en
secuencias de tres veces por año, en fechas similares, un
ejemplo de paquete de datos es mostrado en la Fig. 2.
Además es necesario un paquete de imágenes adicionales
para hacer pruebas en el software y se obtengan resultados
visibles en las primeras pruebas, este paquete de imágenes
es la que contiene al lago Chinchaycocha en Junín.
El programa LandSat está compuesto por los últimos
sensores TM, TM+, la calidad de imágenes del sensor
TM+ fue disminuida desde mayo de 2003, por la falla en el
instrumento Scan Line Corrector (SCL-off) debido a esto
las imágenes tomadas desde julio de ese año presentan
unas franjas de datos erróneas (gaps). Este proyecto hace
uso de las imágenes tomadas por el Sensor TM, para evitar
el coste computacional de corregir el SCL.
Figura. 2. Paquete de Imágenes Satelitales por Banda del Sensor
TM.
Un paquete de datos generado desde el servidor Glovis
USGS es mostrado en la Fig. 3, los principales archivos del
paquete
son
las
bandas
espectrales
(e.g
LT50070692008122CUB00_B7.TIFF) y la que contiene
toda la información del paquete de datos, llamado archivo
de Metadatos.
LT50070692008122CUB00_B7.TIFF
LT50070692008122CUB00_B6.TIFF
LT50070692008122CUB00_B5.TIFF
LT50070692008122CUB00_B4.TIFF
LT50070692008122CUB00_B3.TIFF
LT50070692008122CUB00_B2.TIFF
LT50070692008122CUB00_B1.TIFF
LT50070692008122CUB00_VER.JPG
LT50070692008122CUB00_VER.TXT
LT50070692008122CUB00_MTLold.TXT
LT50070692008122CUB00_MTL.TXT
LT50070692008122CUB00_GCP.TXT
README.TXT
Figura 3. Ejemplo de contenido de un paquete de datos del
servidor Glovis USGS.
B.) Estudio del satélite LandSat5
El satélite LandSat5 es parte de la constelación LANDSAT
enviados por los Estados Unidos para el monitoreo de
recursos terrestres. El LandSat5 lanzado en 1984 lleva a
bordo el sensor Tematic Mapper(TM), un avanzado sensor
de barrido multiespectral que opera simultáneamente en
siete bandas espectrales, siendo tres en el visible, una en el
infrarrojo cercano, dos en el infrarrojo medio y una en el
infrarrojo termal.
El estudio del satélite se divide en dos partes, detalles de la
características del sensor y análisis de la Metadata que
acompaña al paquete de datos del sensor.
B.1) Las características de una imagen Satelital son:
Resolución Espacial:
Figura 17. Resultado de segmentación de una laguna usando el aplicativo de software en la Cuenca del rio Santa. Los resultados de análisis temporal para el proyecto, se basan en el estudio de tres lagunas en el departamento de Ancash (Ver anexo1), las lagunas son: Laguna Pelagatos Laguna Paron Laguna Qerocha Los paquetes de imágenes fueron adquiridas con una frecuencia de una vez por año, durante los años 2007, 2009, 2011 desde servidor Glovis USGS. Las lagunas son seleccionadas usando el aplicativo de software, las características resultantes como ubicación, área, perímetro son guardadas junto con la imagen de la laguna segmentada, en las Fig.19 y 20 se muestra las características calculadas para las tres lagunas por año. Figura 19. Áreas calculadas para las lagunas Pelagatos, Paron y Querocha durante los años 2007,2009 y 2011. Figura 20. Coordenadas de Centroides calculados para las lagunas Pelagatos, Parón y Querocha durante los años 2007,2009 y 2011. La ubicación geográfica de los centroides de las lagunas generadas por el software, son guardadas con una extensión compatible a Google Earth; la Fig.21 muestra los resultados de ubicación de las lagunas. Figura 21. Ubicación resultante de las lagunas Pelagatos, Paron y Querocha visualizado en Google Earth. La visualización de los resultados generados es posible con la superposición de los bordes calculados por el software en la imagen a color de las lagunas, la Fig.22 muestra las imágenes de lagunas superpuestas con sus respectivos Figura 22. Imágenes a en falso color de las lagunas Pelagatos(a), Parón (b) y Querocha(c), resaltadas por la segmentación de sus bordes. La obtención de características como área, perímetro, ubicación geográfica e imagen segmentada, es realizada automáticamente por el aplicativo de software propuesto. Acelerando el levantamiento de datos sobre las cuencas hidrográficas del país.y se muestra el proceso
llevado a cabo, además en el anexo se adjunta el código
que lo ejecuta.
Figura 16.Vector de Coordenadas de los Distritos de
Ancash y La Libertad visualizadas en Google Earth.
Fuente: ANA
F.5) Creación de la Base de Datos
Con la validación hecha sobre la zona de laguna
seleccionada por el usuario, sigue la creación de una tabla
con las características de la laguna, un dato importante es
la localización de la laguna en el mapa del Perú. Para esto
importamos un archivo "Mapa_Distrital_Peru.shp" con los
vectores que componen la frontera de los distritos de todo
el Perú, archivo brindado por el ANA, la Fig.16 muestra
las coordenadas de las fronteras de los distritos de Ancash
y La Libertad. Haciendo uso de la función conversor de
UTM a sexagesimales (función implementada adjuntada en
los anexos), las coordenadas del centroide son guardadas
en sexagesimales. Calcular la región, provincia, distrito a
la que pertenece el centroide de la laguna con las funciones
implementadas, para luego guardarlas en la Base de Datos.
El cálculo del área de laguna es realizado con una función
implementada que realiza la equivalencia pixel-metro, el
valor del área es guardado en la base de datos usando
unidades de km.
RESULTADOS
El aplicativo de software con las herramientas para realizar
detección, segmentación y creación de base de datos de
lagunas sobre la cuenca del Rio Santa es finalizado en su
etapa de prueba. La Fig. 17 muestra el aplicativo de
software en funcionamiento sobre la cuenca del rio Santa
en Ancash.
Las primeras pruebas sobre el aplicativo de software se
realizaron usando imágenes del año 2007, en esas
imágenes se lograron segmentar más de 10 lagunas de
considerable tamaño. La Fig.13 muestra la carpeta con las
imágenes resultantes de estas primeras pruebas.
Figura 18. Lagunas segmentadas junto con la imagen
LandSat5 que le dio origen.
IDLandSat
Año
Nombre
Cuenca
Area km^2
bordes.
(a)
(b)
(c)
CONCLUSIONES
IDLandSat
Año Nombre
Cuenca Centroide Latitud Centroide Longtiud
Aplicación de métodos de corrección atmosférica de datos Landsat5 para análisis multitemporal, Brizuela, Armando B.; Aguirre, César A.; Velasco, Inés PERÚ. Instituto Nacional de Estadística e Informática. PERÚ, COMPENDIO ESTADÍSTICO 2008. Lima, Perú. Tulio Chávez; Colonia Ortiz; Loarte Cadenas; Albornoz Albornoz y Alex Zambrano Ramírez. (2011) "Identificación de lagunas de Alta Montaña en el Perú mediante técnicas de Teledetección Espacial y Modelos de Elevación Digital". ANAIS XV SIMPÓSIO BRASILEIRO DE SENSORIAMENTO REMOTO -SBSR. Cem Unsalan and Kim L. Boyer. Multispectral Satellite Image Understanding, Springer, 2011.Gobierno del Perú, 2008.
% Excentricidad e = sqrt((EjeA)^2-(EjeB)^2)/(EjeA); eprima = (sqrt((EjeA)^2-(EjeB)^2)/(EjeB)); % Radio Polar c = EjeA^2/EjeB; % Aplanamiento % alpha = (a-b)/b; % Eliminacion del retranqueo para todos los casos X. X = X -500000; % Elimincacionde retranqueo en Y. if (strcmp(Hemisferio,'Norte')|| strcmp(Hemisferio,'norte')) % Si las coordenadas pertenecen al hemisferio Norte % Y no se modifica. Y = Y; else % Si las coordenadas pertencen al hemisferio sur. % Y = Y -10 000 000; Y = Y -10000000; end lambdaCent = huso*6 -183; % Ecuaciones de Coticchica-Surace phi = Y /(6366197.724*0.9996); v = c * 0.9996/sqrt(1+eprima^2*(cos(phi))^2); a = X/v; A1 = sin(2*phi); A2 = A1*(cos(phi))^2; J2 = phi + A1/2; J4 = (3*J2 + A2)/4; J6 = (5*J4 + A2*(cos(phi))^2)/3; alpha = 0.75*eprima^2; beta = 5*alpha^2/3; gama = 35*alpha^3/27; Bphi = 0.9996*c*(phi -alpha*J2 + beta*J4 -gama*J6); b = (Y -Bphi)/v; epsil = (eprima)^2*a^2*(cos(phi))^2/2; epsilon = a*(1 -epsil/3); n = b*(1-epsil) + phi; deltalamb = atan(sinh(epsilon)/cos(n)); tao = atan(cos(deltalamb)*tan(n)); Longitud = deltalamb*180/pi + lambdaCent; Latitud = (phi + (1 + eprima^2*(cos(phi))^2-1.5*eprima^2*sin(phi)*cos(phi)*(tao-phi))*(tao-phi))*180/pi; end Función obtención de Bordes de una imagen segmentada function [ im1 ] = ObtenerBorde( imb1 ) imb1 = L;imBin = imb1(:,:,1)>0; % Delimitar Bordes de la Region con Operadores Morfologicos % Dilatar y Erosionar con elemento Structurante. se = strel('octagon',3); % DILATAR: Numero de veces dilatar N N = 1; for i=1:N imDila = imdilate(imBin,se); end Universidad Nacional de Ingeniería
IDLandSat Año Nombre Cuenca Area km^2. IDLandSat Año Nombre Cuenca Area km^2
IDLandSat Año Nombre Cuenca Area km^2. 50080662IDLandSat Año Nombre Cuenca Area km^2 "LT50080662
179496006 -77.79363317 "LT500806620 09179CUB00" 2009 Paron Santa -8.992750445 -77.66791335 "LT500806720 09131CUB00" 2009 Querocha Santa -9.717370767 -77.32451465IDLandSat Año Nombre Cuenca Centroide Latitud Centroide Longtiud "LT500806620 09179CUB00" 2009 Pelagatos Santa -8. IDLandSat Año Nombre Cuenca Centroide Latitud Centroide Longtiud "LT500806620 09179CUB00" 2009 Pelagatos Santa -8.179496006 -77.79363317 "LT500806620 09179CUB00" 2009 Paron Santa -8.992750445 -77.66791335 "LT500806720 09131CUB00" 2009 Querocha Santa -9.717370767 -77.32451465
717370767 -77.32451465IDLandSat Nombre Cuenca Centroide Latitud Centroide Longtiud "LT500806620 11137CUB00" 2011 Pelagatos Santa -8.179486595 -77.79499326 "LT500806620 11137CUB00" 2011 Paron Santa -8.993015575 -77.66873322 "LT500806720 11153CUB00" 2011 Querocha Santa -9. IDLandSat Nombre Cuenca Centroide Latitud Centroide Longtiud "LT500806620 11137CUB00" 2011 Pelagatos Santa -8.179486595 -77.79499326 "LT500806620 11137CUB00" 2011 Paron Santa -8.993015575 -77.66873322 "LT500806720 11153CUB00" 2011 Querocha Santa -9.717370767 -77.32451465 2007 2009 2011
| sample_1790 | 0.9947 | arxiv | |
SolarEV City Concept for Paris: A promising idea? 1
Paul Deroubaix
École Polytechnique
PalaiseauFrance
Laboratoire des Sciences du Climat et de l'Environnement
IPSL
CEA-CNRS-UVSQ
Université Paris-Saclay
Gif-sur-YvetteFrance
Takuro Kobashi takuro.kobashi.e5@tohoku.ac.jp
Graduate School of Environmental Studies
Tohoku University
SendaiJapan
Léna Gurriaran
Laboratoire des Sciences du Climat et de l'Environnement
IPSL
CEA-CNRS-UVSQ
Université Paris-Saclay
Gif-sur-YvetteFrance
Fouzi Benkhelifa
NEXQT -Liberté Living Lab
Philippe Ciais
Laboratoire des Sciences du Climat et de l'Environnement
IPSL
CEA-CNRS-UVSQ
Université Paris-Saclay
Gif-sur-YvetteFrance
Katsumasa Tanaka katsumasa.tanaka@lsce.ipsl.fr
Laboratoire des Sciences du Climat et de l'Environnement
IPSL
CEA-CNRS-UVSQ
Université Paris-Saclay
Gif-sur-YvetteFrance
Earth System Division
National Institute for Environmental Studies
TsukubaJapan
SolarEV City Concept for Paris: A promising idea? 1
1 * Corresponding authors Emails: 1 The short version of the paper was presented at ICAE2022, Bochum, Germany, Aug 8-11, 2022. This paper is a substantial extension of the short version of the conference paper. 2 closer to the carbon neutrality goal, there are also implementation challenges for installing PVs in Paris.Urban decarbonizationelectric vehiclesrenewable energyrooftop photovoltaicsParisSolarEV City
Urban decarbonization is one of the pillars for strategies to achieve carbon neutrality around the world. However, the current speed of urban decarbonization is insufficient to keep pace with efforts to achieve this goal. Rooftop photovoltaics (PVs) integrated with electric vehicles (EVs) as battery is a promising technology capable to supply CO2-free, affordable, and dispatchable electricity in urban environments ("SolarEV City Concept"). Here, we evaluated Paris, France for the decarbonization potentials of rooftop "PV + EV" in comparison to the surrounding suburban area Ile-de-France and Kyoto, Japan. We assessed various scenarios by calculating the energy sufficiency, self-consumption, self-sufficiency, cost savings, and CO2 emission reduction of the PV + EV system or PV only system. We found that above a certain roof coverage, that is, 50-60% of the total roof area for Paris or 20-30% for Ile-de-France, PV electricity production regularly exceeds the demand, resulting in a lower self-consumption. Above that roof coverage, feed-in-tariffs (FIT) or storage are needed to further exploit the potential of the PV + EV system. The combination of EVs with PVs by vehicle-to-home (V2H) or vehicle-to-building (V2B) systems at the city or region level was found to be more effective in Ile-de-France than in Paris suggesting that SolarEV City is more effective for geographically larger area including Paris. If implemented at a significant scale, they can add substantial values to rooftop PV economics and keep a high self-consumption and self-sufficiency, which also allows bypassing the classical battery storage that is too expensive to be profitable. Furthermore, the systems potentially allow rapid CO2 emissions reduction; however, with already low-carbon electricity of France by nuclear power, CO2 abatement (0.020 kgCO2/kWh reduction from 0.063 kgCO2/kWh) by PV + EV system can be limited, in comparison to that (0.270 kgCO2/kWh reduction from 0.352 kgCO2/kWh) of Kyoto, also because of the Paris's low insolation and high demands in higher latitude's winter. While the SolarEV City Concept can help Paris to move one stepHighlights• From roof coverage of 50-60% PV production regularly exceeds demand in Paris.• PV + EV system is more effective in Ile-de-France than Paris for larger roof area.• PV + EV system is less effective in Paris than in Kyoto for climate.IntroductionMany state governments including the US, China, India, and Japan have announced so-called "net zero" emission targets by mid-century to steer the world towards an emission pathway consistent with the long-term temperature goal of the Paris Agreement [1,2]. In July 2021, the EU established a legal framework to achieve net zero greenhouse gas (GHG) emissions by 2050 [3], with individual states setting varied target years (e.g. 2045 for Germany; 2050 for France). Net zero targets have also been put forward by regional and local municipalities including Paris and Kyoto. Decarbonization of urban areas is important because CO2 emissions from cities around the world account for 71%-76% of the global CO2 emissions [4], and because first-hand decarbonization measures are often performed through local governments [5]. Increasing zero carbon energy technologies (e.g.,renewables) and improving energy efficiency, as well as electrifying the transport and heat system, are major pillars of decarbonization[6,7]. The SolarEV City concept [8], a novel concept that makes use of synergies between rooftop photovoltaics (PVs) and electric vehicles (Evs) as battery (PV + EV), supports such pillars.When both technologies are combined, EVs can not only eliminate CO2 emission from gasoline/diesel combustion through PVs, but also serve as electricity storage to address intermittency with rooftop PVs [9,10].The first study for the "PV + EV" in a city scale was conducted for Kyoto City, Japan (hereafter, "Kyoto"), which demonstrated that by using 70% of the rooftop area of Kyoto for PVs and converting all passenger vehicles to EVs, Kyoto's CO2 emission from electricity generation and ICEs (internal combustion engine vehicles) can be reduced by 60-74% with 22-37% energy cost reduction in 2030[9]. Then, the analyses were extended to nine Japanese urban areas: Koriyama City, Sendai City, Okayama City, Kyoto City, Kawasaki City, Hiroshima City, Sapporo City, Niigata City, and Tokyo special districts[8]. It was found that the effectiveness of "PV + EV" systems for urban decarbonization is highly variable, depending on the level of urbanization of the cities. For example, Kawasaki and Tokyo are highly urbanized areas with a small rooftop area and the number of vehicles per capita, resulting in relatively limited CO2 emission reduction (54-58%) by the PV + EV systems with energy cost saving of 23-26%. On the other hand, regional cities such as Niigata and Okayama have a larger rooftop area and the number of vehicles per capita, which can yield larger CO2 emission reduction (up to 95%) by the systems with higher energy cost saving of up to 34%.The effectiveness of the "PV + EV" systems also depend on the country specific factors such as electricity
tariff, climate, and urban structures. Chang et al. analyzed five South Korean cities, which indicated "PV + EV" systems can reduce CO2 emissions up to 86% with cost saving of 51% [11]. South Korean Cities have generally higher buildings than those in Japanese cities, which reduces the benefits of "PV + EV" systems than those of Japanese cities [11]. Liu et al. analyzed Shenzhen, China, which is a highly urbanized new city, and found that CO2 emissions can be reduced by 42% and cost saving by 21% through the "PV + EV" system [12]. Dewi et al. evaluated the potentials of the "PV + EV" system for Jakarta, the capital of Indonesia, and found CO2 emission reductions by 76-77%, accompanied by energy cost savings by 33-34% [10].
The study by Arowolo and Perez analyzed Paris, Lyon, and Marseille, France for the effects of "PV + EV" systems [13]. For a half of rooftop available space installed with PVs and a half of passenger vehicles replaced with EVs, they found 20-42% of electricity demand reduction, 43-48% of CO2 emission reduction, and a payback period of 2-3 years by 2030. Although Arowolo and Perez analyzed Paris for the PV + EV system as we did, they did not account for the electricity supply to the city from rooftop PV generation by considering hourly supply-demand balance (self-sufficiency). It is crucial to consider the benefit of electricity supply from PVs with supply-demand balance when evaluating the potential of the system for Paris due to its high-latitude location with strong seasonal variation of solar insolation. Paris can be seen as an iconic city of climate change as it is the birthplace of the Paris Agreement, so is Kyoto for the Kyoto Protocol. Our analysis of Paris and Kyoto may thus be useful for raising awareness of the SolarEV City Concept.
Under the background above, this paper will strive to answer the following questions:
1. How can the SolarEV City Concept (rooftop PV system combined with EVs as battery) contribute to the decarbonization of the City of Paris (high latitude city)?
2. What are the factors that can affect the potential of "PV + EV" for Paris in comparison to those of Ile-de-France and Kyoto?
What would be barriers to implement the SolarEV City Concept in Paris?
This paper is organized as follows. Section 2 describes the methods and materials of this study, including the city of Paris, techno-economic analysis, and scenarios. Section 3 illustrates the results of the analyses of Paris in comparison with those of other regions. Section 4 discusses the implications of the results and barriers to implement such technologies in a city scale. Section 5 concludes the paper.
Methods and materials
2.1. "Paris" and surrounding region, "Ile-de-France"
We studied two areas: Paris "intramuros", i.e. the city without its suburbs, and Ile-de-France, which is the region around Paris. Paris is a highly urbanized area with population of over 2.1 million and located in high latitude (48.9° N, 2.4° W) ( Fig. 1; Table 1). To fully elucidate the potential of rooftop PVs integrated with EVs for Paris, it is useful to consider the surrounding region of Ile-de-France as potential solar power suppliers ( Fig. 1). Ile-de-France (including Paris) covers 18.9% of the population of France (i.e., mainland) [14], which is the largest metropolitan area within the EU. While Paris is an urban area with a high population density and energy intensity, Ile-de-France is mostly a suburban area with a lower population density and energy intensity (Fig. 1).
Public transport is well developed in Paris. In Ile-de-France, on the other hand, residents more frequently use and own passenger vehicles. These differences are apparent in the number of registered vehicles per capita and average driving distances (Table 2). Data for Kyoto is also listed for comparison.
The French government will ban the sales of gasoline and diesel vehicles from 2040. Paris government will start an equivalent ban 10 years earlier, and Ile-de-France government set a ban for diesel vehicle sale by 2030.
Since 2018, a territorial climate-air-energy plan has been adopted in France, mandating inter-municipalities with more than 20,000 inhabitants to establish a global warming mitigation strategy based on renewable energy and energy consumption control. In this context, the city of Paris has announced that by 2050 it will achieve an energy mix of 100% renewables, of which at least 20% will be supplied locally [15]. [17][18][19][20]. A techno-economic analysis is a useful tool to evaluate all these factors and can provide information on whether to invest in projects under consideration [19,21]. We employed a methodology developed in the previous studies [16,22] that has been applied to investigate the future potential of the SolarEV City concept elsewhere. The methodological description here is kept concise at the level required for presenting our results.
Analyses were performed with a publicly available energy-economic software, SAM (System Advisor Model; version 2020.11.29 Revision 2), developed by the U.S. Department of Energy's National Renewable
Energy Laboratory (NREL) [23]. SAM is designed to evaluate the viability of various types of renewable energy projects [24]. The model runs with a given set of parameters or with a range of values for a subset of parameters iteratively. SAM can analyze the system at the scale of the city (or the region) and considers the surplus and deficit only at this level. The model does not account for the surplus and deficit at the household level, which may well occur without any surplus or deficit at the regional level. Thus, the basic assumption is that rooftop PV generated electricity was consumed in a city in the most-efficient way within the framework we considered. The SAM files used for the analyses are available at Mendeley Data [25].
We calculated the cost savings in terms of net present value of cashflow for a project period of 25 years [16], with a nominal discount rate of 2.5%. The potential changes in the costs of centralized electricity production, in particular the cost of maintaining the current means of production, are not considered. The costs of replacing existing gasoline and diesel vehicles with EVs and the resulting saving of fuel costs are treated as the background in our scenarios and are thus not considered in our cost calculations unless otherwise noted. The net present value is expressed in 2019 euros or 2030 euros, depending on the 1 st year of the project. In addition to cost savings, we calculated energy sufficiency, self-sufficiency, self-consumption, and CO2 emission reduction as decarbonization indicators [16]. Energy sufficiency is defined as the total amount of electricity produced by PV in one year divided by the annual electricity demand. Self-sufficiency is the actual electricity coming from PV consumed in a year divided by the annual demand. Self-consumption is the proportion of PV electricity that is consumed within the region considered [16]. More precisely, these indicators [26] can be expressed as:
(%) = {1 − } × 100
where NPV is net present value, N is project period, and AnnualEnergyCostBase is annual energy expense of a base scenario (i.e., annual electricity from power company and gasoline cost).
Energy sufficiency = (EPV-load + Ebattery-load + EPV-gid) /(Eload)
Self-sufficiency = (EPV-load + Ebattery-load)/ (Eload)
Self-consumption = (EPV-load + Ebattery-load)/ (EPV-load + Ebattery-load + EPV-grid)
where Eload = Total electricity load (kWh·yr -1 ) in the city.
EPV-load = Electricity (kWh·yr -1 ) supplied from PV directly to load in the city.
Ebattery-load = Electricity (kWh·yr -1 ) supplied from battery to load in the city.
EPV-grid = Electricity (kWh·yr -1 ) exported from PV to grid out of the city.
The outputs from SAM were used to calculate these indices. We calculated CO2 emission reduction from driving and consumption of electricity to assess the environmental benefits. Kyoto was similarly analyzed [16].
Scenarios
We focused on two illustrative scenarios: "PV only" and "PV+EV". "PV only" assumes a penetration of building rooftop PV. The "PV+EV" scenario assumes a penetration of residential rooftop PV combined with electric vehicles with bi-directional charging (e.g., V2H). In the "PV+EV" scenario, all vehicles are assumed to be electric and connected to vehicle-to-home (V2H) or vehicle-to-building (V2B) systems (bi-directional EV chargers), in which electric vehicles can be used to charge electricity from the rooftop PV and to discharge to the building.
We studied these two scenarios for two areas: Paris "intramuros", i.e. the city without its suburbs, and Ile-de-France, which is the region around Paris, comparing them also with Kyoto [22]. We considered two periods:
2019 (for "PV only") and 2030 (for "PV only" and "PV + EV"). The choice of area affected technical characteristics in the analysis, such as the roof area, the number of cars or the electricity demand. In our analyses, the choice of period only affected the prices, with projections used for the 2030 scenarios, to illustrate the effects of cost decline. For each scenario, we tested a different set of hypotheses on the roof coverage, different technologies ("PV only" or "PV + EV"), cost of technologies ("2019" or "2030"), and feed-in-tariffs ("with" and "without"). As for the techno-economic analysis, we compared the scenarios with a "base" one with the uses of gasoline/diesel engine vehicles and grid electricity [22].
Meteorological data
We used hourly data for the following parameters: diffuse horizontal irradiance (DHI; W/m 2 ), direct normal irradiance (DNI; W/m 2 ), global horizontal irradiance (GHI; W/m 2 ), temperature (°C) and wind speed (m/s). We obtained this dataset for Paris and Ile-de-France (49°N, 002.5°E) for 2019 with a tool SIREN, which calculates these parameters from climate reanalysis data MERRA-2 [27]. However, a direct application of this data can lead to an overestimate of the PV electricity production [9]. Thus, DHI, DNI, and GHI were reduced with a coefficient of 0.8, which was inferred from the analyses for Japanese cities [16]. The calculated capacity factor of 11.1% by SAM was a good agreement with the observed value of 11.0% in 2019 for Paris. The year 2019 was the one with the highest capacity factor in the period 2014-2020 (minimum 9.6% and mean 10.3%). In SAM, we chose the tilt angle of the panel to be 40° and its azimuth to be 180° for Paris and Ile-de-France.
Electricity demand and cost
The hourly electricity demand for Ile-de-France is available for the year 2019 by "Réseau de Transport d'Electricité" [28] (Fig. 2). For 2030, we rescaled the 2019 demand by a factor 1.08 to match the electricity demand of EV for the "PV + EV" scenarios. The increased electricity demand was calculated under an assumed current EV efficiency of 17.2 kWh/100km. This efficiency corresponds to the mean use (mean between winter and summer conditions) of a Renault Zoé in city driving conditions. The driving patterns were assumed to be the same in 2019 and 2030. On the other hand, data for hourly electricity demand were not available for Paris.
However, data for annual demand are given by Enedis, the power grid operator for the whole city [29]. For Paris, we thus used the hourly electricity demand of Ile-de-France multiplied by a factor of 0.18 based on the annual demand data of two regions. For 2030, we calculated that the demand increase due to EV charge is 2%, from deriving distance and EV efficiency resulting in the same scaling factor of 0.18 for Paris.
Concerning the prices of electricity, all our analyses for Paris and Ile-de-France used a weighted average price of 0.16 €/kW from the prices for household (0.178 €/kW) and industry (0.105 €/kW) [30] with annual electricity consumptions of 22.7 TWh and 7.3 TWh in 2019 [31], respectively. When we considered FIT, we used 0.04 €/kWh for both regions, which was an average day-ahead market price of electricity in 2019 for France [32]. We used the same price of electricity in 2019 and 2030. As the price of electricity has been rising in France for the past 30 years [30], particularly strongly in the recent past in the midst of geopolitical turmoil, it is likely to continue rising in the foreseeable future, which adds additional values on decentralized energy systems [17]. corresponds to the use of about 70% of the total rooftop area of the city [16]. In 2019, the cost of a PV-system depends on the surface area of panels for each roof. We used the 5-10 m 2 price (Table 3), which is higher than the price of 10-100 kW (thus 50-500 m 2 ) based on the dataset given by the Apur [34]. Using the higher price, our results on energy cost saving by PV system should be considered conservative. Maintenance prices were given as 22.5 €/kW/yr [34] and assumed to be the same in 2030. BloombergNEF (BNEF) estimates the global price for fixed-axis utility scale PV systems in 2030 to be 69% of 2020 prices (all costs included) [35]. We applied the same reduction to our residential prices, which leads to the prices for 2030 given in Table 3. A conversion rate of 1.12$/€ was used (2019 mean). We assumed that EVs are equipped with a 40kWh battery [16]. We set the power charge to 6 kW, and discharge can be expected with the same power for a V2H system [16]. It was projected that Europe would reach price parity between EV (including home chargers) and ICE during the period 2025-2030 [36]. The additional costs of having EV plus V2H system is estimated to be around 25 €/kWh in 2030 [16]. The cost of battery replacement of 91 € per battery (when the capacity is reduced to 80% of the initial capacity) is included in EV price [16]. We limit the use of EV batteries only in the range from 50 to 95% of their charge to prevent battery degradations and to allow EV owners to use their EVs for short trips anytime.
Number of cars and annual driving distance are given in Table 2. We assumed that the number of cars, the proportion of cars used during weekdays, and the average distance of moving cars in Paris and Ile-de-France would be the same between 2019 and 2030. It should be noted that while Paris and Ile-de-France replace ICEs with EVs, the number of vehicles may be reduced. The city of Paris is promoting the use of bicycles instead of cars, which is also an important decarbonization measure [37]. A decrease in the use of vehicles, therefore an increase of the parked time of vehicles, might raise the potential of "PV + EV". However, a significant change in the number of vehicles would reduce the total battery capacity and thus could affect the results of the "PV + EV" scenario.
Results
Paris vs. Ile-de-France
For Paris, "PV only" scenario can bring benefits already in 2019, and the benefits can further increase in 2030 ( Fig. 3a). There are optimum PV capacities of 2.7 GW and 3.6 GW with FITs for 2019 and 2030, respectively ( Fig. 3a; Table 4). Figure 3b shows that in the "PV only" case, surplus PV electricity start increasing from around 40%. From this point, FIT starts to play an important role to increase NPVs and optimal PV capacity. In addition, above this threshold, self-sufficiency diverts from energy sufficiency, and self-consumption starts to decline (Fig. 3b). Concerning "PV+EV", NPVs become larger than zero above 10% coverage in 2030, and NPVs continue rising above 70% (Fig 3a). Thus, the rooftop PV economics reaches the maximum with the maximum usage of the rooftop area (70%) in Paris by coupling with EVs. Self-consumption is 100% even at the maximum rooftop usage (71%) for "PV + EV" system with self-sufficiency and energy sufficiency being equal (Fig. 3c).
For Ile-de-France, there are optimums for PV capacity in all the scenarios (Fig. 3d). For "PV only", FITs make a difference with a roof coverage of above around 20% (Fig. 3d), which is much smaller than those for Paris owing to larger rooftop area per capita (Fig. 3a). When the rooftop coverage of PV becomes larger than around 20%, PV electricity production becomes greater than the demand in many hours of the year, resulting in a lower self-consumption and a larger difference between self-sufficiency and energy sufficiency (Fig 3e), which occurs in smaller roof area coverage than that of Paris. In addition, NPVs reach peaks in 54% and 60 % rooftop coverage, and abruptly drops, which is the result of EV battery replacement as a large investment for the replacement reduces the optimal PV capacity (Fig 3a). It is noted that energy sufficiency in Ile-de-France reaches 78%, which is much larger than 34% of Paris. Concerning "PV + EV", NPVs become larger than zero above 8-10% coverage in 2030. In contrast to Paris, self-consumption exhibits a slight decrease from 62% of the roof coverage with increasing surplus electricity. Accordingly, self-sufficiency is lower than energy sufficiency above 62 % of the rooftop coverage (Fig. 3f).
The results above indicates that Paris, where energy demand per area is high and the rooftop area is relatively limited, is better suited to have "PV only" below 50% of the rooftop coverage. For Ile-de-France with a relatively large rooftop area, on the other hand, PV-generated electricity can be quickly saturated with a small roof coverage (Fig. 3e). In this instance, PV + EV scenario has more advantages than PV only scenario, as long as the systems will be implemented at a substantial scale (i.e., above the threshold rooftop area). If PV only scenario proceeds further in Ile-de-France, it could lead to an overproduction of electricity, requiring curtailment with reduction in PV economics, as is already happening in some areas with a large amount of renewables. It is noted that NPVs in Figure 3 do not include cost saving from elimination of gasoline/dieses expenses. Thus, rooftop PV + EV owners have larger cost benefits than the results shown in Figure 3.
Paris vs. Kyoto
The potential of the SolarEV City Concept differs not only by the geographical extent as exemplified by the comparison between Paris and Ile-de-France but also climate, latitude, electricity tariff, etc. Therefore, it is useful to compare Paris with Kyoto, Japan, where the SolarEV City Concept was first introduced [9]. There is a large difference in latitude between Paris and Kyoto. As Earth is round and the rotating axis is tilted, higher latitudes experience annually a lesser amount of solar irradiance and larger seasonal change of solar irradiance, which affects energy yields of PV. The slope and azimuth of PV panels also affect energy yields differently in different latitudes (Fig. 4). Flat PV panels in Paris produces about 24 % less energy in a year than that of Kyoto (Fig. 4).
Maximum energy yields can be obtained in a 30˚-50˚ slope in Paris and in a 30˚slope in Kyoto with south faced azimuth (180˚) (Fig. 4), where Paris has still 21% less energy yield than that of Kyoto. However, energy yields on southern faced façades (a slope of 90%) in Paris are only 9 % less than that of Kyoto (Fig. 4), indicating that façade PVs are relatively good options in higher latitudes. On seasonal variation of PV energy yields, Paris has notable decline in electricity generation in winter compared to Kyoto (Fig. 5). The variation can be alleviated by having some slopes, but the winter decline in Paris is rather large, considering large electricity demands for heating. It is noted that wind power generates more electricity in winter in Europe [38]. That can compensate the solar power decline in the region. Kyoto [22]. In Paris, hourly demand variation shows some consistent characteristic through the year with a first peak around noon then another peak around 19:00. During summer, demands are smallest and in winter demand reaches peaks ( Fig. 2 and 6). On the other hand, daily demand profiles in summer and winter are different in Kyoto (Fig. 6). The largest electricity demand comes in summer with one large peak in the afternoon. In winter, two peaks develop, a morning peak around 9 pm and an evening peak around 7 pm. It is interesting to note that a drop in the lunch break only develops in Kyoto not in Paris (Fig. 6). Figure 6 also shows how electricity is supplied from the "PV + EV" system for both cities. In Paris, owing to smaller rooftop area per capita and less PV generation, the "PV + EV" system can only supply 31% of its demand. On the other hand, the "PV + EV" system in Kyoto can supply 76% of electricity demand, which includes the demand from EVs (Table 4 and 5). Figure 6. Hourly demand in a day for different months and annual-mean supply by "PV + EV" in a day.
Electricity supplies from grid, PV, and battery are shown in orange, red, and grey, respectively for the "PV + EV" scenario with FIT in 2030 for both cities. Figure 7 shows cross-spectral coherence [39] between electricity demand vs. temperature and PV generation.
Cross-sectional coherence for temperature vs. demand shows positive coherence (or correlation) in summer and negative coherence (correlation) in winter for periods longer than 64 hours for both Paris and Kyoto (Fig. 7).
Paris shows wider area of significant correlation both in winter and summer for the periods of 64-512 hours and 1024-2048 hours than those of Kyoto (Fig. 7). For the plot of demand vs. PV generation, cross-spectral coherence become less significant except daily periods. Positive coherence becomes significant in Kyoto in summer for the periods of 512 hours, indicating that space cooling demands are coinciding with higher PV generation (Fig. 7). Figure 7. Cross-spectral coherence [39] for demand vs. temperature and PV generation. Allows pointing right indicate in-phase relationships, and vice versa. The areas enclosed with lines are significant in a 95% confidence. X-axis represents time, and y-axis represents periods. Figure 8 shows Kyoto's decarbonization potentials for "PV only" and "PV + EV" in 2018 and 2030 as for Paris and Ile-de-France in Fig. 3. Kyoto's profiles are more similar to the those of Ile-de-France than that of Paris in terms of higher self-sufficiency and surplus electricity ( Fig. 3 and 8). In Kyoto, the "PV + EV" system can provide 76 % (self-sufficiency) of electricity demand including the demands from EVs. In comparison with "PV only" system, coupling PV systems with EV battery can help increase self-consumption from 40 % to 84 % ( Fig. 8 and Table 4). Figure 8. "PV only" and "PV + EV" potentials for Kyoto. "w."
and "w/o" indicate with and without, respectively.
The differences between Paris and Kyoto on the effects of "PV + EV" originate from energy structure of the cities and climate. To understand the influence of climate on the "PV + EV" system for Paris, we apply the energy demand, the number of vehicles per capita (also annual driving distance), and rooftop area per capita of Kyoto to Paris as a sensitivity analysis, such that the energy structure becomes comparable with that of Kyoto in the analysis. Thus, the difference between two cities become only climate [26]. With these settings, selfconsumption, self-sufficiency, and energy sufficiency of the "PV + EV" system for Paris is 87%, 62%, and 71%
for the "PV + EV" system with the full usage (71 %) of rooftop area in the city. The self-sufficiency in Kyoto is 76 % (Table 5), which is higher by 14 points than that of Paris. Our sensitivity analysis indicates that the effects of the "PV + EV" system in Paris are lower than those for the city of Kyoto owing to the climate (e.g., higher latitude).
CO2 emission reductions
France is already quite low carbon in terms of electricity generation owing to accumulated investments on nuclear power plants. In 2019, grid CO2 emission factor for France was 0.063 kgCO2/kWh [40], which can be compared with 0.352 kgCO2/kWh in 2019 for Kyoto [41]. This indicates that the "PV + EV" system can reduce CO2 emission from electricity consumption by 0.020 kgCO2/kWh (= 0.063*0.31, where 0.31 is self-sufficiency for PV + EV) for the Paris's power system and 0.270 kgCO2/kWh (= 0.352*0.76, where 0.76 is self-sufficiency for PV + EV) in 2019 for the Kyoto's. Therefore, the "PV + EV" system in Kyoto, where the current electricity generation has high CO2 emission from coal-and gas-fired power plants, is 13.5 times more effective to lower the mean CO2 content (/kWh) of power generation than that in Paris.
Discussion
Our model calculations showed that developing rooftop PV could bring economic benefits for both Paris and
Ile-de-France. It was estimated to be the case already in 2019 and the benefits could increase in 2030 owing to declining costs. Up to a certain roof coverage, 50-60% of the total roof area for Paris and 20-30% for Ile-de-France, the production does not exceed the demand, resulting in a nearly 100% self-consumption at the macroscopic level. Above such threshold, FIT was shown to play a role. EVs used batteries are another option, which can be more profitable thanks to the combination of EVs with PV through V2H or V2B systems developed at the city or region level. V2H or V2B systems can add value to PV systems, allowing a high self-consumption and self-sufficiency, when the roof coverage exceeds the threshold coverage for the region. The systems also allow bypassing the classical battery storage, which is too expensive to be profitable. Finally, because the electricity production is low carbon in France due to the reliance on nuclear power (70.5% of generated electricity in 2019) [42], solar panels alone do not allow substantial CO2 emission abatements. But the "PV+EV" scenario facilitates further CO2 emission abatements directly or indirectly from the use of EV relative to that of ICE.
Technical difficulties may hinder the implementation of the PV systems on complicated roof surface and V2H and V2B systems in densely populated districts. Grid constraints could also be limiting factors. These factors may work against a widespread use of PV and PV+EV. Furthermore, there are also practical constraints for the implementation of "PV only" and "PV + EV" systems. Wind turbines are not well accepted in some French regions, and solar panels may not be socially accepted in a historic city such as Paris [43]. Most buildings in Paris are under co-ownership that would require an agreement on the PV installation and use, as well as associated cost and benefit sharing. Legal difficulties could also arise, since buildings situated less than 500 m away from a historical monument or landmark must ask for a specific permit for a PV installation. The present roof coverage of PVs is less than 0.3% in Paris today. While the use of EV is becoming more widespread in Paris these days, not all buildings have sufficient parking space for EVs. Such infrastructure constrain may hinder the implementation of V2H systems in Paris. However, such barriers may be lower in Ile-de-France than in Paris.
Even if the systems bring net benefits at some point of the long-term project period, the requirement of a large head investment could also be an economic barrier. To address those issues, strong political decisions, accompanied by legal and financial support and stakeholder engagement, may be needed.
Conclusions
While the SolarEV City Concept can face certain implementation barriers in Paris and Ile-de-France and may only lead to a modest reduction in GHG emissions in France, it can improve overall energy efficiencies by making use of PVs supplemented by the storage capacity of EV and may facilitate a low-carbon shift in transport as part of urban transformation. The SolarEV City Concept can be one of the pillars for transformation toward sustainability and jointly addressed with other pillars. Our analysis suggested that Ile-de-France would be a more promising venue for deploying the SolarEV City approach than Paris, or the deployment should be done in all the Ile-de-France administrative region including Paris or jointly for Paris and Ile-de-France such that large surplus electricity in suburb can be consumed in the center of the city. At the regional level, the storage brought by EVs can be useful with a relatively low rooftop PV coverage in Ile-de-France (20-30%). Ile-de-France is less susceptible to implementation barriers than Paris. Synergies between PVs and EVs cannot be expected in Paris below the rooftop PV coverage of 50%-60% in our estimate. Our analyses indicate that the high-latitude locations of Paris and Ile-de-France is not an advantage for the "PV + EV" system, but it can be complemented with high wind power potential in winter in the region. Although low-carbon electricity is already realized partially in France by nuclear power, the SolarEV City Concept may help take one more step forward toward zero-carbon energy systems in Paris.
Figure 2 .
2Temperature, average daily electricity demand, and daily PV generation for Paris in 2019 and Kyoto in 2018. The data for Kyoto are from [22]. 2.6. PVs The roof areas of Paris and Ile-de-France are 31 and 402 km 2 , respectively [33]. To convert the roof area into the maximum capacity of PV, we used an estimate of 7 m 2 for 1 kWh of PV for both 2019 and 2030, which
Figure 3 .
3"PV only" and "PV + EV" potentials for Paris (left panels) and Ile-de-France (right panels). Note that NPVs do not include cost savings from gasoline/diesel expenens.
Figure 4 .
4Energy yields with different slopes of rooftop PVs with various azimuths. Red lines represent Paris, and blue lines represent Kyoto.
Figure 5 .
5Monthly PV generation with various PV slopes in Paris and Kyoto.
Figure 6
6illustrates average hourly electricity demand variations in a day for different months for Paris and
Table 1 .
1General statistics of Paris, Ile-de-France, and Kyoto. Data for Kyoto are from[16].Table 2. The number of cars, the state of car use, and the average travel distance in Paris, Ile-de-France, and Kyoto. Data for Kyoto are from[16].Paris Ile-de-France Kyoto
Population (million)
2.18 12.2
1.47
Area (km 2 )
105 12,011
827
Density (1000ppl/ km 2 ) 20.6 1.0
1.8
Roof area (km 2 )
31
402
52
Roof area per capita (m 2 ) 14
33
13
Annual Electricity
consumption per capita
(kWh)
6031 6277
5678
Paris Ile-de-France Kyoto
Number of diesel cars (thousand)
250 2,802
-
Number of gasoline cars (thousand)
334 2,525
-
Total number of cars (thousand)
585 5,327
485
Number of cars per capita
0.27 0.44
0.33
Proportion of cars used during
weekdays
0.35 0.63
-
Table 3 .
3Prices of PVs assumed in this study.Paris Ile-de-France
PV, 2019, installation and inverter
included (€/W)
1.9
1.9
PV, 2030, installation and inverter
included (€/W)
1.31
1.31
2.7. EVs and vehicle statistics
Table 4 .
4Decarbonization indicators for Paris and Ile-de-France in 2019 and 2030. Cost-savings include those from gasoline/diesel expenses as in[22]. The percentages indicated for the optimal PV capacity are the corresponding rooftop area in the city.2019
2030
2030
"PV only"
"PV only"
"PV+EV"
Paris
with FIT
without
FIT
with FIT
without
FIT
with FIT
without
FIT
Optimal PV capacity
(GW)
2.7 (44%)
2.5
(44%)
3.6 (58%) 3.2 (52%)
4.4 (71%)
4.4 (71%)
Self-consumption (%)
97
98
87
92
100
100
Self-sufficiency (%)
20
19
24
23
31
31
Energy sufficiency (%)
21
19
28
25
31
31
Cost saving (%)
2
2
5
5
12
12
CO2 emission reduction
(%)
18
17
21
20
51
51
2019
2030
2030
"PV only"
"PV only"
"PV+EV"
Ile-de-France
with FIT
without
FIT
with FIT
without
FIT
with FIT
without
FIT
Optimal PV capacity
(GW)
15 (19%)
14
(17%)
20 (25%)
18 (22%)
48 (54%)
48 (60%)
Self-consumption (%)
97
98
88
92
99
100
Self-sufficiency (%)
20
19
24
23
53
50
Energy sufficiency (%)
21
19
27
25
53
50
Cost saving (%)
1
1
4
4
21
22
CO2 emission reduction
(%)
13
12
14
14
79
77
Table 5 .
5Decarbonization indicators for Kyoto. Cost-savings include those from gasoline/diesel expenses as in[22]. The percentages indicated for the optimal PV capacity are the corresponding rooftop area in the city.2019
2030
2030
"PV only"
"PV only"
"PV+EV"
Kyoto
with FIT
without
FIT
with FIT
without
FIT
with FIT
without
FIT
Optimal PV capacity
(GW)
2.3 (22%) 1.8 (17%) 7.4 (72%) 2.8 (27%) 7.4 (72%) 5.9 (57%)
Self-consumption (%)
88
96
40
80
84
94
Self-sufficiency (%)
29
25
43
32
76
68
Energy sufficiency (%)
33
26
106
40
90
73
Cost saving (%)
4
4
18
11
31
29
CO2 emission reduction
(%)
27
23
40
30
78
70
Declaration of Competing InterestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Data availabilitySupplementary data is available at https://data.mendeley.com/datasets/t93bh6bthj/1.
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| sample_1800 | 0.9398 | arxiv | |
Los Cultivos Mixtos y las Fermentaciones Alcohólicas
Pilar Escalante-Minakata
Vrani Ibarra-Junquera
Facultad de Ciencias Químicas
Universidad de Colima
División de Biología Molecular
IPICyT
Los Cultivos Mixtos y las Fermentaciones Alcohólicas
Alcoholic fermentationswinearomamixed-culturessequential-culturespopulation dynamics
RESUMENLa dinámica poblacional de cultivos mixtos y secuenciales en fermentaciones de mostos de frutas es un problema muy interesante desde el punto de vista teórico y tecnológico. Por cultivos mixtos nos referimos a que se encuentran presentes desde un inicio más de una especie/raza de microbio y por cultivo secuencial a que serán añadidas a lo largo de la fermentación. Dichos procesos tienen un papel fundamental en la industria de bebidas fermentadas, de ahí la importancia de su estudio y modelado. Los modelos de estos procesos deben representar la dinámica de múltiples especies de microorganismos que crecen en una mezcla de sustratos, porque el mosto de frutas esta formado por una proporción importante de hexosas y pentosas. En las bebidas y en general en los alimentos fermentados un aspecto muy importante son las propiedades organolépticas, por ello resulta fundamental estudiar la dinámica poblacional y el impacto de estos consorcios microbianos en el perfil de compuestos volátiles, y su influencia en el perfil sensorial. El objetivo de este trabajo es mostrar un panorama general de estos ecosistemas fermentativos desde el punto de vista biológico, matemático y tecnológico.Palabras clave: Fermentaciones alcohólicas, vinos, aroma, cultivos mixtos, cultivos secuenciales, dinámica poblacional.ABSTRACTThe population dynamics of mixed-culture and sequential-cultures in fruit-must fermentation is a very interesting problem from both the theoretical and technological stand point. By mixed-culture we refer to those fermentations in which more that one strain/species are present from the beginning of the process; and by sequential to those in which different microorganisms are added along the process. These kinds of fermentations play a key role in industry of fermented beverages.The mathematical models of such processes should represent the dynamics of multiple species growing in a mixture of substrates as the fruit must composition includes an important proportion of hexoses and pentoses. Since the flavor is a basic aspect of beverages, and in general of all fermented foods, it is fundamental to study the population dynamics and its impact in the organoleptic properties, through the influence in the volatile compound profile. The goal of this paper is to present a panorama of the investigations of these fermentative ecosystems from a biological, mathematical, and technological stand point.
INTRODUCCIÓN
Durante décadas la investigación en biotecnología se enfocó en cultivos puros, ahora los efectos sinérgicos en cultivos mixtos de microorganismos están siendo objeto de un creciente interés (Schink, 2002). La dinámica del cultivo mixto de microorganismos en mezclas de sustratos es un problema muy interesante desde el punto de vista teórico y tecnológico. Hoy en día se reconoce que para entender la presencia, el crecimiento y el papel que juegan los microorganismos en los bioprocesos se necesita un enfoque de ecología microbiana (Días & Wacher, 2003). Los cultivos mixtos que crecen en mezclas de sustratos juegan un papel fundamental en la bioingeniería.
La producción de bioetanol, es un ejemplo de mucho interés. La materia prima usada en la fermentación para producirlo consiste típicamente en una mezcla de hexosas y pentosas. Por tanto el bioetanol es el producto de la transformación de una mezcla de sustratos mediante microorganismos.
Cuando un microorganismo crece en presencia de al menos dos sustratos, uno de ellos es normalmente agotado primero, lo que resulta en un cambio en la pendiente de la curva de crecimiento de biomasa. La población de levaduras usadas en la producción de bioetanol, a escala industrial, puede variar de acuerdo con las condiciones particulares del proceso de cada planta así como del estrés que el ambiente fermentativo impone a los consorcios de microorganismos. Por ello, las levaduras aisladas de una industria en particular pueden estar adaptadas a dichas condiciones y por tanto son mejores para ese proceso que una cepa comercial pura (da Silva-Filho et al., 2005).
Los alimentos fermentados constituyen igualmente un área de gran interés. Su calidad y producción en condiciones controladas dependen del conocimiento y control de la microbiota presente (Días & Wacher, 2003). Un ejemplo clásico en alimentos fermentados con cultivos mixtos es el yogurt, el cual es el producto de la interacción de Lactobacillus bulgaris y Streptococcus thermophilus (Marshall, 1987). Para obtener una idea más detallada de la organización y dinámica de las comunidades microbianas en alimentos fermentados, será necesaria la detección de su actividad y el papel que esta juega en el producto terminado.
En este trabajo revisaremos tres aspectos fundamentales de las fermentaciones alcohólicas basadas en consorcios microbianos. Primero hablaremos del punto más importante en una bebida: el sabor, ya que éste determinará la aceptación del producto final. Después en la sección "los vinos y la dinámica poblacional" daremos un breve panorama del estado de arte de las fermentaciones alcohólicas que se llevan cabo con cultivos mixtos. Finalmente, en la sección "modelando la dinámica poblacional" presentaremos un panorama del modelado de estos complejos sistemas biológicos.
EL AROMA Y LOS VINOS
Según Abbott (1999) los atributos que más condicionan la aceptabilidad del alimento por parte del consumidor son los relacionados con la calidad sensorial u organoléptica, que incluye la apariencia, la textura, el aroma y el gusto. En este sentido, uno de los rasgos organolépticos más complejos y determinantes de la calidad sensorial es el aroma del alimento, que se puede definir como la sensación global producida por los compuestos que interaccionan con las terminaciones nerviosas sensitivas del gusto, del olfato y la visión (Goff & Klee, 2006). El aroma está compuesto por centenares de compuestos volátiles que pertenecen a distintas familias químicas y que se encuentran en muy variable concentración (Ruiz & Martínez, 1997). La elevada producción y la necesidad de encontrar alimentos aromáticamente estandarizados, requieren herramientas analíticas eficientes para la caracterización y algoritmos que permitan el control automático de la producción. Cabe mencionar que el umbral de percepción de las sustancias que condicionan el aroma puede variar desde µg/l a mg/l, pero no necesariamente por encontrarse en mayor concentración su incidencia será mayor (Riu, 2005). En este sentido, el impacto sensorial esta relacionado con las presencia de compuestos volátiles. Así pues, una de las principales variables a medir es la fracción aromática.
En enología lo usual es clasificar los aromas del vino en función de la etapa en la que se forman. El aroma puede provenir de la fruta, es el llamado aroma primario que incluye dos subcategorías: el varietal (compuestos volátiles libres presentes en la uva que dependerán de la variedad utilizada y sus características) y el prefermentativo (aromas que se liberan de su combinación con otras sustancias llamadas precursores, debido a la actividad enzimática provocada por la tecnología aplicada). El aroma secundario proviene de la levadura que se desarrolla durante la primera fermentación, está ligado a la presencia de ciertos tipos de enzimas y es el aroma mayoritario; y finalmente el aroma terciario o postfermentativo es el que se forma durante la crianza. Este último se desarrolla mediante reacciones químicas y/o bioquímicas a partir de aromas de etapas anteriores (Riu, 2005).
El perfil aromático característico de las frutas depende de una mezcla compleja de compuestos químicos que se va formando durante la maduración del fruto, a través de distintas rutas bioquímicas a partir de precursores de las plantas (Gómez & Ledbetter, 1997;Lund & Bohlmann, 2006). El desarrollo de los aromas en las frutas tiene lugar durante el climaterio, que es el periodo crucial del proceso de maduración. Pequeñas cantidades de carbohidratos, lípidos, proteínas y aminoácidos se catabolizan y dan lugar a distintos compuestos volátiles. La velocidad de formación de estas sustancias aumenta después del inicio del climaterio y el proceso continúa tras la recolección de la fruta hasta que comienza la senescencia (Arthey & Ashurst, 1997). Al influir en la ecología del proceso de elaboración de vino, las levaduras contribuyen al sabor del vino. El metabolismo y la actividad enzimática de cada especie de microorganismo así como las combinaciones de éstas impactan en el aroma. Los característicos sabores frutales del vino se deben principalmente a la esterificación de los alcoholes superiores sintetizados por las levaduras.
LOS VINOS Y LA DINÁMICA POBLACIONAL
La producción de vino es otro proceso de especial interés. Cabe mencionar que el término "vino" se aplica al líquido resultante de la fermentación alcohólica, total o parcial, del zumo de frutas, sin adición de ninguna sustancia. Se pueden encontrar además del vino de uva, vinos de mango y plátano entre otros vinos de frutas. Desde el punto de vista biotecnológico, el vino es el producto de complejas interacciones entre levaduras y bacterias que comienza desde que el fruto está en la plantación y continúa a lo largo de todo el proceso de fermentación, hasta el momento en que el producto es embotellado. En el proceso de elaboración de vino de uva, el tipo y cantidad de aroma depende de varios factores: microorganismos fermentantes, condiciones ambientales (suelo y clima), estado de la fruta, proceso de fermentación, pH del mosto, cantidad de dióxido de azufre, aminoácidos presentes en el mosto (Lilly et al., 2000). En el caso de los vinos de uva está bien estudiado que aunque el tipo de uva y las condiciones de cultivo son claves en el sabor del vino, los microorganismos (en especial las levaduras) tiene un papel muy importante en las características organolépticas (Fleet, 2003). De reportaron que distintos tipos de mezcal joven, reposado y añejo producidos con mosto de Agave salmiana, presentaron diferente composición de compuestos volátiles como etanol, alcoholes superiores y ésteres, y que éstos contribuían de forma importante al perfil sensorial. De estos trabajos se puede concluir que la interacción entre la materia prima y el proceso de elaboración en la bebida son los responsables de las propiedades organolépticas de las bebidas alcohólicas provenientes de la fermentación.
Tradicionalmente la producción de vinos se ha realizado a partir de fermentaciones espontáneas de los mostos llevadas a cabo por cepas de levaduras endémicas residentes en las superficies de las uvas y de los equipos de las bodegas. Dentro de las fermentaciones alcohólicas basadas en consorcios microbianos las fermentaciones espontáneas se pueden considerar las pioneras de la biotecnología. Estas fermentaciones espontáneas de mostos son un complejo proceso que involucra la acción de diferentes géneros y especies de levaduras e incluso bacterias. El equilibrio entre los diferentes microorganismo presentes en la flora inicial, el orden de sucesión entre especies y la diversidad de la flora pueden variar entre un año y otro. Dando así origen a la diferencia en la velocidades de fermentación y a las características del vino de año a otro (Querol et al., 1992(Querol et al., y 1994.
Existen argumentos a favor y en contra de las fermentaciones espontáneas. El principal argumento a favor indica que en estas fermentaciones se consiguen características organolépticas típicas de la zona que no estarían presentes si se utilizara un inóculo de cepas foráneas. Sin embargo la calidad del producto puede ser muy variable. La composición cualitativa y cuantitativa de las microbiota presente a lo largo de la fermentación del mosto puede depender principalmente de los siguientes factores: región de donde es originaria la fruta, procedimiento de producción, tipo de bebida a ser producida, concentración inicial de la microbiota, temperatura, pH, SO 2 , y concentración de etanol (Torija et al., 2001;Granchi et al., 2002).
El uso de inóculos con poblaciones mixtas y/o inóculos secuenciales, constituye una herramienta importante para estandarizar el producto y preservar aquellas características deseables. Seleccionar cepas de una determinada región parece ser la solución para asegurar un producto estandarizado preservando las características organolépticas que distinguen a la zona de producción. Además del Saccharomyces cerevisiae se han reportado muchas otras levaduras presentes en la fermentación del vino: Hanseniaspora guilliermondii, Kloeckera apiculata (Romano et al., 1992(Romano et al., , 1997aZironi et al., 1993;Gil et al., 1996), Pichia anomala (Rojas et al., 2001), Candida stellata, Torulaspora delbrueckii (Ciani & Maccarelli, 1998), Candida valida, Bretanomyces bruxellensis, Rhodotorula aurantiaca, Deckera intermedia (Mateo et al., 1991;) y Candida catarellii (Toro & Vázquez, 2002). Todas estas levaduras mejoran el bouquet del vino, pero no son capaces de terminar la fermentación debido a su poca tolerancia a altas concentraciones de etanol (Clemente-Jiménez et al., 2005). Por está razón, varios autores ya han estudiado fermentaciones usando mezclas de levaduras, ya sea inoculadas simultáneamente (Moreno et al. 1991;Gil et al., 1996;Erten, 2001) o de manera secuencial (Herraiz et al., 1990;Zironi et al., 1993;Toro & Vázquez, 2002). Cabe mencionar que estos trabajos no han sido abordados desde una perspectiva de sistemas dinámicos y no han generado modelos que permitan explorar aspectos de control y propiedades dinámicas. Los mecanismos de interacción de estos ecosistemas de la fermentación incluyen: producción de enzimas líticas, etanol, dióxido de azufre y efectos de tipo "killer"; competencia por los nutrientes, oxígeno, producción de dióxido de carbono.
MODELANDO LA DINÁMICA POBLACIONAL
Es muy importante la identificación y el entendimiento de las interacciones enológicas que ocurren en estos consorcios de levaduras y bacterias. Los trabajos pioneros de Jacob Monod y J. B. S.
Haldane han servido como un punto de inicio de importantes modelos matemáticos que dan cuenta de diferentes aspectos del crecimiento microbiano en monocultivos por lote, lote-alimentado y continuos.
Estos trabajos suponen cultivos puros. Actualmente existe una vasta cantidad de artículos sobre modelos matemáticos de crecimiento microbiano (Nielsen et al., 2003). Sin embargo, en el ámbito de cultivos mixtos la literatura se reduce considerablemente. Por supuesto, en general, cuando la complejidad de un problema crece, la posibilidad de analizarlo en términos precisos disminuye.
En el modelado de la mayoría de estos sistemas biológicos se asume de manera implícita que son de naturaleza continua, aplicando las ecuaciones diferenciales como la herramienta para su modelado.
Las variables analizadas son denominadas estados, y son propiedades tales como la concentración de microorganismo (biomasa en g/l), concentración del producto (g/l), y concentración de sustrato (g/l); y en algunos casos concentración interna de enzimas. Sin embargo todos estos estados son muy difíciles de medir (sino es que imposible) en tiempo real. Se necesitan desarrollar modelos basados en ecuaciones diferenciales ordinarias que contemplen entre sus estados variables que sean fácilmente monitoreables en tiempo real. Dichos modelos permitirían el desarrollo de controladores que hagan frente a las perturbaciones inherentes a estos sistemas.
Se ha descrito como es posible inferir teóricamente la presencia de cultivos mixtos a partir de datos de biomasa total, usando una transformada ondeleta (Ibarra-Junquera et al., 2006ª). La idea central desarrollada por Ibarra-Junquera et al., (2006ª) se basa en el hecho de que todo evento a nivel metabólico (cambio de sustrato) o a nivel de interacciones entre especies (crecimiento mixto con competencia o sin ella) genera la presencia de singularidades en la señal de biomasa total. Es decir, estos eventos se asocian a la presencia de puntos en donde alguna derivada no exista, relacionando así el grado de singularidad a la naturaleza del evento que la provocó. La herramienta usada para detectar la existencia de singularidades y su grado fue la transformada ondeleta, la cual es un análogo de la transformada de Fourier a nivel local. En concreto, Ibarra-Junquera et al., (2006ª) mostraron teóricamente como cambios en la fuente de sustrato provocan singularidades en la segunda derivada de la señal de biomasa total mientras que crecimientos mixtos, sin competencia, inducen singularidades en la primera derivada.
Por otra parte se han realizado trabajados en el caso del mezcal donde se encontró que es posible monitorear en línea el proceso fermentativo a partir de medir el potencial redox durante la fermentación (Escalante-Minakata et al., 2006 b ), asociando la señal de redox a la biomasa total. Ambas herramientas (el potencial redox y la transformada ondeleta) son de gran utilidad para entender la dinámica de las fermentaciones. Al estudiar la dinámica poblacional de las fermentaciones con cultivos mixtos se busca entender y eventualmente manipular (indirectamente) el mecanismo a través del cual una especie de microorganismo impacta a otra y finalmente a las propiedades organolépticas del producto de interés. Para incrementar la producción y la calidad del producto son necesarias técnicas para el monitoreo en línea y el control automático de estos complejos procesos fermentativos. Por otra parte, es importante resaltar que la mayoría de controles que operan actualmente en la industria de los bioprocesos están basados en modelos lineales del proceso, a pesar de que prácticamente todos los procesos biológicos son de naturaleza no lineal. Por ello es de esperarse que estrategias para su monitoreo y control basadas directamente en modelos no lineales muestren considerables ventajas y mejor desempeño en estos procesos fermentativos tan altamente no lineales.
Sin embargo, en la mayoría de los procesos bioquímicos es difícil desarrollar modelos matemáticos, basados en ecuaciones diferenciales ordinarias, que sean razonablemente precisos y cuyos valores estimados de parámetros sean confiables. No obstante, dichos modelos resultan fundamentales para la optimización y el desarrollo de estrategias de control del proceso. En particular en los reactores biológicos las incertidumbres en el modelo se deben a un limitado conocimiento del proceso real, a no linealidades, dinámicas no modeladas, presencia de ruido interno o externo, influencias del ambiente y parámetros variantes en el tiempo. La presencia de tales incertidumbres es la causa del desajuste entre el modelo optimizado y el proceso real, lo cual puede degradar el desempeño del controlador provocando serios problemas de estabilidad en el proceso. Por lo tanto resulta un reto de gran importancia, diseñar esquemas de control para procesos bioquímicos, que sean robustos a incertidumbres en el modelo.
Los primeros modelos de crecimiento mixto en un sustrato único, en quimiostato, mostraron teórica y experimentalmente, que no más de una especie sobrevive, sin importar la velocidad de dilución, ni la concentración de sustrato alimentado (Aris & Humphrey, 1977;Hansen & Hubell, 1980;Powell, 1958).
Sin embargo, yacía una contradicción en este resultado, la llamada "paradoja del plancton" (Hunchinson, 1961). Por ello el problema de crecimiento mixto en una mezcla de sustratos atrajo el interés de muchos matemáticos. Este interés resultó en dos artículos fundamentales, que muestran que en presencia de múltiples sustratos limitantes, es importante especificar los requerimientos nutricionales satisfechos por los nutrientes (León & Tumpson, 1975;Tilman, 1977). Es decir, dos sustratos son mutuamente sustituibles si ambos satisfacen exactamente los mismos requerimientos nutricionales y con ello el crecimiento continúa incluso en ausencia de cualquiera de ellos. Entonces, podemos decir que dos sustratos son complementarios si satisfacen distintos requerimientos nutricionales y con ello el crecimiento es imposible en ausencia de cualquiera de ellos.
En años recientes han surgido modelos matemáticos que describen aspectos fisiológicos del crecimiento microbiano. Hanegraaf et al. (2000), desarrollaron un modelo que describe el mecanismo respiro-fermentativo de una levadura. El modelo toma en cuenta la presencia de múltiples rutas de asimilación de la fuente de carbono y su respuesta ante diferentes concentraciones de sustrato. Sin embargo, estos modelos solo son para cultivos puros, de ahí la importancia de desarrollar nuevos modelos que nos permitan mejorar y entender estos importantes fenómenos enológicos.
CONCLUSIONES
El mercado actual demanda no solo una calidad homogénea en los productos sino una alta calidad y un bajo precio. El estudio, el modelado y el análisis dinámico de los procesos de fermentación basados en cultivos mixtos permitirían no solo elucidar los mecanismos para influir en las propiedades organolépticas del producto final, sino también desarrollar estrategias para su control automático a nivel industrial. Estas herramientas conducirán al desarrollo de métodos sistemáticos de producción que permitan el desarrollo de productos homogéneos a lo largo de los años.
AGRADECIMIENTOS
Los autores agradecen al Dr. Haret Rosu, al Dr. Juan Osuna y a los árbitros cuyos certeros comentarios no hicieron más que enriquecer este trabajo.
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| sample_1801 | 0.6262 | arxiv | |
Traveling planetary-scale waves cause cloud variability on tidally locked aquaplanets
21 Nov 2022 November 23, 2022
Maureen Cohen
School of GeoSciences
The University of Edinburgh Edinburgh
EH9 3FFUK
Centre for Exoplanet Science
The University of Edinburgh
UK
Massimo A Bollasina
School of GeoSciences
The University of Edinburgh Edinburgh
EH9 3FFUK
Denis E Sergeev
Department of Mathematics College of Engineering, Mathematics, and Physical Sciences
University of Exeter Exeter
EX4 4QFUK
Paul I Palmer
School of GeoSciences
The University of Edinburgh Edinburgh
EH9 3FFUK
Centre for Exoplanet Science
The University of Edinburgh
UK
Nathan J Mayne
Department of Astrophysics College of Engineering, Mathematics, and Physical Sciences
University of Exeter Exeter
EX4 4QFUK
Traveling planetary-scale waves cause cloud variability on tidally locked aquaplanets
21 Nov 2022 November 23, 2022Draft version Typeset using L A T E X default style in AASTeX631Exoplanets (498) -Exoplanet atmospheres (487)
Cloud cover at the planetary limb of water-rich Earth-like planets is likely to weaken chemical signatures in transmission spectra, impeding attempts to characterize these atmospheres. However, based on observations of Earth and solar system worlds, exoplanets with atmospheres should have both short-term weather and long-term climate variability, implying that cloud cover may be less during some observing periods. We identify and describe a mechanism driving periodic clear sky events at the terminators in simulations of tidally locked Earth-like planets. A feedback between dayside cloud radiative effects, incoming stellar radiation and heating, and the dynamical state of the atmosphere, especially the zonal wavenumber-1 Rossby wave identified in past work on tidally locked planets, leads to oscillations in Rossby wave phase speeds and in the position of Rossby gyres and results in advection of clouds to or away from the planet's eastern terminator. We study this oscillation in simulations of Proxima Centauri b, TRAPPIST 1-e, and rapidly rotating versions of these worlds located at the extreme inner edge of their stars' habitable zones. We simulate time series of the transit depths of the 1.4 µm water feature and 2.7 µm carbon dioxide feature. The impact of atmospheric variability on the transmission spectra is sensitive to the structure of the dayside cloud cover and the location of the Rossby gyres, but none of our simulations have variability significant enough to be detectable with current methods.
INTRODUCTION
The capabilities of the James Webb Space Telescope (JWST) have raised the prospect of characterizing the atmospheres of transiting exoplanets through transmission spectroscopy (Mollière et al. 2017;Greene et al. 2016;Beichman et al. 2014). Particular interest has focused on the characterization of rocky and temperate planets orbiting at distances from their host stars that would allow liquid water to exist on their surfaces (Gialluca et al. 2021;Morley et al. 2017). A number of terrestrial planets have been found in this range of orbital distances, known as the habitable zone (Kasting et al. 1993), including the non-transiting Proxima Centauri b (Anglada-Escudé et al. 2016) in orbit around the closest star to Earth, Proxima Centauri, and three transiting planets in orbit around the star TRAPPIST-1 (Gillon et al. 2017). These planets are thought to be tidally locked to their host stars as a result of their close-in orbits (Barnes 2017), and indeed tidally locked planets around M-dwarf stars may be the most common type of potentially habitable planet (Dressing & Charbonneau 2015;Kopparapu 2013).
A challenge for transmission spectroscopy of transiting exoplanets is the presence of clouds, which mute spectroscopic features by scattering light isotropically at the level of the cloud deck (Barstow 2021;Helling 2019). Clouds are believed to exist on multiple known exoplanets (Burningham et al. 2021;Helling et al. 2021;Kreidberg et al. 2014). Modelling studies of the impact of clouds on the transmission spectra of water-rich rocky planets have indicated that in most cases it would take anywhere from ten to hundreds of transits to detect atmospheric absorption features using the JWST (Komacek et al. 2020;Suissa et al. 2020;Fauchez et al. 2019). Available observations of the planets in the TRAPPIST-1 system have ruled out hydrogen-rich primordial atmospheres for these planets Garcia et al. (2022); Moran (2018);de Wit et al. (2016), but are unable to break the degeneracy between a cloud-or aerosol-heavy atmosphere, a high molecular mean weight atmosphere, or the absence of an atmosphere, although the JWST may be able to do so in future (Lustig-Yaeger et al. 2019). Some work has offered brighter prospects of the detection of water vapor on arid (icy) planets (Ding & Wordsworth 2022) and found that stratospheric (as opposed to tropospheric) clouds would not necessarily affect observations by the JWST (Doshi et al. 2022). As water-rich planets are expected to form substantial cloud decks, this limitation is a significant obstacle to the detection of atmospheric chemistry and potential biosignatures on water-rich habitable worlds.
One possible avenue for characterizing water-rich planets is temporal variability in cloud cover. Studies of exoplanet variability are extremely limited so far, but variable wind speeds may have been detected on KELT-9b (Asnodkar et al. 2022) and variation in the offset of the peak of the phase curve of HAT-P-7b was reported by Armstrong et al. (2016) and later disputed by Lally & Vanderburg (2022). Some theoretical (Welbanks & Madhusudhan 2022;Powell et al. 2019;Line & Parmentier 2016) and observational (Mikal-Evans et al. 2022;Ehrenreich et al. 2020) studies have found that it may be possible to detect spatial variability in cloud cover at the planetary terminators of large exoplanets. In a one-dimensional model, Tan & Showman (2019) found that cloud radiative feedback can drive atmospheric variability on brown dwarfs and giant planets. Most relevantly, Fauchez et al. (2021) and May et al. (2021) simulated the effect of cloud variability on transmission spectra and atmospheric retrievals of TRAPPIST-1e. In the latter study, general circulation model simulations exhibited cloud cover variability at the planetary limb. The authors combined ten synthetic spectra randomly chosen from a time series of 365 days of the planet's climate and used the resulting composite spectrum to retrieve atmospheric chemical abundances, finding that this did not result in a difference compared to the use of non-variable spectra. However, May et al. (2021) did not study the cause of the cloud variability in their simulations. An understanding of the physics of cloud and climate variability is necessary to confirm that this variability is not noise and to explain why different models predict vastly different degrees of variability.
In this work, we describe a dynamical mechanism driving cloud and climate variability in the atmospheres of moist tidally locked terrestrial exoplanets and investigate its impact on time series of transmission spectra. In Section 2, we describe our general circulation model, simulation parameter space, and radiative transfer scheme for simulating transmission spectra. In Section 3, we outline a feedback loop between cloud radiative effects, incoming stellar radiation, and the dynamical state of the atmosphere that causes back-and-forth propagation of planetary-scale (Rossby) waves and regular variations in cloud cover at the planetary limb. We further discuss the interaction between the propagating Rossby gyres and the dayside cloud structure and simulate time series for the water absorption feature at 1.4 µm and the carbon dioxide feature at 2.7 µm. Our results support the findings of May et al. (2021) and Fauchez et al. (2021) that cloud variability is unlikely to affect JWST observations, except in specific cases where the cloud structure and wave propagation may interact in a fortuitous way. In Section 4, we discuss our results in the context of previous work on Rossby wave structures on tidally locked planets, as well as implications of dynamical variability for the planetary climate and for observational practices. We conclude in Section 5.
METHODS
Model description
Our simulations are based on the Global Atmosphere 7.0 (GA7) configuration of the Met Office Unified Model (UM). Idealized versions of the UM have previously been used to simulate hot Jupiters (Christie et al. 2021;Mayne et al. 2017Mayne et al. , 2014 and terrestrial planets (Braam et al. 2022;Sergeev et al. 2022a;Eager et al. 2020;Boutle et al. 2017). The model uses the ENDGame (Even Newer Dynamics for General atmospheric modelling of the environment) dynamical core to solve the non-hydrostatic, fully compressible, deep-atmosphere Navier-Stokes equations (Wood et al. 2014). GA7 contains parameterizations for sub-grid scale turbulence, convection, non-orographic gravity wave drag, boundary layer processes, precipitation, and clouds. Radiative transfer is simulated using the SOCRATES (Suite Of Community RAdiative Transfer codes based on Edwards and Slingo) community radiative transfer code. All simulations are run (Wilson et al. 2008). The scheme has three prognostic cloud fractions (liquid, ice, and mixed-phase), as well as water vapor and liquid and frozen condensate. These prognostic variables are updated in increments by processes in the model, including advection, convection, and precipitation. The column cloud fraction is determined by exponential random overlap. The moist atmosphere configuration includes water vapor with evaporation and precipitation and an otherwise 100 % nitrogen atmosphere with fixed trace CO 2 . In the TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) (Sergeev et al. 2022b), the UM's cloud scheme produced a mean cloud fraction in the middle of the comparison (60 %), compared to the extremes of the Laboratoire de Météorologie Dynamique -Generic model (LMD-G, at 28 %) and the Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics model (ROCKE-3D, at 77 %).
Simulation parameters
We performed five simulations: 1. A "control" moist Proxima Centauri b with planetary and orbital parameters as described in Anglada-Escudé et al. (2016) (Control ProxB) 2. A "warm" moist Proxima Centauri b with planetary orbital parameters corresponding to the inner edge of Proxima Centauri's habitable zone (Warm ProxB) 3. A "control" moist TRAPPIST-1e with planetary and orbital parameters as described in Gillon et al. (2017) (Control TRAP-1e) 4. A "warm" moist TRAPPIST-1e with planetary and orbital parameters corresponding to the inner edge of TRAPPIST-1's habitable zone (Warm TRAP-1e) 5. A "dry" TRAPPIST-1e atmosphere identical to the control case aside from the dry atmosphere (Dry TRAP-1e) Table 1 lists the values of the parameters varied between each simulation. These parameters were chosen to facilitate comparison with previous UM studies of the two planets. The simulation set-up for Proxima Centauri b is based on Boutle et al. (2017) and Cohen et al. (2022), using a model top of 85 km with 60 vertical levels, quadratically spread to give greater resolution near the surface. The planet is simulated with a slab ocean (Frierson et al. 2006) which has a mixing depth of 2.4 m, representing a heat capacity of 10 7 J K −1 m −2 . The stellar spectrum for Proxima Centauri, modelled as a quiescent M-dwarf, was taken from BT-Settl (Rajpurohit et al. 2013) with T ef f = 3000 K, g= 1000ms −2 , and metallicity = 0.3 dex. The Proxima Centauri b simulations were spun up from an equilibrium state of a previous simulation performed using the UM with the same configuration.
For TRAPPIST-1e, we use the simulation parameters of the TRAPPIST-1 Habitable Atmosphere Intercomparison for both the dry and the moist atmosphere cases (Fauchez et al. 2021;Turbet et al. 2022;Sergeev et al. 2022b;Fauchez et al. 2022). In this instance, the models use 39 vertical levels with a top of 80 km. The planet's surface in the moist case is a slab ocean with a mixing layer of 1 m, representing a heat capacity of 4 × 10 6 J K −1 m −2 . The spectrum is taken from BT-Settl (Rajpurohit et al. 2013) with T ef f = 2600 K and Fe/H=0. The TRAPPIST-1e simulations were spun up from an initial state of an isothermal (300K) dry atmosphere at rest with zero winds, following the THAI protocol . Unlike in the THAI project, our simulations were run with the UM's gravity wave drag scheme switched on, resulting in some differences in the wind structure.
All the simulations correspond to tidally locked planets. The Control ProxB, Warm ProxB, Control TRAP-1e, and Dry TRAP-1e simulations were run until a balance between incoming and outgoing radiation at top-of-atmosphere was achieved. Control ProxB, Warm ProxB, and Control TRAP-1e ran for 6,000 days and the period from day 5,000 to 6,000 was sampled for analysis. The Warm TRAP-1e simulation underwent a runaway greenhouse effect, with convection reaching the model top after approximately 4,000 days. We sampled a 990-day period (day 3,000 to the crash just before day 4,000) and include the results here to study the extreme limit of the habitable zone and in particular the potential effect of cloud variability on observations of close-in rocky planets (Venus analogues). As the Dry TRAP-1e simulation achieved radiative balance faster than the moist atmospheres, we ran the simulation for 4,000 days and used the period from day 3,000 to 4,000 for analysis. In the results reported below,"day 10" and similar formulations refer to the day of the sample period, not the day of the simulation.
NASA Planetary Spectrum Generator
We use the NASA Planetary Spectrum Generator (Villanueva et al. 2018), publicly available at https://psg.gsfc.nasa.gov/ (PSG), to simulate time series of water vapor and carbon dioxide features of the four moist atmosphere simulations as observed by the James Webb Space Telescope's NIRSpec (Near Infrared Spectrograph) instrument. We omit the dry case as it has no time-varying atmospheric chemistry or clouds. The NIRSpec instrument's range covers water vapor features in the infrared at 1.4, 1.8, and 2.7 µm, as well as CO 2 features at 2.1, 2.7, and 4.3 µm (Team et al. 2022). For each simulated atmosphere, we prescribe the orbital, planetary, and stellar parameters shown in Table 1, together with the pressure, temperature, altitude, H 2 O, N 2 , and CO 2 data from the UM. For the Proxima Centauri b simulations, the 85 km model top was sufficient for the PSG to calculate a spectrum, and we use only the model output data. For the TRAPPIST-1e simulations, however, the 80 km model top was slightly too low to enable the PSG to model the spectrum. We used the Met Office's iris package's built-in linear extrapolation method to extend the temperature, H 2 O, ice cloud, liquid cloud, N 2 and CO 2 profiles to one extra atmospheric level with an altitude of 85 km and half the pressure of the layer immediately below (MetOffice 2010). Previous works have used the PSG to generate a spectrum for each grid box and averaged the spectra for a final output representing the signal during transit (May et al. 2021;Suissa et al. 2020;Komacek et al. 2020). To reduce the computational expense of simulating long time series for multiple simulations and absorption features, we instead average the atmospheric values for each day around the limb first, generate a transit spectrum for each day, and extract and plot the absorption features against time. Similarly, a full description of the climatology of TRAPPIST-1e as simulated by the UM with a dry and moist atmosphere is given in Turbet et al. (2022) and Sergeev et al. (2022b), respectively. We give a brief overview of the equilibrium climates of all five simulations here. Figure 1 shows the vertical temperature structure, zonal mean zonal wind, vertical humidity profile, and the spatial distribution of surface temperature of each simulation. All simulations display a nightside temperature inversion, although in the Warm TRAP-1e case it is very small and the temperature profile is nearly identical on the dayside and nightside. The specific humidity profiles are likewise consistent for Control ProxB, Warm ProxB, and Control TRAP-1e, with much greater humidity on the dayside and an arid nightside. Only the Warm TRAP-1e (incipient runaway) simulation has substantial humidity on the nightside. A comparison of the zonal mean zonal wind of the Control vs. Warm ProxB and Control vs. Warm TRAP-1e cases supports an increase in zonal wind speeds for planets orbiting closer in. The Proxima Centauri b simulations have a broad equatorial jet in the troposphere and a series of vertically stacked opposing jets in the stratosphere in a longitudinally asymmetric stratospheric oscillation (LASO) as described in Cohen et al. (2022). In contrast, the Control and Warm TRAPPIST-1e simulations form a mid-latitude Table 2. Mean, maximum, and minimum values for each plot shown in Figure 1. Values are given separately for the substellar and antistellar profiles of temperature and specific humidity.
(kg/kg) 1.5×10 −3 4.9×10 −3 1.0×10 −3 10.5×10 −3 0 Max specific humidity (sub) (kg/kg) 8.2×10 −3 21.0×10 −3 5.0×10 −3 34.5×10 −3 0 Min specific humidity (sub) (kg/kg) 0.5×10 −7 4.8×10 −7 0.1×10 −7 2.5×10 −7 0 Mean specific humidity (anti) (kg/kg) 0.4×10 −4 6.2×10 −4 0.6×10 −4 52.9×10 −4 0 Max specific humidity (anti) (kg/kg) 3.0×10 −4 33.9×10 −4 3.5×10 −4 171.8×10 −4 0 Min specific humidity (anti) (kg/kg) 0.5×10 −7 5.3×10 −7 0.1×10 −7 2.4×10 −7 0 Mean surface temperature (K) 219
tropospheric jet in each hemisphere. In these simulations, unlike in the THAI project, the planet also generates a LASO in the equatorial region due to the acceleration of the flow contributed by the gravity wave drag scheme. The zonal mean zonal wind for the Dry TRAP-1e case differs from that reported in THAI (Turbet et al. 2022) for the equivalent N 2 -dominated atmosphere case. Turbet et al. (2022) reported a stable state with two mid-latitude jets, while our result is a broad equatorial jet more similar to that of Proxima Centauri b or the CO 2 -dominated atmosphere case in Turbet et al. (2022). Recent work has shown that UM simulations of TRAPPIST1-e exhibit climate bistability, with one stable dynamical state corresponding to an equatorial jet and the other to two mid-latitude jets (Sergeev et al. 2022a). It may be that the inclusion of gravity waves, which affect the dynamical structure of the atmosphere and heat transport between dayside and nightside, tipped this simulation into the equatorial jet state. The zonal wind magnitude is in line with that shown in Turbet et al. (2022) and considerably less than that in the moist atmosphere cases. The tropospheric jet structure influences the location and propagation of Rossby wave structures discussed below, as the zonal wind magnitude is a component of the Rossby wave phase speed and Rossby waves can be advected by the flow.
Mechanism of oscillation
All five simulations exhibit the presence of Rossby waves which propagate westwards in the dry case and alternatingly eastwards and westwards in all the moist cases. Figure 2 represents these waves as fluctuations in the mean midlatitude meridional wind at a height of 2.96 km. Investigation of the vertical vorticity profile and inspection of the eddy rotational component at different atmospheric levels showed that the Rossby wave-associated vorticity and wind speeds in the vertical region where clouds form are greatest at this height. Accordingly, single-level plots in our results are shown at 2.96 km. Results for other levels are qualitatively similar but typically of smaller magnitude. In Figure 2, the longitudes at which the mean meridional wind alternates between northward and southward represent the longitudinal range of the oscillation in the moist atmosphere cases. This back-and-forth propagation in the moist atmospheres is regular and associated with periodic climate variability on a planetary scale. To understand the mechanism driving this oscillation, we analyzed and compared the Control and Dry TRAP-1e simulations. Figure 3 shows the wind pattern at 2.96 km for Control TRAP-1e and Dry TRAP-1e at three different simulation times, chosen to correspond to the easternmost, westernmost, and again easternmost location of the gyres in the Control TRAP-1e simulation, covering a full cycle of motion. In the control simulation, Rossby gyres are clearly visible in the northern and southern polar regions of the eastern hemisphere, for example at 60N and 60-90E in Figure 3 a). These gyres propagate eastwards and westwards such that the centers of the gyres shift from between 30-60E to 120-150E on an approximately 20-day cycle. A matching western pair is less apparent due to interactions with other elements of the flow. In the dry simulation, gyres form at lower latitudes, are irregular in shape, and propagate at slow speeds exclusively westwards.
We explain the motion of the gyres using the theory of Rossby waves. Following e.g., Holton & Hakim (2013) or Vallis (2017), the phase speed of Rossby waves is given by:
c p =Ū − β k 2 + l 2 ,(1)
whereŪ is the zonal mean zonal wind speed, β is the Rossby parameter f rac2Ωcosφr (with Ω the planet's rotation rate in radians/second, φ the latitude in radians, and r the planet's radius), and k and l are the zonal and meridional wavenumbers in units of m −1 . To determine why the Rossby gyres oscillate in the moist atmosphere cases only, we compared the Rossby wave phase velocity for Control TRAP-1e and Dry TRAP-1e. Figure 4 shows time series of the phase velocity of the Rossby wave with the highest power spectral density (PSD) in the flow for these two simulations.
To extract the wavenumbers of the highest powered waves in the flow, we first performed a Helmholtz decomposition of the wind field at 2.96 km to calculate the eddy rotational component as in (Hammond & Lewis 2021). We then input the magnitude of the eddy rotational component, which we equate to the Rossby waves, into a 2-D Fourier transform and extracted the zonal (k) and meridional (l) wavenumbers of the wave with the maximum PSD on each simulation day. Finally, we calculated a day-specific Rossby wave phase velocity as per Equation 1 (i.e. the phase velocity varies by day depending on both the zonal wind and the predominant Rossby wave). In this calculation, we used the time-varying daily value of the zonal mean zonal wind U. Figure 4 shows that, in the moist simulation, the Rossby wave phase velocity oscillates between positive (eastward) and negative (westward) values on an approximately 20-day cycle, while it remains negative in the dry case over the same time period. Note that this method only takes into account the phase velocity contribution from the wave with the highest PSD; however, our analysis showed multiple waves present in the flow, occasionally with similar PSDs. This reduces the accuracy of the magnitude of the calculated phase velocity, but does not undermine the qualitative finding that the velocity oscillates in only the moist atmosphere.
For the Control TRAP-1e simulation, the Rossby wave phase velocity oscillates in a band of latitudes between 50-70N/S, with a tendency toward increasingly eastward flow further polewards. A similar analysis for the Control ProxB and Warm ProxB simulations found that the oscillatory latitude band starts at 55N/S and extends to the poles. This is attributable to the larger size of Proxima Centauri b, as the wavenumbers in m −1 vary by latitude and the degrees of latitude for each planet correspond to different distances. The eastern gyres in the Control TRAP-1e simulation are centered around 60-70N/S, while those in the ProxB simulation are centered further equatorwards at 55-60N/S. The latitudinal position may be influenced by the position of the zonal jets on the two planets. On Earth, Rossby waves are associated with the mid-latitude jet stream (Vallis 2017). As seen in Figure 1, Proxima Centauri b's equatorial jet extends to about 55N/S, while the mid-latitude jets on TRAPPIST-1e extend further polewards to approximately the latitude of the Rossby vortices. Previous work simulating TRAPPIST-1e with the UM has also shown that the circulation can take on one of two regimes: a single equatorial jet or two mid-latitude jets (Sergeev et al. 2022a). In the single equatorial jet regime, as in our Proxima Centauri b simulations, the gyres form further equatorwards than in the double mid-latitude jet regime.
The formation of Rossby gyres in simulations of tidally locked planets is believed to be related to the spatially periodic thermal forcing (Showman & Polvani 2011, 2010Gill 1980;Matsuno 1966). As our model's stellar spectra do not vary with time and the planet is tidally locked with zero eccentricity or obliquity, atmospheric processes must be responsible for the temporal variability in our simulations. To determine why the constituent Rossby waves in the wind field (and hence the Rossby wave phase velocity) vary periodically with time, we searched for correlations between quantities thought to play a role in the Matsuno-Gill response to periodic forcing. Figure 5 compares the variations over time of the vertical cross sections of dayside mean air temperature, vertical wind, zonal wind, net surface shortwave flux, and the PSD of the zonal wavenumber 1 Rossby wave (identified as the 1-0 wave) and, separately, the sum of the PSDs of the Rossby waves identified as 1-1, 2-1, 2-2, and 3-2 waves, where the first digit refers to the zonal wavenumber and the second digit refers to the meridional wavenumber. Regular 20-day cycles are visible in all quantities in the moist atmosphere case, but are absent in the dry atmosphere. The air temperature, vertical wind, and shortwave surface heating increases precede the increase in the Rossby wave power. For example, Figure 5 a), c), and g) show a peak in these three quantities at around 10 days, while the spike in the 1-0 Rossby wave (red line in Figure 5 g)) occurs at 18-20 days. This pattern repeats five times over the period displayed in the plots. Figure 6 further shows variability in the dayside mean total (ice and liquid) cloud cover on the same 20-day cycle. The cloud mass fraction grows during the heating/rising and drops during the cooling/subsiding part of the cycle.
We posit an internal feedback between the dayside cloud cover and the intensity of the Matsuno-Gill response. A decrease in cloud cover allows more shortwave radiation to reach the surface, leading to atmospheric heating and subsequent ascending motion of the air mass. The 1-0 Rossby wave responds to the increase in forcing, boosting its power spectral density relative to the other constituent Rossby waves in the wind field. To support this interpretation, we show in Figure 5 g) and h) both the PSD of the 1-0 wave and the summed PSD of a number of other large-scale waves, namely the 1-1, 2-1, 2-2, and 3-2 waves. At the troughs of the cycle, the PSD of the 1-0 wave is roughly equal to that of the other waves combined, and occasionally even drops below it. At the peaks, however, the PSD of the 1-0 wave increases substantially more than that of the sum of the remaining waves, indicating that this wave disproportionately receives energy during the cycle, as would be expected from its direct relationship to the Matsuno-Gill periodic forcing pattern. (Note that in the dry atmosphere case, the PSD of all waves is an order of magnitude smaller than in the moist case despite the larger shortwave flux and atmospheric temperature anomalies, highlighting the important role of moisture.) As longer wavelength Rossby waves have higher westward phase speeds, this shift towards the 1-0 wave contributes to the westward propagation of the gyres. When cloud cover increases again, less radiation reaches the surface, the air mass cools and subsides, and the 1-0 Rossby wave becomes weaker relative to other waves, shifting the Rossby wave phase velocity eastwards. It is possible that the location of the Rossby gyres in turn affects the cloud cover, closing the causal loop, but we believe it is unlikely that the Rossby waves are the only or main factor in the density of the clouds. The zonal wind speed, which influences both the Rossby wave phase velocity and the stability of the dayside cloud cover, is also affected by the changes in the thermodynamic properties of the dayside atmosphere shown above (Figure 5 e)). Untangling these intricate relationships requires a better understanding of the factors controlling the zonal wind speed on tidally locked planets than is currently available. In addition, the cloud layer is likely to be sensitive to multiple processes in the atmosphere in addition to the zonal wind variation, including the intensity of convection, specific humidity, and the advective and radiative time scales.
The period of the oscillation, given in Table 3, varies substantially between the four moist atmosphere cases. Understanding why the period is longer in some simulations is important because a slower oscillation implies the planet will have a longer period of clear skies at the limb, potentially allowing for repeat observations when conditions are favorable. We find that the oscillation period monotonically decreases in parallel with the rotation period, but the relationship is not linear. We expect the rotation period to influence the Rossby wave phase velocity directly through β. However, other factors are clearly in play. While the rotation period decreases by similar amounts (2-3 days) between each simulation, there is a disproportionately large difference between the oscillation periods of the Proxima Centauri b and TRAPPIST-1e simulations. We believe the non-linearity can be explained by the additional influence of the zonal wind on the Rossby wave phase velocity as defined in Equation 1. Figure 7 shows latitude-time diagrams Table 3. Rotation period, period of Rossby gyre oscillation, mean zonal mean zonal wind, mean meridional temperature gradient, and mean northern hemisphere thermal wind for each of the four moist atmosphere cases. The periodicity was determined from the cloud cover oscillation shown in Figure 8. The meaning period for the bottom three quantities was chosen to be the same as in Figure 1, the first 300 days of the sampling period for each simulation.
of the Rossby wave phase velocity for each simulation. Both the eastward and westward phase of the oscillation display higher phase velocities in the TRAPPIST-1e simulations as compared to Proxima Centauri b, accounting for the much shorter oscillation periods of the former. The phase velocities differ because the zonal mean wind, reported in Table 3, jumps significantly between the the Proxima Centauri b (4-5 m/s) and Trappist-1e (15-18 m/s) simulations. The higher zonal mean wind in the TRAPPIST-1e cases may in turn be explained by a larger meridional temperature gradient via the thermal wind balance. The Rossby number for all four moist simulations is small, on the order of 10 −2 , as the characteristic length scale of the phenomenon (the zonal wavenumber 1 Rossby wave) is approximately half the circumference of the planet, while the characteristic zonal wind is on the order of tens of meters per second. This means the geostrophic approximation can be applied and the thermal wind balance equation holds true:
u t = − R d f ∂T v ∂y ∂p p ,(2)
where u t is the vertical gradient of the zonal wind, R d is the gas constant for dry air, f is the Coriolis parameter 2Ωsinφ, ∂Tv ∂y is the mean meridional temperature gradient of a layer, and p is the pressure (Vallis 2017). According to the weak temperature gradient theory applicable to slowly rotating tidally locked planets (Pierrehumbert & Hammond 2019), the equator-pole temperature gradient should increase with increasing rotation rate, which is consistent with the values in Table 3. We used the mean equator-pole temperature gradient to calculate the mean northern hemisphere thermal wind in the final row of Table 3. As predicted, Control TRAP-1e (3.11 m/s) has a higher thermal wind than Control ProxB and Warm ProxB (1.80 and 1.34 m/s). In contrast, Warm TRAP-1e has a weaker thermal wind, even though its meridional temperature gradient is similar to that of Control TRAP-1e (and different from that of both Proxima Centauri b cases). We believe this is due to greater pressure variation within the same vertical range for this near-runaway simulation, combined with the effect of the larger Coriolis parameter in the denominator of 2. These patterns broadly suggest that more slowly rotating planets with weaker equator-pole temperature gradients are likely to have longer oscillation periods and longer windows of cloudless sky at the terminators.
Cloud variability and observables
The migration of Rossby gyres impacts the amount of moisture transport and thus cloud condensate at the planetary terminators. All four of the moist atmosphere simulations display cloud cover variability at the terminators, shown in Figure 8. The Control and Warm ProxB runs in Figure 8 a) and b), respectively, exhibit large fluctuations in cloud condensate in the observable regions of the planet, ranging from near 0 to 7 × 10 −7 kg/kg and 2.5 × 10 −6 kg/kg, respectively, on a time scale matching the migratory cycle of the Rossby gyres (120 days/160 days). The TRAPPIST 1-e simulations do not undergo these long-period cycles, but show regular smaller magnitude fluctuations on an approximately 20-day time scale. Figure 9 depicts the interaction between the wind field and the dayside clouds. Figure 9 a) and b) are two stages in the Rossby gyre migratory cycle for the Warm ProxB simulation, corresponding to a cloud condensate maximum and minimum. During the maximum, the eastern pair of Rossby gyres is at the extreme western part of its propagation path, where it intersects with the region of heavy cloud cover around the substellar point. During the minimum, the gyres are at the extreme eastern part of the propagation path and do not interact with the dayside clouds. In the TRAPPIST-1e case, shown in Figure 6. Vertical profile of dayside mean total cloud cover (ice and liquid) over time for the Control TRAP-1e simulation. As in Figure 5 a) and b), the short vertical range of 0 to 5 km results in discontinuities between vertical levels due to the low resolution of the simulation.
condensate and moisture described in 3.2 and shown in Figures 5 and 6, on which the longer-period effect from the traveling wave structures is overlaid.
The magnitude and periodicity of the variation in cloud cover at the planetary limb is highly sensitive to not only the Rossby wave propagation, but also the dayside cloud structure. As demonstrated by the TRAPPIST-1e cases, the amount of cloud at the terminator will not be affected by the Rossby wave oscillation unless the Rossby gyres form at low or mid-latitudes where they can advect cloud from the substellar region. Figure 10 shows cross-sections of the dayside cloud layer at the equator and at longitude 0 for the four moist atmosphere simulations. The extent of the cloud cover in longitude, latitude, and altitude depends on the temperature and moisture profile of each simulated planet, but as the longitude, latitude, and even peak altitude of the Rossby waves also vary in different simulations, the parameter space of the resulting wave-cloud interaction is complex.
To explore the potential impact of wave-cloud interactions on observations, we simulated transit spectra for the Control ProxB, Warm ProxB, Control TRAP-1e, and Warm TRAP-1e simulations, excluding the Dry TRAP-1e simulation as it does not form clouds. We constructed time series of two absorption features, shown in Figure 11. We chose the water line at 1.4 µm because it does not overlap with any CO 2 features and the CO 2 feature at 2.7 µm because it is a strong line in the available NIRSpec spectrum and does not overlap with the N 2 -N 2 collision-induced absorption line at 4.3 µm. As the CO 2 abundance in the simulations is fixed, variability in the transit depth of this feature can only be due to differences in the muting effect of cloud cover or due to temperature fluctuations and not due to variations in CO 2 content. For the water feature, variations in transit depth may also be due to differences in water vapor content on different days, caused by other factors such as the LASO and random fluctuation (model noise). However, the time series for the H 2 O and CO 2 are well-correlated, supporting clouds as a factor in the variability. In the Control and Warm ProxB simulations in Figure 11 a)-d), the time series show clear long-period variation in addition to small continuous fluctuations, but the relative difference in the transit depths for these simulations is only 4-5 %. The percentage variation for the Warm TRAP-1e simulation is the largest in the comparison at 18-20 %, but the transit depths are profoundly muted compared to Control TRAP-1e because of the high cloud deck visible in Figure 10 d) and h). In addition, while the Control and Warm ProxB time series have extended periods of larger transit depths, corresponding to the longer period of the cloud cover oscillation for this planet, the TRAP-1e runs lack these multi-week periods of stronger transit signals due to their shorter Rossby wave cycle as described in Section 3.2.
DISCUSSION
Our results support the existence of internal atmospheric variability on tidally locked aquaplanets even in the absence of a varying stellar spectrum or stellar activity, rotation with respect to the host star, obliquity, and eccentricity. The stabilizing feedback between the dayside cloud cover and atmospheric temperature, identified in previous work on the inner edge of the habitable zone for tidally locked Earth-like planets (Kopparapu et al. 2016;Yang et al. 2014), induces periodicity in the atmospheric dynamics. Edson et al. (2011) postulated that the large amplitude of the zonal wavenumber 1 Rossby wave on slowly rotating planets with superrotating atmospheres is caused by resonance between this wave and the spatially periodic heating. Our finding of a disproportionate increase in the power spectral density of the 1 − 0 wave directly after an increase in net surface shortwave flux supports their hypothesis. The increase in surface heating is caused by a drop in total cloud cover in the dayside, reducing the cloud albedo. This periodic reduction in cloud cover may be affected by the propagation of the Rossby gyres in a closed feedback loop, but it is likely that other aspects of the circulation, especially the magnitude of the zonal and vertical winds and intensity of convection in the substellar region also play a role. The potential relationship between atmospheric moisture and cloud-radiative feedback is reminiscent of theories of the Madden-Julian Oscillation (MJO) (Zhang et al. Figure 8. Mean cloud condensate (mixing ratio, kg/kg) over time at the planetary limb for each of the four moist atmosphere simulations. Liquid and ice cloud are shown separately. Each type of cloud is averaged over all latitudes and all heights on the eastern and western terminator. The data has been filtered to remove cycles with periods shorter than 10 days. Note the different limits of the y-axis. 2020; Zhang 2005), particularly the moisture-mode hypothesis, which also posits a planetary wave response. As there is no consensus about the mechanism of the MJO and the complexity of the factors influencing the cloud cover on the dayside is high, we limit our analysis to identifying the immediate cause of the Rossby gyre oscillation and its effects on observables, and defer detailed analysis of the moist atmosphere feedbacks between clouds, convection, specific humidity, and the zonal wind to future studies.
Our simulations of transit spectra show that the variable cloud cover caused by traveling Rossby waves could affect transit depths, though for our chosen planets the effect is too small to be observable with current instruments. May et al. (2021) reported a transit depth variation due to cloud cover on the order of 10 ppm for their 10 −4 bars of CO 2 TRAPPIST-1e simulation with ExoCAM (Wolf et al. 2022), which is comparable to the THAI Hab 1 setup (Sergeev et al. 2022b) and to our Control TRAP-1e experiment. THAI Part III (Fauchez et al. 2021) found the standard deviation of the variation of the continuum level for Hab 1 to be 3 ppm for ExoCAM and 1 ppm for the UM, compared to our min-max difference of 1.26 ppm for for the 2.7 µm feature. The slightly smaller degree of variation in our results compared to May et al. (2021) is in line with the finding in Sergeev et al. (2022b) and Fauchez et al. (2021) that ExoCAM displays the greatest degree of cloud variability out of the four models included in the comparison. Our quantitative findings agree with the results of these previous works and support the conclusion that atmospheric variability due to clouds will be below the noise floor of JWST.
From a qualitative perspective, the impact of Rossby waves on observations is highly sensitive to the location of both the Rossby gyres and the cloud deck. If clouds form on or extend to the planetary terminators, migrations by Rossby gyres could regularly clear this region for periods of time as long as the planet's transit. Without prior knowledge of the cloud structure, cycle duration, and cycle phase, it is impossible to predict when such clearing events might occur and to time observations to avoid flattened, featureless spectra due to clouds (Garcia et al. 2022;Diamond-Lowe et al. 2018;de Wit et al. 2016;Kreidberg et al. 2014;Knutson et al. 2014). However, as the body of data from transit spectroscopy grows, atmospheric and climate variability should be considered when combining or interpreting data from different observing periods. In addition, as our theoretical understanding of climate variability on exoplanets improves, it may be beneficial to obtain data from consecutive transits instead of randomly chosen ones, as consecutive observations are more likely to represent a real atmospheric state rather than an averaged, composite one.
Traveling Rossby waves could also affect the chemical composition of the planet's atmosphere. Several studies using chemistry-climate models have found that different chemical environments form on the dayside and nightside of tidally locked planets due to the presence or absence of photochemistry (Braam et al. 2022;Yates et al. 2020;Chen et al. 2018). In particular, the nightside gyres can build up high concentrations of species that are destroyed on the irradiated dayside. In our simulations of TRAPPIST-1e, however, the nightside gyres frequently travel back and forth over the eastern terminator, exposing chemically enriched nightside air to radiation. This process may reduce chemical differences between the dayside and nightside, leading to a more homogeneous planetary climate.
The specific features of this atmospheric oscillation, including the period, the latitudes and longitudes of the Rossby gyres, their size, the distance they travel, and how much cloud (if any) they advect are dependent on model setup, especially the cloud parameterization. The THAI project found significant differences in the cloud water paths predicted by the four models included in the intercomparison, with the UM in the middle of the pack (Sergeev et 2022b). The location of the Rossby gyres also differs between models and between simulations with varying parameters. To date, only Skinner & Cho (2022) have studied the Rossby wave lifecycle in a tidally locked planet simulation. In their high-resolution, hot gas giant simulations, Rossby gyres (or "modons") fully circumnavigate the planet in the westward direction, periodically dissipate, and then reform and begin circulating again. We did not observe circumnavigation even in a matching high-resolution simulation performed with our control Proxima Centauri b model. Numerous factors such as the temperature structure of the atmosphere and the presence of clouds may influence the motion of Rossby waves in simulations of tidally locked planets. A better understanding of the sensitivity and evolution of these waves in atmospheric models of tidally locked planets is key to understanding climate variability and a fruitful avenue for future work.
CONCLUSION
We describe a mechanism in the atmosphere of tidally locked terrestrial exoplanets in which feedbacks between clouds and incoming stellar radiation influence the dynamical state of the atmosphere, especially the zonal wavenumber-1 Rossby response to the thermal forcing, leading to alternating eastward and westward propagation of the Rossby gyres previously characterized as largely stationary. The oscillation in the location of the Rossby gyres can affect the distribution of clouds if the path of the Rossby gyre migration intersects with the dayside cloud cover. In our simulations of Proxima Centauri b, this interaction results in periodic clear and cloudy days at the planet's eastern terminator, while in our simulations of TRAPPIST-1e, the Rossby gyres are located too far polewards to interact with the dayside clouds. Time series of synthetic spectra generated for a 300-day sample of the climate oscillation confirmed that the variation in cloud cover and atmospheric humidity associated with the feedback mechanism results in a timevarying transmission spectrum, but the magnitude of the variation in transit depths is too small to be detectable for our simulated planets.
This study and our previous work in Cohen et al. (2022) identify physical mechanisms of variability which cause cycles in the planetary climate even in idealised exoplanet models without eccentricity, obliquity, or changes in the stellar spectrum. More complex environments on real planets are no doubt subject to additional sources of variability. As the body of exoplanet observations grows in the age of JWST and other upcoming telescopes, consideration of long-term climate variability and of weather on other planets can help interpret observations taken at different times, construct time series, and inform observing and data processing practices. Time series of 2.7 μm CO2 feature h) CO 2 feature, Warm TRAP-1e Figure 11. Time series of the 1.4 µm water absorption feature and 2.7 µm CO2 absorption feature for the Control ProxB, Warm ProxB, Warm TRAP-1e, and Control TRAP-1e simulations. In a)-d), a sample of 300 days is taken to cover the 157.5 and 120 day oscillation periods in the Control and Warm Proxima Centauri b simulations, respectively. In e)-h), a sample of 100 days is taken to cover the 19.4 and 16.2 day periods in the Control and Warm TRAPPIST-1e simulations.
Climatology Boutle et al. (2017) present a detailed climatology of Proxima Centauri b as simulated by the UM.
Figure 1 .
1Comparative climatology of the five simulations, showing (from left to right) the vertical temperature profile at the substellar and antistellar point, the zonal mean zonal wind, the vertical water vapor profile at the substellar and antistellar point, and the surface temperature. From top row to bottom row: Control ProxB, Warm ProxB, Control TRAP-1e, Warm TRAP-1e, Dry TRAP-1e. All values are 300-day means.
Figure 2 .
2Time-longitude diagrams of the mid-latitude (55 to 85N) averaged meridional wind at an altitude of 2.96 km above the surface. Positive values correspond to northward flow, while negative values represent southward flow.
Figure 3 .
3Wind vectors for Control TRAP-1e simulation on days 0, 10, and 20 and Dry TRAP-1e simulation on days 0, 30, and 60.
Figure 4 .
4Time series of Rossby wave phase velocity of the primary wave in the flow at 56N for Control and Dry TRAP-1e simulations.
Figure 9 cFigure 5 .
95) and d), the Rossby gyres are too far polewards to interact with the dayside cloud cover. The short-period cycles shown inFigure 8c) are likely a direct reflection of the fluctuation in cloud Top three rows: Vertical profiles of dayside mean air temperature, vertical wind, and zonal wind over time for the moist atmosphere Control TRAP-1e and the dry atmosphere Dry TRAP-1e (left and right, respectively). The vertical range of a) and b) is 0 to 5 km to better show the temperature oscillation near the surface. Due to the relatively low resolution of our simulations, this close-in view results in discontinuities between vertical levels. The discontinuities are not visible in c)-f) because the vertical range shown in 0 to 35 km. Bottom row: Time series of the dayside mean net downward shortwave flux close to the planet's surface (black), shown with the power spectral density of the zonal wavenumber 1 Rossby wave (red) and the sum of the power spectral density of the waves with zonal and meridional wavenumbers 1
Figure 7 .
7Latitude-time diagrams of Rossby wave phase velocity for each simulation at h=2.96 km height. Positive values correspond to eastward flow, while negative values represent westward flow.
Figure 9 .
9Wind vectors overlaid on the total cloud condensate (ice and liquid) at the given height for Warm ProxB and Control TRAP-1e simulations. The images are daily snapshots chosen to illustrate the eastmost and westmost phases of the Rossby gyre migration for each planet.
Figure 10 .
10Longitudinal and latitudinal cross-sections of the dayside cloud layer for the four moist atmosphere simulations. The total cloud is the sum of ice and liquid cloud condensate. The images depict 120-day means.
Table 1. Model parameters for all simulations at a resolution of 2 • latitude by 2.5 • longitude. The substellar point is defined to be at 0 • longitude and latitude, while the antistellar point is located at 180 • longitude and the eastern and western terminators at 90 • E and 90 • W, respectively. "Days" refers to Earth days throughout this work.The UM has a fully prognostic cloud scheme, the Prognostic Cloud fraction and Prognostic Condensate (PC2) schemeParameter
Control ProxB Warm ProxB Control TRAP-1e Warm TRAP-1e Dry TRAP-1e
Semi-major axis (AU)
0.0485
0.0423
0.029
0.025
0.029
Stellar irradiance (W m −2 )
881.7
1100.2
837.7
1392.9
837.7
Orbital period (Earth days)
11.2
9.2
6.1
4.2
6.1
Rotation speed (rad s −1 )
6.501×10 −6
7.933×10 −6
1.192×10 −5
1.746×10 −5
1.192×10 −5
Eccentricity (·)
0
0
0
0
0
Obliquity (·)
0
0
0
0
0
Radius (km)
7160
7160
5797
5797
5797
Acceleration due to gravity (m s −2 ) 10.9
10.9
9.1
9.1
9.1
CO2 (ppm)
378
378
400
400
400
Number of levels (·)
60
60
39
39
39
Model top (km)
85
85
80
80
80
m/s Horizontal wind, day 0, h=2.96 km a) Control TRAP-1e, day 0 Horizontal wind, day 0, h=2.96 km d) Dry TRAP-1e, day 0 Horizontal wind, day 10, h=2.96 km b) Control TRAP-1e, day 10 Horizontal wind, day 30, h=2.96 km e) Dry TRAP-1e, day 30 Horizontal wind, day 20, h=2.96 km c) Control TRAP-1e, day 20 Horizontal wind, day 60, h=2.96 km f) Dry TRAP-1e, day 60180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Longitude
90S
60S
30S
0
30N
60N
90N
Latitude
Total cloud a d horizo tal wi d, day 410, h=2.96 km kg/kg c) Control TRAP-1e, day 410 Total cloud a d horizo tal wi d, day 420, h=2.96 km kg/kg d) Control TRAP-1e, day 42020 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Lo gitude
90S
60S
30S
0
30N
60N
90N
Latitude
Total cloud a d horizo tal wi d, day 410, h=1.45 km
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
10 −4
kg/kg
a) Warm ProxB, day 410
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Lo gitude
90S
60S
30S
0
30N
60N
90N
Latitude
Total cloud a d horizo tal wi d, day 500, h=1.45 km
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
10 −4
kg/kg
b) Warm ProxB, day 500
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Lo gitude
90S
60S
30S
0
30N
60N
90N
Latitude
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
10 −4
20 m/s
180W 150W 120W 90W 60W 30W
0
30E 60E 90E 120E 150E 180E
Lo gitude
90S
60S
30S
0
30N
60N
90N
Latitude
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
10 −4
al. Total cloud at longitude 359.0 Total cloud at longitude 359.0 Total cloud at longitude 359.0 10 −4 kg/kg c) Control TRAP-1e Total cloud at longitude 359.090S 60S 30S
0
30N 60N 90N
Latitude [deg ees]
0
5
10
15
20
Height [km]
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
a) Control ProxB
90S 60S 30S
0
30N 60N 90N
Latitude [deg ees]
0
5
10
15
20
Height [km]
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
b) Warm ProxB
90S 60S 30S
0
30N 60N 90N
Latitude [deg ees]
0
5
10
15
20
Height [km]
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
90S 60S 30S
0
30N 60N 90N
Latitude [deg ees]
0
5
10
15
20
Height [km]
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
d) Warm TRAP-1e
180W
90W
0
90E
180E
Longitude [deg ees]
0
5
10
15
20
Height [km]
Total cloud at latitude 1.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
e) Control ProxB
180W
90W
0
90E
180E
Longitude [deg ees]
0
5
10
15
20
Height [km]
Total cloud at latitude 1.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
f) Warm ProxB
180W
90W
0
90E
180E
Longitude [deg ees]
0
5
10
15
20
Height [km]
Total cloud at latitude 1.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
g) Control TRAP-1e
180W
90W
0
90E
180E
Longitude [deg ees]
0
5
10
15
20
Height [km]
Total cloud at latitude 1.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
10 −4 kg/kg
h) Warm TRAP-1e
Transit depth [ppm] Mean = 17.87 Max = 18.30 Min = 17.57 Diff = 0.73 Time series of 1.4 μm H2O feature a) Water feature, Control ProxB Transit depth [ppm] Mean = 31.15 Max = 31.89 Min = 30.69 Diff = 1.20 Time series of 2.7 μm CO2 feature b) CO 2 feature, Control ProxB Transit depth [ppm] Mean = 17.96 Max = 18.25 Min = 17.54 Diff = 0.71 Time series of 1.4 μm H2O feature c) Water feature, Warm ProxB Transit depth [ppm] Mean = 24.68 Max = 25.22 Min = 23.94 Diff = 1.28 Time series of 2.7 μm CO2 feature d) CO 2 feature, Warm ProxB Transit depth [ppm] Mean = 15.51 Max = 15.82 Min = 15.19 Diff = 0.63 Time series of 1.4 μm H2O feature e) Water feature, Control TRAP-1e Transit depth [ppm] Mean = 31.06 Max = 31.79 Min = 30.41 Diff = 1.38 Time series of 2.7 μm CO2 feature f) CO 2 feature, Control TRAP-1e Time series of 1.4 μm H2O feature g) Water feature, Warm TRAP-1e0
50
100
150
200
250
300
Time [days]
17.6
17.7
17.8
17.9
18.0
18.1
18.2
18.3
0
50
100
150
200
250
300
Time [days]
30.8
31.0
31.2
31.4
31.6
31.8
0
50
100
150
200
250
300
Time [days]
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.2
0
50
100
150
200
250
300
Time [days]
24.0
24.2
24.4
24.6
24.8
25.0
25.2
0
50
100
150
200
250
300
Time [days]
15.2
15.3
15.4
15.5
15.6
15.7
15.8
0
50
100
150
200
250
300
Time [days]
30.4
30.6
30.8
31.0
31.2
31.4
31.6
31.8
0
50
100
150
200
250
300
Time [days]
6.00
6.25
6.50
6.75
7.00
7.25
7.50
7.75
8.00
Transit depth [ppm]
Mean = 7.09
Max = 7.95
Min = 6.02
Diff = 1.93
0
50
100
150
200
250
300
Time [days]
We acknowledge the funding and support provided by the Edinburgh Earth, Ecology, and Environmental Doctoral Training Partnership and the Natural Environment Research Council [grant number NE/S007407/1]. We also kindly acknowledge our use of the Software: We used the Iris python package to manage and analyse model output data (MetOffice 2010). We used the windspharm python library to perform Helmholtz decompositions to characterise the mean circulation(Dawson 2016) and NASA's Planetary Spectrum Generator to simulate transit spectra(Villanueva et al. 2018)
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| sample_1837 | 0.5952 | arxiv | |
Knowledge for a warmer world: A patent analysis of climate change adaptation technologies
April 22, 2022 21 Apr 2022
Kerstin Hötte
Oxford Martin Programme on Technological and Economic Change
University of Oxford
UK
Institute for New Economic Thinking at the Oxford Martin School
University of Oxford
UK
Faculty of Business Administration and Economics
University of Bielefeld
DE
Su Jung Jee
Institute for New Economic Thinking at the Oxford Martin School
University of Oxford
UK
School of Management
Faculty of Management, Law & Social Sciences
University of Bradford
UK
Knowledge for a warmer world: A patent analysis of climate change adaptation technologies
April 22, 2022 21 Apr 20221 arXiv:2108.03722v2 [econ.GN]Climate ChangeAdaptationInnovationPatent DataTechnology-Science InteractionsR&D Policy
Technologies can help strengthen the resilience of our economy against existential climate-risks. We investigate climate change adaptation technologies (CCATs) in US patents to understand (1) historical patterns and drivers of innovation; (2) scientific and technological requirements to develop and use CCATs; and (3) CCATs' potential technological synergies with mitigation. First, in contrast to mitigation, innovation in CCATs only slowly takes off, indicating a relatively low awareness of investors for solutions to cope with climate risks. Historical trends in environmental regulation, energy prices, and public support can be associated with patenting in CCATs. Second, CCATs form two main clusters: science-intensive ones in agriculture, health, and monitoring technologies; and engineering-intensive ones in coastal, water, and infrastructure technologies. Analyses of technology-specific scientific and technological knowledge bases inform directions for how to facilitate advancement, transfer and use of CCATs. Lastly, CCATs show strong technological complementarities with mitigation as more than 25% of CCATs bear mitigation benefits. While not judging about the complementarity of mitigation and adaptation in general, our results suggest how policymakers can harness these technological synergies to achieve both goals simultaneously. JEL: O33; O38; Q54; Q55; Q58
Introduction
Climate change is an existential threat to human livelihoods (Bellprat et al., 2019;Ornes, 2018). Recent extreme weather events have shown that significant adaptation is needed to help communities, cities, and economic activity adjust to new climatic conditions (IPCC, 2018). Technological innovation plays an important role in addressing this challenge (Dechezlepretre et al., 2020;Ferreira et al., 2020): climate-smart agriculture helps to adapt to droughts, floods, and increasing threats of pest infestation (Adenle et Kuhl, 2020); new types of hazard defense and weather prediction tools help protect infrastructure and human lives from storms, floods, and heatwaves (UNFCCC, 2006); water conservation and catchment technologies help address water scarcity (Conway et al., 2015); vaccines, new drugs, and preventive public health inventions strengthen people's resistance against infectious diseases and heatwave-induced risks that become more prevalent under climate change (Caminade et al., 2019;Guo et al., 2018). Alongside nature-based solutions and behavioral changes, adaptation technologies are needed to cope with current and future climate risks (UNEP, 2021;UNFCCC, 2006).
Governments under the Paris Agreement committed to strengthening their adaptation capacities, including technological solutions, but progress to achieve this goal has been rarely evaluated at a comprehensive level (Berrang-Ford et al., 2019;Lesnikowski et al., 2017). Measuring progress is important as it helps identify adaptation gaps, enables impact assessments of adaptation strategies, and mutual learning when decision makers share their experience with undertaken adaptation efforts. Here, we systematically take stock of existing technologies for adaptation using patent data addressing three questions:
(
1) To what extent have these technologies been developed and which were the drivers of innovation? (2) How can governments support the development and adoption of these technologies? (3) How do technologies for adaptation interact with climate change mitigation?
Existing studies on climate change adaptation technologies (CCATs) often focused on specific regions, technologies, or climate risks. To date, systematic analyses of innovation in CCATs have been limited (Dechezlepretre et al., 2020;Popp, 2019), not least because, until 2018, there was no classification of CCATs in patent databases. The most closely related study was made by Dechezlepretre et al. (2020) who investigated the diffusion of CCATs using patent data.
Leveraging the recent Cooperative Patent Classification (CPC) of 'climate change adaptation technologies' (Angelucci et al., 2018), we investigated how innovation in various adaptation technologies has changed over time. We analyzed the composition of the scientific and technological knowledge bases of CCATs to show which scientific and technological capabilities are needed to advance, adopt, and utilize CCATs. We further identified technological complementarities between adaptation and mitigation showing in which areas both targets can be achieved at the same time. To the best of our knowledge, this is the first systematic analysis of the current state of technological knowledge for adaptation. From our analysis of CCATs, we have documented five key insights:
1. Despite increased awareness of climate change, patenting in most adaptation tech-nologies has not experienced a surge in the past two decades, much unlike patenting in climate change mitigation which has been increasing significantly. 2. Adaptation technologies form two clusters: those that are science-intensive (healthrelated adaptation, agriculture, and indirectly enabling technologies for weather forecasting and natural resource assessment) and those that are engineering-based (adaptation in coastal, infrastructure, and water supply). The qualitative details of the knowledge base reveal scientific and technological requirements needed to develop, adopt, and utilize these technologies and inform policy makers how to facilitate advancement and transfer of adaptation technologies. 3. Invention in various CCATs greatly differ by magnitude: Adaptation related to human health has the highest number of patented inventions (>16k patents), followed by agriculture (8k). Coastal adaptation has the lowest number of patented inventions (<0.9k). 4. Since mid-2000s, more than 40% of adaptation patents have been reliant on government support, which is about 10% higher than average (Fleming et al., 2019b). For most mitigation technologies, the reliance on government support is much lower during the same period, except for nascent mitigation technologies such as carbon capture and storage (CCS). 1 5. 26% of all adaptation technologies simultaneously help with mitigation. The highest overlap exists in infrastructure, where 70% of adaptation patents also help reduce emissions. Many of these inventions came as byproducts of innovations developed to cope with environmental regulation and high energy prices. The observation that 26% of adaptation technologies simultaneously contribute to mitigation is of high theoretical and practical importance. In many theoretical discourses, climate change adaptation and mitigation were treated as substitutes (Barrett, 2020;Reyer et al., 2017). Our results question this perspective. We argue that well-designed policy can encourage innovations that meet the twin goals of adaptation and mitigation simultaneously.
We documented a substantial scope for technological complementarity between certain adaptation and mitigation options. While not promising a universal solution for all adaptation and mitigation options, we illustrate examples of how emission-increasing maladaptation can be avoided (Barnett and O'Neill, 2010). 2 For example, thermal insulation in buildings achieves both: adaptation to heatwaves and emission-reduction through energy savings, while air-conditioning would be an example of maladaptation. Energy-intensive desalination to cope with water scarcity, another example of maladaptation, can be complemented with the integrated use of solar PV. Our analysis identifies additional cases, for example in agriculture, infrastructure, and clean production where public R&D support can encourage inventions that meet adaptation and mitigation goals at the same time.
As technological development is path-dependent (Arthur, 1994;Ruttan, 1997), subsequent technological development cumulatively builds on pre-existing technology and knowledge. Technology choices in the early phase of development are essential to prevent lock-in effects in adaptation options that undermine mitigation efforts or in mitigation strategies that increase vulnerability against climate change.
The remainder of this paper is structured as follows: In the next section 2, we offer an introduction to the economics of adaptation, mitigation, and technology. In section 3 we describe the methodology and data. Section 4 outlines the results, first documenting innovation trends in adaptation (Section 4.1), continuing with an analysis of the technological and scientific base (Section 4.2), and ending with an analysis of adaptation-mitigation complementarity (Section 4.3). Section 5 concludes.
Background
Adaptation and the role of technology
Governments typically employ a portfolio of different actions to adapt to climate change. For instance, these portfolios can comprise of behavioral and nature-based solutions, technological adaptation of physical infrastructure, and insurance-like mechanisms that facilitate the economic recovery after the occurrence of an extreme event (Berrang-Ford et al., 2019).
Behavioral solutions can comprise of awareness and information campaigns that strengthen the risk-preparedness in the face of wildfires, storms, and floods; or teach the population about appropriate behavior during heatwaves (Valkengoed and Steg, 2019). Naturebased solutions for adaptation either strengthen the resilience of ecological systems, such as through biodiversity protection, or leverage the provision of ecosystem services for water supply or green zones to alleviate heatwaves in urban areas (Seddon et al., 2020;Sharifi, 2021). Technologies for adaptation comprise both high-tech and low-tech solutions, and even non-patented technological solutions (Dechezlepretre et al., 2020;IPCC, 2022;UNFCCC, 2006). Next to these, financial instruments and social safety nets play a crucial role, as financial and economic capabilities are essential to enable recovery after extreme weather events. These instruments consist of, for example, weather insurances in agriculture or real-estate, but also public recovery schemes. Furthermore, poverty reduction is an effective adaptation strategy, which is most prevalent in lowincome countries (Linnerooth-Bayer and Hochrainer-Stigler, 2015).
However, these adaptation options interact and mutually enhance their effectiveness. Behavioral risk-preparedness is easier to achieve if technologies provide reliable weather forecasts (Valkengoed and Steg, 2019), and the costs of financial insurance schemes can be significantly reduced if technological adaptation strengthens the resilience of physical assets against extreme weather (Mills, 2007).
In this study, we focus on patented technological solutions for adaptation. Technological solutions are appealing when other adaptation options are prohibitively expensive or infeasible, and they bear the potential to overcome some of the limits to adaptation.
For example, two-thirds of the world's cities are located on coastlines, which are vulnerable to sea level rise. Relocating assets and citizens is often infeasible or prohibitively expensive due to financial and social constraints (Fankhauser and McDermott, 2016). Many nature-based solutions like the restoration of mangroves for flood protection, agroforestry dealing with water scarcity, or green zones in cities to alleviate heatwaves, only work provided that extreme weather events are sufficiently moderate (Thomas et al., 2021). In a world with ongoing climate change as currently projected (IPCC, 2018;Steffen et al., 2018), societies need to prepare for weather events that exceed these limits. In these situations, technological solutions can play an important role (IPCC, 2022;Tompkins et al., 2018).
Adaptation and mitigation: Substitutes or complements?
Although it has been said that -given our current knowledge-mitigation remains the cheapest and best adaptation, climate change is already happening today at a worrying pace and societies need to adapt to these unavoidable changes.
In the literature, the relationship between climate change mitigation and adaptation is an interesting controversy. Theoretical studies suggest that mitigation and adaptation efforts can be considered as strategic substitutes, as increased mitigation efforts reduce the need for future adaptation, while future adaptation may compensate for the lack of mitigation today (Barrett, 2020;Buob and Stephan, 2011;Reyer et al., 2017;Vuuren et al., 2011). Game theoretical considerations suggest that policymakers' ambitions to mitigate climate change may be undermined by the prospect of future technological solutions that neutralize the negative impact of climate change (Barrett, 2020;Buob and Stephan, 2011).
This line of argument was believed to undermine the progress of international climate negotiations about mitigation and underpinned ethical concerns about research on climate engineering (Svoboda, 2017) and adaptation (Reyer et al., 2017). The controversy about adaptation-mitigation trade-offs is of very practical relevance today, acknowledging that adaptation is a necessity of both today and the future (Barnett and O'Neill, 2010;IPCC, 2022). Research has shown that short-term mitigation policies may undermine the future adaptation. For example, the production of carbon-neutral biofuels or rapid deforestation to sequester carbon may come with the cost of biodiversity losses, which may be essential to assist ecological systems in adapting to changing climatic conditions (Chisholm, 2010;Jeswani et al., 2020). Other examples of maladaptation are emission-increasing solutions for adaptation, such as energy-intensive desalination techniques to improve water supply or air-conditioning in response to heatwaves (Barnett and O'Neill, 2010).
However, theoretical models upon which the trade-off considerations build are difficult to calibrate for three major reasons:
(1) The models explore a trade-off between current costs of mitigation compared to future costs of adaptation. This valuation is highly sensitive to the appropriate choice of the discount rate which is empirically controversial (Gollier and Hammitt, 2014). Moreover, those making decisions about adaptation and mitigation may be disparate as adaptation benefits are mostly locally specific, and often private, while climate change mitigation contributes to a global (uncertain) public good (Abidoye, 2021).
(2) The economic impact of climate change is subject to uncertainty: Once tipping thresholds in the climate system are crossed, it may become unpredictable and an existential threat to human livelihood, which may be beyond the scope of any available and expected technological solutions (Lenton et al., 2019).
(3) Existing models suggest that investments made in mitigation cannot be spent on adaptation and vice versa. However, empirically mitigation and adaptation are not necessarily mutually exclusive and examples exist where adaptation efforts contribute to mitigation and vice versa (Berry et al., 2015;Sharifi, 2021;Spencer et al., 2017).
We provide evidence that the trade-off consideration may need to be reconsidered as we identify adaptation-mitigation complementarities in R&D and show in which areas these co-benefits can be harnessed. In addition, we state that some examples of emission-increasing maladaptation can be a matter of technology choice, for example in desalination or air-conditioning (see Barnett and O'Neill, 2010).
Methods
Data sources
We used US patent data from the US Patent and Trademark Office (USPTO) and GooglePats compiled for an earlier project (Hötte et al., 2021b;Hötte et al., 2021c). We used USPTO data since most high-value inventions are filed in the US, and US patents can be regarded as a good proxy for the global technological frontier (Albino et al., 2014). To ensure the uniqueness of inventions, we used the patent DOCDB family ID of patents downloaded from PATSTAT (Spring 2021 version) as the unit of analysis (Kang and Tarasconi, 2016;Office, 2021). 3 We supplemented the patents with CPC classifications obtained from the master classification file (April 2021 version) provided by USPTO. 4 To identify adaptation and mitigation technologies, we used the CPC Y02tags (Angelucci et al., 2018;Su and Moaniba, 2017).
We obtained 37,341 unique patents that are tagged as technologies for adaptation to climate change as indicated by the CPC tag Y02A. We categorize them as patents for coastal adaptation (Y02A1), water supply and conservation (Y02A2), infrastructure resilience (Y02A3), agriculture (Y02A4), human health protection (Y02A5), and indirectly enabling technologies such as weather forecasting, monitoring, and water-resource assessment (Y02A9) (see A.1 for a detailed overview). We also sourced mitigation-related patents distinguishing technologies at the 4-digit level (buildings (Y02B), CCS (Y02C), energy-saving ICT (Y02D), clean energy (Y02E), clean production (Y02P), clean transportation (Y02T), and clean waste (Y02W)(see Angelucci et al., 2018;Veefkind et al., 2012). The tagging scheme for climate change mitigation and adaptation technologies is based on the search algorithms that identify mitigation-and adaptation-related CPC symbols, IPC symbols, and keywords (see Angelucci et al., 2018;Veefkind et al., 2012). Our analysis relies on the CPC version from April 2021.
The USPTO regularly re-classifies patents whenever a new version of the CPC system becomes available. Hence, old and new patents are assigned to technology classes according to uniform principles (Lafond and Kim, 2019). This enables the identification of the technological ancestors of today's inventions. For example, early patented inventions in windmills are the technological ancestors of today's high-tech wind turbines (cf. Hötte et al., 2021c). An adaptation-related example is health-related patents for improvements in medical compounds developed in the late nineteenth century to fight cholera. These inventions build the foundations of today's technology to fight infectious diseases. Similarly, many inventions in agriculture (e.g. ecological buffer zones or organic fertilizers), water conservation, and insulation in buildings have their origins in the nineteenth century.
Some of the patents in our data serve multiple adaptation purposes. We doublecounted these patents, arguing that knowledge is non-rival and patents that serve multiple adaptation purposes contribute equally to the knowledge base of these CPC 6-digit categories. This argument is further supported by the high variation in the value of patents: patents with a higher number of co-classifications tend to represent more valuable inventions (Lerner, 1994;Méndez-Morales et al., 2021;Sun et al., 2020). In our data, 295 out of 37,341 unique patent families are multi-purpose adaptation technologies, i.e. are assigned to two or more 6-digit Y02A-classes. 5 We further supplemented the data with information on the reliance of individual patents on governmental support (Fleming et al., 2019a;Fleming et al., 2019b). Patents are defined as being reliant on governmental support if at least one of the following five conditions hold: (1) The patent is directly owned by a governmental institution.
(2) Governmental support is explicitly acknowledged in the patent document. (3) The patent cites a patent owned by a governmental institution or that acknowledged governmental support. (4) The patent cites research published by a governmental institution. (5) The patent cites research where governmental support is mentioned in the acknowledgments. The first two conditions are related to the patents created by direct financial support of the government and the last three conditions are related to the patents being reliant on prior knowledge created by financial support of the government. Although there can be other routes of governmental support such as human-or facility-based ones, we focus on the direct financial support and prior knowledge base support, main areas of governmental support that can be captured comprehensively at the patent-level.
To analyze the technological and scientific knowledge base, we used data on (1) citations from patents to patents from Pichler et al. (2020) and (2) citations from patents to science provided by Marx and Fuegi (2020b).
The scientific base
To describe the scientific base of adaptation, we used data on citations from patents to science. Citations in a patent can be made in the text body or at the front page of a patent, and can be added by the applicant or patent examiner. We included all types of citation into our analyses. Marx and Fuegi (2020c) extracted the citation links using a sequential procedure based on text recognition and matched the data with the scientific database Microsoft Academic Graph (MAG) (Sinha et al., 2015). The matching procedure is probabilistic. Marx and Fuegi (2020c) tagged citation links with a so-called confidence score, which indicates the precision and recall rate of the matching (more detail available in Marx and Fuegi, 2019;Marx and Fuegi, 2020a). We only included patents with a confidence score > 4 which is associated with a precision rate of more than 99%. The citation links are complemented with meta-information on the scientific paper that is cited, e.g. title, DOI (if available), outlet, publication year, and scientific field of research.
We analyzed the scientific base in two ways: (1) We computed time series of the share of the number of citations to papers to the number of total citations to patents and papers. The data are aggregated into 5-year bins gathering all patents classified as certain adaptation technology that were granted during the considered period. (2) We provided a qualitative description of the science base. Every paper is tagged by the Web-of-Science (WoS) category into which the article is classified. The assignment of WoS categories to papers is made on the paper level (further explanations are provided in Hötte et al., 2021c). We used this information to show, for each type of adaptation technology, the six most often cited WoS fields as a share in all scientific citations during the different time periods.
Adaptation-mitigation complementarities
Analyzing the technological base of patents relies on the hierarchical CPC system, which classifies patents into broad sections (A-H, Y) which are sequentially sub-divided into classes, sub-classes, groups, and sub-groups. The section 'Y' is a special, cross-sectional tagging scheme that is used to identify climate-related technologies. We removed 'Y10'tags from our analysis because these tags are assigned to patents for technical reasons (for example to ensure compatibility with other classification systems).
Patents can be classified into multiple CPC classes. Co-classification indicates interdependence among different technologies. We used co-classification data to identify patents that are tagged as adaptation and mitigation technologies. We call these patents 'dual purpose' technologies.
To better understand overlaps in the knowledge base of adaptation and mitigation technologies, we used backward citations. The cosine similarity of two technology types is computed as the normalized dot product of the vectors of backward citation shares made to 4-digit CPC classes for the technological similarity and to WoS-fields for scientific similarity. We rely on the methodology used in Hötte et al., 2021c to create similarity networks. We illustrated the pairs of 6-digit mitigation and adaptation complements that show strong overlaps in their technological and scientific knowledge base.
Results
A slow start for adaptation
We analyzed the technological frontier in climate change adaptation by looking at patents granted by the USPTO that are tagged as technologies for adaptation to climate change. This leads to a population of 37,341 unique patent families that are explicitly recognized as technologies that help in climate change adaptation. We also collected 408,348 unique patent families related to climate change mitigation to explore the technological relationship between mitigation and adaptation.
Currently, there are six main categories of climate change adaptation patents: (1) coastal adaptation, (2) water supply and conservation, (3) infrastructure resilience, (4) agriculture, (5) human health protection and (6) indirect adaptation i.e. measurement technologies such as weather forecasting, monitoring invasive species, and water-resource assessments (see UNFCCC, 2006 and A.1 for details).
In Fig. 1, we show on the left-hand side the evolution of patents in mitigation and adaptation technologies as identified by 4-digit CPC codes. At the right-hand side, we show analogous figures for different adaptation technologies at the more disaggregate 6-digit level. The upper two figures 1a and 1b show the number of annually granted patents since the mid-nineteenth century. In the mid row, we show these time series measured as a share in all annually granted USPTO patents.
Until the second half of the twentieth century, patenting in mitigation and adaptation ranged at very low levels, both in absolute patent counts and measured as a share. The only exception is renewable energy with a share of up to 4% already in the late nineteenth century. This share corresponds to the level of clean energy inventions today. The historically high share is in line with previous research and historical accounts showing that patenting for energy technologies like windmills and water wheels was already very prevalent in the nineteenth century (Hötte et al., 2021c).
Since the early twentieth century, we observe the number of annually granted patents in mitigation and adaptation to grow slowly. However, when showing these inventions as a share in all US inventions, we find the growth of green inventions to be nonmonotonous.
Patenting in climate change mitigation began growing after the 1950s. After then, patenting in mitigation technologies experienced several periods of acceleration, such as during the Oil Crisis of the 1970s (Geels et al., 2017;Grubler et al., 2012). Since the 2000s, patenting in climate change mitigation (especially in energy and transportation) increasingly took off.
For adaptation, we find that inventions have not increased substantially over time except for the category of health-related technologies (Fig. 1d). Adaptation has seen only modest increases in response to the oil price crisis and in the subsequent decades. In 2020, about 0.5% of all US patents were classified as being helpful for adaptation, while q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q (b) Adaptation patents counts q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q . 1a (1b) shows the number of annually granted US patents (unique by DOCDB patent family) in 4-digit mitigation and adaptation (6-digit adaptation) technologies since 1836. Fig. 1c (1d) shows the number of 4-digit mitigation and adaptation (6-digit adaptation) patents as a share of all US patents. Fig. 1e (1f) shows the share of these patents that relies on governmental support in 1935-2017 (see Sec. 3.1 for a definition). Note that the axes may differ in scale due to differences in the data by time coverage and scale.
green energy and transport patents account for more than 3% and 2.5% and exibited a steep increase since the 2000s (Fig. 1c, 1d).
Among the adaptation technologies, health-related adaptation dominates by the number of patents. With more than 16,300 unique patents over the full time horizon, health accounts for more than twice as many patents as agriculture (8,089 patents), which is the second largest category. Coastal adaptation is the smallest category with only 857 unique patents (Table A.1). These differences may not only reflect high levels of innovative activity in health-related adaptation but also the fact that these technologies can be more effectively protected through patents compared to the other technologies (Cohen et al., 2000). Moreover, as coastal adaptation has public goods characteristics which may explain that private incentives for innovation -and patenting-can be relatively dampened. Patenting in adaptation related to water and infrastructure peaked in the 1980s but subsequently tapered off.
Drivers of innovation in adaptation and mitigation
Previous research has shown that innovation and patenting in green technologies respond to price signals and the size of the market for the technology (Acemoglu et Popp, 2002). The market size of a technology can grow through an increased demand, for example induced by environmental disasters (Miao and Popp, 2014) or regulatory pressure (Andreen, 2003;Kemp et al., 2000). These drivers may explain patterns in the time series data.
Health-and water-related adaptation rose in the aftermath of the first regulatory initiatives by the US government to reduce the pollution of the air and water resources by industrial processes (e.g. the Clean Air Act in 1963 and Clean Water Act in 1972). The majority of health-related CCATs during the 1960-1980s are air-pollution control technologies, and water-related adaptation technologies comprise many inventions for water treatment and pollution control (see A.1). Innovation in pollution-control technologies is one response to regulatory pressure (Andreen, 2003;Kemp et al., 2000) with an enhanced technological capacity for health-and water-related adaptation as a byproduct.
The rise in infrastructure adaptation can be associated with the Oil Crisis. Increased energy costs in response to that crisis were an important driver of energy-saving innovations (Hassler et al., 2021;Popp, 2002). Patents for infrastructure adaptation comprise many energy-saving insulation technologies, for example preserving thermal comfort in buildings or making power lines for energy transmission more robust (see A.1).
Innovation can be also triggered by an entrepreneurial state (Mazzucato, 2013) that actively engages in basic and applied research and creates markets for novel technological solutions. Many of the early inventions in low-carbon energy technologies during the 1950s and 1960s can be attributed to upcoming government-led initiatives in nuclear energy (Cowan, 1990), but also in renewable energy technologies emerging from early US government initiatives from the Department of Energy and the US space program (Mazzucato, 2013).
Reliance on public support
Patenting in adaptation strongly relies on governmental support with over 40% of patents since mid-2000s being linked directly or indirectly to government support (Fig. 1e). This is about 10% higher than the value for average patents in the US (cf. Fleming et al., 2019b). Indirect adaptation and health-related adaptation show the highest levels of reliance on public support (Fig. 1f). For many climate change mitigation technologies, by contrast, we observe a lower reliance on public support today compared to earlier periods. Especially clean energy and green ICT were heavily supported in the past, but have seen a significant private-sector take off. Mitigation technologies with insufficient market demand (e.g. CCS) show comparably high levels of public support as adaptation technologies.
The reliance on public support serves as an indicator of the stage of market development: if sufficient market demand for a technology exists, innovators have a commercial interest to develop these technologies and the reliance on public support is low. In contrast, if markets are underdeveloped (as in the case for adaptation and CCS), the public sector can play a critical role to stimulate innovation (cf. Mazzucato, 2013).
Reliance on public support also includes the reliance on research that is funded by the government. As we shall see below in 4.2 and A.2.2, adaptation technologies are more science-reliant than many other technologies. This contributes to the relatively higher reliance on public support of adaptation technologies (but also of science-reliant CCS), but the time trends suggest that this is not sufficient to explain this pattern. For example, for both clean energy and green ICT, the science reliance increased over time, but we observe a decreasing reliance on public support. Moreover, among the different categories of adaptation technologies, we also find that technologies like coastal, waterrelated, and infrastructure adaptation exhibit relatively higher shares of reliance on public support despite low levels of scientificness.
The knowledge base of adaptation
To study the knowledge base of adaptation technologies, we combine data on patent citations, co-classifications (Hötte et al., 2021b), and science citations (Marx and Fuegi, 2020c). Citations from patents to science indicate the scientific origins of patented inventions (Ahmadpoor and Jones, 2017;Meyer, 2000). Similarly, citations from patents to other patents describe technological base of patented inventions (Jaffe and De Rassenfosse, 2019;Verhoeven et al., 2016).
Reliance on science: Two clusters
We find that adaptation technologies, as reflected by patents, can be grouped into two clusters: (i) science-intensive technologies (agriculture, health, and indirect adaptation); and (ii) engineering-based technologies (coastal, water, and infrastructure).
We measure the scientificness of adaptation technologies by the share of patent citations to science over the sum of citations to other patents plus citations to science. This ratio indicates to which extent a patent relies on science rather than applied technological development as encoded in patent citations (see Hötte et al., 2021c). The evolution of the CCATs' scientificness over time since 1976 is shown in Fig. 2. Coastal, water, and infrastructure adaptation technologies exhibit low shares of citations to science (0-5%) while health, agriculture, and indirect adaptation are highly science-intensive (50-80%). This reflects the idiosyncratic nature of different technologies. To be specific, science-intensive adaptation technologies include, for example, crops that are climate resilient, treatments for diseases that will become more prevalent in hotter temperatures, and complex early warning and monitoring systems. By contrast, engineering-based adaptation, which relies significantly less on science, includes technologies such as fixed construction to provide flood defense, cliff stabilization, water purification, and methods to strengthen the resilience of infrastructure.
The rise in share of citations to science for agriculture and health in the 1970s-1980s coincides with the rise of the US biotechnology. This period was characterized by many spin-offs from universities and public research laboratories that undertook innovation in basic necessities (Powell et al., 1996;Powell et al., 2005). Even within the engineering-intensive adaptation technologies such as water and infrastructure adaptation, we observe that these technologies became more science-intensive. We find that this phenomenon is related to the increased scientificness of chemistry-reliant waterconservation technologies (such as desalination, reverse osmosis), advances in material sciences for infrastructure adaptation, and increased interactions between developments in science-reliant solar photovoltaics with water and infrastructure adaptation, for example to supply energy for water treatment or heating and cooling in buildings.
Coastal adaptation, the smallest category in our sample, did not show an increase in its reliance on science. This is exceptional as an increasing reliance on science is a general trend in innovation during the second half of the twentieth century (Hötte et al., 2021c). This indicates that other knowledge sources rather than science are important for patented technologies in coastal adaptation, although interpretations must be made with caution due to the low number of patents.
Composition of the scientific base
We studied the knowledge base of adaptation showing which fields of science are cited by adaptation technologies over time (Fig. 3). This gives an idea of the scientific disciplines policymakers can support to strengthen innovation in adaptation technologies. Complex technologies require a so-called absorptive capacity to be effectively used and further developed (Caragliu and Nijkamp, 2012;Cohen and Levinthal, 1990;Criscuolo and Narula, 2008). In many environmental technologies, off-the-shelf solutions available on global markets require adaptive innovation to become useful under locally specific conditions (Popp, 2020). Hence, having expertise in scientific fields that are relevant for adaptation can spur the adoption, adaptation, and indigenous development of CCATs and ensure their maintenance. This can facilitate the efficient transfer of CCATs to regions where being exposed to climate risk, which is particularly urgent in many developing countries (Adenle et Huenteler et al., 2016;A. Lema and R. Lema, 2016). These regions can stimulate adoption of adaptation technologies by investing in laboratories of local universities or public research institutions having relevant scientific understanding and thereby stimulate the transfer of adaptation skills to the local community.
Distinguishing between applied and basic research following Persoon et al. (2020), we find that science-intensive CCATs (agriculture, health, and indirect adaptation) rely mostly on basic research, while adaptation technologies with a low science-intensity (coastal, water, and infrastructure) build to a higher extent on applied research.
Among the science-intensive CCATs, both health and agriculture largely build on biochemistry and molecular biology. Health adaptation further relies on immunology, oncology, and virology, while agricultural adaptation further relies on plant sciences. Indirect adaptation technologies which cover monitoring, assessment, and forecasting technologies rely on physics-related areas such as electrical engineering and optics, which form foundations of sensor and measurement technologies. Further, they build on biologyrelated areas such as biochemistry and immunology. Manual inspections of patents reveal that indirect adaptation technologies cover not only weather forecasting and monitoring technologies but also bioinformatics technologies for medicine and chemical assessment. Therefore, university or public research laboratories in the field of biochemistry or molecular biology would be a good starting point for transferring many of the science-intensive adaptation technologies to the regions in need of such skills and knowledge (Adenle et al., 2015).
In engineering-based CCATs, applied sciences dominate. Coastal adaptation relies on several different types of engineering (civil, electric, environmental, and geological), but it also has weak linkages to some basic research of meteorology, maths, geosciences and environmental science. Water-related adaptation also relies on engineering but also basic research in chemistry, which is relevant for water conservation, filtration, recovery, and desalination that make use of chemical processes. The scientific knowledge base of infrastructure adaptation consists of material science, thermodynamics, construction, and electrical engineering, among other fields. To sum up, to transfer the engineering-based CCATs to the regions in need, the role of laboratories in the engineering department of local universities will be particularly important, though basic science is also necessary in some fields. For example, in regions at high risk of sea level rise, civil engineers, and geologists in local universities may work together to efficiently adopt and advance technologies for coastal adaptation, and to adapt them to locally-specific conditions. Similarly, in regions where water adaptation is urgent, chemical engineers in the local universities may play a pivotal role in facilitating the adoption and further development of water adaptation technologies.
Composition of the technological base
A single patent can belong to multiple technology classes, reflecting a combinatory nature of knowledge creation (Nelson and Winter, 1985). Investigating co-classification patterns of adaptation patents can reveal technological capabilities other than Y02A that are needed to develop each type of CCAT. In addition, the co-classification patterns can be also interpreted as reflecting the promising fields of technological convergence with adaptation technologies (e.g. Jee et al., 2019). Therefore, organizations equipped with capabilities in fields frequently co-classified with Y02A can be understood as being in a competitive position in developing and exploiting adaptation technologies. Motivating these organizations, particularly in the private sector, to engage in the development of adaptation technologies can be a reasonable direction to spur innovation in climate change adaptation. In addition to encouraging the supply side, governments can also stimulate targeted foreign direct investments (FDI) or foreign licensing and connect these organizations with potential regions where demand exists, the regions being exposed to a higher risk of a certain type of climate change (Ferreira et al., 2020;Popp, 2020;Saggi, 2002). Targeted technology-transfer policy may not only stimulate the diffusion of environmentally related technologies, but also spur technological learning and indigenous innovation by local firms. Fig. 4 shows the overall patterns of co-classification for each type of CCAT. For example, we can see that the vast majority of coastal adaptation patents are co-classified as fixed constructions technology. 6 The results imply that firms with fixed construction engineering skills are in a good position to develop and utilize coastal adaptation technologies. Targeted government support on these firms to motivate their investment in coastal adaptation technologies and to match them with regions with high risk of sea level rise would play an important role in stimulating innovation in coastal adaptation.
Many indirect adaptation patents are co-classified as physics (see Fig. 4). In-depth analysis with further technological details (see SI.2) shows that this is due to technological interdependencies between indirect adaptation and applied physics including measurement, detection, and prediction technologies. Therefore, to stimulate innovation in indirect adaptation, governments can incentivize firms with advanced skills in measurement, detection, and prediction to invest in indirect adaptation technologies, as well as connect these firms to regions where precise, timely sensoring and forecasting of climate disaster are critical. Fig. 4 also shows the extent to which different categories of adaptation patents are labeled as mitigation patents, indicated by purple color. The next section explores this duality in more detail.
Complementarities with mitigation
We next focus on complementarities between adaptation and mitigation technologies to inform technology-choices that help achieve climate change mitigation and adaptation at the same time. We use two different approaches: (1) analyzing patents that are co-classified as adaptation and mitigation technologies to identify 'dual purpose' technologies, and (2) examining the extent to which adaptation and mitigation technologies rely on similar technological and scientific knowledge (i.e., cite the same patents and papers). The knowledge base similarity of adaptation and mitigation technologies helps understand how mutual knowledge spillovers between adaptation and mitigation can be stimulated. For example, public support may be directed towards the fields in which both adaptation and mitigation rely on.
Adaptation technologies with mitigation co-benefit
Starting off with co-classifications, we find that many adaptation patents except for those in indirect adaptation include a significant proportion of dual purpose patents helping in not only adaptation but also mitigation (purple bars in Fig. 4). In total, 26% of adaptation patents are co-classified as mitigation patents, showing that more than a quarter of adaptation technologies have the potential to be used in both adaptation and mitigation areas (Table 1). The highest overlap is in infrastructure adaptation where 70% of the patents are co-classified as mitigation technologies. For example, thermal insulation in buildings achieves both adaptation and mitigation purposes: it preserves thermal comfort during extreme temperature events, but it may also help reduce energy consumption and associated emissions. This is an example of how maladaptation relying on the intensified use of air-conditioning to cope with heatwaves can be avoided (Barnett and O'Neill, 2010).
Other illustrative examples are extreme weather resistant electricity grids that rely on insulation technologies that help reduce energy losses during the transmission through the grid, or integration of production and use of renewable energy into buildings for heating and cooling purposes. For health-, agriculture-, and water-related adaptation, roughly 20% of patents simultaneously serve mitigation purposes (Table 1). Co-benefits in health adaptation arise for example from clean transportation that reduce emissions. This represents a preventive intervention improving public health as air-pollution control helps prevent respiratory and cardivascular diseases. Research has shown that these diseases increase the vulnerability to heatwaves and some infectious diseases (Harlan and Ruddell, 2011), including Covid-19 (Domingo and Rovira, 2020).
In agriculture, we find technologies that improve the climate resilience of plants can simultaneously sequester carbon. Some technologies that contribute to an improved handling of bio-related waste or energy efficiency of greenhouses can simultaneously be used in cooling systems for food storage.
In addition, some adaptation technologies used for water treatment, purification, and desalination also help reduce emissions in wastewater and solid waste treatments. Barnett and O'Neill (2010) mentioned energy-intensive desalination as an example of emission-increasing maladaption. Our analysis shows that mitigation-friendly alternatives exist, combining renewable energy with desalination.
By contrast, the occurrence of dual purpose technologies is relatively weak in coastal (8%) and indirect adaptation technologies (1%).
When examining the degree to which mitigation patents can be co-classified as adaptation patents, we find that CCS, clean buildings, and waste management related mitigation technologies include 8By the number of patents, clean transportation, efficient production, and low-carbon energy patents have significant co-classification with adaptation. However, due to the large number of patents in these categories the share of co-classification is low, ranging between 1-3%.
The fact that some adaptation technologies bear mitigation co-benefits does not tell us much about the climate impact of the remainders beyond examples mentioned in the literature on maladaptation. We cannot say -based on our analysis-whether mitigation technologies that are not co-classified as adaptation have a negative or positive impact on the economy's climate resilience. While not judging whether adaptation and mitigation are complements in general, we show that some adaptation-mitigation options are complementary. Complementarity may be a matter of technology choice and our analysis identifies areas that are promising to achieve adaptation-mitigation co-benefits.
Although our analysis shows the technological potential to achieve both adaptation and mitigation goals, the absence of co-benefits does not necessarily imply an inferior technology choice. Other factors such as competing policy objectives, economic constraints, different time horizons, and locality of events may constrain the set of available technology options. For example, health-related adaptation technologies to cope with risks from vector borne diseases are urgent in some developing countries although disconnected from any mitigation technology. For nuclear energy, in some countries, political objectives to achieve short-term mitigation may weigh higher than the long-term resistance to climate change. At least in the short term, adaptation co-benefits of nuclear energy are absent and there is good reason to believe that these technologies rather undermine than strengthen the vulnerability against extreme climate shocks (Hanski et al., 2018;Jordaan, 2018). Nevertheless, short term mitigation benefits of this technology are strong and -assuming a positive mitigation impact-it also contributes to adaptation in the long run if it helps reduce the impact of climate change.
Potential knowledge spillovers between mitigation and adaptation
We investigate the extent to which different mitigation and adaptation technologies build on a common knowledge base. To identify domains of shared knowledge, we analyze similarities of the technological and scientific knowledge base for pairs of different adaptation and mitigation technologies. Previous research has shown that similarities enable knowledge spillovers across technologies at the organizational, regional, and national level, and they are an indicator of absorptive capacity as it is easier for firms, industries, and countries to adopt a new technology if the adopter has pre-existing relevant knowledge (Caragliu and Nijkamp, 2012;Cohen and Levinthal, 1990;Criscuolo and Narula, 2008). This also matters for policy: if two technologies build on the same knowledge sources, R&D policy may focus on these areas to support the development of both technologies at the same time.
In Fig. 5, we illustrate knowledge similarities through network plots and correlation charts. Similarities are measured via backward citation patterns: two technologies are more similar if they rely more on common sources of knowledge. This is measured by the cosine similarity based on shares of citations to CPC 4-digit technology classes ( Fig. 5(a)) and citations to scientific Web of Science (WoS) fields ( Fig. 5(b)).
The upper two figures show similarity networks. A link between a pair of technologies indicates the cosine similarity of their references to scientific fields and technology classes, respectively. For clarity, only the most significant links are shown. 7 The widths of connecting edges are proportional to the degree of similarity and the node sizes are proportional to the number of patents. The node colors indicate the 4-digit technology class (i.e., red for adaptation, gray for buildings, black for CCS, blue for green ICT, green for energy, orange for production, yellow for transport, and brown for waste).
The lower two figures illustrate the numerical values of the cosine similarity of adaptation (columns) and mitigation (rows) technologies at the 6-digit level. The letters in the beginning indicate the type of mitigation technology (B for buildings, C for GHG disposal, D for green ICT, E for energy, P for production, T for transport, and W for waste). Our similarity analysis shows:
(1) Citing similar patents, mitigation technologies for energy efficiency in buildings and green ICT have a similar technological knowledge base to infrastructure-related adaptation technologies. Technologies that reduce transmission losses and improve the energy efficiency of ICTs rely on similar technological knowledge as technologies that strengthen the resilience of physical infrastructure to extreme weather events. The same holds for insulation, efficient heating, and renewable energy in buildings.
(2) Clean energy, especially clean combustion and bio-fuels, exhibits strong scientific similarities with science-intensive adaptation technologies such as agriculture, health, and indirect adaptation. This is particularly due to their common reliance on chemistry (see Section 4.2 and for more detail SI.8
in the Supplementary Material).
(3) Water-related adaptation technologies exhibit a high degree of scientific similarity with clean industrial processing technologies for metal and oil, with waste treatment, and CCS. This can be explained by their joint reliance on chemistry. We also observe a high potential for scientific and technological knowledge spillovers between water adaptation and clean energy that mostly arise from interactions with non-fossil fuels and renewables. Our data shows that examples of energy intensive water treatment technologies like desalination explicitly make use of photovoltaics, which explains their reliance on the same science (see A.1 and for more detail in the Supplementary Material).
q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.
(4) We observed the rise in mitigation technologies for clean production that have adaptation co-benefits (see orange node in ). Not surprisingly, the spillover potential is highest in between adaptation and mitigation in agricultural production. In addition, we observe a large potential for technological knowledge spillovers between enabling technologies in production and various fields of adaptation. This suggests that there is a high potential to harness knowledge spillovers and to realign efforts to mitigate emissions in production processes with adaptation goals.
This analysis suggests that many adaptation and mitigation technologies in various domains share a common knowledge base. The reliance on similar technological and scientific knowledge suggests that R&D investments in one area have positive side effects on another. Economically, the existence of positive knowledge spillovers is a justification for higher levels of public support, as the social returns of these investments exceed those from investments in technologies that show a lower spillover potential (Aldieri et al., 2019).
Discussion
Despite the urgency of climate change and the substantial long-term economic benefits of adaptation (Tall et al., 2021), the study of innovation in adaptation has attracted relatively little scholarly attention (Dechezlepretre et al., 2020;Popp, 2019) and markets for adaptation technologies seem underdeveloped given their benefits (Dechezlepretre et al., 2020). However, this is likely to change: the requirement of countries to disclose their adaptation plans under the Paris Agreement (Berrang-Ford et al., 2019;Lesnikowski et al., 2017), increasing awareness of firms' climate risks and efforts by regulators to make risk disclosures mandatory will incentivize the public and private sector to take action towards adaptation (Goldstein et al., 2019;Smith, 2021). This study offers the first systematic analysis of adaptation technologies and their knowledge base addressing three questions.
First, we asked: To what extent have these technologies been developed, and which were the drivers of innovation? We find that patenting in most adaptation technologies did not increase substantially over the past decades, with the exception of health-related and indirect adaptation. Historically, we observed several phases of increased inventive activity, especially since the late 1960s and during the Oil Crisis in the 1970s. The 1960s were the starting date of many environmental initiatives including regulatory measures such as the Clean Air Act from 1963 and Clean Water Act from 1972. As discussed above, many adaptation technologies, especially in water and health, interacting with pollution control bear a positive externality improving the environmental quality. Despite not providing causal evidence, the rise in certain water and health adaptation technologies we observe might be a byproduct of environmental regulatory policy.
Similarly, our analysis revealed that many solutions for adaptation, especially in infrastructure and agriculture, have the potential to simultaneously improve energy efficiency. Many other technologies integrate off-grid renewable energy into their processes, for example for desalination, food processing and conservation, or cooling and heating in buildings. High prices for fossil fuel energy during the Oil Crisis stimulated investments in energy efficiency and the demand for alternative energy solutions, which offers one explanation for the rise adaptation, again as a byproduct of the seemingly unrelated energy price.
Second, we addressed the question: How can governments support the development and adoption of these technologies? Our analysis has further revealed that public R&D support may be supportive for early-stage technological development. This is particularly important for science-intensive technologies, as private sector incentives to engage in basic research with uncertain returns are limited. Agriculture, health, and indirect adaptation technologies are highly science-intensive, while adaptation for coastal defense, infrastructure, and water is rather engineering-based.
Analyzing the scientific base of adaptation, we have further discussed that scienceintensive CCATs rely more heavily on basic rather than applied sciences. This gives insights into policies for transferring adaptation technologies to regions in need. Local universities and public research institutions equipped with relevant scientific knowledge base (e.g., biochemistry and molecular biology for science-intensive CCATs) can be key actors in facilitating technology transfer, as they contribute to the regional absorptive capacity for science-intensive technologies. An analysis of co-classification patterns of adaptation patents helps identify organizations with complementary technological capabilities, which can be used to develop and exploit different adaptation technologies, for example firms with construction skills for coastal adaptation. Above, we discussed directions in which the government should provide targeted support for both supply and demand of adaptation solutions to stimulate innovation in climate change adaptation.
Finally, we wanted to find out: How do technologies for adaptation interact with climate change mitigation? From a technological perspective, climate change mitigation and adaptation are complements: on average, 26% of adaptation technologies also help in mitigation. In some sub-fields such as infrastructure-adaptation, the complementarities are particularly large, with 70% of adaptation patents simultaneously contributing to climate change mitigation. Well-designed policy may exploit and strengthen these complementarities to ensure that climate change technologies serve the twin goals of adaptation and mitigation.
Adaptation-mitigation co-benefits have been recognized in many adaptation case studies (Berry et al., 2015;Kabisch et al., 2017;Sharifi, 2021). Our analysis shows that this can be also seen systematically in aggregate data. This enables a systematic understanding of the drivers of innovation behind adaptation and shows many examples of how adaptation and mitigation efforts can be aligned. We have also seen that adaptation technology development often came as a byproduct of other economic trends. Identifying complementarity with other larger technological developments, for example in artificial intelligence and biotechnology, may help to make R&D for adaptation more effective. Furthermore, systematic analyses of technological overlaps of adaptation with response strategies to major shocks such as Covid-19, the Ukraine war, or financial crises can also mobilize additional financial resources to create a resilient economy.
Conclusion
In this paper, we have taken stock of the current technological frontier of adaptation technologies. We have shown that -compared to mitigation-innovation in the field of adaptation has not yet taken off. In the analysis, we have identified and discussed major drivers of innovation in adaptation such as responses to regulation and shocks in the market, but we also highlighted a prominent role of the government stimulating the development of these technologies.
Our analysis has further shown how governments can effectively stimulate the development and adoption of technologies through targeted investments in scientific and technological capacities, and we discussed how this can help enable technology transfer to countries where adaptation needs are high.
Finally, we addressed the nexus between climate change mitigation and adaptation and have shown that -from a technological perspective-adaptation and mitigation efforts may be complementary. However, this may be a matter of technology choice and our analysis may provide guidance on how these choices can be made to achieve mitigation and adaptation objectives at the same time.
This study is limited to the technological frontier of adaptation as reflected in patent data. Although the granted patents capture inventions that have high (perceived) market value, patent data as a measure of innovation has well-documented limitations (OECD, 2009) being biased towards the technological frontier solutions and being silent about other aspects such as nature-based or behavioral solutions. A promising avenue for future research is to develop measures for these other solutions of adaptation that can be systematically compared to the technologies analyzed in this paper. This would help understand the multiple trade-offs and synergies among different solutions for adaptation and their interaction with mitigation, which is highly relevant to address the climate challenge in an efficient way.
Data availability
The research data including R-scripts used for the data compilation and empirical analysis are publicly available under a CC-BY-4.0 license to ensure the full reproducibility of the results and re-use (Hötte et al., 2021a). The data can be downloaded here: https://doi.org/10.4119/unibi/2958327.
Acknowledgments
The authors want to thank Sugandha Srivastav who significantly contributed to an earlier version of this article, in both intellectual and practical ways. Further gratitude is owed to Anton Pichler and François Lafond whose work on an earlier project contributed significantly to the methodological basis of this work. The authors also want to thank Matthias Endres, Peter Persoon, Vilhelm Verendel and their colleagues from the Institute for New Economic Thinking (INET), the Oxford Martin Pogramme on Technological and Economic Change (OMPTEC), and Future of Work for helpful feedback. Gratitude is owed to Elizabeth Champion for her proofreading assistance. K
A.2 Additional results
A.2.1 Summary statistics of adaptation and mitigation patents
In Table A.1, we summarize the adaptation patents (at the DOCDB family level) granted over the full time horizon covered by our analysis. We have a relatively low number of patents in coastal adaptation (857) and the largest number of patents in health adaptation (16,363). We also report the number of patents that make at least one citation to science, the share of patents that cite to science, the number of scientific citations, average number of citations made by patents, average number of citations made by citing patent and the share of patents that are reliant on governmental support. Overall, we find that patents relying on public support tend to be more science intensive (i.e., exhibit a higher share of science reliant patents and make more citations to science than others). Fig. A.1 (Fig. A.2) shows time series plots of counts of 6-digit adaptation (4-digit adaptation and mitigation) patents (blue line) and counts of patents that cite at least one scientific paper (orange line) at a logarithmic scale. Among the adaptation technologies, adaptation in agriculture and health are the oldest technologies with first patents being granted in the mid 19th century. Indirect adaptation technologies emerged in the 1960s and exhibit a strong reliance on science. While agriculture, health and indirect exhibit exponential growth, the other three technologies rather stagnated for a long time. Post-2005, the number of annually granted patents was increasing.
A.2.2 The scientificness of adaptation and mitigation over time
Clean energy technologies show historically a relatively high number of patents, and also for adaptation, mitigation related to buildings, production and transport, patenting began already during the nineteenth century. Green ICT and CCS are the by far youngest technologies starting off in early to mid-twentieth century. For all technologies, we observe an increasing reliance on science starting off from the 1950s. The reliance on science has been increasing for all technologies, though we observe a strong heterogeneity across technology groups with adaptation, clean production, and CCS having the highest share of patents that make at least once citation to a scientific article (see also Table A.2).
In Fig. A.3 we show an alternative measure of the scientificness of patents given by the ratio of citations to science over the sum of citations to patents and science. This figure confirms the pattern observed before with adaptation showing the highest reliance on scientific rather than applied knowledge, but also CCS, clean production, energy, waste and green ICT to become increasingly scientific. However, as seen in Section 4.2, the there is a high heterogeneity across subfields as technology. For example, the high science intensity of adaptation is mainly driven by health technologies and previous research has show that solar PV and biofuels are key drivers of the scientificness of clean energy technologies (Hötte et al., 2021c). q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.01 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.01 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 Notes: These figures illustrate technological and scientific similarities among adaptation technologies and among adaptation and mitigation technologies at the 6-digit CPC level. We use a cosine similarity-based methodology as explained in Hötte et al., 2021c. Mitigation technologies are ranked by the row-sum in a decreasing order, i.e. technologies with a higher the spillover potential across all types of adaptation technologies rank higher. Column-wise reading illustrates for which types of adaptation technology the highest spillover potential is found. The letters preceding the name of the technology type indicate the type of 6-digit mitigation or adaptation technology (i.e., A for adaptation, B for buildings, C for capture and storage of greenhouse gases, D for green ICT, E for energy, P for production, T for transport and W for waste). Notes: These networks illustrate technological and scientific similarities of different types of adaptation and mitigation technologies. The networks are based on the shares of (a) citations to CPC 4-digit technology classes and (b) citations to scientific fields (WoS). A link between a pair of technologies indicates the cosine similarity of their references to scientific fields (scientific similarity) and technology classes (technological similarity). For clarity only the most significant links are shown. The widths of connecting edges are proportional to the degree of similarity and the node sizes are proportional to the number of patents. The node colors indicate the 4-digit technology class (red for adaptation, gray for buildings, black for CCS, blue for green ICT, green for energy, orange for production, yellow for transport, and brown for waste). Notes: The networks illustrate the technological and scientific similarity of different adaptation and mitigation technologies computed on the basis of (a) citations to CPC 4-digit technology classes and (b) citations to scientific fields (WoS). A link between a pair of technologies indicates the cosine similarity of their references to scientific fields (scientific similarity) and technology classes (technological similarity). To simplify the representation, only the most significant links are shown. The widths of connecting edges are proportional to the level of similarity and the node sizes are proportional to the number of patents. The node colors indicate the 4-digit technology class (red for adaptation, gray for buildings, black for CCS, blue for green ICT, green for energy, orange for production, yellow for transport and brown for waste).
SI.1 Relative frequencies of adaptation and mitigation patents
SI.1.1 Additional information on the science base of adaptation
Technological similarity by CPC4 citations
SI.1.3.3 Co-classification of dual purpose patents
Figure 1 :
1Patented
Fig
Fig. 1a (1b) shows the number of annually granted US patents (unique by DOCDB patent family) in 4-digit mitigation and adaptation (6-digit adaptation) technologies since 1836. Fig. 1c (1d) shows the number of 4-digit mitigation and adaptation (6-digit adaptation) patents as a share of all US patents. Fig. 1e (1f) shows the share of these patents that relies on governmental support in 1935-2017 (see Sec. 3.1 for a definition). Note that the axes may differ in scale due to differences in the data by time coverage and scale.
Figure 2 :
2Science Science-intensity of different adaptation patents measured by the share of citations to science in the number of total citations (sum of citations to other patents and scientific articles).
Figure 3 :
3Composition of scientific knowledge base by scientific fields
Figure 4 :
4Co-classification of adaptation technologies
Figure 5 :
5Technological
. 108 ...
108.H. acknowledges support from OMPTEC and Citi. S.J. acknowledges support from Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A3A03037237). Y02A CPC COOPERATIVE PATENT CLASSIFICATION Y GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS (NOTES omitted) Y02 TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE (NOTES omitted) Y02A TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE NOTE This subclass covers technologies for adaptation to climate change, i.e. technologies that allow adapting to the adverse effects of climate change in human, industrial (including agriculture and livestock) and economic activities. 10/00 at coastal zones; at river basins 10/11 . Hard structures, e.g. dams, Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping 20/00 Water conservation; Efficient water supply; Efficient water use 20/Rainwater Relating to industrial water supply, e.g. Extreme weather resilient electric power supply systems, e.g. strengthening power lines or underground power cables 30/24 .
Figure
Total number of patents by technology type and number of these patents that cite to science over time at a logarithmic scale.
Figure
Total number of patents by technology type and number of these patents that cite to science over time at a logarithmic scale.
Figure A. 3 :
3ScienceNotes: Science-intensity of different 4-digit adaptation and mitigation patents measured by the share of citations to science in the number of total citations (sum of citations to other patents and scientific articles).
Figure SI. 1 :
1Relative frequencies of different technologies Notes: These pie charts illustrate the relative frequencies of different types of mitigation and adaptation technologies. The figures at the left show pie charts for all Y02-tagged technologies (with adaptation technologies (Y02A) indicated in red color). The figures at the right show these numbers for the subset of adaptation technologies.
Figure
Figure SI.3: Scientific & technological similarities of adaptation & mitigation in 1976-2005
Figure
Figure SI.4: Scientific & technological similarities of adaptation & mitigation in 2006-2020
Figure
SI.5: Cosine similarity networks of mitigation-adaptation complements
FigFigure
.SI.5 illustrates scientific and technological similarities between mitigation and adaptation technologies at the disaggregate level (6-digit CPC) using the subset of adaptation patents with mitigation co-benefit.Fig. SI.6 illustrates technological and scientific similarities of mitigation and adaptation technologies using the full sample of mitigation and adaptation technologies.SI.6: Cosine similarity networks of mitigation and adaptation technologies
Figure SI. 9 :
9Co-classification of adaptation technologies with mitigation co-benefitNotes: This figure shows the 8 most frequent co-classifications (3-digit CPC classes) of adaptation technologies that are simultaneously classified as mitigation technology.
Figure SI. 10 :
10Co-classification of dual-purpose adaptation and mitigation technologiesNotes: This figure shows the 8 most frequent co-classifications (3-digit CPC classes) of dual-purpose adaptation and mitigation patents, i.e. patents that are simultaneously classified as adaptation and mitigation technology.
Notes: These figures show the 8 most often cited scientific fields (by Web-of-Science categories). The numbers on top of each bar indicate the number of papers cited by patents granted in the respective time period. The size of the colored fields in each bar plot indicates the share of citations that goes to the respective WoS field. Black color is used for the residuum of fields that are cited less often than the 8th most often cited field.Coastal
1976−1990
1991−2005
2006−2020
16
37
186
Eng. Civil
Eng. Elec.
Eng. Environ.
Eng. Geological
Environ. sci.
Geosciences
Maths., Appl.
Meteorology
Water
1976−1990
1991−2005
2006−2020
79
479
4810
Biochem. & Mol. Bio.
Chem.
Chem., Physical
Energy & Fuels
Eng. Chemical
Eng. Environ.
Environ. sci.
Materials sci.
Infrastructure
1976−1990
1991−2005
2006−2020
64
329
1950
Chem., Physical
Construct. Tech.
Energy & Fuels
Eng. Elec.
Materials sci.
Maths.
Polymer sci.
Thermodynamics
Agriculture
1976−1990
1991−2005
2006−2020
294
35467
103941
Agronomy
Biochem. & Mol. Bio.
Biotech. & Microbio.
Chem., Physical
Environ. sci.
Fisheries
Microbiology
Plant sci.
Health
1976−1990
1991−2005
2006−2020
3932
109923
341316
Biochem. Methods
Biochem. & Mol. Bio.
Biotech. & Microbio.
Immunology
Infect. Diseases
Microbiology
Oncology
Virology
Indirect
1976−1990
1991−2005
2006−2020
329
10357
58333
Biochem. & Mol. Bio.
Chem., Analyt.
Endocrin. & Metabol.
Eng. Elec.
Immunology
Meteorology
Oncology
Optics
Notes: These figures show the co-classification of adaptation technologies at the CPC section level (1-digit). The numbers on top of each bar indicate the number of patents granted in each sub-period. Note that the bar plots rely on the number of co-classifications. Patents that serve multiple adaptation purposes, i.e. are classified into multiple adaptation technology types, are double-counted. The size of the colored fields in each bar plot indicates the share of co-classifications for different subgroups by adaptation technology type.Coastal
1976−1990
1991−2005
2006−2020
207
300
431
Water
1976−1990
1991−2005
2006−2020
1467
1773
4592
Infrastructure
1976−1990
1991−2005
2006−2020
1605
1889
3294
Agriculture
1976−1990
1991−2005
2006−2020
2206
3476
5742
Health
1976−1990
1991−2005
2006−2020
1899
8076
19597
Indirect
1976−1990
1991−2005
2006−2020
198
801
3264
Fixed Constructions
Perform. Operations & Transp.
Climate Change Mitigation
Physics
Chemistry & Metallurgy
Human Necessities
Mechanical Engineering
Electricity
Textiles & Paper
Table 1 :
1Overview statistics of dual purpose patentsNotes: This table summarizes the subsets of dual purpose patents, i.e. patents that are simultaneously classified as adaptation and mitigation technology. The upper part of the table shows these patents from the angle of adaptation, the lower part from the angle of mitigation technologies. Column Share dual purpose shows the share of dual purpose patents in all patents. Column Citing/total patents shows the ratio of patents that cite at least one scientific paper over the number of all patents. Column Share gov. supported shows the share of patents that benefited from governmental support. The rows Gov. support: Yes and No show statistics for the subset of patents that do and do not rely on public support, respectively. Sum of the number patents in each sector is not exactly same with the number of all patents because a patent can be classified into multiple sectors at the same time.Total
patents
Share dual
purpose
Citing/total
patents
Share gov.
supported
Dual purpose adaptation technologies
Coastal
71
0.08
0.11
0.30
Water
926
0.20
0.25
0.32
Infrastructure
3276
0.70
0.10
0.17
Agriculture
1768
0.22
0.21
0.23
Health
3668
0.22
0.19
0.20
Indirect
39
0.01
0.54
0.69
Gov. support (No)
6440
0.27
0.10
Gov. support (Yes)
1657
0.17
0.41
All
9645
0.26
0.23
0.20
Dual purpose mitigation technologies
Buildings
3033
0.07
0.09
0.16
CCS
429
0.08
0.44
0.46
Green ICT
15
0.00
0.67
0.36
Energy
920
0.01
0.24
0.31
Production
1356
0.02
0.25
0.23
Transport
2821
0.03
0.12
0.14
Waste
1071
0.05
0.24
0.27
Gov. support (No)
6440
0.02
0.10
Gov. support (Yes)
1657
0.02
0.41
All
9645
0.02
0.29
0.20
Notes: These figures illustrate technological similarities of different types of adaptation and mitigation technologies that are complements, i.e. simultaneously classified as adaptation and mitigation technologies. The figures are based on shares of (a) citations to CPC 4-digit technology classes and (b) citations to scientific fields (WoS). The upper two figures show similarity networks. A link between a pair of technologies indicates the cosine similarity of their references to scientific fields and technology classes, respectively. For clarity only the most significant links are shown. The widths of connecting edges are proportional to the degree of similarity and the node sizes are proportional to the number of patents.05
0.14
0.24
0.33
0.42
0.51
0.61
0.7
0.79
0.89
0.98
Coastal
Water
Infrastructure
Agriculture
Health
Indirect
P Chemicals
E Non−fossil fuel
P Agriculture
T Air transport
W Indirect
W Wastewater
W Solid waste
P Metal proc.
P Oil refining
C CCS
C CCS
E Combustion
B Insulation
B Renewables
T Road transport
(b) Scientific similarity
The node colors indicate the 4-digit technology class (i.e., red for adaptation, gray for buildings, black
for CCS, blue for green ICT, green for energy, orange for production, yellow for transport, and brown
for waste). The lower two figures illustrate the numerical values of the cosine similarity of adaptation
(columns) and mitigation (rows) technologies at the 6-digit level. The letters in the beginning indicate
the type of mitigation technology (i.e., B for buildings, C for GHG disposal, D for green ICT, E for
energy, P for production, T for transport, and W for waste).
Structural elements or technologies for improving . . using natural or recycled building materials, e.g.thermal insulation
30/242
. . Slab shaped vacuum insulation
30/244
straw, wool, clay or used tires
30/249
. . Glazing, e.g. vacuum glazing
30/254
. . Roof garden systems; Roof coverings with high
solar reflectance
30/27
. Relating to heating, ventilation or air conditioning
[HVAC] technologies
30/272
. . Solar heating or cooling
30/274
. . using waste energy, e.g. from internal combustion
engine
30/30
. in transportation, e.g. on roads, waterways or
railways
30/60
. Planning or developing urban green infrastructure
40/00
Adaptation technologies in agriculture, forestry,
livestock or agroalimentary production
40/10
. in agriculture
40/13
. . Abiotic stress
40/132
. . . Plants tolerant to drought
40/135
. . . Plants tolerant to salinity
40/138
. . . Plants tolerant to heat
40/146
. . Genetically Modified [GMO] plants, e.g.
transgenic plants
40/20
. . Fertilizers of biological origin, e.g. guano or
fertilizers made from animal corpses
40/22
. . Improving land use; Improving water use or
availability; Controlling erosion
40/25
. . Greenhouse technology, e.g. cooling systems
therefor
40/28
. . specially adapted for farming
40/51
. . specially adapted for storing agricultural or
horticultural products
40/58
. . . using renewable energies
40/60
. Ecological corridors or buffer zones
CPC -2021.02
1
A.1 Y02A classes and definitions
This list is downloaded from: https://worldwide.espacenet.com/classification?
locale=en_EP#!/CPC=Y02A [April 2021].
Y02A
40/70
. in livestock or poultry
40/76
. . using renewable energy
40/80
. in fisheries management
40/81
. . Aquaculture, e.g. of fish
40/818
. . . Alternative feeds for fish, e.g. in aquacultures
40/90
. in food processing or handling, e.g. food
conservation
40/924
. . using renewable energies
40/926
. . . Cooking stoves or furnaces using solar heat
40/928
. . . Cooking stoves using biomass
40/963
. . Off-grid food refrigeration
40/966
. . . Powered by renewable energy sources
50/00
in human health protection, e.g. against extreme
weather
50/20
. Air quality improvement or preservation, e.g.
vehicle emission control or emission reduction by
using catalytic converters
50/2351
. . Atmospheric particulate matter [PM], e.g. carbon
smoke microparticles, smog, aerosol particles,
dust
50/30
. Against vector-borne diseases, e.g. mosquito-borne,
fly-borne, tick-borne or waterborne diseases whose
impact is exacerbated by climate change
90/00
Technologies having an indirect contribution to
adaptation to climate change
90/10
. Information and communication technologies [ICT]
supporting adaptation to climate change, e.g. for
weather forecasting or climate simulation
90/30
. Assessment of water resources
90/40
. Monitoring or fighting invasive species
CPC -2021.02
2
Table A .
AThe row entry All corresponds to total numbers for columns total patents, citing patents and scientific citations and to averages for the other columns. We double-count patents that fall into multiple adaptation technology categories, i.e. totals in row All are smaller than the sum of totals by technology type. The rows Gov. support: Yes and No show statistics for the subset of patents that do and do not rely on public support, respectively. The data on government support is only available for the period 1928-2017, i.e. the patent counts do not sum up.1: Overview of adaptation adaptation technologies
Technology
Total
patents
Citing
patents
Citing/total
patents
Scientific
citations
Citations
per patents
(all)
Citations
per patents
(citing)
Share Gov.
support
Coastal
857
62
0.07
328
0.38
5.29
0.18
Water
4678
720
0.15
14173
3.03
19.68
0.22
Infrastructure
4671
421
0.09
3828
0.82
9.09
0.16
Agriculture
8089
2482
0.31
149341
18.46
60.17
0.23
Health
16363
9331
0.57
490310
29.96
52.55
0.39
Indirect
2978
1749
0.59
72759
24.43
41.60
0.58
All
37341
14681
0.30
730739
12.85
31.40
0.31
Gov. support (No)
21706
5717
0.26
158897
7.32
27.79
Gov. support (Yes) 9853
6911
0.70
480611
48.78
69.54
Notes: This table summarizes the characteristics of patents classified as climate change adaptation
technologies. The categories are distinguished at the 6-digit CPC level. The column Citing patents
shows the number of patents that rely on science, i.e. make at least one citation to the scientific
literature.
Table A .
A2 summarizes all Y02-tagged technologies in our data differentiating between different types of mitigation and adaptation technologies.Fig. SI.1shows a pie-chart illustrating the relative frequencies of different types of mitigation and adaptation technologies at the aggregate and disaggregate level.
Table A .
A2: Overview of adaptation and mitigation technologiesTechnology
Total
patents
Citing
patents
Citing/total
patents
Scientific
citations
Citations
per patents
(all)
Citations
per patents
(citing)
Share Gov.
support
Adaptation
37341
14681
0.39
672420
18.01
45.80
0.31
Buildings
43371
6243
0.14
39477
0.91
6.32
0.16
CCS
5111
2074
0.41
22261
4.36
10.73
0.34
Green ICT
32735
8281
0.25
55787
1.70
6.74
0.11
Energy
166061
40075
0.24
417128
2.51
10.41
0.32
Production
83967
27315
0.33
310779
3.70
11.38
0.21
Transport
109997
10457
0.10
70373
0.64
6.73
0.19
Waste
22368
4361
0.19
33671
1.51
7.72
0.19
All
445689
98084
0.26
1621896
4.17
13.23
0.23
Gov. support (No)
272606
46150
0.17
378647
1.39
8.20
Gov. support (Yes) 81245
36919
0.45
1005000
12.37
27.22
Notes: This table summarizes the characteristics of adaptation and mitigation technologies at the
aggregate 4-digit CPC level. The column Citing patents shows the number of patents that rely on
science, i.e. make at least one citation to the scientific literature. The row entry All corresponds to
total numbers for columns total patents, citing patents and scientific citations and to averages for the
other columns. We double-count patents that fall into multiple technology categories, i.e. totals in row
All are smaller than the sum of totals by technology type. The rows Gov. support: Yes and No show
statistics for the subset of patents that do and do not rely on public support, respectively.
Table SI .
SI1 gives an overview of the characteristics of the data on citation links from
patents to science in our data showing the number of patents that cite science, the num-
ber of different papers being cited, the number of citation links, the number of citation
links with the highest reliability score, the average confidence score, the percentage share
of citations made by the applicant and by the examiner, and the percentage of citations
made on the front page of the patent and in the text body. Interestingly, science citations
in science-intensive technologies (agriculture, health, indirect) are most often made by
the applicant (63.6-83.5%) while citation links in technologies with low science reliance
(coastal, water, infrastructure) are mostly added by the patent examiner (24.4-35.7% of
citations made by the applicant).
Table SI .
SI2 summarizes the age characteristics of science-reliant patents and papers being cited. The oldest science reliant patents were granted between 1935 (agriculture) and 1965 (coastal). The oldest scientific papers cited are from the nineteenth century.
Table SI .
SI2: Age characteristics of science-reliant adaptation patents and cited papersTable SI.3 the most frequently cited scientific fields by adaptation technology. Biochemistry and molecular biology turn out to be the by far most often cited field of research.Technology
Oldest
patent
Youngest
patent
Avg year
patent
Oldest
paper
Youngest
paper
Avg year
paper
Table SI .
SI3: Most frequently cited WoS fields Notes: This table shows the number of citations from patents to different scientific fields. The third and fourth columns show the number of citations that the WoS field has received by patents in each adaptation technology field and by patent from all adaptation technology fields, respectively.Technology
WoS field
# citations
(by tech)
# citations
(total)
Coastal
Environmental Sciences
39
3,660
Water
Eng., Chem.
2,777
4,368
Infrastructure
Energy & Fuels
474
3,000
Agriculture
Biochem. & Molec. Biology
68,260
231,750
Health
Biochem. & Molec. Biology
144,666
231,750
Indirect
Biochem. & Molec. Biology
18,447
231,750
All
Biochem. & Molec. Biology
231,750
231,750
Table SI .
SI4 shows the most important journals cited by adaptation patents.Table SI.6shows the most science-reliant patent, i.e. the patent making most scientific citations and tableSI.5 shows the papers that have been most important for different types of adaptation technologies.
Table SI .
SI4: Most frequently cited journals This table shows the journals that are cited most frequently. The third and fourth columns show the number of citations that the journal has received by patents in each adaptation technology field and in all adaptation technology fields, respectively. PNAS is the abbreviation of Proceedings of the National Academy of Sciences of the United States of America.Technology
Journal
# citations
(by tech)
# citations
(total)
Coastal
Electrochimica Acta
10
10
Water
Desalination
1,087
1,087
Infrastructure Science
113
113
Agriculture
PNAS
10,483
10,483
Health
PNAS
22,732
22,732
Indirect
PNAS
2,967
2,967
All
PNAS
36,267
36,267
Notes:
Table SI .
SI5: Most frequently cited papersSI.1.2 Co-classification of adaptation technologiesFig. SI.2 shows the relative frequencies that adaptation technologies are co-classified with other CPC classes at the 4-digit level.SI.2: Co-classification of adaptation technologies Notes: These figures show which technology subgroups are most often co-classified with adaptation technologies. Technology subgroups are identified by the 4-digit CPC code. The numbers on top of each bar indicate the number of patents granted in each sub-period. Note that the bar plots rely on the number of co-classifications where patents that belong to multiple classes are double-counted. The size of the colored fields in each bar plot indicates the share of co-classifications for different subgroups by adaptation technology type. Co-classifications made for technical reasons (e.g. to ensure the compatibility with other classification systems) are excluded (see 3.3). Black color is used for the residuum of groups that do not belong to the 8 most often co-classified technology groups. The letters in the beginning of the verbal description of each technology group indicate the broad CPC section with A for Human Necessities; B for Performing Operations; C for Chemistry; D for Textiles; E for Fixed Constructions; F for Metallic Engineering; G for Physics and Y as general tagging scheme for cross-sectional technologies (including Y02-tagged green technologies).SI.1.3 Dual purpose technologies for mitigation and adaptationSI.1.3.1 Technological and scientific similaritiesTechnological and scientific knowledge spillovers are likely to occur if knowledge bases of two technologies are sufficiently similar such that the knowledge is mutually useful.Fig. SI.3 and SI.4 show the scientific and technological similarities among adaptation technologies and among adaptation and mitigation technologies at the 6-digit CPC level for the subperiods 1976-2005 and 2006-2020. The rows with mitigation technologies are ordered by their cumulative cosine similarity with adaptation technologies, i.e. by the row sum showing those technologies with the highest overlap with adaptation first. An extract with the fifteen highest scoring technologies is shown inSec. 4.3 in the main text.Technology
Paper title
Year
WoS field
#
cit.
(techn)
#
cit.
(total)
Coastal
Characterization Of Dredged River Sediments
In 10 Upland Disposal Sites Of Alabama
1995
Construction &
Building Tech.
5
5
Water
The Philips Stirling Engine
1991
Thermodynamics 66
66
Infrastructure
Conventional Wallboard With Latent Heat
Storage For Passive Solar Applications
Figure Coastal
Notes: These figures illustrate technological and scientific similarities among adaptation technologies and among adaptation and mitigation technologies at the 6-digit CPC level. We use a cosine similarity-based methodology as explained inHötte et al., 2021c. Mitigation technologies are ranked by the row-sum in a decreasing order, i.e. technologies with a higher the spillover potential across all types of adaptation technologies rank higher. Column-wise reading illustrates for which types of adaptation technology the highest spillover potential is found. The letters preceding the name of the technology type indicate the type of 6-digit mitigation or adaptation technology (i.e., A for adaptation, B for buildings, C for capture and storage of greenhouse gases, D for green ICT, E for energy, P for production, T for transport, and W for waste).0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coastal
Water
Infrastructure
Agriculture
Health
Indirect
A Coastal
A Water
A Infrastructure
A Agriculture
A Health
A Indirect
P Chemicals
E Non−fossil fuel
W Wastewater
W Solid waste
P Agriculture
P Metal proc.
C CCS
C CCS
T Road transport
E Combustion
B Heating
P Mineral proc.
P Oil refining
E Conversion
T Air transport
T Indirect
P Goods
E Indirect
B Renewables
B Insulation
E Renewables
W Indirect
B Appliances
E Nuclear
B Indirect
B Lighting
P Sector wide
T Waterways
T Railways
P Enabling
E Transmission
B Power managem.
D Effic. communic.
D Effic. computing
B Misc.
B Elevators
D Misc. ICT
D Misc. ICT
Life−Saving/Fire−Fight F Machines/Engines B Phys./Chem. Proc. Y Green Tech. C Water Treatm. Phys./Chem. Proc. F Cool & Heat Y Green Tech. C Water Treatm. Food Treatm. F Heat & Ventil. B Phys./Chem. Proc. F Cool & Heat Y Green Tech. C Water Treatm. Phys./Chem. Proc. B Separation Solids Y Green Tech. C Water Treatm.Adaptation
1976−1990
1991−2005
2006−2020
3246
5870
15071
F Combustion
C Fertilisers
F Heat & Ventil.
F Machines/Engines
B Phys./Chem. Proc.
F Cool & Heat
Y Green Tech.
C Water Treatm.
Buildings
1976−1990
1991−2005
2006−2020
1508
1729
3162
A Agriculture
E Building
E Doors & Windows
H Electr. Power
F Heat Exchange
F Heat & Ventil.
F Cool & Heat
Y Green Tech.
CCS
1976−1990
1991−2005
2006−2020
60
217
1208
F Combustion
F Combustion
C Inorg. Chemistry
A Green ICT
1976−1990
1991−2005
2006−2020
0
0
59
E Building
G Computing
H Electr. Comm.
H Electr. Power
G Spec. Ict
A Medical/Vet. Sci.
G Signalling
Y Green Tech.
Energy
1976−1990
1991−2005
2006−2020
1006
985
3117
C Fertilisers
F Heat Exchange
F Heat & Ventil.
F Motors
B Production
1976−1990
1991−2005
2006−2020
939
1418
2755
A Agriculture
C Fertilisers
A Transport
1976−1990
1991−2005
2006−2020
389
1952
6268
F Combustion
C Inorg. Chemistry
F Machines/Engines
G Measure & Test
B Phys./Chem. Proc.
F Cool & Heat
Y Green Tech.
B Vehicles
Waste
1976−1990
1991−2005
2006−2020
616
1086
2465
A Agriculture
B Packing
B Disp. Solid Waste
C Fertilisers
B
The technology class CCS also includes the capture and storage of non-carbon greenhouse gases such as SO 2 or SF 6 . We use the term CCS to simplify the notation. 2 Note that the definition of maladaptation goes beyond emission-increasing adaptation but includes any adaptation action with adverse side effects. In this article, we refer to subset of emissionincreasing adaptation when using the term maladaptation.
Throughout this document, we use simple DOCDB patent families as the unit of analysis, but we use 'patent' for 'patent family' as shorthand. 4 https://bulkdata.uspto.gov/data/patent/classification/cpc/
Note that we applied the same double-counting rule for mitigation patents that are classified into multiple 4-digit subclasses of Y02.
Coastal adaptation significantly relies on solutions that are difficult to patent as well, such as mangrove reforestation and nature-based solutions. We should note thatFig. 4includes a bias towards coastal adaptation solutions that are patentable, rather than the hard to be patented solutions.
We use the median weight of connecting links as significance threshold and show only those links whose weight is larger than that.
Author contributionsK.H. developed the research idea, study design, visualized the results, and wrote the initial draft. K.H. and S.J. compiled and analyzed the data. S.J. validated the results. All authors contextualized the results, reviewed, and edited the manuscript.Competing interests statementThe authors do not have any competing interests to declare.ReferencesOnline Supplementary MaterialKnowledge for a warmer world: A patent analysis of climate change adaptation technologiesKerstin Hötte, Su Jung Jee, Sugandha Srivastav(1)unique patents, (2) unique papers, (3) citation links, (4) citations with highest confidence score (CS = 10), (5) the average confidence score, (6) the share of applicant and (7) examiner added citations (remaining share is of unknown type), (8) share of citations made exclusively in the text body or (9) front page of the patent document (remaining shares account for citations made in both). Notes: This table shows the papers that are most frequently cited by adaptation patents. Year indicates the publication year of the paper and WoS field indicates the Web-of-Science field of research by which the paper is categorized. The fifth and sixth columns show the number of citations that the paper has received by patents in each adaptation technology field and in all adaptation technology fields, respectively. Notes: Columns show (1) patent family number (DOCDB), (2) patent title, (3) full CPC code(s), (4) grant year of the patent and (5) the number of citations made by the patent.
Dual purpose technologies for mitigation and adaptation. . . . . , 48SI.1.3 Dual purpose technologies for mitigation and adaptation . . . . . . . . . 48
Technological and scientific similarities. . . . . . . . . . . . , 48SI.1.3.1 Technological and scientific similarities . . . . . . . . . . . . . . . 48
2 Science base of dual purpose technologies. . . . . . . . . . , 54SI.1.3.SI.1.3.2 Science base of dual purpose technologies . . . . . . . . . . . . . 54
Co-classification of dual purpose patents. . . . . . . . . . . , 56SI.1.3.3 Co-classification of dual purpose patents . . . . . . . . . . . . . . 56
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Scientific base of mitigation technologies with adaptation co-benefit Notes: This figure shows the 8 scientific fields (Web-of-Science categories) that are most frequently cited by patents for mitigation that have a co-benefit for climate change adaptation. S I Figure, 8Figure SI.8: Scientific base of mitigation technologies with adaptation co-benefit Notes: This figure shows the 8 scientific fields (Web-of-Science categories) that are most frequently cited by patents for mitigation that have a co-benefit for climate change adaptation.
| sample_1842 | 0.9993 | arxiv | |
Analyzing At-Scale Distribution Grid Response to Extreme Temperatures
Sarmad Hanif
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Monish Mukherjee
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Shiva Poudel
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Rohit A Jinsiwale
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Min Gyung Yu
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Trevor Hardy
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Hayden Reeve
Pacific Northwest National Laboratory
902 Battelle Boulevard99352RichlandWAUSA
Analyzing At-Scale Distribution Grid Response to Extreme Temperatures
Preprint submitted to Applied Energy December 9, 2022 arXiv:2212.03997v1 [eess.SY] 7 Dec 2022 Electrification, Distributed Energy Resources.Distribution GridsExtreme TemperaturesResilience Event
Threats against power grids continue to increase, as extreme weather conditions and natural disasters (extreme events) become more frequent. Hence, there is a need for the simulation and modeling of power grids to reflect realistic conditions during extreme events conditions, especially distribution systems. This paper presents a modeling and simulation platform for electric distribution grids which can estimate overall power demand during extreme weather conditions. The presented platform's efficacy is shown by demonstrating estimation of electrical demand for 1) Electricity Reliability Council of Texas (ERCOT) during winter storm Uri in 2021, and 2) alternative hypothetical scenarios of integrating Distributed Energy Resources (DERs), weatherization, and load electrification. In comparing to the actual demand served by ERCOT during the winter storm Uri of 2021, the proposed platform estimates approximately 34 GW of peak capacity deficit 1 . For the case of the future electrification of heating loads, peak capacity of 78 GW (124% increase) is estimated, which would be reduced to 47 GW (38% increase) with the adoption of efficient heating appliances and improved thermal insulation. Integrating distributed solar PV and storage into the grid causes improvement in the local energy utilization and hence reduces the potential unmet energy by 31% and 40%, respectively.
Electrification, Distributed Energy Resources.
Introduction
Extreme events are becoming more and more frequent, to the level that they may not be ignored while planning and operating future power systems [2]. Unsurprisingly, planning and operating the power grid to account for these extreme conditions is becoming one of the most critical challenges for power system's planning and operation entities (e.g., system operators and utilities) [3,4,5]. Similarly, the need for methods and tools to help plan and operate power systems for extreme weather events is also of immense need [6]. As the fundamental planning variable for the power grid is the electricity demand, estimating and predicting a region's electricity demand during an extreme event may prove crucial for deploying resources to combat against predicted extreme events. Moreover, the adversity of an extreme event is usually characterized by the amount of unmet load, before, during and after the event and consequently how many customers were left without access to power, and for how long. Hence, the ability to gauge the increase in system demand due to an extreme event scenario is of great importance to grid planners and analysts. This paper presents the results of a modeling and simulation platform which captures distribution grid demand during an extreme weather event. Utilizing the platform, the paper then explores distribution grid conditions, such as losses and grid violations, during such an event and system net demand under hypothetical DER and retrofit scenarios. We chose to focus on the distribution grid demand modeling for two reasons. First, distribution grids face the greatest level of disruption during extreme events [7,8]. Second, distribution grids are located closest to the consumers, which allows more detailed modeling of consumer actions and strategies to better represent the overall demand dynamics. Although there can be many types of extreme conditions, (e.g. hurricanes, super-storms etc.), this paper focuses on extreme temperatures. This is motivated by the fact that even though extreme temperatures may not be considered as a natural disaster, they may end up causing the same level catastrophic disruptions (e.g., see the impacts of a recent events of winter storm Uri in Texas [9] 2 .
In the literature there exists two general approaches to estimating large, regional electricity demand due to extreme temperature. First are the topdown models which may consist of deploying regression expressions of demand against historical temperatures [1], machine-learning methods to predict outages [12,13], and classical short-term forecasting techniques [14]. For extracting large-scale grid response, these models are adequate, as the diversity of the large population averages out the individual, sometimes atypical, demands. However, these models do not represent detailed physical knowledge of consumers and hence are unable to be predict demand for conditions for which limited to no data exists. As a result, such models may not be suited to include impacts of resilience-mitigation actions, such as demand response techniques, and local generation adoption. The second approach, modeling from the bottom-up, uses physics-based demand modeling to represent the physical behavior of electrical devices. For example, modeling temperature dynamics inside a house to predict the operational state of an HVAC system and it's corresponding power consumption. Authors in [11,15] demonstrated how energy requirements for buildings can be estimated using a physics-based building energy simulation tool. Authors in [11] focused on heat waves, whereas [15] utilized the energy models of commercial building to develop occupant's resilience metrics. Note that these physics-based modeling environments may also be used to generate data for regressionbased/machine-learning models and it may end up providing further insights on variables governing electricity demand during extreme events.
The above outlined approaches for estimating power demand during extreme events do not consider power-system-specific interactions. These interactions are important for not only representing the impact of grid mechanisms (e.g. fault isolation) during a resilience event, but also to include grid physics (e.g. losses) which may impact the overall electric power demand. Transmission grid models and mechanisms have been deployed in the literature, such as in [16]. These models have been developed, following the success of large-scale open-source synthetic grid models [17,18] and power flow modeling tools [19]. The choice of a transmission grid model to determine grid response may be motivated by managing the complexity of the model, as extreme events impact a large fraction of population. However, as discussed earlier, distribution grid representation is crucial for estimating demand, as most of the outages happen at the distribution grid level and directly impact consumers connected to it. Moreover, distribution grids are inherently very different than transmission grids. For example, in distribution grids, condi-tions such as voltage drops due to higher loading level and resultant losses occur more regularly as compared to transmission grids. Similarly, there may exist very different timing and impacts of a utility's resilience measures in distribution grids which may impact the overall unmet load during a resilience event. To this end, a large co-simulation platform is proposed to capture the interaction of both the transmission and distribution systems [20,21]. However, existing platforms' distribution grid models are not yet tested in terms of 1) benchmarking it against a known extreme temperature event, 2) investigating alternative future DERs and load electrification scenarios and observing their impact on key event metrics.
In this paper, we address the above-mentioned need for a reliable at-scale distribution grid response estimation on two fronts. First, we present a modeling and simulation platform that supports physics-based load models in a distribution grid simulation environment to demonstrate large-scale system response to extreme temperatures. Second, to support analytical capabilities of the presented platform, alternative scenarios of future DERs, building weatherization, and load electrification are analyzed in terms of their impact on distribution grid demand estimation during an extreme weather event. The analysis performed in this paper consists of reproducing Texas conditions during winter storm Uri of 2021 and is compared against published data for predicted loads in [1] and actual outage data from Electricity Reliability Council of Texas (ERCOT) in [22]. To limit the scope, this paper focuses on physical power grid interactions (e.g. reactive power flows, losses, and violations) impacting the overall power demand and does not consider conventional (e.g. switch operations, feeder isolation etc.) and contemporary (e.g. utilizing demand flexibility) measures for coping with resilience. Hence, to allow for future work aiming to investigate conventional and emerging resiliency strategies (such as demand flexibility) the presented modeling and simulation platform capture the dynamics and control of the distribution system and DERs.
The rest of the paper is organized as follows. Section 2 explains the modeling and simulation platform used in this paper. Section 3 demonstrates the scenarios analyzed in the paper. Section 4 presents results and Section 5 concludes the paper and provides plausible future works directions.
Modeling and Simulation Platform
This paper's presented modeling and simulation platform is a customized version of the Transactive Energy Simulation Platform (TESP) [23], which is a co-simulation tool, allowing multiple state-of-the-art simulation tools to exchange information with each other and obtain a high-fidelity power system simulation. Figure 1 gives an overview of the components from (TESP) that were utilized in this paper. The platform consists of two simulators: 1) a weather simulator and 2) a power flow simulator. A message bus is used to exchange information between these simulators. The overview of the component of the platform is provided next. Refer to Section 6 for overview on the key modeling aspects of the platform and [24] for the detailed information on population calibration for large-scale simulation study.
Power Flow Simulator
Load Modeling. GridLAB-D TM is central to this paper's modeling and simulation platform, as it provides the capability to obtain weather-dependent load profiles of distribution grids power demand. This is enabled by GridLAB-D's modeling of temperature-dependent thermostatic loads, such as water heaters and the heating, ventilation, and air-conditioning (HVAC) systems inside a building's thermal envelope with modeled thermodynamics. In general, GridLAB-D uses a mixture of ZIP (constant impedance, current, and power) loads, plug loads, and thermostatic loads to represent the total load for a single house. As the HVAC load is one of the largest loads and is highly sensitive to outdoor temperatures, we present a brief overview of its modeling procedure in Section 6.3. The implementation of the latest GridLAB-D residential load models can be found in [25] and the accuracy of the model to represent residential load dynamics has been provided in [26]. For this paper, GridLAB-D is used to first calibrate/fine-tune distribution grid load against historical data and then used to extract grid response under various hypothetical scenarios. The following characteristics of GridLAB-D allows to perform such analysis.
• There are three heating technologies modeled in GridLAB-D: gas heater, heat pump, and resistance heating. As heat pumps are more efficient than resistance heating, the percentage of heating equipment ownership can be adjusted and its impact on the overall distribution grid load can be measured.
• GridLAB-D utilizes the Equivalent Thermal Parameter (ETP) model to estimate the HVAC load for the house. The ETP model parameterizes house insulation using "R" values, which can be adjusted to represent a high or a low insulation level of the house. These values can be adjusted to obtain an appropriate response of house insulation on the distribution grid load.
Feeder Modeling. In order to set up the case-study to perform the desired simulation and grid response, prototypical feeders [27] are populated with GridLAB-D house models. Appropriate house models, based on the combination of water heater, HVAC, lighting load, and plug loads with their activity schedules (e.g., water draw, internal mass due to occupancy, etc.) were specified. The rating of the loads and the activity schedules are assigned based on the statistical distribution of the housing population of the region to be modeled. Based on the selected house model, the service transformers, fuses, and circuit breakers are also sized to allow the distribution feeder to host the additional load. Relevant to the resilience analysis, the typical feeder modeling procedure described above was modified. This was done because during the preliminary analysis of power flow conditions of the feeders, it was observed that the ratings of the distribution system components (lines, transformers) of the prototypical feeders were not adequate enough to generate the peak load which was observed during the Winter storm Uri. Though for this level of abnormally high load, due to tripping of certain protection equipment, it may be a realistic response of the distribution grid, however, 1) it does not help for the goal of this paper to provide an accurate estimation of the required level of infrastructure upgrade to avoid such an extreme condition, 2) as well as does not allow to estimate the maximum aggregated response of the grid to the extreme event. As these evaluations are the goal of this paper, we oversize transformers and lines to allow for hosting such large loads in the distribution grid.
Weather Simulator. As shown in Fig. 1, the required external weather information for simulating distribution grid response is coordinated by the message bus through the weather simulator. For this work, time-indexed files in a ".csv" format are used by the weather simulator which provides information such as temperature, humidity, solar insolation, pressure, and wind speed, to be utilized as input for the power flow simulator. In Section 3.2, an example of how weather data was collected to generate the required extreme weather information, is to be included in the presented platform. Figure 2 shows the overall scenarios presented in this paper. First, a simulation configuration for the region of interest is fine-tuned to obtain a calibrated response model of the respective grid area of the interested region. Following the modeling and simulation additions explained in Section 2 to capture the impact of extreme weather event, the calibrated simulation model is simulated using the extreme weather. This represents the business-as-usual (BAU) distribution grid model's response to extreme weather. Using this model for representing system demand for extreme conditions, we present two future load pathways, 1) an electrification pathway and 2) a higher renewable DER deployment pathway. We demonstrate the impacts of these pathways on the overall system demand during the extreme weather condition. The modeled region for all scenarios is taken as the ERCOT region, with the extreme condition taken as winter storm Uri of 2021.
Scenario Analysis
Modeling Assumptions. As the focus of this paper is on demonstrating the capability of the modeling and simulation platform to reproduce, predict and estimate the impact of extreme events under different grid configurations, the following assumptions are made:
1. To obtain a counter-factual baseline response of the grids if they had not failed, it is assumed that consumer devices and grid infrastructure continues to operate during an extreme event. That is, no damage to utilities and consumers is assumed and consequently, no loss of load is assumed. 2. For Solar PV and behind-the-meter battery, the efficiency do not reduce due to snow. However, solar PV profiles are generated using temperature and irradiation data (as described in Section 3.2), which is represented by Texas' actual recorded temperature, demonstrating reduction in available PV power production during the winterstorm Uri. 3. For HVAC systems, no external damages due to extreme weather is assumed. However, as a direct consequence of modeling the Coefficient of Performance (COP) as a function of operating condition, HVAC response does reflect performance degradation as a result of operating in extreme winter temperatures 4. No advanced control algorithms for coordinating the response of the DERs are explored and only the local controllers built in the power flow simulator (GridLAB-D) are modeled. These controllers include, the thermostat controller of HVAC and water heater. The unity power factor controller for Solar PV and battery. The legacy voltage controllers (discrete step-size) for capacitor banks and transformer regulators. While this help in obtaining a realistic distribution grid response as the commonly available local controls in the grid, it also equips the analysis to be compared against future external control development to improve grid response to extreme weather, e.g. controls to extract demand-side flexibility. 5. As shifting demand (exercising demand-side flexibility) is out of the scope of this paper and is recognized as a key future work, we assume that consumers pre-defined thermostat settings remain same during the extreme weather event. Adjusting these controls to adapt to extreme temperatures is recognized as a key future work. 6. The control of the behind-the-meter storage is assumed to be done by a utility and it is assumed that it stays invariant during an extreme event. It is assumed that storage owners are instructed by the utility to charge/discharge during day/night-time to take advantage of the excess/unavailable solar power and there exists enough incentive for the consumers to participate in this activity. It is assumed that the utility provides signals for charge/discharge to consumers with enough diversification to avoid creating a new peak of charge/discharge.
Distribution Grid Response Calibration
This case is modeled to calibrate the response of the distribution grid, by comparing it with the recorded historical data. Figure 3 shows the modeled region of this paper using 8 representative regions in Texas. The distribution grid modeling of these regions follows the procedure outlined in [24], and its brief overview is given in Section 6.1.
Distribution Grid Business-As-Usual (BAU) Response Under Extreme
Event Modeling This case demonstrates "what would have happened if there was no loadshed in the region during an extreme event -given the existing grid infrastructure and load composition?" The case uses same customer population as in case 1. As shown in Fig. 3, each ERCOT region is assigned a specific weather region [22]. This information was used to collect weather data for the 2021 Texas Vortex Freeze condition. Data for 5-minute resolutions temperature, humidity, and wind speed data was sourced from NOAA archives [28], and average atmospheric pressure data from [29] and was assigned to the geographically closest region. Fig. 4 shows the temperature profile for the region modeled after the Dallas area during the extremely low-temperature event observed in Texas in February 2021.
Case 1 -Electrification of Space Heating
This case models the cases when all the population uses electric heating systems (heat pump or resistance) for electrification. Figure 5 shows approximately 36% of end-users in the ERCOT region uses gas heating, which is distributed evenly between heat-pump and resistance heating.
Case 1a -Space Heating Electrification with Improved Insulation
This sub-case models improved insulation of building stock in addition to the electrification of space heating. This is done by assuming that buildings meet code requirements consistent with construction after the year 2000 and hence adopt higher insulation levels in their thermal envelope. As a result, the chosen R-values of this scenario are shown in Fig. 6, where it can be seen that they on average increase by approximately 22.9 to 63.9 % for this highly-insulated case. Therefore, it is expected that this scenario case will have lower heating demand during extreme weather. Even though thermal insulation levels are improved, the heating system technology ratio (heat pump versus resistance heating) distribution is kept the same as the standard electrification case 1.
Case 1b -Space Heating Electrification with Improved Heating Tech-
nology This scenario models the customer population without resistance heating, i.e., all customers are equipped with heat pump systems for heating to maximize the system efficiency. See Fig. 5 for comparison of heating technologies installed under different scenarios. To not have a bias in the intra-technology efficiency improvement, the efficiency of a heat pump (COP) is still populated using the statistical distribution of the business-as-usual scenario.
Case 1c -Space Heating Electrification with Improved Heating Technology and Insulation
This scenario combines the improved thermal insulation and heating technology scenarios to demonstrate the grid response under efficient electrification directives. That is, all the population uses heat pumps for heating as well as retrofitted high-insulated buildings.
Case 2 -Integration of Distributed Solar PV
This scenario augments the resilience scenario with distributed solar PV. To model the distributed solar PV, 40% of houses are assumed to have rooftop solar PV panels. To demonstrate the geographic diversity, randomly generated azimuth angle, tilt angle, and geographic location was deployed in PySAM's PVWatts calculator [30] to produce a 5-minute solar profile for each region. Using the statistics on distributed PV penetration rate and total customers, solar profiles are scaled to be inputted in GridLAB-D. The detail of distributed modeling is provided in [24]. All distributed solar PV is assumed to be operating under a unity power factor.
Case 2a -Integration of Distributed Solar PV with Behind-the-Meter
Storage This scenario includes behind-the-meter distributed storage across 50% of houses in the grid. It is assumed that no house gets then more than 1 battery. Each battery is modeled as a direct-current electro-chemical device with a specified charge/discharge efficiency, inverter efficiency, power rating, and energy rating. The battery population follows the distribution of a mean 13.5/5 kWh/kW rating with a +/-20% range. All batteries are modeled with discharge efficiency of 96% and inverter efficiency of 98%.
As the goal of this scenario is to complement distributed solar PV in the distribution grid, the charge and discharge signals for batteries are generated based on observing the solar PV profiles. That is, the charging signal is sent during the day times and discharged during the evening/nighttime. This process is automated using another feature of GridLAB-D, where a randomized schedule for each object can be generated by defining the base schedule and individual object's skew parameter to represent shift (delay/advance) from the base schedule. Following this, we generate each battery's charge/discharge schedule using a base charge/discharge schedule and
Results
Distribution Grid Model Response Calibration
The historical data for comparison is taken from [22]. To demonstrate that the presented platform is versatile and can represent diverse grid conditions, first, we present a comparison against business-as-usual conditions. Figure 7 and Fig. 8 shows comparison for a typical 10 days of summer and winter load. As a reference of how the simulated load changes with the temperature, average of modeled 8 weather regions temperature profiles is also plotted in Fig. 7 and Fig. 8 3 . For more insights on the potential validity of 3 Note that in the actual simulation, each region gets to have its own weather simulation. simulation modeling and platform of this paper, interested readers are referred to [31], where a much more detailed population calibration and fine tuning for the ERCOT region for for the year 2016 was performed. Both comparisons demonstrate that simulated demand matches well with the historical data (within approx. 10% and 20% error of instantaneous peak and valley loading level prediction for summer and winter population, respectively). However, the simulation does perform better for the summer-time period. For both seasons, ERCOT load composition in terms of its mod- eled end-uses is shown in Fig. 9 and Fig. 10. The simulated aggregated load profile for the ERCOT region is also compared with the recorded load. Due to the modeling and simulation platform's capability to model weather sensitive-load, it can be seen that due to cooling and heating needs, HVAC load increases during day-time in summer and during night-time in winter, respectively. Note that, a small offset between the sum of all end-use load and "Modeled Load" in Fig. 10 is due to the distribution grid losses. As mentioned in the motivation section of this paper, this capability has been made possible due to the deployment of power flow simulator in the simulation and modeling platform. Figure 11 compares the simulated load profile with the actual (with outages) and predicted load data (without outages) for the Texas region, during the extreme winter temperatures in 2021.The actual load (with outages), i.e., the demand that was served by ERCOT during the extreme winter temperatures is taken from [22]. For extreme weather prediction comparison purposes, data from [1] is used to represent a "without outages" condition.
BAU Modeled Case Under Extreme Conditions
In [1] used a regression-based load model to predict ERCOT load during winter storm Uri if there had been no outages. The presented comparison of this paper with [1] successfully demonstrates that the presented modeling and simulation platform while modeling at-scale physics-based distribution grid loads, is also able to capture aggregated load modeling trends, as proposed in the state-of-the-art literature. From Fig. 11, it can be seen that the simulated load matches well with the predicted load from [1]. As the prediction model in [1] was only presented for the days when outages were experienced, both predicted and actual loads are the same on the non-outages days. The simulated load shows that as temperatures drop to historic low values, the demand increases to represent the increased heating demand. From the 13 th of February onward, the ERCOT system started experiencing outages, which is not captured in the simulation model.
Space Heating Electrification and Efficiency Measures Cases (Case 1,
1a, 1b and 1c) Figure 12 shows simulated load time-series for extreme temperature days for all cases associated with space heating electrification and relevant measures and their comparison to BAU modeled case under extreme conditions of Section 4.2. The results from electrification cases are summarized below:
• Case 1, which considers all space heating electrified without any measures, models the highest peak load of ∼122 GW. This is an increase of 52.5% as compared to the peak load obtained from BAU modeled case (∼80 GW). All peak loads occur at the same time during 15 th February.
• Measures of improving only insulation (Case 1a), heating system technology (Case 1b), and combination of these measures (Case 1c) predicts ∼118 GW, ∼108 GW and ∼99 GW of peak load, respectively. That is, as compared to Case 1, Cases 1a, 1b and 1c, decreases the peak load by 3.4%, 12.9%, and 18.8%, respectively. Eventually, Case 1c, which can be considered as an efficient space heating case, models an increase of 23.7%, as compared to BAU modeled load.
• As a comparison between higher insulation levels (Case 1a) versus better heating equipment (Case 1b), it can be seen that for extreme winter temperatures, better heating equipment (case 1b) reduces the electrified load levels more than higher insulation (case 1a). However, during usual winter temperatures (other than 13 th -20 th February), both cases (case 1a and 1b) yield almost the same system loading. As an example how HVAC load and dynamics change due to the change in the parameters of houses, Section 6.4 provides an example of a house modeled in with (Case 1a) and without (Case 1) high insulation. Figure 13 shows simulated load time-series for extreme temperature days for all renewable integration scenarios and their comparison with the BAU case. Summary of the results from the simulation of these cases are:
Distributed PV and Storage Integration Cases (Case 2 and 2a)
• Distributed PV reduces the load during day-time, due to solar PV production, however, as expected, it has no impact during evening and night-time peaks.
• Distributed storage helps to flatten the net load, by charging during the day-time and discharging during the evening-night-time. This has a positive impact during nights of the extreme temperature days, e.g., 15 th , 16 th and 19 th February. The highest peak load for BAU modeled case, distributed PV (Case 2) and distributed PV with storage (Case 2a), all occur around 5-6 am of 15 th February, during these times there was neither considerable solar PV production nor distributed battery discharging energy available. To visualize this better, this interplay between the charging/discharging of distributed batteries and the solar PV production can be seen in Fig. 14, where to distinguish load and local generation support, aggregated solar PV production and discharging is shown as negative, and charging as positive values.
Case Comparisons Summary
In this section, for extreme winter temperature days (13 th -20 th Februaary), we compare all alternative cases on renewable integration and load electrification (Case 1, 1a, 1b, 1c, 2, 2a) against the 1) BAU modeled load case and 2) ERCOT supplied demand.
Comparison Against BAU Modeled Case
As compared to BAU modeled case, Figure 15 and Fig. 16 show predicted demand and its corresponding energy difference of alternative future cases, respectively. Maximum (∼45 GW) and minimum (∼18 GW) load difference is observed for case 1 and Case 2, respectively. The inclusion of local generation in the form of distributed PV (Case 2) along with storage (Case 2a), reduces the total energy demand, as the net power imported from the upstream of the grid reduces. From Fig. 16, it can be seen that Case 2a has a higher negative energy difference as compared to Case 2. This is because with the presence of storage (Case 2a), the higher utilization of PV and local load supply by batteries reduces grid losses and hence its overall demand. Figure 17 shows in relative percentage, how alternative future scenarios changes grid violations and losses. The 5% above/below and 5.8%/8.3% above/below voltage violations ranges are taken from standards voltage limits to be maintained and avoided, respectively [32]. Due to large space heating electrification load, a very high percentage of low voltage counts occur (500% increase from BAU modeled case). Interestingly, the reductions in the above-voltage violations count occur with improved heating technology (Case 1b) is more than with improve insulation (Case 1a) which is due to improved dynamics of the heating equipment. The inclusion of PV (Case 2), increases the above-voltage violation counts, as injecting local power causes rise in voltage. Comparing to BAU case, with the inclusion of storage (Case 2a), all voltage violations counts and losses are reduced.
Comparison Against Actual ERCOT Supplied Demand During Winter
Storm Uri In this subsection, we compare the difference of all alternative future cases against the actual demand that was supplied in ERCOT during the winter storm Uri. In doing so, we attempt to demonstrate how the presented analytical capability of this paper could be utilized to explore "what-if" scenarios of the required system flexibility, considering a retrospective extreme weather type. Figure 18 and Fig. 19 shows the difference of supplied ERCOT demand and its cumulative energy. BAU modeled load case demonstrates that ∼30 GW of maximum instantaneous load (∼2.2 TWh energy) was potentially unmet during the winter storm, which could have jumped to ∼77 GW (∼6.5 TWh energy ) for the electrified case (Case 1). For both Case 2 and Case 2a, the inclusion of local energy production and utilization bring the potential unmet energy to ∼1.5 TWh and ∼1.3 TWh, which is a decrease of 31% and 40%, as compared to BAU modeled case, respectively.
Conclusion & Future Work
The paper presented at-scale analysis of distribution grid system demand during extreme weather conditions. The proof-of-concept was demonstrated Figure 18: Load difference of alternative modeled cases with actual ERCOT supplied load for extreme weather days Figure 19: Energy difference of alternative modeled cases with actual ERCOT supplied load for extreme weather days on winter storm Uri of February 2021. A modeling and simulation platform was presented which was shown to be extensible by constructing alternative future scenarios and their impact on the overall system demand during extreme conditions. The paper demonstrated that a physics-based at-scale modeling and simulation platform can realistically capture complex interactions between grid infrastructure, their operations procedures and the external influences. Hence, such a platform is advocated to investigate the resulting distribution system loads associated with future DER scenarios and mitigation schemes during extreme weather events. We demonstrate this in the paper by showing how electrification of the loads and the integration of renewable energy influence load dynamics and utilization of local generation on the grid infrastructure. Future works will be targeted towards the control of grid infrastructure, specially demand-side resources, to address challenges associated with grid resilience.
Appendix
Modeling and Simulation Platform Implementation Overview
In the current implementation of the presented platform Section 2, the message bus consists of Hierarchical Engine for Large-scale Infrastructure Co-Simulation Hierarchical Engine for Large-scale Infrastructure Co-Simulation (HELICS) [33], which serves as a bridge to exchange relevant information between these two simulators and controls the flow of the simulation at the desired time step (30-seconds for this paper). For the power flow simulator, we use GridLAB-D, due to its capability to model the weather-dependent load dynamics [34]. For the weather simulator, we use time-indexed data files in a ".csv" format with the relevant information required by the power flow simulator. The results of the simulation platform are stored in a ".h5" file format and a post-processing script is written to visualize them. Depending upon the study case, (e.g. business-as-usual, extreme conditions, higher penetration of solar photo-voltaic (PV), etc.), a Python script was used to coordinate and set-up the simulation platform.
ERCOT Distribution System Modeling
This section gives a brief overview of the modeled region. For a detailed explanation of the process, the interested readers are referred to [24].
To capture the system demand of Texas due to extreme events, similar to [24], multiple Regions were modeled and aggregated to represent the total system load. A summary of each modeled Region is presented in Table 1.
Each Region consists of multiple prototypical feeders as the backbone infrastructure (e.g., topology, rated equipment loading, power conversion elements, and power delivery elements) [27]. Statistical data available for the region, number/types of customers (residential, customer, and industrial), and the peak load of the region. The "Feeder Generator" process shown in Fig. 1 then distributes the population of the feeder with the houses, to match the rated load of the distributed houses with the statistically observed load region. With this process, the GridLAB-D model gets populated with both residential and commercial loads with their corresponding ETP model and its relevant parameters to reflect desired loading characteristics of the Region. The parameters are extracted using building types, their construction year, the HVAC system installed and its efficiency, referred to as Coefficient of Performance (COP). Collectively, all Regions ended up modeling 11929 buildings (residential and commercial), among which 8952 HVAC units and 4923 water heaters were modeled. To manage the complexity and accuracy of the desired load response, a lower number of GridLAB-D houses were modeled than the recorded total number of customers in the modeled region. A scaling factor was then used to represent the modeled load at the Region level. For example, for the residential load of the Region, the final load profile's scaling factor is calculated as: Total Residential Customer in the Region/(Residential Customers Fraction Among Total Customers × Number of Residential Homes Modeled in GridLAB-D). As aggregated residential and commercial load is then obtained, a constant industrial load (due to lack of data) is then added to obtain the total Region load.
GridLAB-D ETP Model Overview
GridLAB-D models two types of loads. One with the control loop and the other without the control loop. ZIP load objects (constant impedance, current, and power) are modeled to model the end-use loads such as lights and plugs. Thermostatic loads (HVAC and water heaters) are modeled with the control loop. With the combination of the HVAC and ZIP model, the total load is modeled, and the corrected voltage response is provided to capture the impact of load on the power flows. One of the largest loads in the house is the HVAC load and as it is sensitive to outdoor temperature and helps the simulation platform to capture the impact of extreme weather conditions, a small overview of the model is given next.
GridLAB-D models the HVAC system using the equivalent thermal parameter (ETP) approach. This captures the essential response of the house under various circumstances such as weather, occupant behavior, appliances, heating, ventilation, and air-conditioning (HVAC) system operation to analyze the grid operation [35]. Fig. 20 illustrates the ETP model of a house in GridLAB-D and the following equations explain how dynamics of loads are captured:
Q A -U A (T A -T O )-H M (T A -T M )-C A d dt T A = 0 (1) Q A = Q H + (1 − f i )Q I + (1 − f s )Q S (2) U A = A g U g + A d /R d + A w /R w + A c /R c + A f /R f + 0.018ACH (3) d dt T A = 1 C A (Q A -U A (T A -T O )-H M (T A -T M ))(4)
Overall, the electrical power consumed by the HVAC system is calculated by the system rated power and fan power. In addition, it considers motor losses that are related to the efficiency of the induction motor when the electric cooling system or heat pump for heating is utilized.
To provide a better quality of indoor circumstances, HVAC systems operate to cool or heat the buildings. The ETP model expresses the physical characteristics of the house with a state-space control form. The heat balance (conservation of energy) for the air temperature node T A is represented as (1). It is determined by how much thermal energy is stored in the air and mass of the building and how much heat can gain or lost from outside based on the actual physical properties of the building. For example, internal mass surface conductance H m is the total heat transfer coefficient by the building surface (exterior walls, interior walls, ceilings). Total heat gain to the indoor air Q A is estimated by the heat gain or loss from non-HVAC equipment Q I , solar radiation Q S , and the HVAC operation Q H as shown in (2). Total heat loss coefficient U A is the sum of all heat loss coefficients through the envelope of the building (walls, windows, doors, ceilings, floors, and infiltration air flows). Eventually, the indoor air temperature (T A ) changes can be estimated by heat gain or loss through the envelope of the building, weather conditions, internal heat gain, and HVAC operation as shown in (4). Figure 21 shows the indoor air temperature (top subplot) and HVAC loads (bottom subplot) for comparison between non-insulated building (Case 1) and high-insulated building (Case 1a). It highlights how the insulation affects the indoor air temperature and HVAC loads in the same building. Both buildings are heated with a heat pump with electric resistance auxiliary backup. The indoor air temperature in both cases was maintained in the desired temperature range by operating the heating systems, except for the extreme outdoor air temperature times (around 2/15 to 2/16). Also, at the extreme outdoor air temperature duration, both cases provided heating with the heat pump and the auxiliary system together, and it resulted in a high HVAC load. When it got warmer from 2/21 to 2/22, both buildings didn't require heating during the daytime but the non-insulated building (Case 1) operated heating during the night. The highly insulated building (Case 1a) maximized the benefits of thermal mass by reducing the heat flow between the indoor space and ambient so it preserved the daytime indoor temperature longer from outdoor air temperature fluctuations. Eventually, the non-insulated building (Case 1) required more heating operation. In addition, the HVAC system size in the non-insulated building (Case 1) is even larger than the highly insulated building (Case 1a) since it requires more heating/cooling, thus it resulted in a huge difference in HVAC loads between the cases.
Impact of Insulation on HVAC load and Indoor Temperature Dynamics of a Building
Nomenclature
Figure 1 :
1Modeling and simulation platform of this paper.
Figure 2 :
2Modeled cases of the paper.
Figure 3 : 8 -
38Node Model of ERCOT region
Figure 4 :
4February 2021 Temperature in Dallas,TX
Figure 5 :
5The fraction of heating system comparison in cases
Figure 6 :
6R-values comparison between standard population and high-insulation population a random skew parameter (+/-2 hours).
Figure 7 :
7Simulated versus recorded load comparison for summer season
Figure 8 :
8Simulated versus recorded load comparison for winter season
Figure 9 :
9ERCOT load decomposition for summer time period.
Figure 10 :
10ERCOT load decomposition for winter time period.
Figure 11 :
11Simulated load for extreme condition and its comparison with actual (with outages) and predicted (without outages[1]) load.
Figure 12 :
12Simulated load profiles for the electrification scenarios and its comparison with BAU modeled case under extreme weather conditions.
Figure 13 :
13Simulated load profiles for distributed PV and storage integration adoption cases and its comparison to BAU Modeled load under extreme weather days.
Figure 14 :
14ERCOT load decomposition for the integration of distributed PV and storage (Case 2a).
Figure 15 :Figure 16 :
1516Load difference of alternative modeled cases with BAU modeled case for extreme weather days Energy difference of alternative modeled cases with BAU modeled case for extreme weather days
Figure 17 :
17Comparison of grid violations and losses for alternative modeled cases with BAU modeled case.
Figure 20 :
20ETP model of a house in GridLAB-D, refer to Section 6.3 for more information on ETP model development.
Figure 21 :
21Indoor air temperature (top subplot) and HVAC load (bottom subplot) for comparison between non-insulated (from Case 1) and high-insulated building (from Case 1a).
Table 1 :
1Region characteristics Region number (Utility Type) Modeled Feeders Modeled Houses Modeled Area Scaling FactorRegion 1 (Urban)
R4-12.47-1
R4-12.47-2
893
Dallas, TX
3816.95
Region 2 (Urban)
R5-12.47-1
R5-12.47-2
1308
Houston, TX
2351.17
Region 3 (Rural)
R5-12.47-5
1539
Lamar, TX
58.14
Region 4 (Rural)
R5-12.47-5
1539
Midland, TX
479.44
Region 5 (Urban)
R5-12.47-1
R5-12.47-2
1308
Hays, TX
1395.95
Region 6 (Urban)
R4-12.47-1
R5-12.47-1
1525
Val Verde, TX
67.95
Region 7 (Suburban)
R5-12.47-5
1539
Nueces, TX
895.00
Region 8 (Rural)
R5-12.47-5
1539
Presidio, TX
23.55
Internal gain fraction to mass f s Solar gain fraction to mass H M Internal mass surface conductance Q A Total heat gain to the indoor air Q H Internal heat gain by HVAC operation Q I Internal heat gain by non-HVAC equipmentA c
Area, ceilings
A d
Area, doors
A f
Area, floors
A g
Area, windows
A w
Area, walls
ACH Air changes per hour
C A
Total air mass
f i
Q S
Solar radiation
R c
R-value, ceilings
R d
R-value, doors
R f
R-value, floors
R w
R-value, walls
T A
Indoor air temperature
T M
Building mass temperature
T O
Outdoor air temperature
U A
Total heat loss coefficient (conductance)
U g
U-value, windows
Heat waves are potentially also fall into this category, but historically have been dealt better by utilities, e.g. see California responses[10,11]).
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| sample_1864 | 0.8028 | arxiv | |
Applications of Intelligent Systems in Green Technology
Sahil Mishra sahilmishra32@gmail.comsanjayauce@gmail.com
Department of Computer Science and Engineering
Design and Manufacturing
Indian Institute of Information Technology
KurnoolAndhra Pradesh
Sanjaya Kumar Panda
Department of Computer Science and Engineering
Design and Manufacturing
Indian Institute of Information Technology
KurnoolAndhra Pradesh
Applications of Intelligent Systems in Green Technology
13 Electronics and Telecommunication Engineering Division Board Annual Technical VolumeIntelligent systemsGreen technologyWater pollutionSoil pollutionSustainability
Intelligent Systems (ISs) are technologically advanced machines, which perceive and respond to the environment around them. They are usually of various forms ranging from software to hardware. ISs are generally the fusion of Artificial Intelligence (AI), robotics and Internet of things (IoT). In order to strengthen ISs, one of the key technologies is green technology (GT). It refers to the continuously advancing methods and materials, which cover techniques for producing energy to non-toxic cleaning products. It may also be broadened to saving energy, and reducing toxic and waste materials in the environment. The motto of GT can be achieved by using the ISs. In this paper, we present various applications of ISs in GT. Moreover, we discuss various possible solutions using ISs in order to overcome the on-going real-life problems.
INTRODUCTION
Intelligent Systems (ISs) and Green Technology (GT) are the two-most emerging technologies in the field of information and communications technology. These technologies have been expanding their horizon. For instance, earlier, we just used to have simple feature phones, which could just make calls and receive calls. But now, we can do a lot of things using smart phones, which is beyond our expectations. ISs are increasingly entering our lives and pose the ability to learn from the experiences (i.e., historical data) and respond accordingly. In general, ISs consists of AI, robotics and IoT [1][2][3]. While AI helps a system to understand and react to certain circumstances, being just a firmware, it cannot do a lot of things [3]. Therefore, robotics does its job by taking necessary physical actions to respond to those circumstances. However, the problem is the communication among various devices constituting the system. Here, IoT plays an important role to smoothen the process of communication between the devices [2]. When these three are combined, they constitute ISs. However, IS is strengthened using one of the associated technologies, namely GT. It is the use of technology to protect the earth and the environment. It can be done in various ways. But, the most important issue to protect the environment is getting rid of all sorts of pollution. If it is not possible completely, then we have to reduce it to a tolerable limit. Similarly, deforestation needs to be fixed on urgent basis. We can use ISs to solve the above issues. There are various ways to achieve our goal.
Pollution, Deforestation and their Causes
Earth is not what it was a million years ago. With the advancement of technology, we have been benefited a lot, but simultaneously, it has caused a lot of adverse effects on our planet's unique environment. Industrialization has led to a lot of pollutants in the air, water and soil. Vehicles are contributing as the major sources of air pollutants [3]. Even the area of agriculture is making a huge contribution of pollutants in all the three forms. Moreover, the burning of fossil fuels, mining, use of pesticides, fertilizers and use of plastic are also major pollutants. We need to fix it if we want to keep this earth habitable.
Deforestation means cutting of trees at an alarming rate [4]. It has led to a loss of habitat of flora and fauna, increase in greenhouse gases, erosion of soil and a lot more adverse effects. It is mainly caused by natural causes, like floods, parasites, etc. and human activities, such as agricultural expansion, cattle breeding, dam construction, infrastructure development, mining, oil extraction and timber extraction.
Both pollution and deforestation together have caused the rate of temperature to double in the last 50 years [5]. In this century, the computer models predict that the average temperature of earth will increase between 1.8° and 4.0° Celsius [6]. Many countries have faced the hottest days in their respective histories in 2019. Other models suggest that we will reach 7° Celsius above preindustrial levels by 2020 [7]. We can use the ISs in various ways to control the types of pollution and deforestation up to some extent.
Controlling Air Pollution using Intelligent Systems
Many metropolitan cities in various countries have started facing the adverse effects of air pollution, like Beijing, New Delhi etc. These cities are some of the most polluted cities of the world. Their main cause of pollution is basically vehicles and industries [3]. In order to control the pollution, the following ways may be adopted.
Firstly, if we can predict the severity of air pollution in different regions in advance, then we can shut down all the factories and restrict the usage of vehicles during that period of time. This system can be implemented using deep learning models, like Recurrent Neural Networks (RNN) [8].The input vector data may comprise of various features, like vehicles on weekdays, vehicles on weekends, factories working hours, temperature, pressure, crop season timings, amount of gases in the atmosphere to name a few. The reason to use RNN is that we have sequential data about each day/hour.
Another change that can be done is increasing the usage of electric vehicles or vehicles driven by some renewable energy. If not possible, then the vehicles can be equipped with a system, which can detect at what speed the level of pollutants emitted by the vehicles may increase, before it actually increases. In order to implement it, the best model may be any ensemble model, which tries to improve the performance by combining the various models. The ensemble model may consist of Model A (say) to check whether all the gear mechanisms are intact and properly working. Model A can be implemented by using Gated Recurrent Unit (GRU) over Convolutional Neural Network (CNN), so that snapshots can be taken at different moments of time from a video and it can be trained using the sequence of images to check how the gear system behaves over time. This system may be used in factories to check for any fault, which may occur in the machines in the future. This can also prevent energy loss due to faulty parts or parts which may fail in the future. Another model, say B may be used to check the air pressure in tires and respective pollutant emission. On the other hand, Model C may be used to check the density of lubricant and any dirt present in it, thus predicting emission of pollutants.
ISs can be implemented as an application of AI on traffic signal system to get rid of traffic jams. Most of the times it happens that the traffic light is red on one side with a lot of traffic and it is green on the other side, where traffic is very less. It is also a cause of pollution as the vehicles' engines were on at that time, which unnecessarily releases a lot of pollutants in the air. Therefore, object detection along with localization can be used to check the density of the vehicles and give priority to that road, where density is more. It can also be helpful in giving way to emergency vehicles, like ambulances, fire-fighting van etc. Moreover, ISs can be implemented in such a manner that the engine of the vehicle automatically turns off, when it is not moving for some duration of time.
Road accidents are also a cause of traffic jams, which leads to air pollution. Therefore, a camera can be put in various accident-prone roads, which can detect accidents automatically and inform the nearby medical help team. This can be implemented using CNN on snaps of videos.
Solving Water Related Issues using Intelligent Systems
Controlling Water Pollution
The oceans are now at dangerous levels with cargo transport, offshore drilling and trash. For instance, one garbage truck of plastic is put into the oceans every one minute, which results eight million metric tons of plastic annually [9]. To remove garbage from the ocean, we need to put some drones over the ocean to detect garbage floating on its surface. The autonomous floating garbage trucks can be deployed in the areas of ocean, where there is a lot of garbage [10]. This garbage truck pulls the floating garbage, mainly plastic, by the floating rope towards a collector, which is usually a container ship. Further, this waste is recycled.
Machine Learning (ML) can be used to detect the garbage flowing into the ocean from the various places and thus knowing what sources are present in those places, which release such waste products. It can also help in determining the actions and behaviours of people in those places. This may help in preventing the waste from those sources and getting drained into water bodies. Further, it can be recycled.
Groundwater contamination can be checked using its chemical composition. But, it's not easy to extract ground water at various places and check its composition easily as it changes with time. Therefore, we can develop a system to find chemical composition using temperature, electrical conductivity and potential of hydrogen (pH) levels as input vectors. Any ML or Deep Learning (DL) model can be suitable for this task.
Coastal area's ground water quality also needs to be checked and predicted in future for usage, because the salinity of the sea also pollutes the ground water near it. We need to implement RNN to predict the future contamination as the pollutants are added and cleaned regularly. For this, we require a time-based sequential data. The input vector may comprise of location of pumping stations, previous salinity, dissolved mineral concentrations, temperature and chlorophyll levels.
River water pollution also needs to be checked as most of the cities in North India get water supply from rivers. Water quality variables, like pH, total dissolved solids, chemical oxygen demand, etc. can be taken as input vectors and the prediction of dissolved oxygen and biological oxygen demand can be made using them. The Artificial Neural Network (ANN) model can be used to make predictions. Moreover, the presence of bacteria can be done using the same model.
Minimizing Water Wastage
ML US alone wastes 7 billion gallons of potable water per day, which is about 11000 swimming pools [11]. We can install sensors in houses to check for daily water usage and wastage. It will strike an alarm if the water is being wasted. The amount of waste water will be determined based on the previous usage, number of people living in the houses and their daily usage. For this, we use Long-Short Term Memory (LSTM) model or GRU, which uses the data collected by the sensor.
Preventing Ground Water Wastage
Chennai has almost run out of ground water and it will completely run out by 2020 [12]. Despite being near coastal areas, this metropolitan city faces water issues every year. On the other hand, it gets flooded in the monsoon. The main reason behind this is that most of the city roads and footpaths are made up of concrete, which prevents the rainwater to go into the ground. The same situation is with Hyderabad, which will run out of groundwater very soon.
There are various solutions to these problems. The ground water level usually falls in summer, especially when the demand is high. Therefore, we can build a predictor to predict when the supply is going to be more. At that time, we can get alternate sources to supply the affected areas. This will reduce the load on the groundwater supply system and prevent the chaos caused due to water shortage. The input vector for the predictive model may be the pumping rate of the affected areas. We can also install rainwater syringe [13] in the areas, which may lose groundwater in the future.
Controlling Soil Pollution using Intelligent Systems
The main sources of soil pollution are chemicals, leaching of wastes from landfills, oil and fuel dumping, pesticides or direct discharge of industrial wastes. To curb soil pollution, immediate measures need to be taken failing which flora is going to die very soon. Firstly, we can deploy a device to check the soil composition timely and predict when it becomes polluted. Here, we can also know that where do the pollutants come and what period of time the amount of pollutants is more. For this, we can implement RNN model as the input is time-based. This system can also be used to track waste leaking from landfills.
The main cause of soil pollution in agricultural lands is the uncontrolled usage of pesticides by the farmers. This is not only damaging the soil, but also poisons the crops and make them unfit to be consumed. Therefore, we can develop a model to suggest them the specific pesticides along with quantity that are required by the crops based on the images of the crops. The best model in this case is CNN, which will take images of crops as input to predict the diseases, and output the quantity and name of the pesticides required. The same case is also applicable to fertilizers, but they cannot be predicted just by using images of crops. We need to get the soil composition too. It is not easier to get the composition of soil quickly. As a result, we can develop a system to find chemical composition using temperature, electrical conductivity and pH levels as input vectors. This data can be easily obtained using sensors and can be used to predict the soil composition along with the name and quantity of fertilizers required.
SUSTAINABLE LIFE USING INTELLIGENT SYSTEMS
Sustainable living is the lifestyle, which focuses on reducing the usage of earth's natural resources at the individual level and social level. The basic goal of it is to reduce carbon foot printing.
There are a lot of ways to achieve it. First and the foremost thing is to predict the demand and supply of resources around the globe. It has been seen many times that this demand and supply miscommunication or broken chain has led to economic chaos. For instance, tomato crop demand and supply chain. This crop is affected by weather conditions. On the other hand, heat waves ripe it before time. Thus, farmers are forced to sell it at lower prices due to unavailability of cold storage, while consumers pay a high price for it. The areas where this crop has produced more, it is sold at very lesser prices and thus farmers get almost zero profit. On the contrary, it reaches very late after getting to know the amount of shortage, which is a long time after being bought from the farmers. Therefore, farmers sometimes destroy their crops and they don't get enough profit. This is seen more as a national economic loss, but it is more loss of earth's natural resources.
Rice, sugarcane and tomato crops require lot of water. If we destroy them, then it means the wastage of potable water, which was used. It also leads to the wastage of earth's natural resources. Moreover, a lot of fertilizers would have been used to harvest the crops, which would have again degraded the soil quality. Therefore, if we develop some system to predict demand and supply of various things across the globe and arrange the proper transportation facilities for them, then it can minimize loss of energy and make it useful in other places.
Sustainable development is not only affected by crop price inflation, but also by disease outbreaks. Many of the diseases are often concentrated among the poorest populations in the world. The disease outbreaks generally result in loss of life at a large scale, which pollutes various natural resources. If the dead bodies are not disposed off properly, then soil, air and water can get contaminated. It will also affect various parts of the world.
Using historical data, if we can predict the time, period and region of outbreaks in advance, then we can save a lot of natural resources. This prediction system still difficult to implement as it needs a lot of data to be trained. Fortunately, world health organization tries to prevent such outbreaks and reduce epidemics. Still, a lot of epidemics is occurred in various parts of the world and building a system to predict such epidemics in advance may save the lives of hundreds of people.
CONCLUSION
In this paper, we have discussed two key technologies, namely ISs and GT. As green earth is the need of the hour, ISs can be applied to the field of GT. Moreover, as the time is passing, the earth is slowly becoming inhabitable. Therefore, people should understand that their irresponsibility is causing harm to the environment. AI can be used in making our earth a better place to live for our future generations. We can use it in various ways like to curb all types of pollution (i.e., air, water and soil). AI tools like ML and DL can be used to predict the severity of pollution in advance. They can also be used to check the source of pollution from various sources. They can even be used to predict the behaviour of people towards environment based on their activities. With the help of robotics, AI gets a helping hand to clean the environment and IoT can make various system communications, thus forming a group of ISs. These ISs can play a major role in helping to reverse the effects of human activity on the environment. They can even suggest us do's and don'ts in future to prevent any chances of future catastrophe.
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Kerala Man Innovates Rainwater Syringe By Accident, Restores 300 Cr Litres in 30. Kerala Man Innovates Rainwater Syringe By Accident, Restores 300 Cr Litres in 30
| sample_1875 | 0.7672 | arxiv | |
Spatio-temporal influence of solar activity on global air temperature
Samuel T Ogunjo stogunjo@futa.edu.ngsamuelt.ogunjo
Department of Physics
Federal University of Technology
PMB 704Akure, Akure
Ondo State
Nigeria
A Babatunde Rabiu
Centre for Atmospheric Research
National Agency for Space Research and Development
Anyigba
Kogi State
Spatio-temporal influence of solar activity on global air temperature
2 Preprint submitted to Elsevier November 27, 2022solar cyclesunspot numberF107 indexspace -earth coupling * Corresponding author
Previous studies on the impact and influence of solar activity on terrestrial weather has yielded contradictory results in literatures. Present study presents, on a global scale, the correlation between surface air temperature and two solar activity indices (Sunspot number, 'Rz', and solar radio flux at 10.7, 'F10.7' ) at different time scales during solar cycle 23. Global air temperature has higher correlation values of ±0.8 with F10.7 compared to Rz (±0.3). Our results showed hemispheric delineation of the correlation between air temperature and solar activity with negative correlation in the southern hemisphere and positive correlation in the northern hemisphere. At the onset of the solar cycle, this hemispheric delineation pattern was prevalent, however, an inverse hemispheric delineation was observed at the recession of the solar cycle.
INTRODUCTION
The Sun influences weather on Earth through changes in solar irradiance, variability in solar ultraviolet, and effect of galactic cosmic rays (Mufti and Shah, 2011). The direct and indirect impact of solar activity on Earth's climate is important, hence, the need for continuous monitoring of solar activity. It is pertinent to estimate the contribution of solar activity to global warming and climate change. Over the years, scientists have developed indices to measure and quantify solar activity. One of the most common indices for solar activity is the sunspot number, Rz. Sunspots are regions of reduced temperature on the Sun photosphere. Sunspot number Rz, was one of the earliest proxies for solar activity with data as far back as the 16th century. The solar 10.7 cm radio flux (F10.7 ) is defined as the measurement within one hour, of all emissions on the solar disc at a wavelength of 10.7 cm (Tapping, 2013). The F10.7, has been found to be a better representation of solar activity than Rz (Mielich and Bremer, 2013;Okoh and Okoro, 2020). A similar, E10.7 index based on the extreme ultraviolet radiation 10.7 cm radio flux has also been proposed (Tobiska et al., 2000). The flare index is a short-lived solar activity to quantify the daily flare activity over a 24-hour period (Kleczek, 1952). The total sunspot area, obtained by measuring the area of each sunspot group, has been proposed as a measure of solar activity (Sarychev and Roshchina, 2006). These indices provide a means to quantify the effect of solar activity on atmospheric parameters.
The impact of solar activity on atmospheric variables has been investigated.
Values of coefficient of determination r 2 between Rz and rainfall were found to be 0.89 in Rome using long term data (Thomas, 1993). Correlation coefficient between Rz and rainfall in India has been reported to be in the range -0.14 to +0.29 (Ananthakrishnan andParthasarathy, 1984), 0.199 (Hiremath andMandi, 2004), ±0.2 (Chattopadhyay and Chattopadhyay, 2011), −0.41 − 0.55 (Hiremath, 2006), -0.76 to -0.86 (Selvaraj et al., 2009), ≤ 0.35 (Chakraborty and Bondyopadhyay, 1986), and 0.145 (Jain and Tripathy, 1997). The differences in correlation coefficient values in India could be attributed to different time periods, different number of locations, and method of computation considered. In other regions of the world, correlation values between Rz and annual rainfall has been reported as -0.1 for Southern Brazil (Echer et al., 2008), 0.48 − 0.99 for several African countries, (Fleer, 1982), 0.40 in Portugal (Lucio, 2005), -0.10 in Santa Maria (Rampelotto et al., 2012), and 0.24 in Italy (Mazzarella and Palumbo, 1992). Sunspot activities have also been reported to have correlation with lake volumes/water levels, river flows (Mauas et al., 2011), . Furthermore, the impact of Rz has been reported on large scale teleconnection patterns such as El Ninosouthern oscillation (ENSO) (Zaffar et al., 2019), North Atlantic Oscillations (Hern´andez et al., 2020;Kuroda et al., 2022), and Pacific Decadal Oscillation (PDO) (Ormaza-Gonz´alez and Espinoza-Celi, 2018).
One of the greatest interest in Sun-Earth relationship, is the influence of solar activity on tropospheric temperature. The solar contribution to tropospheric temperature has been estimated to be 7% (Solomon et al., 2007), 30% (Solanki and Krivova, 2003), 41% (De Jager et al., 2010), and 60% (Scafetta, 2010). The correlation between mean global air temperature and sunspot number has been estimated at 0.27 (Valev, 2006). Correlation values reported between Rz and air temperature at various location and time periods include +0.57 (Sch¨onwiese, 1978), +0.5 (Blanco and Catalano, 1975), -0.42 Rabiu et al. (2005), -0.26 Rabiu et al. (2005), and +0.66 (Echer et al., 2009). Another approach to estimating the influence of solar activity on air temperature is using the length of the solar cycle. Solheim et al. (2012) observed significant negative trend between Norwegian air temperature and length of previous solar cycle but not with the current solar cycle. The study did not give information about the variation of correlation values for different regions of the world. A high correlation was observed between solar cycle length and air temperature in the northern hemisphere (Friis-Christensen and Lassen, 1991). This correlation between solar cycle length and air temperature have also been confirmed at Northern Ireland (Butler and Johnston, 1996), Svalbard at 12-year lag (Solheim et al., 2011), and Qinghai-Xizang railway at 5-year lag (Li et al., 2004). Correlation between Rz and winter temperature has been estimated as −0.3 in Canada (Laing and Binyamin, 2013), +0.42 in Holland (De Jager, 1981), and −0.91 to −0.63 in Bulgaria (Georgieva et al., 2005).
Weather across the world is connected. Previous studies on the relationship between Rz and air temperature have largely focused on aggregated data and specific locations. However, it is imperative to study the interaction of solar on global weather to determine large scale patterns and trends. This makes it difficult to make inference on the global impact of solar activity. The aim of this study is to characterize the relationship between solar and geomagnetic activities and global air temperature at long term, seasonal and annual time scales across the world. This will give insight into the contribution of solar and geomagnetic contributions to climate activities across different regions of the world.
METHODOLOGY
For this study, Rz and F10.7 were used as proxies for solar activity during solar cycle 23 (1997 -2008 The Spearman correlation (ρ) was used in this study. It is defined as (1) The values of ρ are in the range ±1. Negative values denotes negative correlations between the two variables which implies that an increase in one variable corresponds to a decrease in the other variable. The significance of the correlation was computed using the two tailed p-value. In this study, all results were considered at 95% confidence interval.
RESULTS AND DISCUSSION
The spatial variation of significant correlation of air temperature with Rz and
CONCLUSION
There has been no scientific consensus on the impact of solar activity on atmospheric weather. In this study, we have investigated the correlation between surface air temperature and two solar activity indices (Rz and F10.7) on the global scale during solar cycle 23. This approach will help identify large scale patterns which can give more insight into the relationship between atmospheric weather and solar activity. Our study was conducted at seasonal, annual, and long term time scales for a clearer understanding. Our results showed hemispheric delineation at seasonal, annual, and long term considerations. Furthermore, while the years preceding the solar minimum showed preference for positive correlations in the north and negative correlations in the south, the receding years favours the opposite.
Disclosures
The authors declare no financial interests or conflict of interests in this manuscript.
Data, Materials, and Code Availability
Data used in this study is publicly available and links have been provided in the manuscript.
based on the Lloyd's season where J-season includes May, June, July, and August; D-season months are November, December, January, and February; while the E-Season months are March, April, September, and October.
Figure 1 :
1Spatial variation in significant correlation at 95% confidence interval between air temperature and (a) Rz and (b) F10.7.
F10. 7 Figure 2 :Figure 3 : 7 Figure 4 :
72374during the entire solar cycle 23 is shown inFigure 1. The correlation of air temperature with Rz showed hemispheric delineation. The northern hemisphere showed negative correlation with air temperature on both land and sea while a positive correlation was prevalent in the southern hemisphere. However, the hemispheric delineation was not obvious in the correlation of air temperature with F10.7 index. The highest negative correlations with Rz index were found in the tropical region. This implies that Rz play a significant role in the climatology of the tropics. Regions with high significant positive correlations between air temperature and Rz include areas around Celebes sea (Pacific Ocean) and Queen Elizabeth Islands in North America. The correlation between F10.7 and air temperature were not found to be significant over major continental land masses except tropical land masses. The tropical land and oceans showed similar significant negative correlation with F10.7 index as in the Rz index. The only significant positive correlation between air temperature and F10.7 index were also around Celebes sea (Pacific Ocean) and Queen Elizabeth Islands in North America.The correlation between global air temperature and Rz were also considered at the three seasons (Figure 2). In the J-season, significant negative correlations were predominant in many regions. Significantly high negative correlations were found across the equator except the Indian Ocean. Regions north and southeast of Australia showed significantly high positive correlations between air temper-Seasonal spatial variation in significant correlation at 95% confidence interval between airtemperature and Rz ature and Rz index. During this season, significant correlations were not found over the continental land masses except in Greenland and small regions in Africa and Europe. During the D-season, there were no significant negative correlations in the Pacific Islands, as in the J-season. However, significant high positive correlations were found in the Queen Elizabeth Islands, west of Greenland. Unlike the J-season, significant negative correlations were found in south Atlantic Ocean and Indian Ocean. Also, larger portion of North America showed significant correlations. The correlations around the Equator were found to be weaker and not predominant as in the J-season. Correlations between air temperature and Rz during the E-Season were generally subdued with less spatial coverage compared to the J-season and D-season. The negative Equatorial correlations and positive Pacific Island correlations were observed to be weakest during this season. The correlation between air temperature and F10.7 index (Figure 3) at the three seasons showed identical patterns with the Rz correlations. In Figure 4, the annual correlation between global air temperature and Rz were considered from 1997 to 2008. The correlation values were found to be in the range ±0.32. Hemispheric delineation were pronounced at the onset of the solar cycle from 1997 to 1999. Specifically, the northern hemisphere were observed to have predominantly significant positive correlations while the southern hemisphere we found to have prevalent significant negative correlations. In 2000, although the hemispheric delineation was present, they were observed only on continental land mass and the Arctic Ocean. However, in 2001 the correlations were only observed on large water bodies. From 2002 to 2005, there were sparse Seasonal spatial variation in significant correlation at 95% confidence interval between air temperature and F10.Spatial variation of significant correlation between Rz and air temperature at 95% confidence interval for each year in solar cycle 23 spatial distribution of significant correlations between air temperature and Rz index. The year 2002 witnessed the sparsest spatial distribution of correlation values as only Equatorial Atlantic Ocean and a few other locations were found to be correlated. In 2003, the continental land mass of Africa, Europe, Australia, Asia, as well as North America and the Arctic sea showed significant correlation values. However, significant correlation values were not observed in the Arctic Ocean but over South America in 2004. In 2007 and 2008, there was an inversion of the hemispheric delineation. During 2007 and 2008, significant negative correlations were observed in the Northern Hemisphere while significant positive correlations were found in the Southern Hemisphere. However, the spatial distribution of the inverse hemispheric delineation was smaller in 2008 compared to 2007.
Figure 5 Figure 5 :
55showed the spatial correlation between global air temperature and F10.7 index for each year in solar cycle 23. The years 1997 to 1999 showed similar patterns as observed in the correlation with Rz but with higher values. In 2001, the continental land mass in the northern hemisphere which did not show significant correlations under Rz were found to exhibit negative correlations with F10.7 while the continental land mass in the southern hemisphere showed positive correlations. During the year 2002, an inverse hemispheric delineation was observed with negative correlations in the northern hemisphere and positive correlations in the southern hemisphere. This implies that F10.7 contribute more to global air temperature compared to Rz index. Sparse spatial distribution of correlation values were also observed in the years 2003 to 2006, with Spatial variation of significant correlation between F10.7 and air temperature at 95% confidence interval for each year in solar cycle 23 13 2005 showing the highest distribution. The correlation values in 2007 and 2008 also showed inverse hemispheric delineation but with larger spatial distribution compared with Rz.
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| sample_1882 | 0.8862 | arxiv | |
Wind to start the washing machine? High-Resolution Wind Atlas for Finland
Xu Yang xu.1.yang@aalto.fi
Dept. of Computer Science
Dept. of Computer Science
Aalto University Espoo
Finland
Yu Tian yu.tian@aalto.fi
Aalto University Helsinki
Finland
Alexander Jung
Dept. of Computer Science
rd Irene Schicker Dept. of Postprocessing GeoSphere Austria Vienna
Aalto University Helsinki
Austria, Finland
Wind to start the washing machine? High-Resolution Wind Atlas for Finland
Index Terms-fossil fuel freerenewablewind energyex- ploratory data analysissmart grid
The current fossil fuel and climate crisis has led to an increased demand for renewable energy sources, such as wind power. In northern Europe, the efficient use of wind power is crucial for achieving carbon neutrality. To assess the potential of wind energy for private households in Finland, we have conducted a high spatiotemporal resolution analysis. Our main contribution is a wind power map of Finland that indicates the availability of wind power for given load profiles. As a representative example of power load, we consider the load profile of a household appliance. We compare this load profile against the wind power available nearby the weather stations of the Finnish meteorological institute.
I. INTRODUCTION
The efficient use of renewable energy is a key component for the green transition of current fossil-fuel based industries to achieve carbon neutrality [1]. Wind energy is a main source for renewable energy in Nordic countries such as Finland, especially during winter months [2]. According to the up-todate statistics(2022), wind power has covered 14,1% of the Finnish electricity consumption [3].
A key challenge in the efficiently using of wind energy is its spatio-temporal variability. In general, wind energy is available at locations and during times, which may not always match the end-user's needs (household appliance). The transfer of wind energy across space and time requires well-designed power grids and efficient storage facilities such as batteries [4,5].
Since the transmission of wind energy incurs losses [6], it is beneficial to consume the wind energy near its production sites.This highlights the importance of site selection for wind power plants, which often requires corresponding estimation of wind production. Previous studies [7]- [10] have found that Weibull distribution is a useful tool for the evaluation of wind resources for chosen sites, due to its ability to properly fit wind data as a probability distribution function.
Historical wind speed observation data of Malaysia has been used to evaluate wind power density and inform wind power plant site selection in [11]. The authors of [12] combined geographic information systems with multi-criteria decision making to optimize the site selection in Thailand. These works use a long-term average perspective, based on the statistics of wind speed and power production. In contrast, we are interested in the short-term availability of wind power to operate household appliances, equipped with modest battery capacity.
Our work is most closely related to recent efforts in generating various instances of a wind power atlas [13,14]. In particular, the NEWA and ERA5 reanalysis data sets have been proposed for wind analysis fields with a temporal resolution of 30 and 60 minute intervals, respectively, and spatial resolutions of 3 and 30 km, respectively. In contrast to these existing works, our approach uses a higher temporal resolution with 10 minute intervals. On the other hand, our approach focuses on local wind power generation dictated by the locations of weather stations operated by the Finnish Meteorological Institute (FMI).
Contribution. This paper provides the results of an exploratory data analysis using freely available weather data provided by FMI. The aim of this analysis is to generate a high-resolution wind-power map for Finland. For each FMI station we determine the fraction of the year 2021 during which an appliance with a given power profile could be powered solely from wind power.
Notation. We denote the first n natural numbers starting with 0 as [n] := {0, . . . , n − 1}. V for wind speed, P for wind power, and E for energy are used throughout the paper. Other symbols are defined as required.
II. PROBLEM SETTING
We consider the simple power system depicted in Figure 1 during discrete time instants t = 0, 1, . . .. The absolute time difference between any two consecutive time instants t and t + 1 is ∆t = 10min. The system includes a wind power plant that delivers the power P (w) t at time instant t. We consider a wind power plant of type Nordex N100/25000 https://www.thewindpower.net/ turbine en 224 nordex n100-2500.php that is mounted at a height of 100 m.
The system in Figure 1 also includes a load that is characterized by a power profile P t . The surplus (if any) power is used to load a battery whose energy level is E
(b) t .
such as a dishwasher or washing machine (see Figure 2). The power profile of the load has finite support of T a time instants,
P (a) t = 0 for t / ∈ {0, 1, . . . , T a }.
Consider some candidate time instant t s ∈ [365 · 24 · 6] during the year 2021. Starting at t s we try to run the load P (a) t . We assume the battery is empty when starting the load and ignore any power leakage,
E (b) ts = 0, E (b) t+1 = min E (b) t + P (w) t −P (a) t−ts ∆t, E bat for t > t s . (1) We define the candidate starting time t s as suitable if E (b) t ≥ 0 for t ∈ {t s , t s + 1, . . . , t s + T a }.
The useful annual fraction of the year 2021 is defined as
ρ := t s ∈ [365 · 24 · 6] : t s is suitable 365 · 24 · 6(2)
Note that the fraction ρ depends on the battery capacity E bat , the load profile P (a) t and the available wind power P (w) t . Section III discusses different choices for the batter capacity E bat and and load profiles P
III. METHOD
To determine the useful factions ρ (i) nearby FMI station i = 1, 2, . . ., we estimate the available wind power from the wind speed observations at a height of 10 m. Section III-A explains the pre-processing of raw weather observations, including the imputation of missing observations, extropalation of wind speed at 10 m to 100 m, and the estimation of wind power generation at 100 m. Section III-B discusses representative power load profiles that we will use for computing the useful fractions and generating the wind power atlas.
A. Pre-Processing Wind Observations
We downloaded wind speed observations V t (height = 10 m) at time instants t = {0, 1, . . . , 365 · 24 · 6} during year 2021 at different FMI stations from the web interface https://en. ilmatieteenlaitos.fi/open-data. In a next step we excluded any weather station for which more than 3% wind observations were missing. The resulting 165 FMI weather stations, indexed i = 1, 2, . . . , 165, are then used to construct the wind atlas in Section IV.
Data Imputation. For some weather stations, the wind speed observations are missing (we also treat negative wind speed values as missing values) at some time instants. We choose to impute missing wind observations via linear temporal interpolation [15]. If we denote t m and t n the time instants just before and after the time instants of missing observations,
V t = V tm −V tn t m −t n · (t−t m )+V tm for t ∈ {t m +1, . . . , t n −1}. (3)
From Wind Speed to Wind Power.: We use the "1/7 wind power law" [16] to extrapolate the wind speed measured at the height of 10 m to the expected wind speed at 100 m (the wind turbine hub height):
V 100 = V 10 · 100 10 α(4)
with α = 1/7.
The estimated wind speed V 100 at each time instant t is then combined with the power curve of the turbine Nordex N100/25000 to obtain an estimate for the generated power P (w) t . In particular, the estimated power P delivered by the turbine for an estimated wind speed in the range
V j < V 100 < V j is P = P j − P j V j − V j · V 100 − V j + P j(5)
Here, P j and P j denote, respectively, the nominal wind power delivered at wind speeds V j and V j .
B. Power Load Profiles
We use the open dataset https://www.kaggle.com/datasets/ uciml/electric-power-consumption-data-set to construct two prototype load profiles P represents an entire single-family household. Single Appliance. We extracted the load power profile P (dw) t ( Figure 2 ) of a dishwasher from the dataset [17]. The overall duration of the dishwasher process is 75 minutes with time intervals of 1 minute. To align the different time intervals of dishwasher load profile and wind speed records from FMI, wind speed is assumed to be constant during each 10 min time interval. Based on this assumption, we implemented (1) on a 1-min interval to run the corresponding numerical experiments.
Entire Household. Figure 3 depicts a representative load profile P [17]. The duration of the profile P (house) t is T a = 24 · 6 time instants.
IV. WIND POWER ATLAS FOR FINLAND
Numerical experiments were then conducted to explore fine-resolution temporal and spatial variations of the wind power resource in Finland via virtually running this dishwasher process according to Eq. (1) and Eq. (2). Table I shows useful annual fractions at FMI weather stations, given different battery capacities. The useful fractions increase as the battery capacity increases until a certain value (between 800 and 1000Wh) is reached. Increasing battery capacity beyond this value has no effect on the resulting useful annual fractions. Figure 4 is a map of Finland, in the location of FMI weather station i, a red dot is added as a marker; the marker size represents the corresponding useful annual fraction ρ (i) . The map clearly indicates that wind power has a high availability in regions along the coastline and in the northern parts of Finland.
We also did further analysis to explore the periodic variation of useful fractions over 24 hours of the day and 12 months of the year. Figure 6 shows an example weather station (see Figure 2) could have been powered only from wind power (using a battery capacity E bat = 1000Wh). Each dot represents an FMI weather station, indexed by i = 1, . . . , 165 and its radius is scaled by ρ (i) . Sotkamo Tuhkakyla where useful annual fraction is 0.7, but the distribution over 24 hours is quite uniform. To quantize the uniformity of the distribution for each station, information entropy is applied; in particular, the following formula is used to calculate the entropy
H = − 24 i=1 p i log p i
where p i is the fraction of useful starting time points that fall into the ith hour of a day during 2021.
The result shows the entropies for all weather stations included in this study are larger than 0.97, indicating the distribution of useful starting time points is quite uniform over the 24 hours of a day.
Whereas the distribution characteristic over 12 months of the year is different. Figure 5 (a, b, c) show significant seasonal trends in some weather stations, and the trends match the general characteristics of wind speed in Finland: From Table II, we can see compared to running a dishwasher, larger battery capacity is needed to fully exploit the wind resources to provide power for an entire house with profile P Comparison with NEWA and ERA5. While wind speeds observations from FMI have a high temporal resolution (10min intervals), they only allow for a poor spatial resolution of the resulting wind power atlas. Some sites are quite close to each other, with distances less than 1km, and some sites are far away from their neighbors, with distances larger than 50km, though generally, the sites are well distributed. Thus, the wind atlas in Figure 4 and 7 are mostly useful for wind turbine locations nearby FMI weather stations. One possible extension of our approach would be to use high-resolution wind reanalysis data sets to interpolate between FMI weather stations. To this end, we compared FMI observation with reanalysis datasets from NEWA [13] and ERA5 [14], which use the Weather Research and Forecasting Model (WRF) and the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (ECMWF-IFS), respectively. As NEWA only updated the reanalysis dataset to the year 2018, so we also downloaded corresponding data of the year 2018 from FMI for comparison. From Figure 8 and 9, we can see NEWA data and ERA5 data generally compare well to FMI observations except for some northern FMI stations of Finland.
V. CONCLUSION
We have used open weather data from the FMI to construct a wind power atlas for Finland. Unlike existing approaches for constructing a wind power atlas, our method employed a high temporal resolution that allows to verify whether a particular load profile could be powered solely by a wind turbine (combined with a battery storage capacity). Our results indicate that wind power has a high availability in regions along the coastline and in northern parts of Finland. We highlight that our analysis was exploratory using historical observation data from previous years. As an important next step, we will consider the short-term predictability of wind power in Finland.
for time instants t ∈ [T a ].The total duration (in absolute time) of the load profile is T a · 1min. An example for the load is a household appliance arXiv:2303.04403v1 [math.NA] time t which is used to serve a load with prescribed power profile P (a)
used to determine the useful annual fractions ρ (i) nearby FMI weather stations, indexed by i ∈ {1, 2, . . .}.
Fig. 3 :
3Load profile of a representative household during an entire day which corresponds to a duration of T a = 24 · 6 time instants (10 minute intervals).
Fig. 4 :
4Spatial distribution of useful annual fractions ρ (i) of 2021 during which the load profile P(dw) t
Fig. 5 :
5Distribution of useful starting points over 12 months at some weather stations (plots a,b,c) and a comparison between average wind speed and electricity demand of year 2021 (plot d) average wind speed of March and October is relatively higher (year 2021)(Figure 5 (d)). A further comparison with the trend of electricity demand in Finland (year 2021) shows during the summer months (June, July, and August), lower electricity demand is aligned with lower wind speed, but the trend is not quite consistent during winter months when the electricity demand achieves peaks. Electricity demand data is from FinGrid open database [18].
Fig. 6 :
6Distribution of useful starting points over 24h in Sotkamo Tuhkakyla weather station.
.
Similarly, a map (Figure 7 ) is generated to visulise the useful annual fractions of 2021.
Fig. 7 :
7Spatial distribution of annual useful fractions ρ (i) of 2021 during which the load profile P (house) t (seeFigure 3) could have been powered only from wind power (using a battery capacity E bat = 2500Wh). The markers (red dots) represents FMI weather stations, indexed by i = 1, . . . , 165. The marker size (radius) is scaled by ρ (i) .
Fig. 8 :
8Comparing modelled wind speed from NEWA with FMI wind speed observations during Year 2018 at Helsinki Kumpula) Fig. 9: Left: ERA5 reanalysis data for the average wind speed at 10 m height during year 2021. Right: Dots represent FMI weather stations with dot color represents the average observed wind speed at 10 m height during year 2021.
TABLE I :
ISummary statistics for the useful fraction of 2021 to run a dishwasher (seeFigure 2) only with wind power.Battery capacity Min fraction Max fraction Mean
std
200Wh
0.14
0.96
0.66
0.19
500Wh
0.18
0.97
0.70
0.18
800Wh
0.20
0.97
0.72
0.18
1000Wh
0.21
0.97
0.72
0.17
1500Wh
0.21
0.97
0.72
0.17
2000Wh
0.21
0.97
0.72
0.17
TABLE II :
IIUseful annual fractions in FMI weather stations to provide wind power for an entire house, given different battery capacities.Battery capacity Min fraction Max fraction Mean
std
1000Wh
0.17
0.97
0.68
0.18
1500Wh
0.19
0.97
0.70
0.18
2000Wh
0.19
0.97
0.71
0.18
2500Wh
0.20
0.97
0.72
0.17
3000Wh
0.20
0.97
0.72
0.17
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| sample_1887 | 0.9562 | arxiv | |
Green Federated Learning
Ashkan Yousefpour
Shen Guo
Ashish Shenoy
Sayan Ghosh
Pierre Stock
Kiwan Maeng
Schalk-Willem Krüger
Michael Rabbat
Carole-Jean Wu
Ilya Mironov
Meta
Green Federated Learning
CCS CONCEPTS • Computer systems organization → Distributed architectures• Computing methodologies → Machine learning• Hard- ware → Power and energy• Social and professional topics → Sustainability KEYWORDS Sustainability, Green AI, Federated Learning
The rapid progress of AI is fueled by increasingly large and computationally intensive machine learning models and datasets. As a consequence, the amount of computing used in training state-of-theart models is increasing exponentially (doubling every 10 months between 2015 and 2022), resulting in a large carbon footprint. Federated Learning (FL) -a collaborative machine learning technique for training a centralized model using data of decentralized entities -can also be resource-intensive and have a significant carbon footprint, particularly when deployed at scale. Unlike centralized AI that can reliably tap into renewables at strategically placed data centers, cross-device FL may leverage as many as hundreds of millions of globally distributed end-user devices with diverse energy sources. Green AI is a novel and important research area where carbon footprint is regarded as an evaluation criterion for AI, alongside accuracy, convergence speed, and other metrics.In this paper, we propose the concept of Green FL, which involves optimizing FL parameters and making design choices to minimize carbon emissions consistent with competitive performance and training time. The contributions of this work are two-fold. First, we adopt a data-driven approach to quantify the carbon emissions of FL by directly measuring real-world at-scale FL tasks running on millions of phones. Second, we present challenges, guidelines, and lessons from studying the trade-off between energy efficiency, performance, and time-to-train in a production FL system. Our findings offer valuable insights into how FL can reduce its carbon footprint, providing a foundation for future research in the area of Green AI.
INTRODUCTION
Federated learning (FL) is a distributed learning paradigm where a large number of client devices, such as smartphones, collectively train a machine learning model using data located on client devices. User data remains on client devices, and only updates to the model are aggregated within a centralized model at the server. FL has emerged as a practical privacy-enhancing technology for on-device learning [1]. Many real-world models have been trained using FL, including language models for predictive keyboards on Google Pixel, † Kiwan Maeng is currently with Pennsylvania State University. Work done when Kiwan Maeng was a postdoc researcher at Meta.
Apple's iOS, and Meta's Quest [2,3,4,5], Siri personalization [6], advertising, messaging, and search on LinkedIn [7].
While FL -when coupled with technologies such as secure aggregation and differential privacy [1,8,9,10] -can be a practical solution to enhance user privacy, the training process in FL can result in non-negligible carbon emissions. A recent study has shown that training a model with FL can produce as much as 80 kilograms of carbon dioxide equivalent (CO 2 e), exceeding that of training a higher capacity model, a large transformer, in the centralized training setting using AI accelerators [11]. The relative inefficiency is attributable to several factors, including the overhead of training using a large collection of highly heterogeneous client hardware, additional cost for communication, and often slower convergence.
Federated Learning's global carbon footprint is expected to increase as the industry increasingly adopts FL and more machine learning tasks shift away from the centralized setting. This is especially concerning since renewable sources of electricity may not be available in all locations, making Green FL a challenging goal to achieve [11,12]. Taking advantage of opportunities for efficiency optimization in FL is of paramount importance to make on-device learning greener.
Recently, there has been growing interest in quantifying and reducing the carbon emissions of machine learning (ML) training and inference in the datacenter setting [13,14,15,16,17]. However, the carbon footprint of Federated Learning (FL) and the factors that contribute to carbon efficiency in FL have yet to be thoroughly explored. Prior works have offer preliminary findings, either quantified the carbon effects of FL only in a simulation setting or with several simplifying assumptions [12,11], offering only a partial picture. These works focused on measurements and opportunity sizing, and restrained from exploring dimensions of the design space toward realizing Green FL. This paper presents a holistic carbon footprint analysis of a production Federated Learning (FL) system that operates on hundreds of millions of clients training on a real-world task. This is the first study that provides a comprehensive view of Green FL by characterizing the emission profile of all major components involved, including the emissions from clients, the server, and the communication channels in between. To this end, we instrument and profile all major components of the FL system.
An important finding of our analysis is: the carbon footprint of an FL task is highly correlated with the product of its running time and the number of users active in training (i.e., concurrency). We discuss this in more detail in Section 5. We also provide an in-depth analysis of the multi-criterion optimization between carbon emissions, time to convergence, and training error. Figure 1 presents results of measuring a production FL task for a range of hyperparameters. We can see that the number of rounds and concurrency are both positively correlated with the carbon footprint, and keeping one of these parameters constant, the Figure 1: Carbon emissions of (synchronous) FL: the more rounds is required to reach a target accuracy and the higher the number of users active in training (i.e., concurrency), the higher is the carbon emissions. Each point represents a training run with a different hyper-parameter (grouped by concurrency with marker colors and symbols). The graph shows the carbon emissions (Y axis) and the rounds to reach a target accuracy (X axis) for a language modeling FL task.
relationship is nearly linear (see, for instance, the line corresponding to concurrency set to 200). These points become more evident throughout the paper. Other findings are the following:
• Compute on client devices, and the communication between the clients and the server are responsible for the majority of FL's overall carbon emissions (97%). The carbon footprint attributable to the server-side computation is small (∼1-2%), while client computation is almost half of the contribution (∼46-50%). Upload and download networking costs are approximately 27-29% and 22-24%, respectively. • Asynchronous FL is faster than synchronous FL as it advances the model more frequently in the face of stragglers, but it comes at the cost of higher carbon emissions. • Different training configurations that achieve similar model accuracy can have substantially different carbon impact, by up to 200×, demonstrating the importance of hyperparameter optimization. • To minimize the carbon footprint of FL, reduce training time, and achieve a high model quality, FL developers must focus on lowering the training time, e.g., through the right choice of the optimizer, learning rates, and batch sizes, while keeping the concurrency small. • Carbon footprint of a language modeling FL task running for several days at scale is of the order of 5-20 kg CO 2 e, similar to that of producing 1 kilogram of chicken [18].
Contributions
To the best of our knowledge, this is the first study to measure carbon emissions at scale for an industrial FL system across a range of hyperparameters. Our findings can help identify challenges and encourage further research towards the development of more sustainable and environmentally friendly FL systems. Our main contributions can be summarized as follows:
• We present a comprehensive evaluation of the carbon emission of a full production FL system stack by presenting the emission profile of all major components involved, including the emissions from clients, the server, and the communication channels in between. No prior work has done a carbon measurement study on a real-world FL production system at scale. • Our empirical observations lead us to propose a set of key findings for Green FL, which identify the levers that have the most significant influence on the carbon footprint of FL. • We propose a model that predicts the carbon footprint of an FL task prior to actual deployment. • We show that using our recipe for Green FL, we can reduce the carbon footprint of FL training pipelines by as much as 200× while achieving similar model quality performance.
BACKGROUND
Climate change is a pressing global issue believed to be caused by human activities such as burning fossil fuels, deforestation, and agriculture, which all emit greenhouse gasses (e.g., CO 2 and methane). Climate change has significant impacts on human communities, as well as on ecosystems and biodiversity. Mitigating harmful emissions is essential in addressing climate change [19,20]. Green AI is the use of AI techniques and technologies in a way to reduce their environmental impact and promote sustainability in AI [21,22]. Some examples are developing more energy-efficient algorithms and hardware, and reducing the carbon footprint of data centers. With the rapid growth of AI (e.g., the amount of compute for training state-of-the-art models doubled every 10 months between 2015 and 2022 [23]), it is imperative to understand the environmental implications, challenges, and opportunities of AI. By making AI more sustainable, we can reduce its environmental impact while also reaping the benefits that AI has to offer.
A related line of work addresses communication efficiency or model compression for FL [24,25,26,27]. Historically, the primary objectives of these techniques have been cost reduction and not carbon emission savings per se. Quantifying and reducing the carbon emissions of FL is our primary objective. Although one might argue that renewable energy can power centralized AI systems [28,29,30], providing FL with renewable energy is inherently more challenging, as end-user devices are tied to their local energy mixes whose carbon footprint must be taken into account. In this paper we set out to study the problem of Green FL, present challenges, guidelines, and the lessons learned from realizing the trade-off between energy efficiency, performance, and time to train in a production FL system.
INDUSTRY-SCALE FEDERATED LEARNING 3.1 Federated Learning Platform
Our company's production FL stack is built based on Papaya [31], a recently proposed system for running federated learning and analytics tasks across millions of user devices. Papaya comprises two major subsystems: a server application that runs on a data center server and a client application that runs on end-user devices. In this study, we set out to measure the energy consumption and carbon footprint of both client-side and server-side resources used during training of a model in the federated learning system Papaya.
The overall architecture of Papaya is presented in Figure 2. The Papaya server has three main components: Coordinator, Selector, and Aggregator. There is one Coordinator, and the number of Selectors and Aggregators scales elastically based on the workload demand. The Coordinator assigns FL tasks to Aggregators based on load and assigns clients to tasks based on demand. Selectors report available clients and route clients to their assigned aggregator. Aggregators execute the client protocol, aggregate updates, and optimize the FL model. Regarding energy and carbon footprint, Aggregators and Selectors are responsible for the majority of processing and heavy lifting. The Coordinator is responsible for assigning FL tasks to Aggregators and clients to FL tasks, and centralized coordination.
Concurrency vs. aggregation goal. A device must meet a defined set of criteria to participate in FL training. Eligible devices report their availability to the Coordinator, which subsequently selects a subset of available devices for training. Concurrency is the maximum number of clients that can train simultaneously. The aggregation goal denotes the minimum number of client responses that must be received at the server before it updates the model.
In asynchronous FL, based on the FedBuff protocol [9], a new device is immediately selected for training as soon as the server receives a client response. Therefore, the number of devices training at any given time essentially equals to the concurrency. Once the aggregation goal is met, the server model is updated, and clients selected thereafter receive the updated model. However, clients chosen earlier may still be training using the previous version of the server model, leading to a phenomenon called staleness [9].
In contrast, synchronous FL [10] proceeds in discrete rounds. At the beginning of a round, the server distributes the same model to a number of devices equal to the concurrency. At the end of the round, the server updates its model if it has received updates from at least as many users as the aggregation goal; it is worth noting that users may drop out during the round due to various reasons (such as the device no longer being idle or connected to Wi-Fi). In synchronous FL, the concurrency is also referred to as users per round, and it is usually greater than the aggregation goal (a process called "over-selection") to account for the possibility of devices dropping out mid-round [32].
Large-scale FL Task: Language Modeling
In all experiments for this study, we train a character-aware language model for a next word prediction task, similar to Kim et al. [33]. This model computes the probability of a sequence of words = 1 , . . . , autoregressively as:
( ) = =1 ( | < ).
More specifically, we use a character-level CNN with multiple filters, followed by a pooling layer that computes the final word embeddings. These are then encoded using a standard LSTM-based neural network that captures the sequential information in the input sequence. Finally, we use an MLP decoder followed by a softmax layer that converts the word-level outputs into final word-level probabilities over a fixed vocabulary. Using the notation where • denotes the length of the sequence seen so far, • ,1 , ,2 , . . . , , are the characters of the -th word in the input sequence, • is the length of the -th word, • is the embedding for the -th word, • ℎ is the hidden state, • is the state of the LSTM for the -th word, • is the weight matrix, • ( +1 | ≤ ) is the probability of the next word in the sequence computed using the MLP decoder and softmax layer, then the model can be expressed as follows:
= CNN( ,1 , ,2 , . . . , , ) , ℎ = LSTM(ℎ −1 , −1 , ) ( +1 | ≤ ) = Softmax( ℎ ) Perplexity( 0 , 1 , . . . , ) = −1 =0 ( +1 | ≤ ) −1/ .
Perplexity measures the degree of uncertainty of a language model when it generates a new token averaged over sequence lengths. Formally, perplexity is defined as the normalized inverse probability of sequences.
In our experiments, the available client pool is in the order of tens of millions of end-user devices. Roughly 2 million devices (Android smartphones) are selected to participate in each experiment.
Instead of using the users' data for mobile keyboard predictions, which could raise privacy concerns, we use publicly available, representative data downloaded to the user devices before training. We used pushift.io's Reddit FL benchmark dataset [34] in all experiments 1 . This dataset is publicly available, previously collected, and currently hosted by pushift.io, consisting of user comments on reddit.com. Thus this dataset has a natural non-IID partitioning and is representative of a real-world data distribution for mobile keyboard predictions. It also exhibits the archetypal power-law phenomenon of the number of comments per user. The dataset comprises millions of users, with an average of 34 samples per user. Each device participating in the FL is randomly assigned an anonymized user id from the pushift.io's Reddit dataset to use as their training data.
Stopping Criteria. We run an FL experiment until either the language model reaches a target perplexity on a hold-out test set, or a maximum time limit of 2 days is reached. We set the target perplexity to be 175 or lower for our tasks and stop the task when the perplexity is at or lower than the target for five consecutive rounds.
Due to the large number of experiments in this study, we set the target perplexity higher and the time limit shorter than those of the typical production models. The carbon emissions of the at-scale production models of the same task are expected to be roughly 10× higher than the numbers reported in this study.
Experiment Parameters
We explored different settings of hyperparameters, separately optimizing for model performance, time to reach target accuracy, and carbon emission. We discuss these choices next.
For the optimizer running on the clients, we use SGD with no momentum. Alternatives (e.g., Adam) require additional on-device memory for the optimizer state (i.e., momentum buffers). Another important consideration is that in scenarios where clients possess limited data (which is often the case), they may not execute sufficient local steps to leverage the benefits of the momentum buffers. In such cases, the momentum-based optimization techniques may not be as effective.
For the server optimizer, we wanted to be as general as possible, and we chose Adam for the server updates [35]. Adam is more general than SGD or SGD with Momentum, and the parameters of Adam can be chosen to essentially replicate the performance of SGD or SGD with Momentum [36]. On the server side in FL, we do not see any evidence that using a more compute-intensive optimizer has any significant impact on carbon emissions, although it should help the other dimensions -reduce time to reach a target accuracy and improve overall accuracy. Our setup, the server updating the global model using the Adam optimizer and the clients using SGD, is called FedAdam [35].
We carefully evaluated hyperparameters for all applicable settings. We experimented with synchronous FL and asynchronous FL. For synchronous FL, the baseline implementation is FedAvg, whereas for asynchronous FL, it is FedBuff [9]. However, since we use Adam as the server optimizer, both synchronous and asynchronous FL get the benefits of adaptive optimizers and perform better than their baselines. The hyperparameters are listed in Table 1.
MEASUREMENT METHODOLOGY
This section describes the measurement methodology we used to obtain our production FL stack's energy and carbon emissions.
End-user Device Resource Measurements
The FL software stack has a client runtime that executes on enduser devices for FL training tasks. To enable accurate measurement The logger records events happening on the production FL client runtime. The logger is based on a generic logging system used widely in our production client runtimes and has minimal resource footprint. The generic logging system guarantees that the events are defined, created, and processed consistently across all the apps and services. The logger runs in parallel with an FL session. The downstream of the logger is a server-side database to store the logs sent from the client runtime logger.
Accounting for geography. In cross-device FL, an end-user device participates in an FL round when it is idle, charging, and on an unmetered network (e.g., Wi-Fi). Since the device is in the charging mode for FL, considering the source of energy for charging results in a more accurate carbon footprint estimate. To this end, we also consider the country where an end user connects from when the device is charging, since different countries have different carbon intensities. Carbon intensity reflects the amount of CO 2 emitted per unit of energy. We obtained country-level carbon intensities using the most recent reported year, e.g., 2020 or 2021, by Our World in Data [37].
Power profile of a phone. Several methods exist to get the compute and communication power of end-user devices. One may try to approximate the power consumption of phones based on modeling different components, e.g., Wi-Fi units and TCP/IP layers [38], although these models may not be accurate. Another approach is to estimate the power drainage by looking at the phone's battery level over time. This method is a coarse-grained and noisy proxy to power consumption, as the battery life also depends on factors such as the age of the battery and ambient temperature. Moreover, the battery drain may differ for the same app usage across devices.
A more reliable method is using an Android phone's power profile. The power profile is an XML file (typically named power_profile.xml) that Android device manufacturers must provide to specify parameters of different electronic components and the approximate battery drainage caused by these components over time [39]. This is the method we adopt as it provides accurate data for phone power consumption based on manufacturer information. We extract from power_profile.xml the power consumption of the CPU and Wi-Fi components. (Papaya utilizes CPU for FL training on the device.)
The listing below illustrates a snippet of a power_profile.xml for Google Pixel 7.
<?xml version="1.0" encoding="utf-8"?> <device name="Android"> . Diversity of Android devices. There are more than tens of thousands of distinct Android device models (also observed in [40,7]), and obtaining the power profiles for every device model that participated in our experiments would not be feasible. We instead focus on a subset of representative mobile phones-210 most commonly seen Android phones in the language modeling FL task in production. These devices represent more than 20% of the total devices participating in the FL task in production. Power profiles for these devices are available from several sources [41,42,43,44].
We impute values for phones with missing power_profile.xml files using corresponding numbers from devices with the same SoC or similar phones with comparable characteristics.
Wi-Fi Power. From the power_profile.xml file, we use the fields wifi.active, wifi.controller.rx, wifi.controller.tx, and wifi.controller.voltage to determine the communication power of the Wi-Fi, as these fields report the current and voltage when transmitting or receiving data [45]. The receiving power of an end-user phone would be
user_rx = ( + ) × ,
where , , denote wifi.active, wifi.controller.rx, wifi.controller.voltage, respectively. The transmission power is computed similarly with wifi.controller.tx as user_tx = ( + ) × .
CPU Power. For estimating the CPU power of phones, we need to know the compute resource pattern of the language modeling task on the phones. We did a field study on a few phones running the FL language modeling task for this. We used the Perfetto tool for profiling and analyzing the resource usage trace and confirmed that the FL task runs when the device is idle, and it runs on the "big" cluster of the CPU. The following is a representative example. Google Pixel 3 based on the Qualcomm SDM845 Snapdragon 845 SoC has two CPU clusters: a "small" cluster with four 1.8 GHz Kryo 385 cores for efficiency and a "big" cluster with four 2.8 GHz Kryo 385 cores for performance. Figure 3 shows a snapshot of the 8 cores of the phone when running an FL task. Cores of the big cluster (cores 4 through 7) are running the FL task and are at the maximum frequency of 2.8GHz. Figure 4 confirms that when the phone is idle, the big cluster is idle and running at a lower frequency of 0.8GHz.
The power_profile.xml file has currents for all CPU clusters running at different frequencies. We find the total current by adding these values (concretely, cpu.cluster_power.cluster, cpu.active, and cpu.core_power.cluster) corresponding to the highest frequency belonging to the "big" cluster. Hence for FL training on the device, the current for CPU is the addition of the values in these 3 fields. We use Watt's law to convert current to power and assume that the phones operate at 3.8V [46].
By multiplying the power and the FL session duration obtained from the logger -namely upload time, download time, and processing time -we can get the energy consumption for an FL session on a phone. We additionally confirm that the values resulting from this methodology are consistent with those reported in previous studies [11,47,48].
Server Resource Measurements
We measure the carbon footprint of the server as follows. There are three main server components in the Papaya stack: Aggregator, Coordinator, and Selector. The most power-intensive computations happen in the Aggregator and Selector, while the Coordinator is responsible for matching FL tasks to clients and Aggregators and orchestration. To ensure accurate measurements of power consumption, we monitored the physical servers that run the FL task (Aggregator and Selector). We describe our methodology for measuring the carbon footprint of an individual task on these servers.
Aggregator. To accurately estimate the carbon footprint of a single task on the physical servers, we measure the CPU utilization of the Aggregator during the execution of the language modeling FL task. We use the CPU utilization as a proxy for the power consumption specifically attributable to the FL task being executed on the server.
We consider the periods where the Aggregator runs only the language modeling FL task. First, we identify the Aggregator that runs a particular FL task. Next, we select a "stable" period when there is no failure, and the Aggregator is relatively underloaded. It is important to consider this period since the Coordinator reassigns FL tasks when it detects failed or overloaded Aggregators [31], hence tracking an FL task would not be feasible. We observe that utilization of the Aggregator for the language modeling FL task is less than 1%, which also includes background processes. To get a conservative upper bound, we assume that server utilization is 1% for the FL task. (Looking ahead, small errors in the estimate of the server utilization have a negligible impact on the results due to the small footprint of the server compute.)
Knowing the hardware specification of the physical servers running Aggregator, at 1% utilization, we measured Aggregator's power consumption for running the language modeling FL task at 45W. We multiply this number by the Power Usage Effectiveness (PUE) of our datacenters, 1.09, which accounts for the additional energy required to support the datacenter infrastructure (mainly cooling) [29].
Load balancing and other techniques of Papaya may impact where the Aggregator and Selector run. However, for this study, we assume they run uniformly across different datacenters. We use the weighted average carbon intensity model to account for the carbon intensity of different Meta datacenters that reside in different locations and regions [49]. We obtain the weighted average of the carbon intensities of the countries where Meta datacenters are located, and the weight is the number of datacenters in that country.
Selector. Since most of the processing happens in the Aggregator, the Aggregator's carbon footprint dominates that of the Selector. We conservatively assume the same carbon footprint value for the Selector as for the Aggregator.
Networking Infrastructure Measurements
For the networking and infrastructure resources, we adopt the standard methodology that considers all hardware assets on the path between the end-user and the FL server, namely, access, metro, edge, and core networks [50,51,52,11]. The access network is the first network user connects to, and it typically includes ADSL Ethernet, Wi-Fi access point, or 3G/4G/5G access point. The metro and edge network aggregate traffic from several users' access points, regulate access and usage, and represent the gateway to the global Internet, which consists of an edge Ethernet switch, broadband network gateways (BNGs), and edge routers [50]. The core network, consisting of core routers, is the backbone of the Internet, connecting the metro and edge network to the datacenter. Schematically for cross-device FL we can have: client → Wi-Fi access point → edge Ethernet switch → BNG → edge routers → core routers → edge routers → data center Ethernet switch → data center. In this setting, power consumption of the networking infrastructure connecting the end-user to the FL server in the datacenter can be obtained using the energy-per-bit model, as [52,50]:
network = ( + as + bng + + + ds ) × ,
where is the bandwidth usage of the FL session, is the number of edge routers, is the number of core routers, and , as , bng , , , ds denote the energy per bit of the Wi-Fi access point, the edge Ethernet switch, the BNG, an edge router, a core router, and data center Ethernet switch respectively [50]. We adopt constants from Vishwanath et al. [50]. The bandwidth usage of the session, , can be calculated using the model size divided by the upload or the download time.
CARBON EMISSIONS OF FL
In this section, we present the results of our study and measurements. We use CO 2 -equivalents (CO 2 e), a standardized measure to express the global-warming potential of various greenhouse gases as a single metric. Carbon dioxide (CO 2 ) is not the sole greenhouse gas contributing to climate change. There exist other gases that also have a significant impact on the environment, and the aggregate effect of all these gases is quantified as CO 2 e: the number of metric tons of CO 2 emissions with the same global warming potential as one metric ton of another greenhouse gas.
Estimating Carbon Emissions of Industry-scale FL System
We quantified the carbon emissions of our synchronous and asynchronous FL system through hundreds of experiments, each with a different set of hyperparameters. First, we illustrate the total carbon impact of synchronous and asynchronous FL. Figure 5 shows the carbon emissions of synchronous and asynchronous FL training in our production stack to reach a target perplexity of 175. We have tuned both methods by finding the choice of hyper-parameters that led to the lowest time to target perplexity, as also used in Huba et al. [31]. In this setup, concurrency and aggregation goal are both set to 1,000.
We can see that synchronous FL has a smaller carbon footprint compared to asynchronous FL. This is in contrast to the faster convergence of asynchronous FL (2.4 hours), which involves more model updates at the server (100). Asynchronous FL converges faster to the target perplexity due to its fast model updates. Due to its frequent iterations, asynchronous FL involves more clients. This result shows a fundamental trade-off between synchronous and asynchronous FL: if tuned well, asynchronous FL is faster than synchronous FL as it advances the model more frequently in the presence of stragglers, but it comes at the cost of higher carbon emissions.
We can also see that the majority of the carbon footprint is contributed by the client compute -consistent with FL's pushing the AI processing to the edge of the network. The server compute is a small fraction of the carbon emissions as shown in Figure 5 and other experiments. We observe that client compute and the communication between the clients and the server are responsible for the greatest share of FL's overall carbon emissions (97%). The carbon footprint from the server-side computation is small (∼1-2%), while client computation contributes to almost half of the overall carbon footprint (∼46-50%). Upload and download networking costs are approximately 27-29% and 22-24%, respectively. Figure 6 illustrates the carbon emissions of synchronous and asynchronous FL training in our production stack after a fixed time -after 4 and 10 hours. In this experiment, instead of fixing the target perplexity and evaluating on training time, we fix the training time and measure the carbon emissions and the achieved perplexity (lower is better). The test perplexity is computed using data from 20 held-out clients. Because test perplexity with so few clients is noisy and can vary significantly from round to round, we smooth the test perplexity using an exponentially-weighted moving average with parameter = 0.3 and declare that the test perplexity target has been reached when the smoothed test perplexity achieves the target. Asynchronous FL can advance the model faster and reach a lower perplexity at the cost of more carbon footprint. After 10 hours, synchronous FL is able to catch up to asynchronous FL with a similar perplexity of 120. The same contribution ratio among client compute, server compute, upload and download networking costs can be seen here too.
In the rest of the experiments, we fix the target perplexity while evaluating carbon emissions and training time.
Some Parameters Matter More
In our study on hyperparameters in FL tasks, we observed that some parameter choices have a greater impact on carbon footprint than others. Specifically, the parameter of concurrency plays a significant role. The relationship between concurrency and carbon emissions in synchronous FL is depicted in Figure 7, where we observe that as concurrency increases, so does the carbon footprint. Higher concurrency leads to more devices training simultaneously, resulting in increased resource utilization and only partially offset with potentially faster convergence. We note that the time to reach a target accuracy decreases only up to concurrency of 800, illustrating diminishing returns in training speed. Diminishing returns in training speed as a function of increasing the number of clients training in parallel is analogous to a similar phenomenon in large-batch training [31,32,53].
Among the parameters of FL system design, we found that concurrency and time to reach a target accuracy, which translates to the number of rounds for synchronous FL and wall-clock time for asynchronous FL, have the most significant impact on carbon emissions. Conversely, other parameters such as learning rates, batch sizes, aggregation goals, and local epochs impact the convergence of the FL model towards the target accuracy, which in turn influences the time required to complete the training process. While these parameters do not directly affect carbon emissions, they do indirectly influence the overall training speed. Therefore, it is recommended that these parameters be included in the "time" and "performance" aspects of the multidimensional design in Green FL. On the other hand, concurrency impacts both time and carbon emissions directly and should be given greater consideration in FL system design for reducing carbon emissions.
Predicting Carbon Emissions of FL
We put forth a model of the relationship between time-to-convergence, model performance, and carbon emissions. By leveraging our model, FL practitioners can effectively forecast the carbon emissions of their system before initiating the training process.
We observed that concurrency is the most significant determinant of FL's carbon emissions. It has the largest effect on the resources, since concurrency most directly corresponds to the resource utilization of clients. While higher concurrency accelerates model convergence, it results in significantly higher carbon emissions. For instance, increasing concurrency by 10× increases the resource usage by 10× while only reducing the convergence time by 1.5× or 2×. Therefore, the overall benefits of higher concurrency, considering resource consumption, do not scale linearly increasing concurrency has diminishing returns considering convergence, model performance, and carbon emissions. Higher concurrency reduces training duration, but increases resource usage even more.
To understand the relationship, we assume that the carbon emissions have a linear relationship with the product of concurrency and the number of rounds (or duration) it takes to reach a target accuracy. We validate our hypothesis in Figures 8 and 9. Figure 8 shows the relationship between the product of rounds and concurrency and the carbon emissions for download, upload, and client compute in synchronous FL (carbon emissions of server compute is negligible). Different points on these scatter plots represent different training runs of the language modeling FL task. We use linear regression to find the fitting line that shows the aforementioned relationship. Figure 8 also shows the 2 values of the models, which is a goodness-of-fit measure for the linear regression models. We can see high 2 values for the linear regression models, confirming the product of rounds and concurrency is a good proxy to predict the carbon footprint of synchronous FL. Figure 9 shows a similar linear regression model for asynchronous FL. Since there is no concept of rounds in asynchronous FL, we treat duration (hours to reach a target accuracy) as an explanatory variable for the carbon footprint of asynchronous FL. We also see high goodness of fit ( 2 values) for these models. Hence, the product of duration and concurrency is a good proxy to predict carbon footprint of asynchronous FL.
In Figure 10, we present an overview of the design space for Green Federated Learning (FL) and highlight the trade-off between time, performance, and carbon emissions in asynchronous FL (the design space for synchronous FL was previously illustrated in Figure 1). The scatter plot depicts various training runs of the FL task conducted through asynchronous FL, with different marker colors and symbols representing distinct concurrency values. Each point represents an experiment with a different hyper-parameter; we group the points by concurrency. We observe that the points corresponding to the same concurrency follow a linear trajectory, where higher concurrency leads to a steeper slope, implying a faster rate of CO 2 e accumulation. The cumulative carbon footprint of the task is a function of both its running time and the rate of carbon Concurrency=50 Concurrency=100 Concurrency=200 Concurrency=300 Concurrency=800 Concurrency=1000 Concurrency=1300 Concurrency=1500 5 Figure 10: Carbon emissions of asynchronous FL increase linearly with the product of the time it takes to reach a target accuracy and concurrency. Each point represents a training run with a different hyper-parameter (grouped by concurrency with marker colors and symbols), its carbon emissions (Y axis, in kg CO 2 e) and the time it takes to reach a target accuracy (X axis, in hours). The more time is required to reach a target accuracy and the higher the concurrency, the higher is the carbon emission.
emission increase. Our analysis identifies concurrency and time to convergence as the two critical parameters for carbon emissions. While the former is under the direct control of the FL engineer, the latter is more indirect and reliant on the appropriate selection of hyperparameters. In particular, the high concurrency regime (which may be desirable, for instance, for its more robust privacy guarantees) puts a higher premium on hyperparameter tuning as longer training time translates into a larger carbon footprint.
RELATED WORK
To the best of our knowledge, our work is the first to conduct a large-scale carbon emission characterization of an industry-scale FL stack and different hyperparameters. We explore ways FL can be made more energy-efficient ("greener") through the right selection of FL parameters and design choices. There has been growing interest in quantifying and reducing the carbon emission of machine learning (ML) training and inference in the datacenter [13,14,15,54,17]. Nevertheless, the carbon footprint of FL has not yet been explored well. Prior works only quantify the carbon effect of FL in a simulation setting under several simplifying assumptions [12]. Other studies explore different ways for minimizing the energy footprint of client devices in Federated Learning [55,56,57], though not at large-scale scenarios like this study. Another work did a preliminary study of carbon emissions of FL [11]; however, the authors also did not do their carbon emissions as comprehensively as our study does, as we log the FL session information and use the actual power measurements of the devices.
We take a data-driven approach to quantify carbon emissions of FL by directly measuring a real-world FL task at scale running on millions of user devices. We present challenges, guidelines, and lessons learned from studying the trade-off between energy efficiency, performance, and time to train in a production FL system.
Other related work could be the works on compression and quantization [27,25]. Compressing the communications between the server and the clients could further reduce the carbon emissions of the FL training pipeline while presumably maintaining high model utility. For instance, we observed that the carbon emissions of communication in some settings could contribute to up to 60% of the total emissions. Hence, reducing them by, say, a factor 4 with int8 [58] would reduce the total emissions by a factor of 1/(.4 + 0.6/4) = 1.82.
CONCLUSIONS AND FUTURE WORK
In this paper, we demonstrate how different FL parameters and design choices can impact the carbon footprint of a production FL system. Our empirical approach quantifies carbon emissions by directly profiling a real-world FL task running on millions of user devices. These measurements inform our guidelines and lessons learned on the trade-off between carbon emissions, target accuracy, and time to train in a production FL system.
We acknowledge that this study, like any, has some limitations. Recall that we used the power profiles of the 210 most commonly seen device models to obtain estimates of upload, download, and compute power for typical devices. We noted that these 210 devices represent 20% of the total devices participating. The carbon emissions values we report based on these values are estimates. Although it is possible that the absolute carbon emissions would change if power profiles for additional devices were available, we believe that the same trends and overall conclusions hold.
As future research directions, we suggest investigating how compression and quantization techniques could apply to Green FL, potentially reducing the carbon footprint of the communication stack (at the expense of increasing client-side computations). Alternative FL architectures, such as secure aggregation via cryptographic computations, federated ensemble learning, or federated split learning, present intriguing challenges as well. Additionally, we encourage the research community to consider the impacts of differential privacy on the landscape of Green FL. Differential privacy would introduce privacy as an additional criterion, alongside accuracy, carbon, and time. Finally, we urge FL practitioners to consider the carbon footprint of their systems in their decision-making process.
Figure 2 :
2Overall architecture of our production FL stack, based on Papaya[31].
Figure 3 :
3A snapshot of the 8 cores of the phone when running an FL task. Cores of the big cluster (CPUs 4 through 7) are running the FL task and are at the maximum frequency of 2.8GHz.
Figure 4 :
4A snapshot of the 8 cores of the phone when it is idle. The cores of the big cluster are idle.
Figure 5 :
5Carbon emissions of SyncFL and AsyncFL to reach a target perplexity. The text above the bars shows the time and rounds it takes to reach the target perplexity.
Figure 6 :
6Carbon emissions of SyncFL and AsyncFL after a fixed training time. The text above the bars shows the perplexity of the model at the specified time (lower is better).
Figure 7 :Figure 8 :Figure 9 :
789Higher concurrency leads to more carbon emissions. The numbers above bars are the time (in hours) it takes to reach the target accuracy. Carbon emission of synchronous FL is linearly correlated with the product of rounds it takes to reach a target accuracy and concurrency. Carbon emission of asynchronous FL is linearly correlated with the product of the time it takes to reach a target accuracy and concurrency.Consistent with prior research, the present study indicates that larger values for local epoch do not yield improvements in training efficiency, particularly within the context of non-IID at-scale FL systems characterized by heterogeneous data and systems. On the contrary, larger local epoch values result in a marked increase in carbon emissions, largely attributable to the corresponding rise in client compute. Therefore, we recommend using smaller values for the local epoch, specifically in the 1 to 3 range.
arXiv:2303.14604v1 [cs.LG] 26 Mar 2023216
Carbon Emissions (kg CO2e)
0
0.2
0.4
0.6
Rounds to Target Accuracy
0
50
100
150
200
Concurrency=50
Concurrency=100
Concurrency=200
Concurrency=300
Concurrency=800
Concurrency=1000
Concurrency=1300
Concurrency=1500
3
Table 1 :
1Hyperparameters and their values explored in the experiments. Aggregation goal is expressed here as a percentage of concurrency.of compute time, upload, and download duration, we implemented a logger that records the vitals of the FL session, including the country from which the device is connected for the FL training, the model of the device, model download time, model upload time, and total duration of a single FL session. We use this information for power measurements of the devices.Hyperparameter
Values
server learning rate 0.0001, 0.001, 0.005, 0.01, 0.1, 1
client learning rate
0.0001, 0.001, 0.01, 0.1, 0.5, 1
local epoch
1, 3, 5, 10, 15, 20
batch size
8, 16, 32
Adam 1
0.1, 0.5, 0.7, 0.9
Adam 2
0.9, 0.99, 0.999
concurrency
50, 100, 200, 300, 800, 1000, 1300, 1500
aggregation goal
8%, 10%, 25%, 50%, 65%, 77%, 80%, 85%, 100%
Table 1
1Concurrency
Client Compute
Server Compute
Upload
Download
50
0.011799
0.000415
0.007513
0.008009
100
0.022022
0.000652
0.010833
0.010400
200
0.015755
0.000497
0.009454
0.007891
300
0.042568
0.001353
0.024112
0.023665
800
0.055558
0.002001
0.042957
0.035411
1000
0.081274
0.002551
0.047613
0.041832
1300
0.143102
0.004142
0.070423
0.063725
1500
0.141950
0.004657
0.098224
0.071627
Carbon Emissions (kg CO2e)
0
0.1
0.2
0.3
0.4
Concurrency
50 100 200 300 800 1000 1300 1500
Client Compute
Server Compute
Upload
Download
4 h
3 h 2.7 h
2.9 h
2 h
3.7 h
5.1 h
2.5 h
Meta was not involved in the collection of data from Reddit.
ACKNOWLEDGMENTSWe would like to thank Pavel Ustinov, Kunal Bhalla, and Vlad Grytsun for the discussions and their invaluable help in this work; Harish Srinivas, Sam Lurye, Anthony Shoumikhin, Kaikai Wang, and Dweep Gogia for their continued support and for sharing their expertise; Karthik Prasad, Graham Cormode, Ramya Raghavendra, Arnald Shaju Samthambi, and John Nguyen for their insightful ideas and comments. We also like to thank Grace Nichols, Ajay Chand, Jesse He, Riten Gupta, Bharati Sethiya, and Gilbert Sanchez for helping us in mobile phone measurements.
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| sample_1899 | 0.985 | arxiv | |
Climatic implications of a rapid wind/solar transition
Peter D Schwartzman
Department of Environmental Studies
Knox College
61401GalesburgIllinoisUSA
David W Schwartzman
Department of Biology (Emeritus)
Howard University
20059WashingtonDCUSA
Xiaochun Zhang xczhang@carnegiescience.edu
Department of Global Ecology
Carnegie Institute for Science
Stanford University
94305StanfordCaliforniaUSA
Climatic implications of a rapid wind/solar transition
1
A transition to a fully global renewable energy infrastructure is potentially possible in no more than a few decades, even using current wind/solar technologies. We demonstrate that at its completion this transition would terminate anthropogenic carbon emissions to the atmosphere derived from energy consumption in roughly 25 years as well as double current global energy production. This result would provide all human energy needs worldwide and additional energy required for climate adaptation as well as carbon sequestration from the atmosphere to bring down the atmospheric carbon dioxide (CO 2 ) concentration to safer levels. The implementation of this energy transition in the near future would maximize the probability for achieving a less than 2 deg C, with a potential 1.5 deg C limit, increase to global temperature over the pre-industrial level by 2100. Our best case scenario utilizes less than 3% of current annual global energy consumption per year with an annual reinvestment of 10% of its growing renewable capacity to make more of itself.
The detrimental impacts of continued fossil fuel consumption particularly with respect to climate change makes a transition to global zero-carbon energy supplies urgent (Hansen et al 2013). Several studies have already demonstrated a path to a global renewable energy (RE) infrastructure in no more than a few decades (Jacobson and Delucchi 2009;Jacobson and Delucchi 2011;Delucchi and Jacobson 2011;Schwartzman and Schwartzman 2011). This transition will require inputs of fossil fuel energy, since the current zero-carbon energy capacity is far from sufficient for the task (Jacobson and Delucchi 2009; Jacobson and Delucchi 2011). Meeting the challenge of energy poverty in the developing world will require the provision of a global level of roughly 3.5 kW per person, corresponding to the minimum required for a world standard high life expectancy (Smil 2008). Here we present the modeling results of a transition to a global wind/solar infrastructure including its climatic impacts. We conclude this transition can be completed in less than 30 years, terminating energy poverty as well as providing additional energy required for climate adaptation and carbon sequestration from the atmosphere to bring down the atmospheric CO 2 concentration to safer levels. The implementation of this energy transition in the near future would maximize the probability for achieving a less than 2 deg C, with a potential 1.5 deg C limit (COP21 2015) to global temperature increase over the pre-industrial level by 2100.
In this study, given anticipated global population growth and assumed rapid phase out of high carbon footprint fossil fuels, we calculate global energy usage and concomitant carbon emissions into the atmosphere. Further, using modeling techniques developed by Myhrvold and Caldeira (2012), we estimate the warming expected with these greenhouse forcing contributions. Our analysis clarifies several critical variables, including the following, each determined incrementally over the entire period until the culmination of transition: (a) the amount of energy required (in comparison to current levels and broken down by type); and increments in both (b) global CO 2 and methane (CH 4 ) atmospheric concentrations; and, (c) global surface temperatures.
Our modeling will hopefully provide an optimal path to be considered by policy makers regarding the implementation of the decarbonation of global energy and its replacement by renewable supplies.
In Schwartzman & Schwartzman (2011), the transition to a future world with 100% renewable energy is modelled using differential equations which allow the computation of the global power capacity of solar energy infrastructure as a function of inputs of fossil fuels and reinvestments of the created renewable energy capacities. Using conservative values of known parameters from existing renewable technologies, in particular, lifespan of photovoltaic panels and wind turbines and the energy return on energy invested (EROI) ratios, they found that very small inputs of current energy consumption per year (~1.0-2.5%) and modest reinvestments of the newly formed solar infrastructure (~10-15%) are sufficient to produce a solar energy infrastructure capable of supplying more than twice modern energy levels on a time scale of 20-30 years. Lifespans of renewable energy technologies were assumed to be 20 to 25 years and the composite EROI ratios for photovoltaic, concentrated solar plants (CSP), and wind farms were taken to be 20:1 to 25:1. Given their already current robust research and development programs, the anticipated improvements in renewable energy technologies will likely make these seemingly dramatic projections quite conservative, as future technologies are implemented.
Myhrvold and Caldeira (2012) model energy transitions, computing warming impacts from carbon emissions for their simulations. However, there is a significant difference between their bootstrapping scenario and our modeling in which the renewable energy capacity exponentially created replaces carbon energy, not leaving it to suddenly disappear at the end (Schwartzman and Schwartzman 2011). Thus, we expected that our solar transition scenarios will commonly result in carbon emissions and resultant warming impacts smaller than the results from their bootstrapping approach. The modeling in previous papers (Schwartzman andSchwartzman 2011, 2013) provided the maximum fossil fuel inputs, hence by inference rough estimates of the maximum global temperature increases, for rapid RE transitions. Here we include in the modeled transitions scenarios with differentiated consumption values of each type of fossil fuel with specified emission factors and compute temperature increases using a climate model. Rapid phase out of coal and other high carbon footprint fuels with conventional liquid oil making up the slack until full wind/solar replacement should have significant future climate consequences because of both the lower C emissions of conventional liquid oil and the complete termination of fossil fuel use in 20-30 years, and this difference informed our modeling.
Starting with the distribution of 2012 energy forms (see Supplemental Table S1) and the UN's best projections for global population growth (WPP 2013), we construct the following seven scenarios: (1) slow initial reductions in fossil fuel energy use in the near-term (fifteen years) followed by rapid reductions (over the next ten years) concomitant with aggressive reinvestment of RE to make build additional RE power capacity; (2) slow initial reductions in high carbon emitting fossil fuel energy use and small increases in lower carbon emitting fossil fuels in the near-term followed by rapid reductions concomitant with less aggressive reinvestments of RE to build additional RE power capacity; (3) similar to (2) in fossil fuel usage but with aggressive reinvestment of RE to make build additional RE power capacity (in the near-term); (4) similar to
(1) with slightly slower initial decreases in lower carbon emitting fossil fuels and an even greater reinvestment of available RE resources (for 3 different values of NG greenhouse emissions, resulting in 4a, 4b, 4c, representing lower, middle, and high values of CH 4 emission factors, respectively) and more aggressive RE reinvestment for more RE; (5) similar to (3) but with faster ramping down of NG use and more aggressive RE reinvestment for more RE; (6) maintenance of 2012 emissions density levels (both CO 2 /kWh and kWh/person) as total energy consumption increases according to "business as usual" (with same distribution of energy forms as in 2012); and, (7) maintenance of 2012 emissions density (CO 2 /kWh) levels with no increase in production (i.e., "no change" for present). Supplemental Table S2 (see supplement) provides the rate of change in use for each fuel type and time interval of the transition; Scenarios 6 and 7 are not included as they do not have preset changes by fuel type. The first four scenarios reduce high carbon emitting fossil fuels much faster than lower carbon emitting fossil fuels. The growth of RE supplies in Scenarios (1) to (5) were computed using different annual growth assumptions (see Supplemental Table S2). While this approach did not use the differential equations of Schwartzman and Schwartzman (2011), the RE levels computed are consistent with those of Schwartzman and Schwartzman (2011) using conservative assumptions regarding input parameters (Table 1). Obviously, climate change concerns motivate the faster initial declines in the high carbon emitting energy forms (see Supplemental Table S1 for the CO 2 and CH 4 emissions by energy type). However, given some recent findings establishing a much higher level of CH 4 emission from natural gas (NG) extraction and use (Howarth 2014; Howarth 2015), scenarios 5a, 5b and 5c differentiate between NG and conventional oil, reducing the former at the same rate as coal and unconventional oil and increasing the latter in the short term, to ensure that enough RE infrastructure is built out early.
Figures 1a-1f shows the output of the seven scenarios, run for twenty-five years into the future, for six important variables: total energy; percentage of energy from energy sources (% RE), power per capita; change in atmospheric CO 2 concentrations, change in atmospheric CH 4 concentrations, and, temperature change. Table 2 shows only the final values after 25 years in the RE transition. Notice that scenarios 1 and 6 result in equivalent changes in total energy and power per capita but have differences otherwise. The drop in total energy after year 15 (for scenarios 2 and 3) are a result of dramatic declines in fossil fuel use after year 15. Notice that these "dips" are quickly removed once the renewable energy capacity grows to a sufficient scale to replace them. Our optimal scenarios 4a-c and 5a-c arrive at similar total energy levels as scenarios 1, 3 and 6 but do so without the instabilities found in these and usually with a markedly lower CO 2 and CH 4 concentration change and a lower temperature increase (except in the case of highest CH 4 emissions from NG, e.g., 4c and 5c, where CH 4 levels can become appreciable after 25 years). In particular, scenarios 4a-b and 5a-b exhibit increases approximately 3-4x smaller than "business-as-usual" and "do nothing," and much smaller than other RE scenarios (other than 1). Not surprisingly then, we observe that these scenarios result in much less warming than the other scenarios as well (~0.26K versus 0.5-0.6K for scenarios 6 and 7 and 0.30-.36K for the other RE scenarios). For 4c and 5c, the two high NG CH 4 emission scenarios, we begin to see temperature changes comparable to other RE transition scenarios but much less than "businessas-usual" and "do nothing." In all cases, the benefits of 4a-b and 5a-b (and of the other RE scenarios) start to accrue between 10-15 years after the starting point of introduction of policies to modify fossil fuel use and renewable energy installation. Figure 2 shows the differences between 4a-c and 5a-c in terms of atmospheric CO 2 and CH 4 concentrations over the 25 year transition to RE. For scenario 4a, the amount of oil and NG required to reach the 93% RE (with total energy 2.1 times larger than 2012 levels) in 25 years is 2,228 EJ for conventional oil and 1,649 EJ for NG, amounting to 18% and 11% respectively of their reserves (Hansen et al 2013).
Note that the CH 4 peaks and then declines rapidly during the transition because of its significantly lower atmospheric lifespan than CO 2 . Scenario 4a serves as our optimal path to an energy system run almost entirely solar and wind energy that would be self-sustaining; 4b, 5a and 5c scenarios also get us to the same point with a bit more climate change, while 5c provides a more optimal path if CH 4 emissions from NG are at the very high end of current estimates. It provides for sufficient power per capita, reaching 90% of the minimum required, 3.5 kW/capita, for world standard high life expectancy (Smil 2008, Schwartzman and Schwartzman 2011) in just 10 years and exceeded it by 30% at the end of the 25 year transition, hence providing additional energy, compared to the present baseline, needed for climate adaptation, and carbon sequestration from the atmosphere to bring down the atmospheric CO 2 concentration to safer levels. The actual level of this increment needs study but some preliminary estimates are now available. For example, if 100 billion metric tons of carbon, equivalent to 47 ppm of atmospheric CO 2 , were industrially sequestered from the atmosphere it would require 5.9 to 18 years of the present global energy delivery (18 TW), assuming an energy requirement of 400 to 1200 KJ/mole CO 2 (House et al. 2011;Zeman 2007). This requirement would of course be reduced by the use of agriculturally-driven carbon sequestration into the soil.
A shift to wind and solar-generated electricity as an energy source could reduce the required power level by 30% once a global system is created (Jacobson and Delucchi 2009;Jacobson et al. 2014). And, it should be noted that scenario 4a does not result in a reduction in total energy production at any point in the transition (note that scenario 2 does not meet the criteria for sufficient energy production over the twenty-five years). Scenario 4a reduces future temperature change by more than half, especially when compared to the "business-as-usual" model. It is important to note that our greenhouse gas model is the same as Ricke & Caldeira (2014) and Zhang et al. (2014), so the decadal lapse rate in peak warming from CO 2 emission found in Ricke and Caldeira (2014) must be contemplated in our case as well. Lastly, humans have the fossil fuel resources today to build the solar/wind infrastructure necessary to make the transition complete. For scenario 4a, 18% of global reserves of conventional oil are used to completely terminate fossil fuel consumption (1). Thus, if implemented, scenario 4a provides for a meaningful means to a world divorced from nearly all fossil fuels and their negative climate implications within a quarter decade.
Already available reliable and cheap storage technologies, along with tapping into geothermal energy, will facilitate the expansion of these renewables ( A comparison of our current fossil fuel "energy in" (to produce and invest in future fossil fuel) to our anticipated "energy in" to create wind/solar capacity (as determined by current EROIs, ~20-25, as stated earlier) convinces us that the energy needed for storage and grid modernization is already freed up in the early phases of wind/solar transition, recognizing the role of aggressive energy conservation in buildings, transport and other sectors. Today, we estimate that ~5 to 10% of total fossil fuel consumption goes as "energy in," assuming a conservative EROI of petroleum and coal (10 to 20) (Hall et al 2014), neglecting the ~14% of total energy consumption derived from other sources such as nuclear power and hydropower (BP 2015). In comparison, in our conservative "best case" scenarios (either 4a or 5a), the percentage of required energy "going in" annually to build the large scale renewable capacity (in ~25 years)
is ~2-3% of present energy consumption level and a reinvestment of ~10% of wind/solar capacity, both annually. Interestingly, this ~10% of wind/solar capacity which is reinvested annually, which is comparable to today's present energy consumption level reinvestment, is sufficient to make RE capacity sustainable even with a growing population and changes in affluence worldwide.
Is a doubling of present energy consumption in 25 years ending up with a composite of RE technologies a wild stretch of the imagination? We note that wind power alone could supply this level of energy generating capacity several times over (Lu, McElroy and Kiviluoma 2009).
Consider the following example, suppose 5 MW capacity wind turbines supply all this energy, with a 35% capacity factor. Then 36 TW, double the present primary energy consumption would require 21 million wind turbines produced in 25 years, assuming the lifespan of this technology exceeds this timespan. We submit that this production is within the technical capacity of the global economy, noting that 90 million cars and commercial vehicles were globally produced in 2014 alone (2014 Product. Stat.).
We demonstrate that the following outcomes are technically achievable using current wind/solar power technologies in the next 25 years, if this transition commences in the near future: (1) the virtually complete elimination of anthropogenic carbon emissions to the atmosphere (derived from energy consumption); (2) the capacity for maximizing the probability of achieving a less than 2 deg C, with a potential 1.5 deg C limit to global temperature increase over the pre-industrial level by 2100, taking into account the approximately 0.
Methods
We programmed the energy scenarios within the context of our solar transition model as follows so as to approximate these outcomes in 25 years: (a) CO 2 emissions should drop by more than 90%; (b) energy production should exceed 900 quads (more than 67% higher than 2012 levels) and be over 95% from renewable sources; (c) energy consumption per capita should exceed 3 kW per person as this has been shown to the approximate consumption level required to get people out of energy poverty reaching world standard life expectancy values (Smil 2008; Schwartzman and Schwartzman 2013; increased during the early stages of the transition in order to enable the faster development of RE infrastructure and increased assurances that total power available will be sufficient to provide every human with this level of power over the entire duration of the transition). Note that since nuclear, biomass, biofuels, hydropower, and geothermal power will not be necessary to make the transition (only accounting for 11% of 2012 energy production), consumption of each of them is kept constant at starting levels for the duration of our model (25 years). For each scenario, we estimate the total annual CO 2 and CH 4 atmospheric contribution (in Tg) over the course of the transition (see Supplemental Table S3).
Energy data from 2012 was used (BP 2013) instead of the most recent data available (2014;
BP 2015), but using 2014 data would not change our conclusions. The global primary energy consumption in 2014 was 2.7% greater than for 2012, with less than 1% increase in each fossil fuels fraction of the total consumption in 2014. Our modeling results would be only slightly different, and the same outcome at 25 years would be obtained with a slightly higher phaseout of fossil fuels in the earlier years.
In the estimation of these emissions levels, we made the following assumptions: (a) no CO 2 production in operation of solar PV, concentrated PV, wind turbines, or nuclear (IPCC 2007); (b) CO 2 emissions from unconventional NG (via hydraulic fracking) is assumed to be equal to conventional NG (though research suggests that it may be significantly higher due to leakage (Caulton et al 2014;Howarth 2014); the latter estimates that they are equal to or greater than coal, for a few decades after consumption); (c) CO 2 emissions from modern biomass is assumed to be the same as traditional biomass; and, (d) CO 2 emissions from unconventional oil will be comparable to emissions from coal. Details of inputs and assumptions are provided in Supplementary file. Having computed the greenhouse gas contributions to the atmosphere, we estimate the actual ambient concentration of CO 2 and CH 4 in the atmosphere given these fossil fuel derived inputs using a technique described in the Supplementary file. (t) = e (-t/12.4) where G(t)'s represent the concentration of CO 2 and CH 4 respectively, at any given time t after a unit release of each of these gases in the atmosphere at time t = 0. Table S2 (in supplement) provides the incremental atmospheric increases of CO 2 and CH 4 (in ppm) during the transition.
References
With these future atmospheric greenhouse gas concentrations in hand, we determine temperature changes expected in the global atmosphere using modelling techniques developed by Myhrvold and Caldeira (2012). We use a simple one-dimensional heat equation with
Neumann boundary conditions to estimate the impact on climate of GHG emissions.
where f = 0.71 is the fraction of the earth covered by ocean, and, ρ and c p are the density and heat capacity of seawater, respectively. The maximum depth z max is chosen as 4,000 meters. RF(t) is radiative forcing. The calculation of radiative forcing follows the IPCC's approach (IPCC 2013).
The climate sensitivity parameter (λ) is 1.051. The ratio of adjusted radiative forcing to the classical radiative forcing derived from the IPCC formula is 0.775. The thermal diffusivity (kv) is 4.24×10 3 m 2 /s. Please note that, "when appropriately calibrated, these simple equations closely follow the global mean temperature results of more complex 3D coupled atmosphere-ocean simulations" (10) NG: -25% (10); Oil-c: -25% (15) 31% 15%/5%* Note:
Oil-u represents unconventional oil, such as that obtained via tar sand or shale; Oil-c represents conventionally extracted oil NG represents Natural Gas RE represents wind and solar installation *15% for the next 5 years and 5% for the last 10 years 4a-4c differ only in the CH 4 emission value used (0.47 g/MJ, 0.78 g/MJ, 2.48 g/MJ respectively for 4a, 4b and 4c) 5a-5c differ on in the CH 4 emission value used (0.47 g/MJ, 0.78 g/MJ, 2.48 g/MJ respectively for 5a, 5b and 5c)
Budischak et al 2013; Jacobson et al 2015; Fairley, 2015). A big enough array of wind turbines, especially offshore, can likely generate a baseload supply without the need to supplement it with separate storage systems (Kempton et al 2010; Archer and Jacobson, 2007). Further, with the progressive expansion of a combined system of wind, photovoltaics and concentrated solar power in deserts a baseload will be created, simply because the wind is blowing and the sun is shining somewhere in the system linked to one grid (e.g., MacDonald et al 2016; Jacobson 2016). Meanwhile baseload would be supplemented by petroleum, with coal phasing out first, on the way to a completely wind/solar global energy infrastructure. The costs for the challenges of intermittency and grid modernization should be absorbed from savings achieved from energy efficiency/conservation and the reduction of health costs corresponding to progressive reduction in air pollution (UNEP Year Book 2014), with a systematic reduction of the subsidies going to fossil fuels, direct and indirect, estimated to be over $5 trillion/year (Coady et al 2015).
8 deg C in the pipeline as heat already stored in the ocean (Chen and Tung 2014; Rogelj et al 2013) if anthropogenic CO 2 is sequestered from the atmosphere on a continuing basis for roughly 100 years into the future (Cao and Caldeira 2010; Gasser et al 2015); and, (3) the provision of the minimum per capita energy consumption level required to achieve the world standard high life expectancy. There is more than sufficient reserve of the lowest carbon footprint fossil fuel, conventional oil, to make this transition possible. We are not naïve to believe that the formidable political economic obstacles do not exist to implementing this transition. Nevertheless, its chances improved with the news that in 2014 over 100 GW of new wind/solar capacity excluding large hydropower was created (Frankfurt 2015), coupled with the apparent stabilization of global CO 2 emissions from the energy and industrial sector in 2014 and 2015 (Jackson et al 2016).
the expected release of CO 2 and CH 4 in the use of various energy sources; values used in the model used here to determine future atmospheric concentrations of these gases. S2 Model Scenarios, Rates of Growth/Decline per Year Details the annual rates of change of fossil fuels and RE (renewable energy) used in the model over the lifespan of the model. S3 Scenario Output (in 5 year increments) Details the output of the model's seven scenarios with snapshots of annual values each five years during the duration of the transition to nearly 100% RE (or similar percentages of RE as now, in Scenarios 6 and 7) Supplemental text: The amount of CO 2 and CH 4 in the atmosphere at any point in time can be estimated by a convolution of the emissions over time with an impulse response function kernel that describes the atmospheric lifetime of each of the two principal GHGs: m(t)= The change of GHG in atmospheric concentration is: C(t) = m(t)/molarmass/molesinatm/fillfactor where molarmass is molar mass of CO 2 (44.01 g/mol), or CH 4 (16.0426 g/mol). molesinatm is amount of moles in atmosphere, fillfactor is atmospheric to tropospheric abundance, in atmospheric concentration of a given greenhouse gas depends on many factors, including changes in concentrations of other GHGs and in the climate. Nevertheless, following the IPCC we approximate the change in GHG concentrations by a simple impulse response function (Prather, Holmes and Hsu 2012; Joos et al 2013; IPCC 2013).
(
Caldeira and Myhrvold 2012). While the individual contributions of black carbon (warming) and SO 2 (cooling) are large, the net climate effect of black carbon and SO 2 emissions is small, so these impacts on warming are not included, likewise other trace gases (Zhang, Myhrvold and Caldeira 2014).
Figure 1
1Figure 1 Output of seven transition scenarios a. Total Energy Produced (EJ) Globally. b. Percentage of Total Energy that is Renewable Energy (RE). c. Power per capita (global). d. Change in atmospheric CO 2 concentration. e. Change in atmospheric CH 4 concentration. f. Change in global temperature.
Figure 2
2Figure 2 Comparisons of optimal scenarios (4a-c & 5a-c): (a) [ΔCH 4 ] and (b) [ΔT].
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Acknowledgements
We would like to thank Ken Caldeira at Stanford University for his support and counsel during
this project.
Author contributions
Competing financial interests
The authors declare no competing financial interests.
Figure & Table Legend
Figures
1 Output of seven transition scenarios. a. Total Energy Produced (EJ) Globally. b. Percentage of
Total Energy that is Renewable Energy (RE). c. Power per capita (global). d. Change in
atmospheric CO 2 concentration. e. Change in atmospheric CH 4 concentration. f. Change in
temperature (global).
2 Comparisons of optimal scenarios (4a-c & 5a-c): (a) [ΔCH 4 ] and (b) [ΔT].
Tables
1 Comparing RE growth in Scenarios (1-3, 4a & 5a) to those of Schwartzman & Schwartzman
(2011)
Details the rate of growth in RE used in the model used in this research as compared to that
observed in previous research
2 End of Transition Scenario Output Details the output of the model's seven scenarios after 25
years of transition to RE.
Table 1
1Comparisons of RE growth in Scenarios (1-3, 4a & 5a) to those of Schwartzman &
Schwartzman (2011)
Scenarios (1-3, 4a and 5a)
Scenario
Energy Ratio*
(1)
2.08
(2)
1.31
(3)
2.28
(4a)
2.13
(5a)
2.13
Schwartzman & Schwartzman (2011)
EROI
F
f initial
Energy Ratio**
25
0.10
0.020
2.2
20
0.15
0.020
2.5
20
0.11
0.028
2.0
Notes:
(a) EROI = Energy Return On (Energy) Invested
(b) F = percentage of RE capacity that is reinvested annually to build infrastructure of new RE
(c) f initial = percentage of fossil fuel consumption (in 2012) that is reinvested annually to build
infrastructure of RE
(d) Energy Ratio = Computed RE (at 25 years)/Total FF energy used (in year 1; 2012)
*This ER is calculated using different scenario rates of the drawdown of fossil fuel consumption
and investments in RE capacity.
**This ER is calculated from the solar calculator (found at http://solarutopia.org/solar-
calculator/) which uses equations provided in Schwartzman & Schwartzman (2011)
Table 2
2Comparing Scenarios at 25 yearsScenario
Total
Energy
(EJ)
%
RE
Power Avail.
(kW/person)
Annual CO2
Emissions
(Pg)
Annual
CH4
Emissions
(Tg)
[ΔCO2],
ppm
[ΔCH4],
ppb
ΔT, °C
1
1,115
92
4.2
2.3
10.1
40
213
0.29
2
704
87
2.6
2.8
12.1
50
287
0.36
3
1,226
93
4.6
2.8
12.1
50
287
0.36
4a
1,141
93
4.3
1.7
7.0
35
159
0.26
4b
1,141
93
4.3
1.7
7.5
35
207
0.27
4c
1,141
93
4.3
1.7
10.1
35
468
0.36
5a
1,142
93
4.3
1.8
7.4
36
153
0.26
5b
1,142
93
4.3
1.8
8.0
36
190
0.27
5c
1,142
93
4.3
1.8
7.0
36
301
0.31
6
1,115
1
4.2
74
257
104
693
0.60
7
537
2
2.0
36
124
78
483
0.49
Table S1 Constants
S1Statistical Review of World Energy BP June 2013 (Online: http://bp.com/statisticalreview) [consumption multiplied by calorific equivalent] B: World Energy Outlook 2012 IEA p. 104. [Best estimate: 2 mb/day "Extra-heavy oil" (includes Canadian oil sands) = 4.47 EJ] C: Renewables 2013: Global Status Report REN 21 (Online: http://www.ren21.net/REN21Activities/GlobalStatusReport.aspx) D: Hansen, J et al 2013 "Assessing 'Dangerous Climate Change': Required Reduction of Carbon Emissions to Protect Young People, Future Generations and Nature PLOS ONE 8(12) e81648 E: Climate Change 2007: Mitigation of Climate Change 2007 IPCC Cambridge University Press F: EIA, Voluntary Reporting of Greenhouse Gases Program, updated Jan. 31, 2011 (obtained Feb. 20, 2014) G: Hodges A W and Rahmani M 2010 Fuel Sources and Carbon Dioxide Emissions by Electric Power Plants in the United States Report FE796 Undated. University of Florida, IFAS Extension. Note: D&F are background sources. H: Myhrvold N P and Caldeira K 2012 Greenhouse gases, climate change and the transition from coal to low-carbon electricity Env. Res. Lett. 7 014019. I1: Coal mining, 2013, EPA (Online: http://www.epa.gov/climatechange/Downloads/EPAactivities/MAC_Report_2013-II_Energy.pdf) I2: Howarth R W 2015 Methane emissions and climatic warming risk from hydraulic fracturing and shale-gas development: implications for policy Energy and Emission Control Technologies 3 45-5 J: IPCC 2006 Guidelines for National Greenhouse Gas Inventories (Online: http://www.ipccnggip.iges.or.jp/public/2006gl/vol2.html) K: Role of Alternative Energy Sources: Hydropower Technology Assessment. 2012 National Energy Technology Laboratory DOE/NETL-2011/1519Used in CO 2 /CH 4 Model
2012
Consumption CO 2 emissions
Sources for
CO 2
CH 4
emissions
Sources for
CH 4
EJ/yr
g/MJ
g/MJ
Coal
156.7
92
A,E
0.18
I1
Natural Gas
125.5
52.4
A,E
0.47
0.78
2.48
I1
I2
I2
Oil
Oil (conventional)
169.5
76.3
A,E
0.18
I1
Oil (unconventional--tar sand)
4.0
92
A,B,E,F
0.18
I1
Uranium
23.5
0
A, G
0
H
Hydropower
31.2
4.69
K (C, G)
0.06
K
Geothermal
2.5
7.14
C, G
0
H
Wind
8.9
0
C, G
0
H
Solar (electricity)
3.3
0
0
H
Photovoltaic (PV)
3.2
0
C, G
0
H
Concentrated
0.1
0
C, G
0
H
Solar (hot water)
8.0
0
C, G
0
H
Biofuels
3.8
49.5
0.01
J
Biodiesel
0.8
49.5
C, G
0.01
J
Ethanol
3.0
49.5
C, G
0.01
J
Biomass
11.9
83.8
0.30
J
Modern
2.6
83.8
C, G
0.30
J
Traditional
9.2
83.8
C, G
0.30
J
Sources:
A:
Table S2 Model
S2Scenarios, Rates of Growth/Decline per YearScenario
Coal & Oil-u
NG & Oil-c
RE
First 15 yrs
Next 10 yrs
First 10-15 yrs
(in parentheses)
Next 10-15 yrs
(in parentheses)
First 10 yrs Next 15 yrs
1
-8%
-25%
-2% (15)
-25% (10)
25%
10%
2
-8%
-25%
2% (15)
-25% (10)
10%
10%
3
-8%
-25%
2% (15)
-25% (10)
25%*
5%*
4a
-8%
-25%
-1% (10)
-25% (10)
31%
15%/5%*
4b
-8%
-25%
-1% (10)
-25% (15)
31%
15%/5%*
4c
-8%
-25%
-1% (10)
-25% (15)
31%
15%/5%*
5a
-8%
-25%
NG: -8% (15);
Oil-c: 2% (10)
NG: -25% (10);
Oil-c: -25% (15)
31%
15%/5%*
5b
-8%
-25%
NG: -8% (15);
Oil-c: 2% (10)
NG: -25% (10);
Oil-c: -25% (15)
31%
15%/5%*
5c
-8%
-25%
NG: -8% (15);
Oil-c: 2%
Table S3 Scenario
S3Output Scenario 1Year
Total Energy
(EJ)
% RE
Power Avail.
(kW/person)
Annual CO 2
Emissions
(Pg)
Annual CH 4
Emissions
(Tg)
[ΔCO 2 ]
(ppm)
[ΔCH 4 ]
(ppb)
ΔT
(°C)
0
537
2
2.4
35.5
124
0
0
0.000
5
526
16
2.3
28.6
105
18
173
0.077
10
643
41
2.7
23.6
91
30
263
0.162
15
762
56
3.0
19.8
80
38
304
0.232
20
809
83
3.1
6.0
25
41
281
0.279
25
1,115
92
4.2
2.3
10
40
213
0.293
Scenario 2
0
537
2
2.4
35.5
124
0
0
0.000
5
561
11
2.4
32.5
123
19
184
0.081
10
629
21
2.6
31.4
127
34
309
0.179
15
747
31
3.0
31.7
134
47
401
0.276
20
553
70
2.1
7.8
33
52
381
0.344
25
703
87
2.6
2.8
12
50
287
0.364
Scenario 3
0
537
2
2.4
35.5
124
0
0
0.000
5
585
14
2.5
32.5
123
19
184
0.081
10
761
35
3.1
31.4
127
34
309
0.179
15
1,220
58
4.9
31.7
134
47
401
0.276
20
1,066
84
4.1
7.8
33
52
381
0.344
25
1,226
93
4.6
2.8
12
50
287
0.364
Scenario 4a
0
537
2
2.4
35.5
124
0
0
0.000
5
551
17
2.4
29.5
110
18
175
0.078
10
755
46
3.1
25.3
99
31
274
0.166
15
840
79
3.3
9.6
33
36
277
0.228
20
939
90
3.6
3.2
12
36
217
0.252
25
1,141
93
4.3
1.7
7
35
159
0.258
Scenario 4b
0
537
2
2.4
35.5
163
0
0
0.000
5
551
17
2.4
29.5
147
18
232
0.085
10
755
46
3.1
25.3
134
31
366
0.181
15
840
79
3.3
9.6
41
36
369
0.248
20
939
90
3.6
3.2
14
36
286
0.271
25
1,141
93
4.3
1.7
8
35
207
0.274
Scenario 4c
0
537
2
2.4
35.5
376
0
00
0.000
5
551
17
2.4
29.5
349
18
544
0.123
10
755
46
3.1
25.3
327
31
870
0.258
15
840
79
3.3
9.6
87
36
875
0.347
20
939
90
3.6
3.2
25
36
664
0.368
25
1,141
93
4.3
1.7
10
35
468
0.360
Scenario 5a
0
537
2
2.4
35.5
124
0
0
0.000
5
541
18
2.3
29.6
97
18
166
0.077
10
749
47
3.1
26.2
81
31
244
0.162
15
862
77
3.4
11.1
40
37
252
0.225
20
944
89
3.6
3.5
14
37
206
0.253
25
1,142
93
4.3
1.8
7
36
153
0.260
Scenario 5b
0
537
2
2.4
35.5
163
0
0
0.000
5
541
18
2.3
29.6
123
18
215
0.083
10
749
47
3.1
26.2
98
31
309
0.173
15
862
77
3.4
11.1
51
37
316
0.239
20
944
89
3.6
3.5
16
37
259
0.267
25
1,142
93
4.3
1.8
8
36
190
0.273
Scenario 5c
0
537
2
2.4
35.5
124
0
0.0
0.000
5
541
18
2.3
29.6
110
18
391
0.106
10
749
47
3.1
26.2
99
31
519
0.211
15
862
77
3.4
11.1
33
37
516
0.282
20
944
89
3.6
3.5
12
37
423
0.310
25
1,142
93
4.3
1.8
7
36
301
0.311
Scenario 6
0
537
2
2.4
35.5
124
0
0
0.000
5
526
2
2.3
34.7
121
19
181
0.081
10
643
2
2.7
42.5
148
37
314
0.187
15
762
2
3.0
50.3
176
57
447
0.313
20
809
1
3.1
53.5
187
78
560
0.451
25
1,115
1
4.2
73.7
257
104
693
0.603
Scenario 7
0
537
2
2.4
35.5
124
0
0
0.000
5
537
2
2.3
35.5
124
20
181
0.083
10
537
2
2.2
35.5
124
36
309
0.188
15
537
2
2.1
35.5
124
51
391
0.292
20
537
2
2.1
35.5
124
65
446
0.392
25
537
2
2.0
35.5
124
78
483
0.488
Note: RE represents "solar" renewable energy (including wind, photovoltaics, and CSP)
| sample_1917 | 0.9999 | arxiv | |
Theoretical foundations of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models
2 Nov 2018
Mark S Williamson
Exeter Climate Systems
College of Engineering, Mathematics and Physical Sciences
University of Exeter
Laver Building, North Park RoadEX4 4QEExeterUK
Peter M Cox
Exeter Climate Systems
College of Engineering, Mathematics and Physical Sciences
University of Exeter
Laver Building, North Park RoadEX4 4QEExeterUK
Femke J M M Nijsse
Exeter Climate Systems
College of Engineering, Mathematics and Physical Sciences
University of Exeter
Laver Building, North Park RoadEX4 4QEExeterUK
Theoretical foundations of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models
2 Nov 2018(Dated: 5 November 2018)Equilibrium climate sensitivityemergent constraintglobal temperature variabilityfluctuation- dissipation theorem
Background: The emergent constraint approach has received interest recently as a way of utilizing multimodel General Circulation Model (GCM) ensembles to identify relationships between observable variations of climate and future projections of climate change. These relationships, in combination with observations of the real climate system, can be used to infer an emergent constraint on the strength of that future projection in the real system. However, there is as yet no theoretical framework to guide the search for emergent constraints. As a result, there are significant risks that indiscriminate data-mining of the multidimensional outputs from GCMs could lead to spurious correlations and less than robust constraints on future changes. To mitigate against this risk, Cox et al 1 (hereafter CHW18) proposed a theory-motivated emergent constraint, using the one-box Hasselmann model to identify a linear relationship between equilibrium climate sensitivity (ECS) and a metric of global temperature variability involving both temperature standard deviation and autocorrelation (Ψ). A number of doubts have been raised about this approach, some concerning the application of the one-box model to understand relationships in complex GCMs which are known to have more than the single characteristic timescale.Objectives: To study whether the linear Ψ-ECS proportionality in CHW18 is an artefact of the one-box model. More precisely we ask 'Does the linear Ψ-ECS relationship feature in the more complex and realistic two-box and diffusion models?'.Methods:We solve the two-box and diffusion models to find relationships between ECS and Ψ. These models are forced continually with white noise parameterizing internal variability. The resulting analytical relations are essentially fluctuation-dissipation theorems.Results: We show that the linear Ψ-ECS proportionality in the one-box model is not generally true in the two-box and diffusion models. However, the linear proportionality is a very good approximation for parameter ranges applicable to the current state-of-the-art CMIP5 climate models. This is not obviousdue to structural differences between the conceptual models, their predictions also differ. For example, the two-box and diffusion, unlike the one-box model, can reproduce the long term transient behaviour of the CMIP5 abrupt4xCO2 and 1pcCO2 simulations. Each of the conceptual models also predict different power spectra with only the diffusion model's pink 1/f spectrum being compatible with observations and GCMs. We also show that the theoretically predicted Ψ-ECS relationship exists in the piControl as well as historical CMIP5 experiments and that the differing gradients of the proportionality are inversely related to the effective forcing in that experiment.Conclusions:We argue that emergent constraints should ideally be derived by such theory-driven hypothesis testing, in part to protect against spurious correlations from blind data-mining but mainly to aid understanding. In this approach, an underlying model is proposed, the model is used to predict a potential emergent relationship between an observable and an unknown future projection, and the hypothesised emergent relationship is tested against an ensemble of GCMs.
find a relationship via a scatter plot between an observable plotted on the x axis and the future projection plotted on the y axis, each point on the plot being one member of the model ensemble. The model ensemble derived relationship or emergent relationship, and the uncertainty in it, can then be determined from regression on the scatter plot. A measurement of the observable in the real world can be combined with the model-derived emergent relationship to produce an emergent constraint on the climate projection. Hall and Qu 3 published one of the first emergent constraints relating the strength of the snow albedo feedback in the seasonal cycle (the observable) to the strength of the snow albedo feedback in climate projections within the multimodel ensemble used in IPCC AR4 5 . Since then many others have been published including studies on sea-ice 6,7 , tropical precipitation extremes 8 , equilibrium climate sensitivity (ECS) 1, [9][10][11][12] , carbon loss from tropical land under warming 13 , zonal shift of Southern Hemisphere westerlies 14 , cloud feedbacks [15][16][17][18][19][20] , strengthening of the hydrological cycle 21 , the climate-carbon cycle feedback 22 and CO 2 fertilization effect 23 , future changes in ocean net primary production 24 , permafrost melt 25 , and changes in natural sources and sinks of CO 2 26 .
Some scepticism about emergent constraints is healthy, particularly when they are not founded on well understood physical processes. There are significant risks that indiscriminate data-mining of the multidimensional outputs from models could lead to spurious correlations 27 and less than robust constraints on future changes 28 . Care is also needed drawing statistical inferences from ensembles of small numbers of models. The problem is compounded if models within the ensemble share common components giving a smaller effective ensemble size [29][30][31] . Observations used to guide model development also may lead to dependencies 32 .
To minimise these risks, a theoretical framework for finding and evaluating emergent constraints is needed. The approach described here involves a form of hypothesis testing, in which an underlying simple, conceptual model is proposed, the model is used to predict an emergent relationship between an observable and an unknown future projection, and the predicted emergent relationship is tested against results from an ensemble of more complex models. Emergent relationships are usually assumed to be univariate and linear, but these are not necessary simplifications.
As an example, we illustrate this theory led approach using simple conceptual models of the global mean temperature as emergent constraints on ECS and test the theoretically predicted relations against observations and the CMIP5 models.
In CHW18, the theoretical linear relationship between a measure of the variability of annual mean global surface air temperature, the observable Ψ, and the equilibrium climate sensitivity (the future projection) was used to derive an emergent constraint on ECS. Colman and Power 33 also found a correlation between the tropical decadal temperature standard deviation and ECS in the CMIP5 models. A number of doubts have been raised about CHW18 34-37 , some concerning the theory and the application of the one-box model to understand relationships in complex GCMs which are known to have more than the single characteristic timescale 38,39 . In section II we investigate whether the relation in CHW18 derived for the one-box model still holds in more realistic yet still analytically soluble conceptual models, namely the often used two-box and diffusion models. It is known the two-box and diffusion models unlike the onebox model are able to reproduce the long term transient behaviour of the CMIP5 GCM abrupt4xCO2 and 1pcCO2 simulations 39,40 . Although we find the one-box linear proportionality between Ψ and ECS is generally no longer true in the two-box and diffusion models, we show the linear proportionality holds to a good approximation for both when the range of their parameters are applicable to the complex CMIP5 GCMs. This gives us increased confidence in the theoretical foundation of CHW18.
It is important to note that each of these conceptual models differ structurally, predict different temperature responses and will not be able to reproduce all of the features of the global mean temperature response. One could loosely view these conceptual models as zeroth order approximations and GCMs as higher order approximations of the real world. The often used quote 'all models are wrong but some are useful' is quite apt as a guiding principle for this manuscript. The usefulness of the model will depend on the question asked of it.
In section III conceptual model predictions are compared with the CMIP5 ensemble and observations, particularly the power spectra and autocorrelation functions. The pink power spectrum of global mean temperature in observations and CMIP5 models can only be reproduced by the diffusion model. However, if one is interested in the shorter time scale behaviour for use as an emergent constraint on ECS, we find the simplest conceptual one-box model will serve as a good approximation.
Also in section III Ψ vs ECS emergent relationships for both piControl and historical CMIP5 experiments are shown. Both have the theoretically predicted linear proportionality although they have differing gradients. This difference in gradient is theoretically expected to scale inversely with the effective forcing and this is also observed in the CMIP5 models.
The current paper can be seen as a companion paper to CHW18, as it examines and tests the appropriateness of the theory used to inform that study.
II. CONCEPTUAL MODELS RELATING GLOBAL TEMPERATURE VARIABILITY TO EQUILIBRIUM CLIMATE SENSITIVITY
Caldeira and Myhrvold 40 (hereafter CM13) fitted three different conceptual models, namely the one-box, two-box and diffusion models to the annual global mean air temperature time series of the CMIP5 abrupt4xCO2 experiments 4 . These fits were then tested against the 1pcCO2 CMIP5 experiments. CM13 showed that while the one-box model was a poor fit to either experiment on longer timescales both the two-box and diffusion models did good jobs. Here we use these conceptual models to analyse the annual global mean air temperature variability in the CMIP5 historical experiments with a view to obtaining ECS as a function of Ψ as found in CHW18 for the one-box model.
Each of the conceptual models have differing numbers of free parameters, the one-box and diffusion model have three and the two-box has five. None of these are assumed to be fixed. These parameters are essentially fitted to each of the CMIP5 models and the observations in the historical period via Ψ (introduced in equation 12). The models are introduced in order of complexity and completeness, the one-box being the simplest analytically while the diffusion model is harder to solve but reproduces more of the observed temperature response.
The historical time series can be approximated as the sum of the responses to the forcing resulting from changes in the atmospheric composition. These include greenhouse gases, tropospheric and stratospheric aerosols from large volcanic eruptions and solar variability. There is also a response to fast, internal variability which is parameterized here as the response to random, white noise forcing. We seek to isolate the response to the latter and relate it to equilibrium climate sensitivity (ECS). A relation between the system response to random fluctuations and its sensitivity, is essentially a fluctuation-dissipation theorem (FDT) 41,42 .
ECS is defined as the equilibrium temperature change due to the constant forcing Q 2×CO2 from the doubling of CO 2 ,
ECS = Q 2×CO2 λ ,(1)
and λ is the climate feedback factor. Linearity of the conceptual models allows each temperature response T i (t) to each forcing Q i (t) to be added to give the total response i.e. if the total forcing is Q(t) = i Q i (t) then the total temperature response is just the sum of the temperature responses to each of the individual forcings T (t) = i T i (t) (principle of superposition). Linearity means that by suitable detrending the response from the trend in emissions can be removed from the total temperature response to leave the residual response, ∆T (t), to the random forcing. For this study, we assume this detrending can be carried out to a good approximation and work with just the residual temperature. For notational ease we also refer to ∆T as T i.e. ∆T := T .
Although the theory we derive here assumes external, random forcing, we have shown that the Ψ-ECS linear proportionality will theoretically become more tightly defined in the presence of common (non-random) forcing across a model ensemble 37 . The gradient of the relationship does however change, being roughly inversely proportional to the amplitude of the forcing (see section III).
The superposition principle implies the response to any forcing can be written as the convolution of the linear response function g(t) (the response to delta function forcing) with the forcing i.e.
T (t) = t 0 g(t − s)Q(s)ds.
(2)
Each model can therefore be characterized by g(t). We will be interested in their response in the stationary limit i.e. when t ≫ τ where τ is the longest timescale in the model. The residual response is found when Q(t) is a Gaussian random variable with zero mean and a standard deviation of σ Q , Q(t) = σ Q dW t , turning equation 2 into a stochastic integral
T (t) = σ Q t 0 g(t − s)dW s(3)
where W s is a Wiener process.
In the following we choose to use the two observables variance σ 2 T and autocorrelation α T (t) as fitting parameters for the conceptual models as they can be easily estimated for a given time series, be it a CMIP5 model or observations. These can be computed for the residual temperature by using equation 3 and the relevant model g(t) via the autocovariance R(t)
R(t) = lim P →∞ 1 P P 0 T (s − t)T (s)ds.
(4)
σ 2 T = R(0),(5)α T (t) = R(t) R(0) .(6)
Another useful quantity we use to compare the simple models to the CMIP5 models and observations is the power spectrum of T , |T (ω)| 2 , which can be found from the Fourier transform of the autocovariance
|T (ω)| 2 = ∞ −∞ R(t)e −iωt dt.(7)
A. Hasselmann one-box model
The simplest, one-box (or one-timescale) model for the evolution of T (t) is
C dT dt = Q(t) − λT(8)
In this model the climate system can be thought of as a single well-mixed box with effective heat capacity C forced by Q(t) and adjusting to this forcing with climate sensitivity λ proportional to the temperature anomaly. The single well-mixed box can be roughly thought of as representing the atmosphere, surface mixed ocean layer and the land. The linear response function for this model is
g(t) = Θ(t) e − t τ H λτ H(9)
where the timescale in the model τ H = C λ and Θ(t) is the Heaviside step function. When the forcing Q(t) is Gaussian white noise, equation 8 is known as the Hasselmann model 43 . Variance and autocorrelation for the one-box model can be computed from equations 3 and 4 to be
σ 2 T = σ 2 Q 2λ 2 τ H ,(10)α T (t) = e − |t| τ H .(11)
These equations can be combined with equation 1 to give 1
ECS = √ 2 Q 2×CO2 σ Q Ψ,(12)
where Ψ is defined as
Ψ = σ T √ − log α 1T ,(13)
and α 1T = α T (1 year). It was equation 12, namely the linear proportionality between the observable Ψ, estimated from timeseries of T and the future projection ECS, that was used to guide the search for an emergent constraint in CHW18. The magnitude of proportionality between Ψ and ECS, the ratio of the effective forcing due to doubling CO 2 and the mean amplitude of the effective forcing in the experiment σ Q , √ 2 Q2×CO 2 σQ cannot be observed but is fortunately weakly correlated to ECS (r = −0.02) across the CMIP5 model ensemble 1 . By linearly regressing Ψ against ECS, the magnitude of proportionality is therefore determined by the model ensemble itself.
The power spectrum of the one-box model is
|T (ω)| 2 = σ 2 Q λ 2 (1 + ω 2 τ 2 H ) .(14)
This model predicts a red power spectrum temperature response, that is, the power scales inversely to the square of the forcing frequency ω.
B. Two-box model
The two-box model 39,44,45 consists of two well-mixed layers, one representing the upper mixed layer of the ocean plus the lower atmosphere, with effective heat capacity C and temperature T , and a second well-mixed box representing the deep ocean with heat capacity C 0 and temperature T 0 . Heat transport between the two boxes is proportional to the temperature difference between the two boxes with constant of proportionality γ. The equations describing the evolution of temperature are therefore
C dT dt = Q(t) − λT − γ(T − T 0 ),(15)C 0 dT 0 dt = γ(T − T 0 ).(16)
This model has a two timescales, a fast τ f and slow one τ s . The linear response function is the sum of the fast and slow modes with amplitudes a f τ f and as τs ,
g(t) = Θ(t) λ a f τ f e − t τ f + a s τ s e − t τs .(17)
This model has been extensively used in previous climate applications and here we use the notation and expressions for the amplitudes and timescales in terms of the quantities in equation 15 as given in Geoffroy et al 39 . They also fitted this model to abrupt4xCO2 CMIP5 experiments for which they found two widely separated timescales, typical values being τ f ∼ 4 yrs and τ s ∼ 250 yrs while the dimensionless mode parameters, a f and a s , were roughly of equal size (a f ∼ 3/5 and a s ∼ 2/5). The autocovariance function for Gaussian white noise forcing can be found by using equations 3 and 4 and in contrast to the one-box model features two modes:
R(t) = σ 2 Q 2λ 2 a 2 f τ f e − |t| τ f + a 2 s τ s e − |t| τs + 2a f a s τ f + τ s e − |t| τ f + e − |t| τs(18)
giving
σ 2 T = σ 2 Q 2λ 2 a 2 f τ f + a 2 s τ s + 4a f a s τ f + τ s ,(19)α T (t) = (a 2 f τ s e − |t| τ f + a 2 s τ f e − |t| τs )(τ f + τ s ) + 2a f a s τ f τ s (e − |t| τ f + e − |t| τs ) (a 2 f τ s + a 2 s τ f )(τ f + τ s ) + 4a f a s τ f τ s .(20)
This general result simplifies for typical fitted parameters to the CMIP5 models 39 as the variance and the autocorrelation are dominated by the fast mode. These can be approximated in the limit (τ s ≫ τ f , a s ∼ a f ) by:
σ 2 T ≈ σ 2 Q a 2 f 2λ 2 τ f ,(21)α T (t) ≈ e − |t| τ f .(22)
The approximate expressions are therefore very similar to the one-box model for the CMIP5 models. Combining these expressions with the equation for ECS gives
ECS = √ 2 Q 2×CO2 σ Q a f Ψ(23)
so that the linear relationship between Ψ and ECS found in the one-box model also approximately holds for the twobox model. The constant of proportionality is however different, it has an extra factor in the denominator a f , which is roughly constant and is approximately a f ∼ λ/(λ + γ) over the CMIP5 model range of parameters. Relative standard deviation in a f is 13%. The reason for the approximate equivalence between the ECS relations in one-and two-box models is due to the wide separation in timescales between the two modes fitted to the CMIP5 models. As in the one-box case, the 'constant' of proportionality between ECS and Ψ, √ 2
Q2×CO 2 σQa f is weakly correlated to ECS (r = 0.03) across the CMIP5 models and one can linearly regress Ψ against ECS for a theoretical emergent relationship.
In contrast to the one-box, the two-box power spectrum is
|T (ω)| 2 = σ 2 Q λ 2 1 + ω 2 (a f τ s + a s τ f ) 2 (1 + ω 2 τ 2 f )(1 + ω 2 τ 2 s ) .(24)
which, depending on the size of terms can give red and ω −4 scaling although when fitted to the CMIP5 models, the spectrum is approximately red.
C. Diffusion equation
The diffusion equation (or heat equation) model 38,40 consists of a continuous vertical layer, z ≥ 0, where radiative forcing at the surface (z = 0) causes heating which is transported down through the water column by diffusion (parameterized by diffusivity D), representing heat uptake by the deep ocean. A mixed-layer surface box has also been added in previous studies to add realism 46-48 although here we use just the diffusion equation for simplicity. The model is described by a partial differential equation:
∂T ∂t = D ∂ 2 T ∂z 2(25)
with flux boundary conditions
−ρc p D ∂T ∂z z=0 = Q(t) − λT (0, t),(26)∂T ∂z z=zmax = 0.(27)
where ρ and c p are the density and specific heat capacity of water respectively. The maximal depth of the ocean, z max , is taken to be infinite. The temperature is now a function of both depth and time, T (z, t) although our interest is only in the surface temperature T (0, t).
In contrast to the one-and two-box models, the ocean is modelled as a vertical continuum rather than a finite number of well-mixed boxes. As heat is diffused down the water column with time, the effective heat capacity increases as the heat sees more ocean. This model can also be thought of as an M -box model where M is very large and each well-mixed box is very thin resulting in a continuum of (M ) timescales. The diffusion model reduces to a one-box model when times of interest are larger than the time taken for heat to be well diffused throughout the water column i.e. when t > z 2 max /D. For ocean depths of z max = 4000 m and typical diffusivities of D = 5 × 10 −5 m 2 s −1 this happens when t > 10,000 years and so this limiting case is not met for the application here.
The linear response function for surface temperature T (0, t) can be found using Laplace transforms on equations 25 and 26 to be
g(0, t) = Θ(t) λ 1 √ πτ D t − e t τ D τ D erfc t τ D(28)
A timescale, τ D , can be identified in this model as τ D = ρ 2 c 2 p D λ 2 . τ D ∼ 25 years for the mean value of D found in CM13 40 . One needs to be aware of an unphysical infinity in g(0, t) at t = 0 because of the time dependence of the effective heat capacity. At t = 0 this results in zero effective heat capacity and therefore an infinite response. In reality energy is not absorbed in an infinitely thin surface layer and thus care needs to be taken when calculating at t = 0.
The power spectrum at the surface can be also be found using either Laplace or Fourier transforms. This is given by
|T (0, ω)| 2 = σ 2 Q λ 2 1 1 + 2|ω|τ D + |ω|τ D .(29)
The diffusion model therefore predicts a pink spectrum i.e. power scales inversely proportional to ω −1 in contrast to the red spectra predicted by the one-and two-box models.
To obtain the autocovariance function at z = 0 we start with the power spectrum and Fourier transform it using equation 7:
R(t) = σ 2 Q 2λ 2 τ D e − t τ D erfi t τ D + 1 π E 1 − t τ D − e t τ D erfc t τ D − 1 π E 1 t τ D(30)
this rather long exact expression can be well approximated more compactly as
R(t) ≈ 2σ 2 Q πλ 2 τ D E 1 πt τ D (31) where the exponential integral E 1 (x) is defined as E 1 (x) = ∞ x e −t t dt.
Unfortunately R(t = 0) = σ 2 T is also infinite because of the unphysical zero effective heat capacity. σ 2 T can however be approximated by taking a very small but finite time, t 0 . Starting with equation 31 and Taylor expanding the exponential integral to zeroth order around t = 0 results in
σ 2 T ≈ 2σ 2 Q πλ 2 τ D −γ EM − log πt 0 τ D (32) ≈ c 0 σ 2 Q πλ 2 τ 1−c 0 c 0 D(33)
where c 0 = −2γ EM −log(πt 0 ), γ EM ≈ 0.577 is the Euler-Mascheroni constant and in the second line, the approximation log x = c 0 x 1 c 0 − c 0 has been used. This approximation gets better for larger c 0 (smaller t 0 ). So for small t 0 34) and the autocorrelation function is
σ 2 T → c 0 σ 2 Q πλ 2 τ D(α T (t) ≈ 2 c 0 E 1 πt τ D(35)
which is purely a function of τ D . Rearranging equation 34 and combining with the equation for ECS (eq 1) gives
ECS = π c 0 Q 2×CO2 σ Q Ψ D(36)
where
Ψ D = σ T √ τ D .(37)
Or in terms of observables
Ψ D = σ T √ π E −1 1 c0α1T 2(38)
where E −1 1 (x) is defined as the inverse of the exponential integral. The linear Ψ-ECS proportionality is not true for the diffusion model. However, comparing eq. 37 with similar for one-and two-box models (eq. 13), if
√ τ D ∝ 1 √ − log α 1T(39)
is approximately true then the linear ECS-Ψ proportionality is also approximately true for the diffusion model. By plotting one against the other in figure 1 this is the case for the range of values of τ D applicable to CMIP5 models (τ D ∈ [10, 60] years in CM13). α 1T is calculated from the exact formula, equation 30.
III. COMPARISON WITH CMIP5 MODELS AND OBSERVATIONS
Theoretical autocorrelation functions and power spectra predicted by the conceptual models are shown in figure 2 for typical values found in fits to the CMIP5 models 39,40 . One-and two-box autocorrelation functions and power spectra are very similar for timescales less than 100 years. Power spectra in these models have the same |T (ω)| 2 ∝ ω −2 red power spectra. In contrast to the box models, the diffusion model has a faster drop off in autocorrelation but a slower approach to equilibrium and a power spectrum that predicts a |T (ω)| 2 ∝ ω −1 pink power spectrum.
For comparison with the conceptual plots, the CMIP5 historical runs (coloured lines) and the HadCRUT4 historical observational dataset 49 (thick black line) are shown in figure 3. The power spectra of the HadCRUT4 observations and CMIP5 models show approximately a |T (ω)| 2 ∝ ω −1 pink spectrum most closely resembled by the diffusion model. The dotted white line is shown as a guide to this proportionality. High sensitivity CMIP5 models also generally have higher autocorrelation. The HadCRUT4 autocorrelation is more representative of the low sensitivity models, consistent with the findings of CHW18.
We have used detrended CMIP5 historical simulations as a comparison to observations can also be made and an emergent constraint obtained. However, conceptual model theoretical relations have been derived assuming white noise external forcing as a parameterization of internal variability. The CMIP5 piControl experiments are the closest analogue to this simplification and one may wonder whether the same relations hold in these experiments as it is known the forced response may not always be the same as the response to internal variability 50,51 . Power spectra and autocorrelation functions for the piControl experiments are broadly the same as figure 3 (not shown). The linear Ψ-ECS emergent relationships are also similarly strong in both piControl and historical simulations having correlations of r = 0.68 and r = 0.77 respectively. The higher correlation in the historical experiment resulting in a reduced uncertainty emergent constraint is theoretically expected when there is common forcing across the model ensemble (see Cox et al 37 ). In this case the common forcing in the historical experiment is provided by the increasing concentrations of greenhouse gases, aerosols and volcanic eruptions.
There are differences in the emergent relationships however. In figure 4 (a) the emergent relationships for the piControl and historical have different gradients. This is due to increased effective forcing in the historical simulations from residual volcanic, aerosol and greenhouse gas forcing remaining after the detrending procedure. table I). The emergent relationship is calculated between 1880-2015 for the historical experiment and for the first 135 years of piControl using the same methodology of CHW18. The gradient of the emergent relationship (dashed line) is theoretically predicted to be smaller with increased forcing in the experiment. This is why the historical run with its volcanic, greenhouse gas, aerosol and internal forcing has a shallower gradient than the control run. (b) is the same plot with Ψ renormalized by the estimated forcing from σN , the standard deviation of the top-of-atmosphere radiative forcing. Emergent relationships then have a very similar gradient illustrating the inverse proportionality of the gradient to the forcing in (a). the CMIP5 models from the net top-of-atmosphere radiative flux N where N ≈ Q − λT with standard deviation σ N .
IV. DISCUSSION AND CONCLUSIONS
All three conceptual models have both physical similarities and deficiencies relative to the CMIP5 models and the real Earth system. The one-box model only really has any physical justification when the timescales of interest are dominated by the well-mixed atmosphere and ocean surface layer. This has led some to question the use of the onebox model by CHW18 to motivate their emergent constraint between equilibrium climate sensitivity (ECS) and Ψ, a statistic dominated by the fast timescale processes e.g. Rypdal et al 36 . However, in this paper we have shown that a near-linear relationship is to be expected between ECS and Ψ for more realistic conceptual models. For the oneand two-box models we were able to find analytical relations to show this. Semi-analytical relations for the diffusion model also show a similar near linear relationship.
Even though a linear proportionality between Ψ and ECS is expected in the conceptual models for regions of parameter space applicable to CMIP5 models, each of the conceptual models predicts different temperature responses. The one-box model cannot reproduce the long timescale behaviour of the two-box or diffusion model and neither the one-or two-box models can mimic the observed and CMIP5 power spectra. Of the three, the diffusion model reproduces the power spectra of the CMIP5 models and the observations most closely although it is more difficult to work with and has some deficiencies as an analogue to the real climate system. Combining a well-mixed atmosphere-surface ocean box with a diffusive continuous deep ocean [46][47][48] , although adding another layer of complexity and making the model less analytically amenable, would add physical realism. We suspect this would produce a similar linear relation to the one-and two-box models as well as mimicking the CMIP5 and HadCRUT4 power spectra due to the timescale separation between surface mixed and deep layers.
In conceptual models, we therefore expect to find emergent relationships between ECS and short-term variability (e.g. as measured by Ψ). However, the underlying models considered here remain deliberately very simple compared to the GCMs we are using to define emergent constraints. It is therefore vital that we continue to check that our conceptual models provide useful insights into the spread of projections from GCMs. We see this as a form of hypothesis testing, in which a conceptual model is proposed, an emergent relationship between variability and sensitivity is predicted based-on that conceptual model, and then that predicted emergent relationship is checked against the ensemble of full-form GCMs. This approach requires that the search for emergent constraints becomes more theory-led than it has been to date, but would also guard against spurious relationships that could easily arise from blind data-mining of the many diagnostics available from modern GCMs. Most importantly, in our view, such theory-led hypothesis testing is much more likely to improve understanding of the climate system than purelystatistically-derived emergent constraints.
−
log α 1Tfor the diffusion model. If these two functions are linearly proportional then Ψ is also linearly proportional to ECS for the diffusion model. Although it is slightly nonlinear, for this range of values (solid line) linearity seems to be a good approximation (dotted line). α1T is calculated from the exact formula, equation 30 with t0 = 10 −6 yrs (∼ 1 min) and τD ∈[10, 60] years. This spans the range of values of τD found in fits to CMIP5 models 40 .
FIG. 2 .
2From equation 12 an inverse relationship with the magnitude of the effective forcing σ Q is expected. When Ψ is divided by the estimated forcing, σ N ∼ σ Q , in figure 4 (b) gradients are very similar. Forcing has been inferred in Autocorrelation, αT (t), (left) and power spectrum, |T (ω)| 2 , (right) for the three conceptual models. λ = σQ = 1 are the same in all curves, while τ = τ f = 4 yrs for the one-and two-box models. For the two-box model τs = 250 yrs and a f = 3/5, as = 2/5 (these are the mean values found by Geoffroy et al 39 in fits to the CMIP5 models). For the diffusion model τD = 25 years. Power spectra and autocorrelation functions are roughly the same for one-and two-box models at timescales less than a decade. For short periods, the diffusion model has a |T (ω)| 2 ∝ ω −1 (power proportional to period) pink spectrum whereas the one-and two-box models show a |T (ω)| 2 ∝ ω −2 (power proportional to the square of the period) red spectra.
FIG. 3 .
3Autocorrelation, αT (t), (left) and power spectrum, |T (ω)| 2 , (right) for the CMIP5 model historical runs. The CMIP5 models used are the same as in CHW18 1 . Red lines are higher sensitivity models (λ < 1 W m −2 K −1 ) while blue lines are lower sensitivity models (λ ≥ 1 W m −2 K −1 ). The black line is the (historical) HadCRUT4 observational dataset. The white dotted line in the right hand power spectrum plot is a guide to show the |T (ω)| 2 ∝ ω −1 pink spectrum predicted by the diffusion model. The power spectra have been smoothed with a 25 point moving average window. . 4. (a) ECS vs Ψ emergent relationships in the historical (blue) and piControl (black) CMIP5 experiments. Each letter plotted is a CMIP5 model and corresponds to the same used in CHW18 (model-letter correspondence is given in
ACKNOWLEDGMENTS
This work was supported by the EU Horizon 2020 Research Programme CRESCENDO project, grant agreement number 641816 (P.M.C. and M.S.W.); the EPSRC-funded ReCoVER project (M.S.W.); the European Research Council (ERC) ECCLES project, grant agreement number 742472 (P.M.C. and F.J.M.M.N.); We also acknowledge the World Climate Research Programmes Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups for producing and making available their model output. and V. Lucarini, "Fluctuations, response, and resonances in a simple atmospheric model,"
TABLE I .
ICMIP5 models used in figure 4 (letters in the first column identify the models) and in CHW18. Values are taken from IPCC AR5 table 9.5 52 .ModelECS (K) λ (W m −2 K −1 ) Q2×CO 2 (W m −2 )a
ACCESS1-0
3.8
0.8
3.0
b
CanESM2
3.7
1.0
3.8
c
CCSM4
2.9
1.2
3.6
d CNRM-CM5
3.3
1.1
3.7
e CSIRO-MK3-6-0
4.1
0.6
2.6
f GFDL-ESM2M
2.4
1.4
3.4
g HadGEM2-ES
4.6
0.6
2.9
h
inmcm4
2.1
1.4
3.0
i IPSL-CM5B-LR
2.6
1.0
2.7
j MIROC-ESM
4.7
0.9
4.3
k MPI-ESM-LR
3.6
1.1
4.1
l MRI-CGCM3
2.6
1.2
3.2
m NorESM1-M
2.8
1.1
3.1
n
bcc-csm1-1
2.8
1.1
3.2
o
GISS-E2-R
2.1
1.8
3.8
p
BNU-ESM
4.1
1.0
3.9
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| sample_1928 | 0.9998 | arxiv | |
Nonparametric approaches for analyzing carbon emission: from statistical and machine learning perspectives
Yiming Ma
Hang Liu
Shanyong Wang
Nonparametric approaches for analyzing carbon emission: from statistical and machine learning perspectives
Linear regression models, especially the extended STIRPAT model, are routinely-applied for analyzing carbon emissions data. However, since the relationship between carbon emissions and the influencing factors is complex, fitting a simple parametric model may not be an ideal solution. This paper investigated various nonparametric approaches in statistics and machine learning (ML) for modeling carbon emissions data, including kernel regression, random forest and neural network. We selected data from ten Chinese cities from 2005 to 2019 for modeling studies. We found that neural network had the best performance in both fitting and prediction accuracy, which implies its capability of expressing the complex relationships between carbon emissions and the influencing factors. This study provides a new means for quantitative modeling of carbon emissions research that helps to understand how to characterize urban carbon emissions and to propose policy recommendations for "carbon reduction". In addition, we used the carbon emissions data of Wuhu city as an example to illustrate how to use this new approach.
Introduction
Climate change due to carbon emissions is causing unprecedented impacts and challenges to human society and the natural environment. Carbon emissions are greenhouse gas emissions produced in various fields and activities, mainly including carbon dioxide, methane, nitrous oxide, etc. China's carbon emissions in 2019 were about 2,777 million tons, accounting for 27% of the world's total, making it the world's top carbon emitter [1] . On September 22, 2020, President of China Xi Jinping announced at the 75th session of the United Nations General Assembly that "China will increase its autonomous national contribution to CO 2 emissions will strive to peak by 2030 and work towards achieving carbon neutrality by 2060." China has implemented a series of strategies, measures and actions to address climate change and participate in global climate governance.
There have been numerous studies on carbon emissions for China at the overall, regional and provincial levels [2][3] . Most of their analysis is based on the STIRPAT model and/or its extended version [4][5] . STIRPAT is an important model for the study of environmental impacts, decomposing them into the products of population size, wealth per capita and technology. In this article, we consider population, affluence, energy intensity, and industrial structure as factors influencing carbon emissions.
In previous studies, population and affluence are the two factors that most directly affect carbon emissions. Dietz et al. [6] believe that population and carbon emissions are proportional within a certain range, but there is a lag between policy interventions on population, and we cannot change the status of carbon emissions quickly by controlling population. In addition, they argue that carbon emissions increase and then remain constant or even decrease as the level of affluence increases. This is because being very affluent means that economic agents are transforming into a service-based economy while having enough capital to pursue energy efficiency. Fan et al. [7] study the impact of industrial structure on carbon emissions in China and point out that the secondary sector is the main source of carbon emissions. Ang [8] states that energy intensity is an important indicator in carbon emissions research, and Rahman et al. [9] argue that reducing energy intensity and using renewable energy can effectively reduce carbon emissions.
A simple and routinely-applied approach for analyzing carbon emission data is to take a log-linear regression to STIRPAT. However, the relationship between carbon emissions and the influencing factors is complex, and there are interactions between the influencing factors. Traditional linear regression methods to build STIRPAT models have the disadvantage of poor fitting accuracy and inadequate explanation. For this reason, this paper aims to provide new modeling ideas and analytical tools for the study of carbon emissions. In particular, we consider various non-parametric methods, including kernel regression, which is commonly used in statistics, and random forest and neural network, which are common in ML.
We collected panel data for ten cities from 2005 to 2019 and modeled them using non-parametric methods and linear regression, finding that neural networks provide the best fit and prediction compared to linear regression method. Based on this, we have analyzed in detail the factors influencing Wuhu and made a forecast of future carbon emissions. We found that under the premise of sacrificing a certain economic development speed, optimizing the industrial structure and improving energy efficiency, carbon emission growth can be significantly controlled.
This article is organized as follows. in Section 2, we describe various methods used to model carbon emissions, including the traditional linear method and non-parametric methods (kernel regression, random forest and neural network). Section 3 describe the sources of the data and provide a brief description and analysis of the data. Section 4 uses the four methods to model the carbon emissions data and select the best method based on the results of the fitting and prediction. Section 5 illustrates how to analyze the influencing factors and forecast carbon emissions based on a neural network model, using the city of Wuhu as an example. Section 6 concludes the paper.
Methodology
It is noted that our main objective is to predict future carbon emissions through modeling and to provide recommendations on carbon emission-related policies. We, therefore, need to model carbon emissions and the factors that influence them and expect the model to have good fit and predictive accuracy. In this section, we describe the modeling methods.
Extended STIRPAT model: linear regression approach
IPAT model ( = ) was first proposed by Ehrlich et al. [10] and the key idea is to decompose the total environmental impact ( ) into the product of the population size ( ), the affluence describing per capita consumption or production (A), and the level of environmental damage caused by technology per unit of consumption or production ( ) [11] . On this basis, an expandable stochastic environmental impact assessment model, called STIRPAT, was proposed by York et al. [12][13]
.
(1)
Here, , , and are still environmental impact, population size, and affluence, respectively, but = ( 1 , . . . , ) in this equation is a -dimensional vector of observed variables representing technology, social organization, culture,and all other factors affecting human impact on the environment other than population and affluence, where denotes the transpose of a matrix and is a positive integer. = ( 1 , . . . , ) is a -dimensional vector of coefficients (or functions) representing their effects. With abuse of notation, means 1 1 · · · . In addition, the subscript and denotes the observational units and time respectively, and represents sum of unexplained component and error. The coefficients and determine the net effect of population and affluence on impact, and is a constant that scales the model. , , , and can be estimated by standard statistical techniques.
In the sequel, we will use this STIRPAT model as a benchmark model to the study of carbon emissions. Its performance, in terms of fitting and prediction accuracy, will be compared with our nonparametric models in Section 4. Let be the carbon emission, the STIRPAT model decomposes in the same way as equation (1), that is,
= ,(2)
where and denote the percentage of secondary sector and energy intensity respectively, and still represents the sum of unexplained components and error.
In fact, represents the industrial structure, i.e. the share of the high carbonemitting industries -industry and construction -in the overall economy, while represents the level of technology (the higher the level of technology the lower the energy consumption is supposed to be). Now we consider the problem of estimating , , , and . The standard practice is to take the logarithm of equation (2), so the extended STIRPAT model becomes
log = log + log + log + log + log .(3)
We can then apply the standard least squares method to estimate the coefficients. However, there are still several problems with this estimate. (i) Time and individual differences cannot be accounted for. The fact that each coefficient is fixed means that changing the same amount of each variable has the same effect on carbon emissions. This contradicts our usual intuition. (ii) The relationship between each variable and carbon emissions may not necessarily satisfy a log-linear relationship.
(iii) The variables are related to each other, which can lead to inaccurate estimates of regression coefficients, increased standard errors, wider confidence intervals and invalid significance tests.
Nonparametric method: from both statistical and ML perspectives
Rather than assuming linear or any other parametric models, we will consider using non-parametric methods (i.e. models not specified by explicit parameters), including the use of statistical and ML methods. We note that here the non-parametric approach no longer looks for an explicit expression; we still build the regression model based on , , and suggested in model STIRPAT (i.e. input , , and and the model will output the emissions ).
Non-parametric statistical method
The kernel regression method is a non-parametric regression method used to find a non-linear relationship between the independent and dependent variables. The essence of the kernel regression method is to use the kernel function as a weighting function to build a non-linear regression model.
Let ( ) = { } =1
be a set of -dimensional vectors of observations drawn from independent variables where = ( 1 , 2 , . . . , ) and is a positive integer, and Then the kernel estimator iŝ
( ) = =1 ( − ) =1 ( − ) , where = ( 1 , 2 , . . . , )
, is the bandwidth (or smoothing) × -matrix which is symmetric and positive definite, is the kernel function with a bandwidth . Briefly, the kernel regression method is a weighted average of local data points; more details can be found in Jaakkola et al. [14] . In practice, we normalize the data before performing kernel regression and use the Gaussian kernel function (i.e.
( ) = (2 ) − /2 | | −1/2 − 1 2 −1 ).
ML methods
Random forest. A random forest is an integrated model consisting of multiple decision trees, which is also a weighted average of response values [15] . Following Athey et al. [16] , the weights are generated by averaging neighborhoods produced by different trees. More precisely, we grow a set of trees indexed by = 1, . . . , and, for each tree, let ( ) denote the set of training examples falling in the same leaf as . Then the weight ( ) ( ; ( ) ), = 1, . . . , is the averaged (over trees) frequency that the training sample falls into the same leaf as , that is,
( ) ( ; ( ) ) = 1 ∑︁ =1 ( ) ( ; ( ) ), where ( ) ( ; ( ) ) := ( ( ) ∈ ( )) card{ ( )} ,
with card{ ( )} denoting the number of elements in ( ). Then the random forest estimator isˆ(
) = ∑︁ =1 ( ) ( ; ( ) ) .
Neural network. A neural network is a hierarchy of interconnected nodes that are weighted and activated on the input data to obtain the final result [17] . Specifically, a neural network consists of three parts: an input layer, hidden layers and an output layer. The input layer receives the input data, the hidden layers process the input data and the output layer generates the final output. In a neural network, each node is connected to all the nodes in the next layer. Each node has a weight that is used to calculate a weighted sum of the nodes in the next layer. These weighted sums are fed into the activation function to produce the output of the nodes in the next layer.
We briefly introduce the workflow of neural network through Figure 1, which shows a simple neural network with one hidden layer. We can observe that the input, hidden and output layers have 1, 3 and 1 neuron(s), respectively. This neural network works as follows. We input a value , which, after linear transformations, yields the inputs of the neurons in hidden layer. Then, after an activation function (·), we obtain three neuron outputs
( 1_1−1 + 1_1 ), ( 1_1−2 + 1_2 ) and ( 1_1−3 + 1_3 ).
The outputs of the hidden layers are transformed linearly into the activation function (·) to get the final output
[ 2_1−1 ( 1_1−1 + 1_1 ) + 2_2−1 ( 1_1−2 + 1_2 ) + 2_3−1 ( 1_1−3 + 1_3 ) + 2_1 ] .
Common activation functions are the sigmod function sigmoid( ) = 1/(1 + − ) and the ReLU function ReLU( ) = ( ≥ 0). In practice, we choose the appropriate activation function according to the task. If we increase the number of hidden layers and the number of neurons per layer, then it is possible to fit complex relationships. Training a neural network is to adjust the weights and drifts so that the neural network conforms to the data distribution. Fig. 1: is the weight and is the drift. It should be noted that the number in front of sliding line "_" represents which layer, the number after that represents the position of the neuron, and the number after connector "-" represents the position of the neuron in the next layer connected. So 1_1−1 represents the weight between the first neuron of the first layer and the first neuron of the next layer. is the activation function, and is the weighted value from the neuron in the previous layer.
Both statistical and ML nonparametric methods can fit complex and nonlinear functional relationships. We use them in the modeling of carbon emissions. We expect the use of non-parametric methods to better fit the data with predicted carbon emissions so that better analysis can be carried out. In Section 4, we compare four methods based on historical data.
Data source and description
Data source
As energy consumption data at the city level is difficult to find, ten Chinese cities (including Wuhu, Hefei, Ningbo, Guangzhou, Qingdao, Tianjin, Chongqing, Beijing, Shenzhen and Shanghai) were selected for the study. Since CEADs [18] currently update city carbon emissions data to the year of 2019, we selected the data of these ten cities from 2005 to 2019. Specifically, note that = GDP , = GDP ind GDP and = GDP , so we should collect the data of , , GDP, GDP ind and . The description and sources of these data are listed in Table 1 In order not to cause misunderstanding, a few points need to be clarified: (i) GDP and GDP ind is calculated using constant 2005 prices; (ii) energy consumption has been converted to standard coal and (iii) data is missing for some cities and years.
Overview of the data
Having collected the data in Table 1, we can calculate population ( ), energy intensity ( ), GDP per capita ( ) and percentage of secondary sector ( ). In addition, we have calculated carbon intensity (i.e. carbon emissions divided by GDP). The results are shown in Figure 2, due to space constraints we only show data of four representative cities: Ningbo, Shanghai, Hefei and Wuhu. The figures show that: 1. The energy intensity of all four cities is on a downward trend, with Wuhu decreasing faster and Shanghai having the lowest energy intensity. 2. These four cities are currently experiencing slow but steady population growth, with Shanghai having the largest population and Wuhu having the smallest. 3. All four cities maintained high growth rates in GDP per capita. 4. Wuhu and Ningbo currently have a higher share of secondary industries, while Shanghai's share is declining. 5. The carbon emission intensity of all four cities is decreasing currently. The carbon emission intensity of Shanghai and Hefei are close to each other; Ningbo and Wuhu are close to each other.
To sum up, Shanghai is China's megalopolis, with a large population and a developed economy. High energy-consuming and high-emission industries such as industry account for a relatively small proportion of the economy as a whole, and the economic focus has shifted to service-oriented industries such as finance. But in fact, most Chinese cities like Wuhu, with a medium population, are still dominated by secondary industries and their economies are in a state of high growth, which brings with it a higher carbon emission intensity. This is the reason for our subsequent focus on Wuhu.
Comparison of modeling methods: fitting and prediction accuracy
We used the four model-fitting methods described in Section 2 to fit the data of the ten cities from 2005 to 2019 and evaluate the goodness of fit of these four methods by comparing simulated emission values with actual emission values. In addition, we consider whether to include city differences as an influencing factor. This is because cities will differ in their expression of the influencing factors; for example, a city using clean energy will emit less carbon than a city using fossil fuels, even for the same energy intensity. We treat the city as a variable added to the model when city differences are considered and do not include the city variable when differences are not considered. We illustrate the goodness of fit here by showing the one-to-one plot in Figure 2, where we let the vertical coordinates be the true emission values and the horizontal coordinates the fitted emission values, so that if the constituent coordinates are closer to a line with a slope of 1 from the origin, the better the fit is. Intuitively, the results of the kernel method are closer to the true values with or without accounting for city differences. Random forest and neural network also perform well when city differences are considered. In addition, we also provide the mean squared error (MSE) and bias in Table 2. We find that the kernel method has the minimum MSE and bias both with and without considering city differences, followed by the neural network method with considering city differences.
This does not indicate that the kernel method is optimal, as it may be over-fitted. In fact, what is more important is that we are more interested in the predictive power of the model. We need predictions of carbon emissions under different future scenarios to provide policy recommendations.
We next investigate the predictive power of the four methods. We note that when city differences are considered, the fit results are better than those without city differences, except for the kernel method, which is close to that when it is not considered. This indicates that differences between cities do exist. Therefore, in the following study, we consider city differences in all methods. We train the model using only data from 2005 to 2017, make predictions for 2018 and 2019, and compare the predictions with real emissions. We show the actual emission values and the predicted emissions from the four methods in Figure 3. We found that the predicted values of neural networks were mostly close to the true values, and the results of random forest methods were often far from the true values, which happened occasionally for kernel regression and linear regression. In addition, bias and MSE are provided in Table 2. Neural network has the minimum MSE and bias, which is a significant advantage over other methods. Kernel methods that perform well in fitting tasks are far inferior to neural networks in prediction tasks. In fact, kernel regression methods suffer from curse of dimensionality in the face of multiple variables [19] . Their great fitting results may due to the over-fitting.
Combining the results of both fitting and prediction, neural networks have better performance and we hence use them throughout the rest of this article. Fig. 3: One-by-one plots of fitted and actual carbon emissions for the different methods. The red dashed line is from the origin with a slope of 1. The first, second, third and fourth rows represent the results of the linear regression, kernel regression, random forest, and neural network, respectively. the first and second columns represent the results of considering city differences and not considering, respectively.
Neural network-based analysis and forecasting
In this section, we analyze the city of Wuhu as an example, focusing on the factors affecting carbon emissions in Wuhu and making predictions. Currently, Wuhu is still an industrial city, with the secondary industry consuming close to 50% of the energy, and over 60% of the energy supply for the whole city is coal. This results in Wuhu having high total carbon emissions and carbon emission intensity. However, there is also some potential for emission reduction, such as improving energy efficiency, optimizing industrial structure and developing clean energy. Most cities in China share these similarities to Wuhu. We further specify the analysis of the factors influencing carbon emissions in Wuhu and the prediction of carbon emissions. This could be a guide for many Chinese cities to reduce their carbon emissions and help China as a whole to reach its carbon peak and carbon neutral targets sooner. We begin with an impact factor analysis.
In previous studies, the modeling has generally taken linear regression approach and used the regression coefficients of the variables to determine the impact of the variables on carbon emissions. However, this is not reasonable because the difference in cities and time, coupled with the existence of interactions between variables, makes it very restrictive to use only one coefficient to account for the effect of the variables on emissions.
Because neural network has no explicit expressions, here we have taken a new approach to quantify the impact of different variables on emissions. That is, for a given city at a given time, all variables are entered into the model unchanged to obtain a baseline value; then when analyzing the impact of a variable on emissions, the other variables are fixed and the value of this variable is increased by 1%, and the output of the modet al this point is compared with the baseline value for that city at that moment in time.
The Wuhu Statistical Yearbook has been updated to 2022 to include data for 2021. We use 2021 data for Wuhu as the baseline data, and both the manipulation of the data and the forecast results are shown in Table 3. Table 3: Results of the significance analysis of the impact factors. In each situation, the value of a variable is increased by 1%.
We find that Wuhu's carbon emissions are insensitive to population, with little or no change. Higher levels of affluence lead to more emissions, which again corresponds to the results of Dietz el at. [6] . An increase in energy intensity also significantly increases carbon emissions. We note, however, that holding other things constant, increasing the share of secondary industry decreases carbon emissions, which we believe is because a higher share of secondary industry does not raise energy consumption, implying that industry is transferred towards less energy consumption, which generally represents less emissions.
In the following, we make predictions for Wuhu's carbon emissions. First, we give a baseline scenario based on Wuhu's historical data and the government's current targets. We do not specify 2020 and 2021 any further because they are available. For 2022 to 2023 we assume a 2% year-on-year decrease in energy intensity, a 5% year-on-year increase in GDP per capita, a constant population and a 1% year-onyear decrease in the share of secondary industry. It should be explained that the population remains unchanged due to previous Chinese family planning policies and the siphoning effect of large cities on Wuhu, which we assume will remain largely unchanged. In addition, we assume that policy interventions are made to promote industrial upgrading and technological upgrading at the expense of some economic growth, so we assume a 4% year-on-year decrease in energy intensity, a 3% yearon-year increase in GDP per capita and a 2% year-on-year decrease in the share of secondary industry and that population remains constant. We put the results in Figure 5. We find that Wuhu's carbon emissions will continue to grow without policy intervention, while with policy intervention, they peak around 2025 and then trend downwards.
Based on the research findings, several policy implications can be drawn. Given the significance of industrial structure on carbon emissions, great measures should be taken to optimize the existing industrial structure. On the one hand, we should limit the development of high energy-consuming and high-polluting industries, vigorously develop green and clean industries and high-tech enterprises, so as to reduce the pro- portion of polluting enterprises in the secondary industry, increase the proportion of clean and high-tech industries in the secondary industry, and improve the greenness of the secondary industry. On the other hand, we should vigorously develop the tertiary industry, increase the proportion of the service industry in the overall economic structure, and moderately reduce the proportion of the secondary industry in the economic structure. Furthermore, energy intensity and carbon emissions are closely related, and measures should be taken to improve energy efficiency and reduce energy intensity. For example, enterprises should be encouraged to strengthen the research, development and application of energy-saving technologies to improve their energy efficiency and resource utilization efficiency. Meanwhile, the application of emerging digital technologies such as big data, cloud computing and artificial intelligence needs to be accelerated to further optimize production processes, increase energy-saving potential and reduce carbon intensity.
Conclusion, implication and limitation
Inspired by STIRPAT, we consider not only linear regression but also the use of statistical and machine learning non-parametric methods to model carbon emissions. Specifically, we model the carbon emission regression using three nonparametric methods: kernel regression, random forest, and neural network, using the factors proposed in STIRPAT as independent variables and carbon emissions as dependent variable, and finally find that the neural network has the best performance (based on data for ten cities from 2005 to 2019). In addition, we quantitatively analyze the factors influencing carbon emissions based on this model and forecast future emissions, which leads to policy recommendations. In general, this study provides new ideas and approaches for carbon emission analysis.
Though this research is meaningful, several aspects should be noted. First, at the time of modeling, there are various factors affecting carbon emissions, while only four influencing factors are considered in this research. Other influencing factors such as energy structure, regional investment scale, and foreign direct investment are not considered. The follow-up study can consider these factors. Second, due to limited access to the carbon emissions data at the city level, the sample used for the model validation is relatively small, which affects the generality of the results to some extent. In the following research, the research sample needs to be further expanded to further enhance the generalizability of the findings.
For example, we could not find the energy consumption data of Shenzhen from 2005 to 2009 and the carbon emission data of Wuhu in 2005.
Fig. 2 :
2Green, purple, cyan and orange represent Shanghai, Hefei, Ningbo and Wuhu respectively.
Fig. 4 :
4Real and predicted carbon emission values for the four methods. Upper panel: results for the year of 2018. Lower panel: results for the year of 2019.
Fig. 5 :
5This is the Wuhu carbon emission prediction curve (to 2030).
.Data Definition
Source
Unit
carbon emission (CO 2 ) Carbon accounts and datasets (CEADs);
Dataset URL: https://www.ceads.net/
ton
GDP gross secondary industry Statistical Yearbook for each municipality
CNY
GDP ind gross secondary industry Statistical Yearbook for each municipality
CNY
energy consumption
Statistical yearbooks for each municipality (Ningbo
energy data is from Ningbo Energy White Paper)
ton
Resident population
Statistical yearbooks for each municipality
Number
Table 1 :
1Definition and source of the data
Table 2 :
2This table provides the predicted or fitted MSE and bias for the different methods. The smallest bias and MSE are shown in bold.
, 2 , . . . , be the corresponding response values drawn from dependent variable.
A city that is of research interest to our funding institute.
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When the Metaverse Meets Carbon Neutrality: Ongoing Efforts and Directions
Fangming Liu
Senior Member, IEEEQiangyu Pei
Shutong Chen
Yongjie Yuan
Senior Member, IEEELin Wang
Senior Member, IEEEMax Mühlhäuser
When the Metaverse Meets Carbon Neutrality: Ongoing Efforts and Directions
JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, DECEMBER 2022 1
The metaverse has recently gained increasing attention from the public. It builds up a virtual world where we can live as a new role regardless of the role we play in the physical world. However, building and operating this virtual world will generate an extraordinary amount of carbon emissions for computing, communicating, displaying, and so on. This inevitably hinders the realization of carbon neutrality as a priority of our society, adding heavy burden to our earth. In this survey, we first present a green viewpoint of the metaverse by investigating the carbon issues in its three core layers, namely the infrastructure layer, the interaction layer, and the economy layer, and estimate their carbon footprints in the near future. Next, we analyze a range of current and emerging applicable green techniques for the purpose of reducing energy usage and carbon emissions of the metaverse, and discuss their limitations in supporting metaverse workloads. Then, in view of these limitations, we discuss important implications and bring forth several insights and future directions to make each metaverse layer greener. After that, we investigate green solutions from the governance perspective, including both public policies in the physical world and regulation of users in the virtual world, and propose an indicator Carbon Utility (CU) to quantify the service quality brought by an user activity per unit of carbon emissions. Finally, we identify an issue for the metaverse as a whole and summarize three directions: (1) a comprehensive consideration of necessary performance metrics, (2) a comprehensive consideration of involved layers and multiple internal components, and (3) a new assessing, recording, and regulating mechanism on carbon footprints of user activities. Our proposed quantitative indicator CU would be helpful in regulating user activities in the metaverse world. IT System (Special-purpose hardware, etc.) Entire Infrastructure (Clean energy, etc.) Non-IT System (Adaptive cooling control, etc.) 40 Mt/yr. End-Device (Integrated Modem, etc.) Networking (Energy recovery, etc.) Application (AI model compression, etc.)Blockchain (Lightning Network, etc.) Infrastructure Layer (IT system, non-IT system, entire infrastructure, etc.) Interaction Layer (End-device, application, networking, etc.) Economy Layer (Blockchain, etc.) 50 Mt/yr. 25 Mt/yr. Deploying special-purpose hardware Graviton3 [40], IBM [41] Dynamic voltage frequency scaling Rubik [42], Gemini [43] AI model compression SmartExchange [44], OFA [45] Server-level (Sec. III-B2) Single-server workload scheduling FineStream [46], Wiesner et al. [47] Cross-server workload scheduling Yi et al. [48], Poly [49] Non-IT system Cooling system (Sec. III-C1) Choosing suitable cooling techniques GreenEdge [50], CoolEdge [51] Adaptive cooling control CoolEdge [51], DeepEE [52] Cooling-aware workload management DeepEE [52], CoolAir [53] Power system (Sec. III-C2) Reducing power mismatches HEB [54], Flex [55] Reducing power losses Panama Power [56]Entire infrastructure (Sec. III-D)
I. INTRODUCTION
The metaverse concept has attracted considerable attention recently. The term originates from the 1992 science fiction novel Snow Crash by Neal Stephenson [1]; it is a portmaneau of "meta" and "universe", and denotes a universal and immersive virtual world [2]. Creating such a virtual world involves Users from all over the physical world are connected together into the metaverse to communicate, work, play, and more [4], [5], [6], [7], [8], [9], [10]. many technologies from artificial intelligence (AI) to extended reality (XR), and many tech companies like Nvidia and Microsoft have paid increasing attention to the metaverse based on their competitive technologies from computing hardware to application platforms. Recently, the COVID-19 pandemic increased the demand for both professional and social online interaction. A prominent example is that the number of daily active users of Roblox, a representative metaverse platform, has grown by 85% in 2020 [3].
The metaverse platforms build virtual worlds for users to connect with others directly online but in an immersive manner over the physical world. Such platforms support extensive daily activities like communication, work, entertainment, trading, etc., as shown in Figure 1. Specifically, Microsoft has developed a virtual collaboration platform Microsoft Mesh where everyone can interact with each other using their avatars while avoiding travelling across the physical world. Users can wear special end-devices running mixed reality (MR) applications, such as HoloLens 2 [9], to achieve lifelike experience. Recently, the BMW Group and Nvidia together built a highly complex manufacturing system with the Nvidia Omniverse platform [11], [12]. In this virtual factory, engineers can simulate and operate the factory collaboratively in real time before putting the factory into practice in the physical world, which contributes to 30% more efficient planning processes [13]. Apart from working online, users can play together in this virtual world. In October 2021, Roblox held its first metaverse music festival World Party, bringing immersive music experiences to users from all over the world [14]. In addition, we can even trade virtual real estate in this virtual world. For example, an anonymous user bought a land next to the famous rapper Snoop Dogg in the metaverse platform The Sandbox with his non-fungible tokens [15]. Fortune predicts arXiv:2301.10235v1 [cs.CY] 18 Jan 2023 that the virtual real estate has the potential to reach several trillion dollars in the metaverse, showing the huge demands for trading [16]. In summary, with the rapid development of the metaverse, we can really enjoy a life online as we wish.
It is generally believed that living online is low-carbon since we can avoid activities like flying across the world and holding physical meetings. These physical activities can generate large amounts of energy consumption and produce lots of carbon emissions. For example, an hour flying comes with around 250 kg CO 2 equivalent based on an estimation [21], and the global carbon emissions produced by aviation in 2020 were reduced by 45% compared to that in 2019 as a result of the COVID-19 pandemic [22]. In addition, according to a recent study, shifting physical meetings to virtual ones can reduce the carbon footprint by as high as 94% [23]. Nevertheless, although the metaverse provides the potential of decarbonization through limiting physical activities, the carbon emissions will still "burst" for supporting the metaverse itself. For example, video streaming is a key technique to the metaverse which provides end-users with a high quality of experience with augmented reality (AR), virtual reality (VR), and MR technologies. However, an estimation shows that four hours of streaming high-quality video (e.g., High Definition (HD) or Ultra HD) a day would result in 53 kg CO 2 equivalent monthly [24]. The carbon issue can get worse when it comes to transactions. To support transactions in the metaverse, the blockchain technology is believed to be indispensable in the metaverse. However, it is astonishing that an Ethereum transaction can generate 329,000× more carbon emissions than a credit card transaction currently [25]. In summary, with the development of the metaverse, considerably increasing carbon emissions would be produced in the foreseeable future.
Facing the serious consequences of global warming and climate change, countries and enterprises have successively put forward the target of carbon neutrality that refers to achieving net-zero carbon dioxide emissions. Tables I and II list the carbon neutrality goals of selected countries and big techs. As we can see, most developed countries have promised to achieve carbon neutrality by the year of 2050, while many tech companies have promised the same no later than 2030. Those techs have already taken various effective actions to become greener. As early as 2016, Alipay's Ant Forest initiative was launched intentionally to make everyone take part in lowcarbon daily activities such as walking and bicycling instead of driving, by rewarding them with virtual "green energy points" that can be translated into real trees thereafter [26]. Google has been contributing to achieving carbon-free energy supply anytime and anywhere in the world and co-launched a 24/7 Carbon-Free Energy Compact [27] in 2021. Although there have been a range of actions to achieve carbon neutrality, the rapid development of the metaverse will bring a critical issue on the way to carbon neutrality as a result of the continuously growing demands for computing power. To realize a green metaverse, therefore, we raise the following questions:
• How much energy will be consumed and how many carbon emissions will be produced by the metaverse? ( §II) • What are the major components of the metaverse and what are their energy consumption and carbon footprint shares? ( §II) • Which green techniques can help drive decarbonization of these components, and how is their applicability when dealing with metaverse workloads? ( §III, §IV, and §V) • What are the limitations of these existing techniques?
( §III-E, §IV-E, and §V-C) • What can we do to realize a green metaverse for the target of carbon neutrality? ( §III-E, §IV-E, §V-C, §VI and §VII) To answer these questions, we examine the carbon issue of the metaverse, provide a comprehensive study of green techniques for the metaverse, provide several insights, and propose future directions tailored to the metaverse.
The rest of this survey is organized as follows. Section II provides an overview of the metaverse, comprehensively investigates the carbon issue of the metaverse from the perspective of its three layers, and briefly discuss ongoing efforts of green techniques. The detailed analysis of those green techniques and their remaining challenges are presented in Section III, Section IV, and Section V. Section VI provides a governance perspective for a low-carbon metaverse. We conclude this survey and present three research directions to a greener metaverse in Section VII.
II. A GREEN VIEWPOINT OF THE METAVERSE FRAMEWORK
In this section, we first provide an overview of the metaverse and define its three carbon-intensive layers. Then, we analyze the carbon issue of building and operating the metaverse by estimating the carbon emissions of those layers in the following years. Finally, we briefly discuss the ongoing efforts to achieve a green metaverse.
A. An Overview of the Metaverse and Its Three Carbon-Intensive Layers
The metaverse refers to a digital virtual world where users gather together to work, study, play, trade, etc., beyond the physical world where we really live. It typically involves two stages, i.e., an offline stage to build the virtual world, and an online stage to operate the virtual world where users can conduct their daily activities. To build the virtual world, large computations are necessarily performed, including AI training, AI inference-based tasks like image recognition and style transfer, 3D rendering, and so on, in order to capture and record key elements from the physical world, convert them into video frames, and render all those frames to construct a 3D virtual world. As an offline process, there is no strong demand for processing latency. After the construction process, users can use their end-devices with avatars to connect to the virtual world and interact with each other. Those end-devices collect all the action information of users from on-board sensors, process them locally or offload them to cloud/edge platforms when the computations become heavy, and generate and render new video frames to display on the end-devices again. As an online process, the end-to-end latency is critical when determining where to perform these computations including AI inference, 3D rendering, video analytics, economic transactions, and so on. There is no doubt that performing the aforementioned computations relies on many technologies. A recent study on the metaverse summarizes eight key technologies to support the metaverse, namely hardware infrastructure, network, cloud/edge, AI/blockchain, computer vision, Internet of things/robotics, user interactivity, and extended reality [28].
From the perspective of functionality and carbon sources of the metaverse, we further propose a metaverse framework with three relatively independent layers as shown in Figure 2, namely the infrastructure layer, the interaction layer, and the economy layer, each of which is composed of several components. Here, we briefly introduce their functionality and main components as follows, and present their carbon footprints in Section II-B.
(1) The infrastructure layer is key to supporting computation in the metaverse in the form of datacenters. As end-devices like mobile phones and headsets typically have limited computing capacity, huge amounts of computations need to be offloaded to datacenters with powerful computing servers and abundant resources. The datacenter facility typically consists of information technology (IT) and non-IT equipment. Specifically, the IT equipment provides the computing, networking, and storage capability, while the non-IT facility is to support the operation of datacenters, such as the cooling system.
(2) The interaction layer is key to supporting communication between users in the metaverse and includes human-computer and human-human interaction. On the one hand, the humancomputer interaction involves both hardware and software components. The former consist of various end-devices like mobile phones and headsets, and the latter refer to diverse kinds of applications running on top of end-devices, such as virtual conferencing and virtual manufacturing. On the other hand, the human-human interaction involves the networking equipment, including cellular modem chips on end-devices and cellular base stations, which provides essential supports for multiplayer interaction in the metaverse.
(3) The economy layer is key to supporting transactions between users in the metaverse. To provide enough transaction security as in the physical world, the economy layer has widely incorporated the blockchain technology. On top of the blockchain, cryptocurrency is a necessary medium for secure transactions between users, while non-fungible tokens are used to prove the ownership rights of users' virtual properties.
Note that such a division covers all the necessary technologies for the metaverse as introduced at the beginning: (1) hardware infrastructure, edge/cloud computing, AI, and computer vision covered in the infrastructure layer, (2) hardware infrastructure, network, AI, computer vision, Internet of things/robotics, user interactivity, and extended reality covered in the interaction layer, and (3) AI and blockchain covered in the economy layer. Some of the technologies like AI belong to more than one layer because of their comprehensive functionality.
B. The "Carbon" Role of the Metaverse
According to Emergen Research [29], the global metaverse market size has reached $63 billion in 2021 and is estimated to reach $1607 billion in 2030. With the rapid evolvement of the metaverse, there will inevitably be high carbon emissions at the same time. In order to undertake effective measures on carbon reduction, we must firstly understand the "carbon" role of the metaverse by speculating its carbon emissions in the following years.
However, it is nontrivial to conduct the estimation accurately as the metaverse is still a newly emerging and constantly evolving concept that covers a wide range of technologies. To reduce the estimation error as much as possible, we speculate the energy consumption and carbon emissions of the metaverse based on the energy figures provided by the following reputable sources: (1) the global IT market size and metaverse market size: a report from The Business Research Company [30] and a report from Emergen Research [29], respectively, (2) the energy consumption of datacenters, enddevices, and networking: articles on Information and Communications Technology (ICT) energy from Huawei Technologies [31], [32], and (3) the energy consumption of the blockchain: a research from the University of Cambridge for calculating the Bitcoin energy [33] and an article from the Technical University of Munich for speculating the overall energy of cryptocurrencies [34]. Note that we take the energy consumption of cryptocurrencies as that of the blockchain since the blockchain is basically used for transactions in the metaverse. Since the energy numbers of cryptocurrencies are only accessible before 2022, we use an exponential function to estimate the future energy consumption based on historical values [35]. By multiplying the energy numbers and the ratio of the metaverse market size to the global IT market size, we can estimate the global energy consumption of the metaverse in each of the three layers from the year of 2022 to 2030. Figure 3 plots the results and growth trend. Based on the estimation, we find that the energy consumption of the infrastructure layer grows relatively proportional to the total energy of the metaverse, and occupies about one fifth all the time. By contrast, the energy consumed by the interaction layer remains at a high level constantly. Although a single end-device usually consumes only several Watts, their huge quantity and a growing demand for data transmission still lead to a high energy share for supporting immersive interaction. Meanwhile, we can see that its energy share, however, drops from about three quarters in 2022 to less than half in 2030. The dropped energy share can be attributed to the faster growth of the economy layer, whose energy consumption increases by over 8× during the eight years. This strong growth is what we have expected, as the current blockchain technology is generally believed to be extraordinarily energy-consuming for the need to perform lots of redundant and useless hash computations.
To quantify the carbon emissions, we should keep in mind that they are not only determined by the energy consumption, but also positively correlated with the carbon intensity of electricity generation which gets decreased due in large part to an increasing share of clean energy. Therefore, based on the energy numbers shown in Figure 3 and the carbon intensity of electricity generation [36], we estimate the corresponding carbon emissions of each layer from 2022 to 2030 as depicted in Figure 4. We find that the carbon emissions of the metaverse will reach as high as 115.30 Mt by the year of 2030. To combat the climate change and achieve carbon neutrality as promised, global CO 2 emissions should be reduced to 23.63 Gt by 2030 [37], in which circumstance the metaverse accounts for nearly 0.5% of the global carbon emissions! We argue that it is increasingly urgent to consider enough green aspects when building and operating the metaverse and devise various green techniques to tackle its carbon issue. Implications The metaverse will account for as high as 0.5% of the global carbon emissions by 2030 unless we take effective preventive measures from now on. First of all, we should call for global attention to its carbon issue and encourage collaborative efforts on green techniques.
C. An Overview of Ongoing Green Efforts for the Metaverse
To address the carbon issue in the IT sector, many green techniques have emerged. As presented in Figure 2, these techniques will help reduce the carbon footprint in the three layers of the metaverse as well. At the infrastructure layer, the techniques can be categorized into the improvement of the IT system, cooling system, power system, as well as the entire infrastructure concerning all of them. At the interaction layer, given the whole process of interaction with others, the techniques include the improvement of end-devices, AR/VR/MRbased applications, and networking. At the economy layer, the techniques mainly refer to the improvement of the blockchain technology. Nevertheless, these existing techniques also show limitations when dealing with metaverse workloads. In the following sections, we will dive into these green techniques for the three metaverse layers by analyzing their applicability and limitations. It is worth noting that our estimation to the energy consumption and carbon emissions of the metaverse in Section II-B would not influence the discussion on green techniques in the following sections. Even if there exists a relatively high estimation error, in view of the growing trend of the metaverse, the carbon footprint of the metaverse will still be large enough to emphasize the importance of green efforts. Replacing instruction set architectures RISC [38] In-memory processing TIMELY [39] III. HOW CAN THE INFRASTRUCTURE BECOME GREEN? Datacenters are the key infrastructure for the metaverse by providing powerful computing capacity [63], [28]. As presented in Section II-A, those large computations from AI-based tasks to 3D rendering have a huge appetite for computing power. However, due to the limited computing and battery capacity of end-devices, it is hard for them to provide real-time metaverse services with a high quality-ofexperience (QoE). A promising solution is to offload most of the computations to the datacenter infrastructure though incurring network latency. For example, 3D rendering is a critical technique for generating the visual content of the metaverse, which requires large amounts of computing power especially when rendering a high-quality frame (e.g., 4K Ultra HD) [64] and thus may need to be conducted in datacenters. In the following, we will first introduce the carbon issue of the infrastructure and then analyze green techniques to improve the energy efficiency of the IT systems, non-IT systems, and the entire infrastructure. In the end, we provide future directions to become green.
A. The Carbon Issue of the Infrastructure
A datacenter is typically composed of the IT and non-IT equipment [65], as illustrated in Figure 5. includes servers, network switches, etc., for providing the computation, network transmission, and storage capacity; the non-IT equipment is to support the IT equipment, referring to the power system, cooling system, fire suppression system, etc. Currently, the global datacenter electricity consumption has already reaches as high as 200 TWh, around 1% of the worldwide electricity consumption and 0.3% of global carbon emissions [66]. With the growing demand of the metaverse and the growing computing power of global datacenters, it is vital to improve the energy efficiency and reduce the carbon footprint of the energy-hungry and carbon-intensive datacenter infrastructure [67].
To this end, we first investigate how to measure the energy efficiency of datacenters. Figure 6 shows the share of energy consumption by source in a typical datacenter [68]. We can find that as the most important part of a datacenter, IT equipment consumes about 50% of the total energy, while among the non-IT equipment, the cooling system plays the dominant role in energy consumption. The power usage effectiveness (PUE) is a commonly used indicator for measuring the energy efficiency of a datacenter as a whole, and is defined as the ratio of the total amount of energy used by the whole datacenter infrastructure to the energy delivered to the IT equipment [69]. It is reported that the energy efficiency of datacenters was generally poor a decade ago: the average PUE in 2011 was as high as 1.89. With the development of modern cooling techniques (e.g., water cooling with warm water [70], free cooling under the sea [71]) and power supply (e.g., renewable energy), the PUE of large-scale datacenters have dropped significantly in recent years, e.g., 1.06 by Google [72]. According to the distance to end-users and the type of provided services, datacenters can be generally classified into edge datacenters and cloud datacenters, both of which play an important role in the metaverse [28]. Specifically, edge datacenters are mainly built for hosting online services while cloud datacenters focus on delay-tolerant offline services. To provide low-latency and high-throughput services to end-users, edge datacenters need to be widely distributed across the network edge near the urban. However, because of the area restriction in the urban, the edge datacenters own limited computing capacity but higher computing density [51], [73]. By contrast, cloud datacenters own massive computing and storage capacity by locating in rural areas, making them cover a wider population but get distant from end-users. A cloud datacenter generally contains thousands to tens of thousands of server racks. Its power rating can reach 10's to 100's of MW [74], which is three orders of magnitude higher than that of an edge datacenter. Figure 7 summarizes the differences in provided services, location, and computing capacity, between edge datacenters and cloud datacenters [75], [76].
Because of these distinctions, cloud and edge datacenters have different levels of energy efficiency and face different opportunities and challenges in carbon reduction. For example, edge service providers sometimes need to over-provision resources to satisfy the strict QoE requirement [75], which in turn leads to extra energy consumption. Therefore, although energy efficient solutions for cloud datacenters have been well studied over the past few decades, some green techniques devised for cloud datacenters may become invalid in edge datacenters considering their distinctions and the carbon issue becomes more serious. For instance, since the free cooling technique is almost unavailable, the PUE of edge datacenters is just as high as 2 [77].
The serious carbon issue pushes us to develop green techniques to reduce carbon emissions from the datacenter infrastructure. As listed in Table III, based on the datacenter architecture and carbon sources, there are extensive green techniques for improving energy efficiency and reducing carbon emissions in multiple levels. Figure 8 shows the key components for carbon reduction of the datacenter infrastructure.
B. Energy Efficiency Improvement of IT Systems
The energy efficiency of IT systems mainly depends on computing servers and each individual component inside servers. We summarize the energy efficiency improvement at the component level and the server level separately.
1) Component-level energy efficiency improvement: To process a certain task efficiently, datacenters have gradually deployed newly-developed special-purpose hardware (e.g., GPU and FPGA) nowadays in addition to CPU [78]. Componentlevel green techniques focus on a single component, including CPU, GPU, memory, and other accelerators through hardware and/or software design.
Replacing instruction set architectures. The evolving of instruction set architectures (ISAs) is a promising way for energy saving. The reduced instruction set computer (RISC) architecture [38] (e.g., used in ARM processors) is recognized as a more energy-efficient ISA than the conventional complex instruction set computer (CISC) architecture (e.g., used in ×86 processors). Because of this advantage, RISC has been widely adopted in end-devices with limited battery capacity. Recently, a growing number of datacenter operators have turned to ARM-based servers for higher efficiency. For example, Cloudflare deployed its edge servers with ARM CPUs (RISC) in 2021 that enables 57% more Internet requests per Watt than the performance achieved by the latest generation of edge servers equipped with AMD Rome CPUs (CISC) [79]. Leveraging RISC-based processors, the metaverse service provider can handle more high-concurrency requests while keeping a small energy footprint in the coming metaverse era.
In-memory processing. Apart from being computeintensive, a lot of metaverse services are also memoryintensive. For example, to enhance the immersive experience, some metaverse applications like cloud gaming will include human-computer interaction using voice, where non-player characters can chat with real players to provide next-step instructions. Therefore, speech recognition is a key technique in the human-computer interaction, but it often incurs a high memory footprint and consumes a large amount of energy [80]. For these memory-intensive metaverse services, it is critical to optimize the memory footprint. Processing-in-memory (PIM) is an emerging technique to improve energy efficiency by reducing data movement between memories and CPUs. Li et al. [39] propose a resistive-random-access-memory (ReRAM) based PIM accelerator with three hardware-based designs to save energy.
Deploying special-purpose hardware. To serve as a foundation for the computational metaverse, various newlydeveloped special-purpose hardware products like Nvidia A100 GPU [81] are promising to be widely deployed in datacenters in addition to general-purpose CPUs [78]. These special-purpose hardware components that cater to the characteristics of a certain type of tasks often achieve a high energy efficiency. For example, Amazon introduces its 3rd generation Graviton CPU (Graviton3) for its cloud datacenters. It is reported that Graviton3 saves up to 60% energy compared to Graviton2 probably due to the integrated special-purpose processors [40]. With an increasing demand for AI-based services, the industry has already developed a variety of specialpurpose hardware that supports low-precision computations of AI workloads to relieve the resource requirement and improve the energy efficiency, such as the NNP I-1000 accelerator designed by Intel [82]. IBM has been empowering CPU chips with AI capability by integrating special-purpose AI chips and aims to boosting energy efficiency by 2.5× each year [83]. Recently, it designs an AI chip with the 7nm technology which supports low-precision computations and achieves up to 16.5 TOPS/W as compared to 3.12 TOPS/W achieved by the widely-used Nvidia A100 datacenter GPU [41]. In addition to hardware designs, most of these components are also integrated with a power management unit, such as FIVR [84], to achieve a dynamic and desired trade-off between energy consumption and performance. These special-purpose components are especially promising for capacity-limited edge datacenters that provide various special metaverse services with stringent performance constraints.
Implications It is especially essential to deploy specialpurpose hardware for both performance and energy efficiency of the metaverse. However, given the various metaverse workloads, metaverse operators need to carefully choose the bestsuitable hardware combinations. Moreover, as such hardware usually brings high capital expenditures, operators should also keep in mind that special-purpose hardware is not a silver bullet compared to more economical CPUs.
Dynamic voltage frequency scaling. Dynamic voltage frequency scaling (DVFS) is a widely-used software-based techniques to improve the energy efficiency of components. Figure 9 illustrates that the power footprint of the Intel Core i5 Processor is positively correlated with its frequency [85]. Based on this observation, DVFS is advanced to reduce the power consumption by dynamically adjusting the voltage and frequency of components like CPUs [42], [43] and other special-purpose hardware including GPUs [86], application specific integrated circuits (ASICs) [87], field programmable gate arrays (FPGAs) [87], etc. However, Figure 9 also shows that a higher energy efficiency usually comes at the expense of performance. It would be more appropriate to implement DVFS carefully on delay-tolerant services, such as background image re-rendering in the offline stage, rather than timesensitive services like cloud gaming and online meeting. The metaverse service providers should accurately estimate the service execution time and carefully balance the energy efficiency and QoS violation rate [88]. Implications DVFS is a widely-used technique to save energy. However, metaverse operators need to carefully incorporate this technique as it usually trades performance for energy efficiency, while metaverse applications tend to place strict requirements. Particularly, even slight performance violations may cause a serious consistency issue as a result of wrong time order of consecutive events in the virtual world.
AI model compression. It is generally believed that the AIbased services play a key role in the metaverse. Nevertheless, their huge energy consumption deserves our special attention as well. For example, when training a large AI model containing 6 billion parameters only to 13% of the whole process, the carbon emission emitted by GPUs will be as much as powering a home for one year in America [89]. The model compression technique has emerged as an effective approach to reduce carbon emissions of model training and inference, by decreasing the size of models and thus the resource and time overhead without significantly affecting the accuracy.
Common model compression techniques include quantization, sparsification, tensor decomposition, and so on [90]. Model compression can help reduce energy consumption of AI-based services by not only relaxing the demand for computing resources, but also eliminating large amounts of data transferring and storage. An effective model compression result usually comes with the hardware software co-design that jointly considers the accelerator architecture. Xia et al. [91] propose a quantization method to reduce the amount of intermediate data and eliminate the power-consuming Digital-to-Analog and Analog-to-Digital Converters on newly designed special-purpose hardware, namely resistive random-access memory (ReRAM). Zhao et al. [44] propose an algorithmhardware co-design framework for energy-efficient inference. Using pruning, decomposition, and quantization jointly, the proposed framework reduces the energy consumption in data movement and weight storage.
The model compression technique is also leveraged when distributing a trained model to various end-devices. To provide AI-based services for end-devices with heterogeneous architectures, conventional approaches usually train a specialized model for each, which causes prohibitive computation and energy overhead. Cai et al. [45] propose a once-for-all network and utilize the pruning method to obtain a sub-network from the once-for-all network for each end-device, which reduces carbon emissions by up to 1300× through avoiding additional training.
2) Server-level energy efficiency improvement: In the server level, energy-aware or carbon-aware workload scheduling is key to increasing the energy efficiency. Workload scheduling is to decide "when, where, and how" the tasks scheduled in server(s) can achieve the least energy consumption and carbon emissions. There are generally two ways to schedule workloads: within a single server and across servers.
Single-server workload scheduling. The service provider can apply resource allocation, workload consolidation, priority-based scheduling, and so on, to manage the server's energy consumption and corresponding carbon emissions. The single-server workload scheduling generally improves the energy efficiency at the expense of the performance. For example, decreasing the quota of computation resources (e.g., GPU memory) for the object detection task will save more energy while hurting the accuracy, which would degrade QoE of the AR service greatly [92]. The metaverse service provider should carefully balance the trade-off between performance and energy efficiency, especially for real-time metaverse services. Prekas et al. [93] propose a latency-critical workload consolidation scheme combined with the DVFS technique for improving energy efficiency. Zhang et al. [46] focus on the emerging CPU-GPU integrated architecture that eliminates frequent communications between CPU and GPU through low-bandwidth and high-latency PCI-e. They advance a finegrained data stream system to schedule workload between CPU and GPU, and achieve 1.8× energy reduction as compared to the stream system based on the original discrete architecture. Wiesner et al. [47] propose a carbon-aware workload scheduling that prioritizes time-sensitive workloads and postpones delay-tolerant ones until the energy source is less carbon-intensive, such as the abundant solar energy during daylight hours.
Cross-server workload scheduling. The service provider would need to place and migrate workloads across servers considering the difference among servers in resource utilization, resource interference, energy efficiency, etc. The performance of the metaverse services often behaviors differently on heterogeneous hardware. For example, the inference time of YOLOv3, a commonly-used object detection model, deployed on Nvidia Jetson Nano is 20× longer than that on Nvidia GTX1060 [94]. The metaverse service provider should capture these heterogeneous behaviors and provide sufficient performance guarantees during the cross-server workload scheduling. Yi et al. [48] design a workload allocation algorithm for long-lasting and compute-intensive tasks. Based on the deep reinforcement learning technique, the proposed algorithm captures the complex power and thermal dynamics of servers, and learns to make efficient workload allocation decisions that achieve a high power efficiency. Wang et al. [49] propose a QoE-aware workload scheduling framework to reduce energy consumption. The proposed framework jointly utilizes GPUand FPGA-based accelerators to cap peak server loads during a day, which reduces the energy consumption by up to 23% with QoE guarantees. Considering the trend that the ISA architecture is evolving in datacenters, Barbalace et al. [95] develop an efficient workload scheduling solution to migrate executions between heterogeneous-ISA servers. The proposed solution can reduce over half of the original energy consumption.
Implications Workload scheduling is a common technique used in datacenters. To schedule various metaverse workloads, service providers need to carefully characterize and categorize these workloads in advance to reach an efficient balance between performance and energy consumption at run time.
C. Energy Efficiency Improvement of non-IT Systems
Besides the energy consumption of IT systems, attention should be paid on the energy efficiency of cooling systems and power systems that are the most power-consuming parts among non-IT systems.
1) Cooling systems: In datacenters, power flows through the IT systems and is transformed into thermal energy, which should be discharged by cooling systems to ensure the safety of IT systems. High-demand metaverse services not only consume a large amount of IT energy, but also increase the pressure of cooling systems.
There are three commonly-used cooling techniques in datacenters: air cooling, liquid cooling, and free cooling. Air cooling is the most widely-used cooling technique in datacenters since it can be deployed in whatever environment. However, air cooling is also the most energy-consuming one because of the low heat conduction capacity of the air, difficulty in controlling the air flow, and so on. Designing a thermal-aware workload scheduling approach is an intuitive way to reduce the energy consumption and improve the efficiency of air cooling in the era of the metaverse. However, it is hard to capture the system dynamics and complexity since metaverse service requests cannot be easily predicted and the cooling energy is affected by multiple factors such as the workload placement and airflow rates. To handle the system dynamics and complexity, Ran et al. [52] propose a deep reinforcement learning based solution to reduce the cooling energy through workload scheduling and cooling adjustment, which achieves up to 15% of the energy savings.
Compared with air cooling, liquid cooling has better efficiency because of the higher density and thermal capacity of the liquid like water. Liquid cooling can be classified as directto-chip cooling and immersion cooling. In a direct-to-chip cooling system, cold liquid removes heat from components through a cold plate which is directly pressed on the surface of each component. While in a immersion cooling system (either single-phase or two-phase), all components are submerged in a thermally conductive dielectric liquid to dissipate the heat. Jalili et al. [96] conduct a comprehensive study on two-phase immersion cooling in terms of performance, costs, etc., which lowers the datacenter PUE by about 14% than that of an air-cooled datacenter. Zhou et al. [50] discuss the energy inefficiency in edge datacenters, and suggest some future trends, such as prioritizing the cooling technique of immersion liquid cooling. However, compared to the directto-chip cooling, immersion cooling places strict constraints on the fluid, tank, etc., which increases the capital expenditure and may prevent large-scale adoption especially in edge datacenters [51]. According to a comprehensive analysis of edge datacenters, Pei et al. [51] find that existing cooling techniques are inefficient for edge datacenters because of the proximity, power density, and diverse edge services. To address the challenges of heterogeneity and high density of edge datacenters, they advance a fine-grained and custom-designed warm water cooling solution with high energy efficiency.
It is worth noting that many natural cooling sources can be leveraged to cool datacenters without additional energy consumption, such as cold air and water. Free cooling aims to make use of external low ambient temperature to dissipate the heat without the refrigeration process [97]. To this end, free-cooled datacenters should be sited in cold locations for access to the free cooing sources. However, there are also some challenges to utilize free cooling. The temperature fluctuation of natural cooling sources during the day would probably reduce the hardware reliability [98]. Besides, the effect of workload placement on the heat recirculation should be also carefully considered to reduce the temperature variation. To handle the above challenges, Nguyen et al. [53] propose a joint management of workloads and cooling control for freecooled datacenters to maintain the air temperature with low cooling energy.
Implications The cooling efficiency is highly dependent on specific datacenter infrastructures and workloads. Thus, we should differentiate between different datacenters that focus on different metaverse services and accordingly adopt a targeted and even customized cooling technique.
2) Power systems: Power supply and distribution systems are essential to daily reliable operations of datacenters. It is of great importance to ensure high availability of the power systems for providing 7×24 metaverse services. To this end, many datacenter operators tend to equip their datacenters with redundant power and cooling capacity. Zhang et al. [55] point out that about 10%-50% of the power resources are typically reserved, leading to a waste of energy and extra expenses. To improve the energy efficiency while ensuring 7×24 reliable services, it is necessary to reduce power mismatches with hardware-or software-based solutions. The hardware-based solutions are to utilize non-IT equipment, such as energy storage, to balance the power demand and ensure the availability. Liu et al. [54] propose to combine super-capacitors with traditional uninterruptible power supply systems, which helps improve clean energy usage and leads to a high energy efficiency. Shen et al. [101] focus on the power management of hardware components, i.e., microprocessors and peripherals, which achieves minimum power consumption under performance constraints. The software-based solutions are to achieve peak shaving through workload management. Zhang et al. [55] introduce "zero-reserved-power" datacenters with availability guarantees. Specifically, they find that there are some software-redundant workloads (i.e., Software-as-a-Service-based workloads like Web search concerning that they are always replicated across multiple availability zones [55]) that can tolerate infrastructure failures, such as 3D rendering in the offline stage. Utilizing these workloads, they propose a workload management solution to reduce the reserved resources and hence decrease the redundant power consumption while ensuring the system availability.
Power losses of the power systems during energy conversion is another important problem in datacenters as it consumes around 10% of total datacenter energy. There are several energy-efficient solutions on various components of power systems, such as uninterruptible power supplies (UPS), transformers, and power distribution units [102]. Recently, Delta and Alibaba introduce a new power supply system with the Panama Power solution that achieves 2% ∼ 4.6% energy efficiency improvement by transforming 10kV alternating current to 240V/336V direct current directly [56].
D. Energy Efficiency Improvement of the Entire Infrastructure 1) Clean energy: The adoption of clean energy can greatly reduce the carbon footprint from the aspect of energy supply because of its much lower carbon intensity than conventional fossil energy sources, as listed in Table IV. Figure 10 plots their energy shares by source in the United States from 1949 to 2021 [100]. We can find a constantly growing share of renewable energy sources, especially after the year of 2007 when the total fossil energy consumption peaks and starts to decline. To combat global warming, it is reported that the clean energy (e.g., renewable energy, nuclear energy, and fossil energy with carbon capture and storage technologies) would need to contribute 70% of the energy demand in 2050 [103]. As a pioneer of green computing, Google achieved carbon neutral as early as 2007, and aims to be carbon free in 2030. The continuous promotion of clean energy plays a key role where Google matches the global energy consumption with 100% renewable energy since 2017 [104].
There also exist many researches demonstrating that the clean energy has great potential for increasing the energy efficiency of datacenters. Deng et al. [105] comprehensively study why, when, where, and how to use renewable energy in datacenters. They highlight the necessity to match multiple energy source supply with variable power demands. Gupta et al. [57] investigate the potential to combine multiple clean energy sources for complementary benefits. Zhou et al. [58] analyze the benefits of fuel cell generation in geo-distributed datacenters for the first time. As the output of the fuel cell is tunable, it can be adjusted to match the time-varying energy demand of datacenters and avoid energy waste.
However, it is challenging for datacenters to use clean energy when managing metaverse services. The generation of renewable electricity highly depends on the weather, and thus the clean energy supply is uncertain, intermittent, and variable [105], [106]. As the metaverse requires 7×24 services and the user requests could be highly dynamic during the online stage, the use of clean energy may cause significant supply-demand mismatches and hurt the reliability of the metaverse. To address these challenges, there are three ways to achieve the service reliability while utilizing the clean energy: predicting the clean power generation, leveraging the energy storage, and utilizing the temporal and/or spatial correlation of the clean energy. In the first approach, the service provider can schedule the workload based on the estimation of renewable energy generation. For example, Aksanli et al. [107] design short-term prediction algorithms for both solar energy and wind energy, and propose a workload scheduling approach to improve the proportion of clean energy usage. However, the prediction accuracy of renewable energy is just passable because of the frequent weather changes [105]. Another potential approach is to use the energy storage technology to bridge the supplydemand mismatches. Ren et al. [108] present an algorithm to carefully decide the energy storage's charging/discharging rate and renewable power capacity. Deng et al. [109] design an online algorithm to decide the UPS's charging/discharging rate and the power procurement considering the time-varying clean energy price, certain volumes of intermittent renewable energy, and the capacity of UPS. The third approach is to utilize the temporal and/or spatial correlation of the clean energy. Some companies build datacenters in a distributed manner for providing a wider range of services. For these geo-distributed datacenters, Zhou et al. [110] find that there is a spatial and temporal variability of the electricity's carbon footprint due to the different fuel mixes of electricity generation among different regions and periods. Leveraging the variability, they design a carbon-aware control framework that jointly reduces power costs and carbon emissions through geographical load balancing, capacity right-sizing, and server speed scaling.
Implications Clean energy is believed to be promising in reducing carbon emissions. However, since different metaverse applications will match different datacenter types as discussed before, e.g., cloud and edge, the supply-demand imbalance across them can reduce the usage effectiveness of clean energy, where energy transmission and storage techniques may help.
2) Heat harvesting: As discussed in Sec. III-C1, the growing demand of the metaverse not only makes the carbon emissions burst but also increases the pressure of cooling systems. What is more, after the IT systems get cooled, the thermal energy tends to be dissipated to the environment directly, which may sometimes have a negative impact on the environment and is energy-consuming [59]. To fully utilize the heat, waste heat harvesting has been emerging in the practice and literature, which is promising to reduce carbon emissions by enabling other industries to leverage this recycled heat, such as warming buildings in some middle-and high-latitude cities.
There are two common ways to realize district heating depending on the servers' distance to buildings, i.e., locally or remotely. Liu et al. [111] propose a concept of "data furnace" which delivers heat to residential buildings by placing servers just in them. In recent years, "data furnace" has been commercialized, e.g., a computing heater by Qarnot [112]. If the servers are far from buildings in the form of datacenters, it is necessary to set up district heating systems to transfer the heat. Chen et al. [59] analyze the feasibility and profitability to harvest heat from datacenters and warm buildings with the help of district heating systems. They propose a market mechanism to motivate datacenter operators to sell waste heat to district heating systems, which not only improves the energy efficiency of datacenters but also reduces the usage of fossil energy in heat generation. To reduce the heat transferring overhead, it is rather practical to recycle heat from edge servers while providing real-time metaverse services, as edge datacenters are typically located in or next to residential/commercial areas. Thanks to the location, the waste-heat recovery system in the Tencent Tianjin datacenter directly brings heating to more than 5,100 local households, saving the high costs for long-haul delivery of the heat [113]. The reduced 52,400 tonnes of carbon dioxide emissions every year is equivalent to the carbon footprint of Portland [113], [114].
Besides harvesting heat for warming, some researches focus on reusing waste heat to generate electricity. Lee et al. [115], [116] leverage thermoelectric generators (TEGs) to recycle heat from microprocessors and power the fans or TECs for cooling. Zhu et al. [60] focus on warm-water-cooled datacenters, and use TEGs to recycle waste heat from the heated cooling water and convert it into electricity. The power reusing efficiency of the proposed approach reaches 14.23% on average.
3) Emerging computing technologies: There are some newly emerging advanced computing technologies that may contribute to energy efficiency improvement and carbon reduction of the datacenter infrastructure.
Cryogenic computing. Recent researches find that cryogenic computing can reduce the component power by about one order of magnitude without performance degradation [117]. However, there could be higher difficulty in managing the cooling system and higher cooling energy consumption to support the extremely low temperature, which may make this technology still be in the pilot phase. Min et al. [61] further propose a CPU microarchitecture under cryogenic computing. Extensive evaluations indicate that it achieves higher performance while reducing both hardware and cooling energy consumption.
Quantum computing. It is recognized that classic computers consume significant amounts of energy especially for high performance computing. With the evolving of the computing technology, quantum computing is believed to provide higher computing capacity with less energy consumption. By leveraging the superposition property as well as other technologies, such as quantum tunneling, quantum bits are exponentially efficient than classical bits. The recent quantum computer Zuchongzhi is estimated to be tens of thousands times faster than the world's most powerful supercomputer by then [62]. Meanwhile, according to an estimation, quantum can reduce energy consumption by hundreds to thousands times [118]. In short, quantum computers are continually advanced and considered to revolutionize the global datacenter energy [119], which also makes sense to the infrastructure for the metaverse.
E. Directions to Become Green
Although there have been extensive studies on green techniques, there are still several challenges in the infrastructure layer. Specifically, we propose an insight into the deployment of special-purpose hardware components in datacenters as these components are becoming increasingly popular to handle specific metaverse workload types.
Insight: Special-purpose hardware is not a silver bullet for metaverse computing. There are many off-the-shelf special-purpose hardware components with different characteristics and they typically achieve a higher energy efficiency when executing certain tasks than general-purpose CPUs. For example, data processing units (DPUs) can perform data processing efficiently while AI accelerators are specially designed for AI tasks. Nonetheless, it is not a good idea to execute all metaverse workloads on these special-purpose hardware components. Firstly, special-purpose hardware components may perform worse than CPUs for some memory-intensive metaverse workloads. A recent work indicates that CPUs achieve much lower inference latency than GPUs when executing memory-intensive AI models like long short-term memory [120]. Secondly, special-purpose hardware components are generally more expensive than CPUs. For example, an A100 GPU costs over $10,000, while a CPU typically costs only a few thousand dollars. Last but not least, as a kind of generalpurpose hardware components, CPUs can carry out a wide variety of tasks so that they are more capable of shaving peak computation demands as the demand of different types of workloads fluctuate.
Direction: On the one hand, datacenter operators should have a knowledge of the provided metaverse services of the datacenter and the required computations (e.g., AI inference and 3D rendering). To make full use of both general-purpose and special-purpose hardware components, it is necessary for datacenter operators to comprehensively consider the performance, cost, energy efficiency, etc., to choose customized hardware combination, i.e., the number of each hardware type in a specific datacenter. On the other hand, it is also necessary for service providers to have a deep understanding of the various components in terms of the energy usage, and accurately measure and disaggregate the energy consumption of metaverse workloads in their life cycles on each component. Note that given the changing amounts of clean energy production and total power supply, the most desired power demand can also vary dynamically. For example, the electricity prices in many European countries are even set negative sometimes in order to maintain a must-run power capacity [121], which indicates that higher energy consumption of datacenters or a lower energy efficiency may be desired in this case. In all, the service providers need to comprehensively consider the performance, energy efficiency, etc., and devise a dynamic service deployment mechanism to schedule various metaverse services to a specific hardware component at run time.
IV. HOW CAN THE INTERACTION BECOME GREEN?
In addition to the datacenter infrastructure, both humancomputer interaction and human-human interaction play a key role in presenting immersive experience to users. The human-computer interaction relies on various end-devices and AR/VR/MR-based applications. The end-devices involve mobile phones, glasses, headsets, sensors, and even motioncapture gloves for lifelike experience [147], while the applications include virtual conferencing, cloud gaming, etc., running on top of these end-devices. Instead of a single user, the human-human interaction provides essential supports for the communication of multi-players in the metaverse. Such support relies on both networking components (e.g., cellular modem chips on end-devices and cellular base stations) and data transmission between these components. Considering the requirements of the metaverse for ultra low latency, high bandwidth, high speed, low jitter, etc., the emerging 5G technology is promising to support large-scale human-human interaction by nature as compared with 4G/LTE [28]. By means of 5G, it is possible to offload computational metaverse workloads like AI-based tasks from battery-constrained end-devices to datacenters and download other players' data at the same time Die shrink 2 nm processor [123] Deploying special-purpose processors Holographic processor [9] Modem chip (Sec. IV-D1)
Using integrated modems Dimensity series [124] Dynamic voltage frequency scaling UltraSave [125] Power management Dynamic search space adaptation [126] Switching between wireless technologies Xu et al. [127], Narayanan et al. [ Power management 5G Power [145] Data transmission (Sec. IV-D2) Energy recovery Wu et al. [146] as discussed in Section III [148]. In the following, we will first introduce the carbon issue of the interaction and then analyze green techniques to improve the energy efficiency of the enddevices, applications, and networking components. In the end, we provide future directions to become green.
A. The Carbon Issue of the Interaction
With the evolvement of the metaverse, users are demanding more advanced interaction technologies for ultimate immersive experience. Meanwhile, there will be inevitably huge global energy consumption and carbon emissions of the interaction. Firstly, although the power consumption of a single enddevice is only several Watts on average [149], the total energy consumption will still be high since the number of end-devices is continually growing, especially for the smartphones and wearable devices like VR headsets. In particular, the number of global mobile devices rises from less than 8 billion in 2016 to more than 12 billion by 2022 [150], while VR and AR headsets are estimated to grow about 10 times from about 11 million in 2021 to 105 million in 2025 [151]. Secondly, the increasing demand for metaverse applications also lead to high energy consumption and carbon emissions. For example, the carbon emissions from streaming workloads in 2018 is almost equivalent to those from France [152]. The real-time interaction among users in the metaverse relies heavily on the streaming-based applications and will raise the carbon emissions further. The second example is the popular computer vision and natural language processing tasks, where the energy consumption of one AI inference execution is gradually approaching and has even surpassed the energy consumption of a human body per second, respectively [153]. This indicates the severe energy burden by AI inference in view of its widespread use as the metaverse continues expanding to benefit everyone. In summary, it is estimated that the global carbon emissions of end-devices will reach about 442 Mt in 2022, comparable to the carbon emissions of Canada [31], [36], [154].
Meanwhile, the proliferation of a sheer number of enddevices and applications to support the metaverse will put increasing pressure on the networking energy usage. According to an estimation by Cisco [150], the global mobile data traffic will increase from 12 exabytes per month in 2017 to 77 exabytes by 2022. Although the energy efficiency of 5G is higher than previous 4G/LTE, the larger antenna numbers, higher base station density, and higher bandwidth [144], as well as the high data transfer demand by the metaverse will make its total energy consumption increase sharply. According to a recent report [155], as compared with a 4G base station, a typical 5G base station increases the energy consumption by up to twice or more. It is estimated that the global carbon emissions of networking will reach about 95 Mt in 2022, comparable to the carbon emissions of Netherlands, and is expected to increase by 2.7× by 2030 [31], [36], [154]. On the other hand, when it comes to end-devices supporting higher band frequencies, Redmi claims that 5G mobile phones tend to consume about 20% more power than 4G ones [156], and real measurement studies conducted by Xu et al. [ Fig. 11. Key components for carbon reduction during the whole interaction process. energy consumption of mobile devices over 5G than 4G.
Facing the severe carbon issue, it is urgent to develop green techniques to reduce carbon emissions from the interaction. As listed in Table V, there have been many studies to improve energy efficiency of end-devices and applications for humancomputer interaction, and networking equipment for humanhuman interaction. Figure 11 depicts these key components for carbon reduction during the whole interaction process. Similar to the PUE used to indicate the energy efficiency of datacenters, the indicator performance per watt (PPW) can be used to indicate the energy efficiency of a particular end-device or its internal hardware component.
B. Energy Efficiency Improvement of End-devices for Human-Computer Interaction
An end-device generally contains various components like processors, memories, modem chips, etc., which dominate its total energy consumption [157]. In addition to green techniques for saving energy directly, the heat harvesting technology, similar to the one used in datacenters, make sense to metaverse users for achieving a longer standby time of their end-devices. In the following, we will discuss green techniques on processors and the heat harvesting technology, and leave the discussion on modem chips, a key networking component in Section IV-D.
1) Processors: Processors are core components for providing computing power in an end-device, including generalpurpose processors (e.g., CPUs) and newly emerging specialpurpose processors (e.g., GPUs, NPUs, DSPs). The latter are designed to execute only specific workloads, and is believed to have a higher energy efficiency.
Heterogeneous processing architectures. There are many techniques developed for general-purpose processors, such as the heterogeneous processing architecture technology and die shrink technology. As a representative architecture, the ARM big.LITTLE is widely used in modern mobile phones [122]. By equipping devices with both energy-efficient and highperformance heterogeneous processors, dynamic task allocation can be realized with this technology to maintain high performance while improving PPW. For the various kinds of metaverse workloads, developers should carefully decide on the best processor candidates.
Die shrink. Although Moore's law may come to an end by around 2025, it is still effective to improve PPW by shrinking the die further [158]. Recently, Qualcomm has announced its Snapdragon 8 Gen 1 processor with the upto-date 4 nm technology [159]. Compared to its previous generation Snapdragon 888 with the older 7 nm technology, this new processor achieves 30% power savings. Furthermore, it is reported that IBM has already created the world's first 2 nm processor in the lab, which can reduce as high as 75% energy at the same performance as compared to the mainstream 7 nm processors [123]. When developing the enddevices for the metaverse, processors with smaller transistors can be preferentially selected to achieve not only higher energy efficiency but also better user experience although there may be potentially higher costs. For example, the 75% energy savings achieved by the 2 nm technology also mean that the battery life can quadruple after the battery gets fully charged. This is especially significant for end-devices with limited battery capacity since users may not want to charge them halfway while enjoying the metaverse.
Deploying special-purpose processors. In addition to the above general-purpose processors, special-purpose processors have gained increasing attention from both academia and industry. These special processors have been recognized to improve energy efficiency significantly and even become the future of computing [160]. Considering the great benefits of the AI technique, AI accelerators are one of the most successful special-purpose processors. Recent works have designed various AI accelerators for enabling highly efficient AI inference on end-devices, such as Google's Edge TPU [161] and Samsung's Exynos 2100 processor [162]. The later incorporates tri-cluster CPUs, a GPU, an NPU, etc., and the integrated NPU improves the energy efficiency to 0.84 mJ per inference [162] from a typical value of tens to hundreds of millijoules [163]. Besides AI accelerators, other studies aim to design special-purpose processors tailored to metaverse devices. For example, Microsoft equips its AR headsets HoloLens [9] with a holographic processing unit that is responsible to process and integrate all the data streaming collected from on-board sensors. This custom processor consumes only less than 10 W, showing its high energy efficiency concerning the huge amount of workloads to be processed [164]. In all, as compared to general purpose processors, these special-purpose processors hold great promise for the metaverse since the enddevices mainly perform specific types of workloads, such as data collecting and AI inference.
Implications Similar to datacenters, it is necessary to deploy special-purpose processors on end-devices for processing various metaverse workloads efficiently. However, it is nontrivial for universal end-devices like mobile phones to balance performance, power demand, energy efficiency, die size, cost, and others when integrating these processors. Thus, more dedicated devices like VR headsets with VR chips need to be studied and developed beyond existing mobile phones.
2) Others: Heat harvesting. Some external components are well studied to power end-devices through heat harvesting. Dai et al. [129] present a TEG-based heat harvesting and reusing framework for mobile phones, and the generated electricity can help extend the battery life. Similarly, Yap et al. [130] leverage TEGs for heat recovery from human bodies. Without any active heat input to TEGs, Raman et al. [165] further show the potential to recycle heat in the dark. In summary, although the generated power is only a few to tens of mW at present, it is still meaningful to make further attempts on the heat harvesting technology, concerning the surprisingly high energy consumption of end-devices (presented in Section IV-A) on the way to the metaverse.
C. Energy Efficiency Improvement of Applications for Human-Computer Interaction
On top of end-devices, there are various metaverse applications, such as virtual conferencing, virtual manufacturing, and cloud gaming. These applications rely on processing technologies such as AI inference and video analytics to generate the content, as well as display technologies including VR, AR, and MR to display the content. In the following, we will discuss green techniques on processing and display technologies.
1) Processing technologies -AI inference: As discussed in Section II-A, the AI technology plays an important role in building a virtual world and virtual persons in the metaverse and afterwards, operating the virtual world in a real-time manner. In addition to datacenter infrastructure, Facebook proposes to deploy AI inference on end-devices to achieve reduced latency and become independent of changeable network conditions [166], which makes sense to metaverse workloads with high requirements on QoE or privacy. Considering the limited computing power and battery capacity of end-devices, many green techniques have been advanced for AI inference. In the following, we will discuss these techniques from the perspective of the application and system levels.
AI model compression. As a common application-level method, AI model compression has been evaluated by many works, and can be divided into several methods, including quantization, sparsification, tensor decomposition, and so on [90]. Qualcomm prompts the quantization method, where the addition and multiplication operations can reduce energy consumption by 30× and 18.5×, respectively, and the memory access energy decreases by up to 4× by leveraging the INT8 formats instead of conventional FP32 formats [131]. Yang et al. [132] develop a specification method that achieves up to 3.7× energy reduction with less than 1% top-5 accuracy loss. Although model compression shows the huge potential in saving energy, there can be perceptual accuracy drop. Depending on the type of metaverse applications and enddevices, developers should make decisions on different model compression methods and their combinations to achieve optimal energy efficiency and accuracy trade-offs.
Collaborative execution. Another application-level method is the device-edge collaborative execution proposed by Kang et al. [133]. Considering that the energy consumption of end-devices comes chiefly from the computation and data transmission, the authors point out that the data transmission energy can be reduced by a large margin through partial offloading, i.e., model layers before the partition point are processed locally, while the rest are transmitted to the cloud/edge platform and processed remotely. The results show that mobile energy consumption can be reduced by 59.5% on average and 94.7% at most. Instead of a single partition point, Eshratifar et al. [134] further consider several partition points depending on the DNN model structure, and achieve up to 32× mobile energy savings. However, although the collaborative execution can save energy of end-devices, there exists extra energy consumption of the cloud/edge platform which is neglected by prior works.
Implications Different from other techniques, collaborative execution involves cloud and/or edge that are/is responsible to process the second part of inference. However, more works are still necessary to investigate this additional part of energy consumption as compared to completely local execution.
Dynamic voltage frequency scaling. The system-level technique DVFS is especially important to end-devices with limited battery capacity, and is well studied for years. Tang et al. [135] investigate the impact of GPU DVFS settings on energy consumption of AI inference tasks. By selecting a proper GPU frequency, they achieve as high as 26.4% energy reduction. Many recent works start to focus on a hybrid solution that considers both model compression and DVFS, which helps achieve different trade-offs. To achieve tradeoffs between energy efficiency and accuracy, Nabavinejad et al. [136] develop an approach to select proper model precision (e.g., INT8 and FP32) and GPU frequency, and the overall energy consumption decreases by up to 28%. Bateni et al. [167] leverage the hybrid solution to achieve a trade-off among energy efficiency, accuracy, and latency, and save the energy by up to 68%. The hybrid solution provides much more candidates for metaverse developers. However, in view of the various metaverse applications and heterogeneous end-devices, it is nontrivial to customize the solution for each applicationdevice combination.
Workload scheduling. As a widely-used system-level technique in both datacenters and end-devices, workload scheduling has been well studied. For end-devices, workload scheduling usually combines with model selection/compression and DVFS. Wang et al. [137] combine workload scheduling with DVFS in view of the widely deployed asymmetric multiprocessors on end-devices, e.g., ARM-based multicore CPUs, and devise an asymmetry-aware partitioning and task scheduling solution. Wan et al. [168] combine application-level model selection and system-level resource allocation. As compared to approaches at either the application or system level, this hybrid solution reduces the energy consumption by over 13%.
Customized AI inference frameworks. Another systemlevel method is developing customized AI inference frameworks, which is of great importance to AI inference-based metaverse applications. Based on TensorFlow, Google develops the TensorFlow Lite framework [138] to enable efficient AI inference on end-devices with computing power and energy constraints. Zhang et al. [169] further devise a framework combined with application-level optimization, such as adaptive model selection. Since these methods improve energy efficiency usually at the expense of performance, metaverse developers should carefully select the components and its frequency that achieves the best energy efficiency and performance tradeoffs.
2) Processing technologies -video analytics: Video analytics leverages the AI technique to complete various computer vision tasks for videos, such as motion detection and behavior tracking [170]. Therefore, many green techniques can be developed based on the properties of video streaming. Feng et al. [139] establish a runtime system to select a compressed AI model dynamically based on the time locality and class skew properties of video streaming, which achieves up to 6.7× energy savings. Song et al. [140] point out that the video frames can be categorized into three types, i.e., I, P, and B frames. Since B frames can be completely reconstructed by I and P frames, AI inference-related computations for the B frames can be significantly reduced. These video-oriented techniques are key to the streaming-based metaverse applications from virtual conferencing to virtual manufacturing.
3) Display technologies: The VR, AR, and MR technologies bridge the virtual and physical worlds, and provide immersive experience to users. Specifically, VR displays a completely virtual world through 360 • video streaming. In comparison, AR needs to place virtual objects in the user's field of view properly after recognizing the surrounding physical environment [171], [172]. MR is regarded as a combination of VR and AR.
Reducing unnecessary data transferring and redundant calculations. To satisfy the strict latency requirements of realtime interaction, current VR and AR devices mainly perform computational tasks locally. For VR devices that support 360 • video streaming, there are abundant computations and data movements between GPUs, DRAMs, and display panels, which wastes huge amounts of energy. Haj-Yahya et al. [141] focus on a new data transferring architecture that demonstrates up to 33% energy savings. Zhao et al. [142] make full use of temporal and spatial correlations of the video to reduce unnecessary computations, which lowers the energy consumption by 17%. For AR devices, object recognition is a key component for the environmental perception. Apicharttrisorn et al. [143] design an object tracking solution to improve energy efficiency while maintaining high detection accuracy by reducing redundant computations. Their real-world experiments show up to 73.3% energy reduction. In view of the popularity of VR, AR, and MR in the metaverse and the increasing bit rates of video frames, there is likely to be huge and probably redundant data transmission, as well as redundant computations for AR applications to conduct AI inference in the background. It is urgent for metaverse developers to adopt more green techniques and put them into practice, while preventing perceptible QoE drops.
D. Energy Efficiency Improvement of Networking for Human-Human Interaction
Although 5G provides many attractive properties desirable to the metaverse, the high energy consumption for transmitting data among end-devices and base stations can generate large carbon emissions as presented in Section IV-A. In the following, we will discuss green techniques on modem chips in end-devices, base stations, and data transmission.
1) Modem chips in end-devices: The energy consumption of end-devices for data transmission comes chiefly from modem chips. There are several green techniques on modem chips at hardware and software levels.
Using integrated modems and dynamic voltage frequency scaling. At the hardware level, with the evolving of the chip technology, instead of building separate 5G modems, Me-diaTek proposes its Dimensity series with integrated modems to reduce the energy consumption [124]. The adopted Ultra-Save technology [125] further saves energy by adjusting the chip frequency dynamically.
Power management. At the software level, to learn the energy share of each networking-related operation, it is necessary to build power models in the first place and then enable power management. In particular, according to a power model developed by 3GPP [126], the control channel monitoring operation dominates the total energy consumption (e.g., over 50%) although this operation only occupies a small portion of time cycles (e.g., about 5%) without any data transmission. This monitoring operations could be reduced on metaverse devices in view of the continuous and stable connection to the virtual world in VR/AR scenarios. For end-devices using different frequency bands, such as mmWave and sub-6 GHz, however, the energy shares of each operation behave differently [126]. This indicates that it would be useful to design custom-designed power management schemes for them, such as discontinuous reception configuration settings recommended by 3GPP [173], and dynamic search space adaptation proposed by Ericsson [126].
Switching between wireless technologies. It is recognized that it is not always efficient to use the 5G signal for communication rather than 4G especially when the throughput is low [127], [128]. Xu et al. [127] advance a dynamic mode switching solution that switches the device to 5G only when the throughput demand is beyond 4G's capacity. The simulation results show that the energy consumption can be reduced by up to 24.8% as compared to using 5G all the time. Narayanan et al. [128] propose a solution for video streaming applications which switches the device to 4G when the predicted 5G throughput is below a threshold. However, switching between 4G and 5G frequently can incur hiccups, which may greatly degrade user experience when users are immersing themselves in virtual roles. Besides, the switches themselves consume significant amounts of energy, which would decrease the benefits from 4G-5G switches. Recently, Kim et al. develop a new material of switches for 5G devices [174] and even 6G ones [175]. The ones for 5G not only deliver a 50× increase in energy efficiency but also realize as high as nanosecond switching speeds, which is promising for the metaverse with continuous multiplayer interaction.
2) Base stations: There are studies focusing on architectural design [144] and power management [145], [176], [177] to save energy of base stations. For metaverse applications, the power management can be one of the key considerations when transferring data between users. Recently, China Tower and Huawei propose their 5G Power solution that enables intelligent peak shaving, intelligent voltage boosting, and intelligent energy storage [145] in an end-to-end manner, which helps save significant costs during retrofitting existing low-capacity site infrastructure. Evaluation results show that this solution is able to save around 4,130 kWh of electricity, and 1,125 kg of carbon emissions per site per year.
3) Data transmission: During data transmission, similar to heat harvesting for end-devices, it also makes sense to recycle energy from the high-frequency radio signals of 5G [178]. Wu et al. [146] further summarize some schemes to improve energy harvesting, such as energy beamforming and channel state information acquisition.
Implications Different from conventional content delivery network (CDN) that distributes just texts, images, and HD or UHD videos, many metaverse applications are built upon extremely high-bitrate videos, such as 16K panoramic videoon-demand and volumetric video streaming [179], [180], which will inevitably bring much higher energy consumption and carbon emissions. Thus, it is urgent to conduct more quantitative measurements on these newly emerging applications under real environment and develop targeted green techniques on the way to the metaverse.
E. Directions to Become Green
Although there have been extensive studies on green techniques, there are still several challenges in the interaction layer. Specifically, we propose two insights into the selection of green techniques and heavy network overhead of the existing CDN technology.
(1) Insight: It is nontrivial to select the best green technique and settings for each metaverse end-device and application. As a large number of new types of metaverse devices and applications start to emerge, such as smart gloves, existing green techniques lack generalizability and scalability. For example, the effectiveness of the AI model compression technique depends on the hardware architecture [90]. That is, an AI model compressed for one hardware type is likely to become less efficient and even inefficient for another, especially the newly-emerged ones with different architectures. However, this will increase the burden of developers as they need to have a rich understanding of various devices and applications and manually select the best green techniques and parameters for each device and application.
Direction: To reduce the burden of metaverse developers, it will be promising to develop a set of automated search engine tools based on intelligent algorithms like reinforcement learning. With such a tool, developers only need to provide necessary inputs like the workload type, hardware type and performance requirements, and the tool can automatically provide suggestions and recommend the best green techniques and parameters.
(2) Insight: The network overhead of the CDN technology gets worse as metaverse users are distributed all over the physical world. It is recognized that CDN can help distribute contents (e.g., 3D background images) based on user preferences in different locations. However, under the scope of the metaverse, users are usually scattered across the physical world, even if they are very close in the virtual world. To this extend, CDN nodes need to cache contents for each user far from each other, which greatly increases the network transmission burden.
Direction: Since metaverse users are typically far from each other in the physical world, green techniques based on edge computing are promising to reduce the network overhead and potential carbon emissions. For example, we can transmit only low-quality frames from the cloud and then perform super-resolution at the edge. In addition, instead of downloading all rendered frames from the cloud, edge nodes can generate subsequent frames based on historical frames and their temporal correlation. The above solutions trade the computation for communication, so developers should ensure a low computing overhead.
V. HOW CAN THE ECONOMY BECOME GREEN?
Similar to the physical world, the metaverse economy requires a financial system to ensure trusted transactions between users and verify their ownership rights. In view of the requirement of high security, the financial system of the metaverse has widely incorporated the blockchain technology. As a virtual currency, the cryptocurrency is a necessary medium for online transactions, and non-fungible tokens (NFTs) are used to prove the ownership rights of users' virtual properties [184]. For example, many metaverse platforms, such as Decentraland, Somnium Space, Nextech AR, etc., have allowed users to buy and sell their virtual properties with blockchain-based cryptocurrencies [185], [186], [187].
The blockchain technology, dating back to 2008, refers to an immutable distributed ledger on a peer-to-peer network which ensures trusted transactions or records with a consensus protocol [188], [189], and achieves adequate security through its natural features as follows. The blockchain consists of a chain, i.e., a sequence of blocks, with the last block containing the hash value of its former block. Thus, a minor modification to a block will change its hash value and thus break the chain. As each worker in the peer-to-peer network keeps a copy of the chain that is synchronized frequently, no one can tamper with data on the chain without paying a huge price (e.g., owning more than half of the total computing power). In despite of the security property of the blockchain, it can cause significant carbon emissions for computing. In the following, we will introduce the carbon issue of the economy layer with the blockchain technology, and then analyze green techniques to improve its energy efficiency. In the end, we provide future directions to become green.
A. The Carbon Issue of the Economy
Although the blockchain technology is desirable to the metaverse, there exists a severe carbon issue. For example, Bitcoin is known for its large amount of carbon footprints on useless hash calculations. According to a study [33], Bitcoin is estimated to consume 126 TWh of electricity in 2021. Since Bitcoin occupies about 68.39% of cryptocurrency mining energy [34], the carbon emissions by all the blockchains for monetary transactions can be roughly estimated as 77 Mt in 2022 and 460 Mt in 2030 [33]. The main reason for the high carbon emissions is that Bitcoin uses proof of work (PoW) as its consensus protocol. All workers in the peerto-peer network can create a new block, and each of them races to solve a complex cryptographic hash puzzle in order to add its own block to the blockchain and get a reward. This process leads to many useless hash computations and thus high carbon emissions. Besides, the problem still remains serious for Ethereum although it has started to replace PoW with more efficient proof of stake (PoS). For example, the carbon footprint of an Ethereum transaction is comparable to about 329,000 credit card transactions currently [25].
Therefore, it is urgent to develop green techniques to reduce carbon emissions from the economy layer. As listed in Table VI, there are green techniques for improving energy efficiency and reducing carbon emissions of the blockchain. Figure 12 shows the key components for carbon reduction of the economy process.
B. Energy Efficiency Improvement of the Blockchain
Many researchers have made efforts on more efficient consensus protocols in the system level and transaction management in the application level.
1) Consensus protocol design and selection: Consensus protocols play a critical role in ensuring the security [190], while higher security usually brings higher energy consumption. Many blockchain platforms, including Bitcoin, Ethereum, etc., adopt different consensus protocols, such as PoW and PoS, with different trade-offs between security levels and the amount of computations, and the latter further determines the energy consumption and carbon emissions. As presented in Section V-A, PoW has an enormous appetite for energy. To achieve an energy-efficient consensus protocol, Sunny King et al. [191] design PoS in PeerCoin. Rather than taking lots of computing power to perform complicated hash calculations, PoS requires workers to place their coins at stake and chooses the block creator by an algorithm based on each worker's stake. Many blockchains and metaverse platforms have adopted PoS to improve efficiency although its security level is lower than PoW. For instance, Ethereum is gradually migrating from PoW to PoS, which will cut the energy consumption by more than 99% [192]. Some metaverse platforms like Decentraland and Somnium Space have chosen to build their financial systems based on Ethereum.
Recently, various consensus protocols have been proposed with different security levels and energy demands. Daniel proposes delegated proof of stake (DPoS), a variant of PoS [193]. It allows workers who hold a stake to vote to elect the block creator, which is proved to achieve higher energy efficiency [190]. In particular, Eleonora et al. [194] [181] propose Proof of Solution (PoSo), a new blockchain consensus protocol where the workers reach a consensus by solving a meaningful optimization problem rather than useless hash calculations as PoW. This could be very useful in the metaverse as there are many optimization problems whose solutions are hard to calculate but easy to verify, such as recognizing the shortest path for guiding the users in the virtual world.
Provided with so many consensus protocols, it is not easy to select the best one for a specific scenario. Bada et al. [182] critically investigate 18 consensus protocols with different estimated energy consumption and propose a framework for selecting a proper consensus protocol. This can be a useful tool for metaverse service providers to realize flexible tradeoffs between security levels and energy consumption.
2) Transaction combination: Combining multiple transactions together can decrease the number of transactions recorded in the blockchain and thus reduce the carbon emissions. Poon et al. [183] describe Lightning Network in a white paper for improving Bitcoin's scalability. Lightning Network allows users to make multiple transactions together and records them as a single transaction by creating a micropayment channel between users. Recently, the Ethereum platform has created its own Lightning Network named Raiden Network [195]. This technique would be desirable to the metaverse as both the demand for transactions and the transaction volume continue growing.
C. Directions to Become Green
Although there have been extensive studies on green techniques, there are still several challenges in the economy layer. Specifically, we propose two insights into handling frequent yet small transactions, and the trade-off between security and carbon emissions.
(1) Insight: It is rather inefficient to conduct a huge amount of transactions frequently for the metaverse. Un-like the physics world, the transaction process in the metaverse relies extensively on the blockchain technology. However, the high-volume, frequent yet small transactions pose a serious problem on efficiency if all the transaction processes are recorded on the blockchain. For example, a Bitcoin transaction consumes up to 1,173 kWh [196].
Direction: In fact, it is not always necessary to record all transactions on the blockchain in real time. Instead, we can merge consecutive and relative transactions in advance before adding them to the chain while ensuring the correctness.
(2) Insight: It is nontrivial to achieve a right trade-off between security and carbon emissions. It is no secret that security is the most important consideration for the economic system. New consensus protocols with fewer carbon emissions often partially sacrifice the security. What is worse, to save costs, some platforms even choose to store users' property just on the platform rather than the blockchain, which reduces carbon emissions by adding only a few blocks on the chain but poses security threats. Recently, an NFT owned by a famous star Jay Chou has been stolen, probably due to the malicious attack to the NFT platform without enough security guarantees [197].
Direction: To achieve a right trade-off between the security and carbon emissions, it is important to enforce different security levels based on the transaction types (e.g., proof of ownership, large-value transactions, daily small-value transactions) by adopting different consensus protocols. For example, large-value transactions have higher security requirements, but the transaction frequency is low, in which case PoW could be more suitable. On the contrary, for daily smallvalue transactions with a high transaction frequency, PoS could be better as the requirement for security is lower. However, the mashup of various consensus protocols place a higher requirement on the management of the blockchain system at the same time.
VI. A LOW-CARBON METAVERSE FROM THE GOVERNANCE PERSPECTIVE
A. Public Policies in the Physical World
In this section, we briefly discuss several public policies to spur energy efficiency and carbon neutrality investments, such as green financing and investing, carbon-neutral bond issuance, carbon trading, and carbon pricing. At the beginning of 2021, China issued its first batch of carbon-neutral bonds that would support carbon-reduction projects [198]. Similarly, as the first greenhouse gas emissions trading system founded in 2005, the European Union Emissions Trading System (EU ETS) aims at greenhouse gas emission reduction under the "cap and trade" principle [199]. Companies regulated by the EU ETS must restrict their carbon emissions within the carbon allowances, otherwise they need to buy these allowances from other companies on the carbon market. The EU ETS has already been proved to be effective and achieves up to 3.8% of EU-wide emission reduction between 2008 and 2016 based on an estimation compared to carbon emissions without the EU ETS [200]. Besides Europe, many other countries and regions have built their carbon emission trading systems [201], such as the US, the UK, China, etc. However, no specific policies have been developed for the metaverse ecosystem currently, which should be put on the agenda.
B. Regulation of Users in the Virtual World
Although users begin to live in a virtual world and everything gets to be unreal, all their actions will generate a certain amount of carbon emissions in the physical world as well. However, for a user activity in the virtual world, its carbon footprint will vary greatly from that occurs in the physical world. For example, doing exercise in the virtual world can lead to relatively high carbon emissions for rendering consecutive video frames, but it only consumes our own body's energy in the physical world. Another example is the way of travelling. In the physical world, hiking only consumes the user's own energy, while flying will bring a lot of carbon emissions. By comparison, due to the need to render a sequence of video frames for a long time, hiking in the virtual world can bring high carbon emissions. Instead, a low-carbon way is to "take a virtual plane", that is to say that the user can directly click a button to arrive at his destination. In this way, travelling all over the world incurs negligible carbon emissions as no real vehicles are needed and only the background image needs to be replaced on the screen.
In view of the difference, a new assessing, recording, and regulating mechanism tailored to the metaverse is necessary. First, we need a new strategy to assess carbon emissions of users' activities and record them through carbon management agencies in the virtual world. Then, we can recommend activities to users based on the recorded carbon information of each activity. Finally, to stimulate users to be aware of their carbon footprints in the metaverse, we can charge them in the physical world or just provide them with a virtual bonus in the virtual world. We further propose a quantitative indicator Carbon Utility (CU), defined as the ratio of service quality brought by activities in the virtual world to the produced carbon emissions in the physical world. This value is affected by the type of activities (e.g., travelling and holding a party), the implementation (e.g., 4K video, 360 • video, and realtime multiplayer interaction), and the energy efficiency of each component in each layer (e.g., datacenters and enddevices). This indicator not only provides information on the carbon bottleneck (i.e., the components with the largest carbon emissions), but also helps the metaverse platform recommend "green" activities to users in the virtual world, and "green" implementations to developers in the physical world.
Implications As the carbon footprint of the same user activity behaves totally differently between in the physical world and virtual world, it is necessary to develop a new assessing, recording, and regulating mechanism on the carbon impacts of these online user activities.
VII. CONCLUSION AND FUTURE DIRECTIONS
With the fast evolvement of the metaverse, it is believed that a growing number of users will join the metaverse when it provides better QoE of working, playing, trading, etc., in the near future. However, we argue that this probably comes at the expense of huge energy consumption and carbon emissions, which will largely hinder the way to carbon neutrality. To better understand this carbon issue, we first split the metaverse into three carbon-intensive layers and estimate their carbon footprints from 2022 to 2030. Our results show that the carbon emissions of the metaverse in 2030 will reach nearly 0.5% of the global carbon emissions if we cannot take effective measures. In view of this critical issue, we then present a wide range of current and emerging green techniques for reducing carbon emissions and analyze their limitations when facing the specific requirements of metaverse workloads. Finally, we propose several insights and future directions to help make each of the layers become green.
As discussed in Section II, the metaverse is built upon a variety of existing technologies. For the metaverse as a whole, each existing green technique still focuses on a single or a few components within a layer, and only takes into account limited performance metrics. We argue that this is no more efficient since the metaverse is an all-inclusive world involving extensive components. For example, the device-edge collaborative execution solution for AI inference is demonstrated to be effective in reducing the device energy but only focuses on end-devices themselves. However, extra energy will be consumed by datacenter servers, switches, etc., which can be large but is neglected by existing literature. Another example is the workload consolidation, which is a general-use approach in datacenters to save the energy of IT systems by reducing the number of active servers. However, it can incur significant hotspots and thus increase the cooling energy consumption. To tackle the issue, we summarize three future directions to improve the energy efficiency of the metaverse as a whole in the following.
(1) Performance metrics to be jointly considered: as a higher energy efficiency can lead to various performance degradation of the metaverse, such as a lower computing speed and a lower security level, we need to consider multiple necessary performance metrics like latency, security, and cost at the same time to achieve a desirable trade-off. However, it is nontrivial to reduce the prohibitively large search space to get an appropriate solution.
(2) Layers and components to be jointly considered: instead of each individual component within a layer on which most ongoing efforts focus, such as processors or cooling equipment, it is necessary to focus on an end-to-end solution that jointly considers all the components and even all the layers to maximize the overall efficiency. To this extend, the first step is to capture the carbon footprint of each component in each layer from a specific metaverse application; the second step is to evaluate the energy efficiency of these components based on the indicators like PUE and PPW; the last step is to feed back, i.e., determine the best green techniques for the application according to the connections between these components, their priorities, the QoE requirement, etc. Since this requires a full knowledge of all the components in the metaverse, training metaverse engineers and developers is the key to the future.
(3) A new regulation mechanism on carbon footprints by the virtual world: since the carbon footprints of various user activities in the virtual world behave differently from that in the physical world, we need to design a new assessing, recording, and regulating mechanism on carbon footprints. Particularly, we propose a quantitative indicator for the metaverse -Carbon Utility, to reflect the carbon intensity of different user activities in the metaverse. Leveraging this indicator, future efforts are required on how to evaluate the service quality and carbon impacts of each user activity. Max Mühlhäuser is currently a Full Professor with Technical University of Darmstadt, where he is also the Head of the Telecooperation Laboratory. He holds key positions in several large collaborative research centers and is leading the Doctoral School on Privacy and Trust for Mobile Users. He and his lab members conduct research on the future Internet, human-computer interaction and cybersecurity, and privacy and trust. He founded and managed industrial research centers and worked as either a Professor or a Visiting Professor at universities in Germany, USA, Canada, Australia, France, and Austria. He is a member of acatech, the German Academy of the Technical Sciences. He was and is active in numerous conference program committees, as an Organizer for several annual conferences and as a member of editorial boards or a Guest Editor for journals, such as IMWUT, Pervasive Computing, ACM Multimedia, and Pervasive and Mobile Computing. He is a Senior Member of IEEE and a Distinguished Member of ACM.
Figure 1 .
1Users from all over the physical world are connected together to communicate, work, play, and more.
Fig. 1 .
1Fig. 1. Users from all over the physical world are connected together into the metaverse to communicate, work, play, and more [4], [5], [6], [7], [8], [9], [10].
Fig. 2 .
2The framework of the metaverse, and the existing green techniques for reducing carbon emissions.
Fig. 3 .
3The estimated energy consumption of the metaverse from the year of 2022 to 2030.
Fig. 4 .
4The estimated carbon emissions of the metaverse from the year of 2022 to 2030.
Fig. 5 .
5Datacenter equipment.
Fig. 6 .
6The energy share by source in a typical datacenter.
Fig. 7 .
7An overview of the datacenter infrastructure for the metaverse.
Fig. 8 .
8Key components for carbon reduction of the datacenter infrastructure.
Fig. 9 .
9The relationship between the frequency and power, and the frequency and performance of the Intel Core i5 processor.
Fig. 12 .
12Key components for carbon reduction during the economy process.
Lin
Wang received the Ph.D. degree from the Institute of Computing Technology, Chinese Academy of Sciences, in 2015. He held positions at Technical University of Darmstadt, SnT Luxembourg, and IMDEA Networks Institute. He is currently an Assistant Professor with the Computer Systems Section, Vrije Universiteit Amsterdam. His research interests include distributed systems and networking. He received an Athene Young Investigator Award from Technical University of Darmstadt in 2018 and a Google Research Scholar Award in 2022.
TABLE I YEAR
ITO REACH CARBON
TABLE III GREEN
IIITECHNIQUES FOR THE INFRASTRUCTURE.Level
Green technique
Work
IT system
Component-level
(Sec. III-B1)
The IT equipmentIT equipment 50%
Cooling system 35%
Power system 10%
Lighting and others 5%
50%
35%
10%
5%
IT equipment
Cooling system
Power system
Lighting and others
Non-IT equipment
TABLE IV THE
IVCARBON INTENSITY OF MAJOR ENERGY SOURCES (IN DESCENDING ORDER IN EACH CATEGORY)[99] Energy source
Conventional non-renewable
fossil fuels
Other non-renewable
sources
Renewable sources
Coal
Oil
Natural Gas
Nuclear
Solar
Geothermal
Biomass
Wind
Hydro
Carbon intensity (g CO 2 eq/kWh)
1,001
840
469
16
22-48
45
18
12
4
1950
1960
1970
1980
1990
2000
2010
2020
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20
40
60
80
100
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Fig. 10. Non-Renewable and Renewable Energy Consumption by Source in the United States from 1949 to 2021 [100].
TABLE V GREEN
VTECHNIQUES FOR THE INTERACTION.Level
Green technique
Work
End-device
Processor
(Sec. IV-B1)
Heterogeneous processing architectures
ARM big.LITTLE [122]
127] and Narayanan et al.[128] also demonstrate the much higherApplication
End Device
Base Station
Data
Transmission
Processor
Modem
Chip
User
For Human-human Interaction
For Human-computer Interaction
TABLE VI GREEN
VITECHNIQUES FOR THE ECONOMY.Blockchain (Sec. V-B)Consensus protocol design and selection Proof of Solution[181], Bada et al.[182] Level
Green Technique
Work
Transaction combination
Lightning Network [183]
User
Consensus
Blockchain Network
Transaction
User
Transaction
estimate the energy consumption of PoW, PoS, and DPoS. The results show that the annual energy consumption of DPoS is the lowest (about 1.2 GWh per year), PoS is sightly higher than DPoS (about 7.3 GWh per year), and both are significantly lower than PoW (about 33 TWh per year). Chen et al.
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His research interests include cloud computing and edge computing, datacenter and green computing, SDN/NFV/5G and applied ML/AI. He received the National Natural Science Fund (NSFC) for Excellent Young Scholars, and the National Program Special Support for Top-Notch Young Professionals. He is a recipient of the Best Paper Award. Hong Kong, 2022. Fangming Liu (S'08, M'11, SM'16) received the B.Eng. degree from the Tsinghua University, Beijing, and the Ph.D. degree from the Hong Kong University of Science and Technology. Wuhan, China12Online Accessed. and IEEE GLOBECOM 2011, the First Class Prize of Natural Science of Ministry of Education in China, as well as the Second Class Prize of National Natural Science Award in China//icapcarbonaction.com/en/[Online Accessed, 12-Jan-2022], 2022. Fangming Liu (S'08, M'11, SM'16) received the B.Eng. degree from the Tsinghua University, Bei- jing, and the Ph.D. degree from the Hong Kong Uni- versity of Science and Technology, Hong Kong. He is currently a Full Professor with the Huazhong Uni- versity of Science and Technology, Wuhan, China. His research interests include cloud computing and edge computing, datacenter and green computing, SDN/NFV/5G and applied ML/AI. He received the National Natural Science Fund (NSFC) for Excellent Young Scholars, and the National Program Special Support for Top-Notch Young Professionals. He is a recipient of the Best Paper Award of IEEE/ACM IWQoS 2019, ACM e-Energy 2018 and IEEE GLOBECOM 2011, the First Class Prize of Natural Science of Ministry of Education in China, as well as the Second Class Prize of National Natural Science Award in China.
He is currently working toward the PhD degree in the School of Computer Science and Technology. Qiangyu Pei received the BS degree in physics from the Huazhong University of Science and Technology. ChinaHuazhong University of Science and TechnologyHis research interests include edge computing, green computing, and deep learningQiangyu Pei received the BS degree in physics from the Huazhong University of Science and Technology, China, in 2019. He is currently working toward the PhD degree in the School of Computer Science and Technology, Huazhong University of Science and Technology. His research interests include edge computing, green computing, and deep learning.
. China. She is currently a Ph.D. student in the School of Computer Science and Technology. Shutong Chen received her B.Sc. degree in the College of Mathematics and Econometrics, Hunan University ; Huazhong University of Science and TechnologyHer research interests include edge computing, green computing, and datacenter energy managementShutong Chen received her B.Sc. degree in the College of Mathematics and Econometrics, Hunan University, China. She is currently a Ph.D. student in the School of Computer Science and Technology, Huazhong University of Science and Technology, China. Her research interests include edge comput- ing, green computing, and datacenter energy man- agement.
| sample_1947 | 0.8137 | arxiv | |
Making AI Less "Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models
Pengfei Li
Jianyi Yang
Mohammad A Islam
Shaolei Ren
UC Riverside
UC Riverside
Arlington
UC Riverside
Making AI Less "Thirsty": Uncovering and Addressing the Secret Water Footprint of AI Models
Source codes: The codes used to generate the results in this paper are available at: https://github.com/Ren-Research/Making-AI-Less-Thirsty
The growing carbon footprint of artificial intelligence (AI) models, especially large ones such as GPT-3 and GPT-4, has been undergoing public scrutiny. Unfortunately, however, the equally important and enormous water footprint of AI models has remained under the radar. For example, training GPT-3 in Microsoft's state-of-the-art U.S. data centers can directly consume 700,000 liters of clean freshwater (enough for producing 370 BMW cars or 320 Tesla electric vehicles) and the water consumption would have been tripled if training were done in Microsoft's Asian data centers, but such information has been kept as a secret. This is extremely concerning, as freshwater scarcity has become one of the most pressing challenges shared by all of us in the wake of the rapidly growing population, depleting water resources, and aging water infrastructures. To respond to the global water challenges, AI models can, and also should, take social responsibility and lead by example by addressing their own water footprint. In this paper, we provide a principled methodology to estimate fine-grained water footprint of AI models, and also discuss the unique spatial-temporal diversities of AI models' runtime water efficiency. Finally, we highlight the necessity of holistically addressing water footprint along with carbon footprint to enable truly sustainable AI.
Introduction
• "Water is a finite resource, and every drop matters." -Facebook (now Meta) Sustainability Report 2020 [1].
• "At AWS, we know that water is a precious resource." -Amazon's Water Stewardship 2023 [2].
• "Fresh, clean water is one of the most precious resources on Earth ... Now we're taking urgent action to support water security and healthy ecosystems." -Google's Water Commitment 2023 [3].
• "Water is a human right and the common development denominator to shape a better future. But water is in deep trouble." -U.N. Secretary-General António Guterres at the U.N. Water Conference 2023 [4].
• "Historic droughts threaten our supply of water ... As the source of both life and livelihoods, water security is central to human and national security." -U.S. White House Action Plan on Global Water Security 2022 [5].
• · · ·
Artificial intelligence (AI) models have witnessed remarkable breakthroughs and success in numerous areas of critical importance to our society over the last decade, including in the ongoing combat against several global challenges such as climate changes [6]. Increasingly many AI models are trained and deployed on power-hungry servers housed inside warehouse-scale data centers, which are often known as energy hogs [7]. Consequently, the environmental footprint of AI models, in particular carbon footprint, has been undergoing public scrutiny, driving the recent progress in AI carbon efficiency [8][9][10][11]. Unfortunately, however, the enormous water footprint of AI models -millions of liters of clean freshwater consumed for generating electricity to power data center servers and for cooling these servers -has remained under the radar, which, if not properly addressed, can become a major roadblock for socially responsible and environmentally sustainable evolution of future AI.
Motivation
Despite the water cycle through our planet's natural ecosystem, clean freshwater resource available and suitable for use is extremely limited and unevenly distributed across the globe. In fact, freshwater scarcity [20,21]. The presence of megawatt data centers clearly results in a huge environmental impact on regional water systems. Additionally, due to the aging public water infrastructure, the need for water conservation remains equally important, even in non-drought areas. For example, in Florida and Singapore, the freshwater shortage is still a key challenge due to the water infrastructure constraints [22,23]. Moreover, it is extremely costly to expand the aging public water infrastructure that is already operating near limits in many parts of the world. The addition of water-thirsty data centers to accommodate new AI model development can certainly worsen the situation.
As one of the most prominent and exponentially expanding workloads in data centers [8,24,25], AI models can, and also should, take social responsibility and lead by example in the collective efforts to combat the global water scarcity challenge by cutting their own water footprint. Despite its profound environmental and societal impact, however, the enormous water footprint of AI models has remained hidden from the AI community as well as the general public. Therefore, it is truly a critical time to uncover and address the AI model's secret water footprint amid the increasingly severe freshwater scarcity crisis, worsened extended droughts, and quickly aging public water infrastructure. The urgency can also be reflected in part by the recent commitment to "Water Positive by 2030" by increasingly many companies, including Google [17], Microsoft [26], Meta [27] and Amazon [2].
Overview of Our Study
Recognizing the enormous water footprint as a critical concern for socially responsible and environmentally sustainable AI, we make the first-of-its-kind efforts to uncover the secret water footprint of AI models. Let us first take the GPT-3 model for language services as a concrete example [28].
• Training: Training GPT-3 in Microsoft's state-of-the-art U.S. data centers can directly consume 700,000 liters of clean freshwater, enough for producing 370 BMW cars or 320 Tesla electric vehicles, and these numbers would have been tripled if GPT-3 were trained in Microsoft's Asian data centers, according to public data sources [18,19,29,30]. 2 If training a similar large AI model elsewhere with average water efficiency of 3.8L/kWh [31], the on-site water consumption can be as much as 4.9 million liters, enough for producing roughly 2,600 BMW cars or 2,200 Tesla electric vehicles. Moreover, training GPT-3 is also responsible for an additional off-site water footprint of 2.8 million liters due to electricity usage (assuming water usage efficiency at the U.S. national average level 1.8L/kWh [32] and power usage effectiveness 1.2). Thus, combined together, this would put GPT-3's total water footprint for training at 3.5 million liters if trained in the U.S., or 4.9 million liters if trained in Asia.
• Inference: ChatGPT needs to "drink" a 500ml bottle of water for a simple conversation of roughly 20-50 questions and answers, depending on when and where ChatGPT is deployed. 3 While a 500ml bottle of water might not seem too much, the total combined water footprint for inference is still extremely large, considering ChatGPT's billions of users.
All these numbers are likely to increase by multiple times for the newly-launched GPT-4 that has a significantly larger model size. But, up to this point, there has been little public data available to form a reasonable estimate of the water footprint for GPT-4.
Next, by using a principled methodology to estimate the fine-grained water footprint, we show concretely that AI models such as Google's LaMDA [34] can consume a stunning amount of water in the order of millions of liters. We also show that WUE (Water Usage Effectiveness, a measure of water efficiency) is varying both spatially and temporally, implying that judiciously deciding "when" and "where" to train a large AI model can significantly cut the water footprint. In addition, we point out the need of increasing transparency of AI models' water footprint, including disclosing more information about operational data and keeping users informed of the runtime WUE. Finally, we highlight the necessity of holistically addressing water footprint along with carbon footprint to enable truly sustainable AIthe water footprint of AI models can no longer stay under the radar.
Background
While the embodied water footprint (e.g., manufacturing of servers and GPUs for training AI models) not directly related to AI model training or inference is part of the lifecycle assessment of environmental footprint and can be of independent interest, we focus on the operational water footprint of AI models directly associated with training and inference. Thus, in what follows, we introduce the basics of data center infrastructure and then describe the way that data centers (and hence, the hosted AI models) consume water. Data center power infrastructure. While data center power infrastructures vary from one to another, a common infrastructure design follows the hierarchical tree type. As illustrated in Figure 2, grid/utility power enters the data center through an automatic transfer switch (ATS) which switches over the main power supply to the backup generator in case of grid power failures. The ATS feeds power to a centralized (or distributed in some systems) uninterrupted power supply (UPS), which supplies "protected/conditioned" power to multiple power distribution units (PDUs) that further deliver power to the computer servers. Meanwhile, the cooling system ensures that the servers are not overheated. The computer servers are where AI models are trained and deployed for inference. These servers may also have specialized designs, including multiple GPUs and/or purpose-built hardware, to speed up AI model training and inference [24]. 2 Without data from the model developer, we set the water usage effectiveness (WUE) as 0.55L/kWh for training in Microsoft's U.S. data centers, and 1.65L/kWh for its Asian data centers based on Microsoft-reported average WUE [30]. The water consumption data for car production is provided by BMW [18] and Telsa [19]. Moreover, in all the estimated water footprints, the overhead for hyperparameter tuning and training failures (if any) is not included. 3 Without data from the model developer, we assume that each inference consumes e = 0.00396kWh energy based on the estimate of [33], the data center's power usage effectiveness (P U E) is 1.2, electricity water intensity factor (EW IF ) for off-site electricity generation is 1.8L/kWh [32], and water usage effectiveness (W U Eon) for on-site cooling is between 0.5L/kWh and 5L/kWh depending on weather conditions. The total water footprint is calculated as e · [P U E · EW IF + W U Eon].
Data center water footprint. We first would like to distinguish water consumption from withdrawal. Water withdrawal refers to getting water from the source (e.g., underground, rivers, sea) [35], and water consumption refers to "losing" water (e.g., by evaporation) in the process of withdrawal and return. Thus, water consumption is the net difference between water withdrawal and return. In this paper, we focus on water consumption, which is consistent with the industry standard [32]. The water consumption in data centers has two parts: on-site direct water and off-site indirect water.
On-site Water
Off-site Water Figure 3: Data center water footprint: on-site water consumption for data center cooling, and off-site water consumption for electricity generation. Multiple AI models are trained and/or deployed in the data center. The icons for AI models are only for illustration purposes.
On-site direct water consumption. Nearly all the server energy is converted into heat that must be removed from the data center server room to avoid overheating. Despite recent advances in cooling solutions, cooling towers are dominantly the most common cooling solution for warehouse-scale data centers, even for some leading companies such as Google [17] and Microsoft [26], and consume a huge amount of water. As illustrated in Figure 3, there are two water loops: one closed loop between the chiller and data center server room, and one open loop between the cooling tower and the chiller. Within the closed loop, water is not lost -it is pumped from the chiller into the data center to cool down the air handling unit's supply air in order to maintain a proper server inlet temperature, and warm water that absorbs the server heat returns to the chiller direction. Through a heat exchanger at the chiller, the heat is transferred from the closed loop to the open loop. Note that the chiller may operate in a "bypass" mode for energy saving when the outside temperature is low. Along the open loop, some of the water gets evaporated (i.e., "consumed") in the cooling tower to dissipate heat into the environment. Additionally, there is a process called "blown down" that drains the cooling water to reduce salt concentration accumulated in the cooling tower and hence also consumes water: the higher water quality, the more cycles of concentrations (i.e., water recirculates more times before "blown down") and hence the less blown-down water [36]. Through evaporation in the cooling tower as well as "blow down", data centers consume a significant amount of freshwater. For example, by one estimate [31] and depending on climate conditions, roughly 3.8 liters of water are consumed for each kWh of cooling load (approximately equal to server energy) by an average data center, resulting in a water usage effectiveness (WUE) of 3.8 L/kWh, while some data centers can even use 5.2 L/kWh [37]. Importantly, the on-site water comes from clean freshwater sources in order to avoid corrosion, clogged water pipes, bacterial growth, etc. While air-side economizers (a.k.a. "free" outside air cooling) do not need cooling towers and hence can reduce on-site water footprint, they often have strict requirements on the climate condition and may not be suitable for all locations. Additionally, freshwater is needed for humidity control to ensure proper server operation in data centers [38].
Off-site indirect water consumption. Data centers are held accountable for carbon footprint because of their (non-renewable) electricity usage. Likewise, electricity generation requires a huge amount of water [35,39], thus resulting in off-site indirect water consumption for data centers [32]. Depending on the cooling technologies employed, different power generation systems (e.g., nuclear, coal and natural gas) consume different amounts of water. Among the non-hydroelectric systems, nuclear power plants typically consume the highest amount of water for producing each kWh of electricity on average, followed by thermoelectricity [35]. The water efficiency metric is called Energy Water Intensity Factor (EWIF) with a unit of L/kWh. Although certain renewable energy generation such as wind turbine and solar PV panels consumes no water for operation, their percentages in the overall electricity generation is still low in most parts of the world. Overall, excluding hydroelectricity (which itself does not consume water for cooling but expedites the evaporation of down streams), the national average EWIF by aggregating different types of power plants in the U.S. is about 1.8 L/kWh [32,39].
Estimating Water Footprint of AI Models
While an AI model's water footprint depends in part on its energy consumption, such dependency is timevarying. As a result, simply multiplying the AI model's energy consumption by a constant and fixed WUE (Water Usage Effectiveness) does not yield an accurate estimate of AI models' water footprint. Next, by accounting for the time-varying WUE, we present a methodology for a fine-grained estimate of an AI model's water footprint.
Methodology
To obtain an AI model's total water footprint, we consider both on-site WUE and off-site WUE.
• On-site WUE. Cooling towers are most commonly used as the heat rejection mechanism for data centers. In general, the on-site WUE of cooling towers depends on multiple factors, such as temperature approach settings (i.e., difference between the cold water temperature and entering wet bulb temperature), cycles of concentrations (i.e., water recirculation times before "blown down"), water flow rate, air pressure, humidity, wet bulb temperature, and wind speed, among many others. Due to the lack of operational data from major data centers, we focus on the impact of outside wet bulb temperature on the on-site WUE, and present an empirical model based on a commercial cooling tower [40]. Specifically, following recommended operational settings, the on-site WUE can be approximated as
W U E on = S S−1 6 × 10 −5 · T 3 w − 0.01 · T 2 w + 0.61 · T w − 10.40 ,
where S is the cycle of concentrations and T w is the outside wet bulb temperature (in Fahrenheit) [15]. The key insight for this formula is that the direct on-site WUE increases with outside wet bulb temperature, as a lower wet bulb temperature makes the water cool down more by the outside air and hence less through evaporation. When T w is sufficiently low, the approximate formula for W U E on can become negative and does not hold -water evaporation may not be needed for cooling in this case, and instead, water is mostly used for humidity control. Additionally, the empirical formula does not apply if the data center uses outside air cooling (e.g., in some of Meta's data centers [27]), and in this case, detailed operational data is needed to construct an accurate model for the on-site WUE.
• Off-site WUE. We now present the off-site indirect WUE measured in terms of EWIF (Electricity Water Intensity Factor). The same way as AI models are accountable for carbon footprint associated with off-site electricity generation, the off-site water footprint should also be taken into account to provide a more comprehensive environmental footprint [32]. Specifically, the off-site WUE depends on the energy fuel mixes (e.g., coal, nuclear, hydro) as well as cooling techniques used by power plants [32,41]. Since electricity produced by different energy fuels becomes non-differentiated once entering the grid, we consider the average EWIF, which can be estimated as
W U E of f = k b k ×EW IF k k b k
where b k denotes the amount of electricity generated from fuel type k for the grid serving the data center under consideration, and EW IF k is the EWIF for fuel type k [42,43]. As a result, variations in energy fuel mixes of electricity generation (to meet various demand levels) result in temporal variations of the off-site WUE. Moreover, the off-site WUE also varies by location, because each fuel type has its own distinct WUE [32] and energy fuel mix is typically different between states as some states may use less water-efficient energy generation than others [15,32,44].
• Water footprint. The on-site direct water consumption can be obtained by multiplying AI's energy consumption with the on-site WUE, while the indirect water consumption depends on the electricity usage as well as the local off-site WUE. Consider a time-slotted model t = 1, 2, · · · , T , where each time slot can be 10 minutes to an hour depending on how frequently we want to assess the water footprint, and T is the total length of interest (e.g., training stage, total inference stage, or a combination of both). At time t, suppose that an AI model uses energy e t (which can be measured using power meters and/or servers' built-in tools), the on-site WUE is W U E on,t , the off-site WUE is W U E of f,t , and the data center hosting the AI model has a power usage effectiveness (PUE) of P U E t that accounts for the non-IT energy such as cooling systems and power distribution losses. Then, the total water footprint W of the AI model can be written as
W = W on + W of f = T t=1 e t · W U E on,t + T t=1 e t · P U E t · W U E of f,t ,(1)
where W on = T t=1 e t · W U E on,t and W of f = T t=1 e t · P U E t · W U E of f,t are the on-site and off-site water footprints, respectively. Our methodology for estimating AI models' water footprint is general and applies to data centers with any type of cooling systems. For example, if the data center uses a cooling tower other than the one we model, we only need a different W U E on,t . Naturally, given more operational data and transparency, both W U E on,t and W U E of f,t can be refined to yield more accurate estimates.
Example: Water Footprint of LaMDA
We now use Google's large language model -LaMDA (Language Models for Dialog Applications) [34]as an example and estimate its water footprint using our methodology. LaMDA uses about 451 MWh for training, but the starting time, specific data center locations, runtime PUE, WUE and EWIF for training and deploying LaMDA are not publicly disclosed. Thus, to estimate the water footprint of LaMDA, we use our empirical model presented in Section 3.1 as well as the state-level EWIF, and consider four different locations of Google's U.S. data centers -Loudoun County (VA), Henderson (NV), Midlothian (TX), and The Dalles (OR). As a result, our estimated water footprint of LaMDA only serves as an approximate reference point for the research community and general public, rather than an accurate calculation that is impossible to know without further transparency from the model developer.
More concretely, we use the hourly weather data [46] and state-level energy fuel mix data [47] for the year of 2022 in each of the chosen data center locations. We obtain the wet bulb temperature from the dry bulb temperature and relative humidity based on [48], and use the EWIF data shown in Table 1 for each energy fuel type. As the EWIF for each energy fuel type depends on the cooling techniques, the EWIF data we use is calculated as the weighted average of the median EWIF in [45] each cooling technique, excluding hydropower. We set the PUE as 1.1 (which is representative of Google's best data center efficiency). Based on the hourly wet bulb temperature and setting the cycle of concentration as S = 5, we use our empirical formula in Section 3.1 to derive the on-site WUE, whose minimum is capped at 0.01L/kWh. With a total training time of consecutive 57.7 days [34], we consider different starting dates and data center locations for training LaMDA, and show the resulting on-site and total water footprints in Figure 4. While it is impossible to know the actual water footprint without detailed information from Google, our estimate shows that the total water footprint of training LaMDA is in the order of million liters. Crucially, we see that different training months and data center locations can significantly affect the water footprint -in general, summer may not be a good time for training large AI models due to excessive on-site water evaporation. Our empirical estimate shows that the highest total water footprint can be more than 3 times the lowest, highlighting the potential of cutting water footprint by judiciously scheduling AI model training.
For comparison, we also show in Figure 4 the estimated carbon footprint for training LaMDA. Note that [34] uses a fixed carbon efficiency of 0.056kg/kWh to calculate the carbon footprint of LaMDA without disclosing further details (e.g., time-varying energy fuel mix). Here, to estimate the carbon footprint of LaMDA, we use the state-level average EWIF to calculate the off-site carbon efficiency by following the approach considered in [43]. 4 While our estimated carbon footprint differs from the value reported by [34], the key message we would like to highlight is that the most carbon-efficient training months and data center location may not be water-efficient. For example, due to the high penetration of solar energy, the carbon footprint of training LaMDA in Nevada is low, but the resulting water footprint can be very high due to high temperatures. This suggests that carbon-efficient scheduling of AI model training may not enable truly sustainable AI.
Limitations of the Existing Approaches
We now review some of the existing approaches to achieving sustainable AI, and discuss their limitations.
Improving on-site water efficiency. The existing approaches to improving on-site water efficiency are mostly from the "engineering" perspective (e.g., improving the data center's cooling tower efficiency) [17, 26,27,49,50]. These water-saving approaches can be viewed as supply-side solutions -saving water while supplying enough cooling to meet the given demand. But, the demand-side management -cooling demands are affected by "when" and "where" AI models are trained and used -is not addressed. While air-side economizers (a.k.a. "free" outside air cooling) can reduce on-site water footprint, they may have strict requirements on climate conditions and still use water for humidity control [27]. For example, even tech giants such as Google heavily rely on cooling towers and consume billions of liters of on-site cooling water each year [17]. Additionally, all these approaches only focus on the on-site water footprint, whereas the off-site water footprint that has time-varying off-site WUE due to variations in energy fuel mixes is not addressed.
Carbon-aware approaches. The existing research on sustainable AI has been primarily focused on AI models' carbon footprint [8][9][10][11]28,29,34]. Nonetheless, despite the correlation between water footprint and carbon footprint, the existing techniques for carbon efficiency do not necessarily equate to optimal water efficiency. This is because WUE varies with time and location in its own unique manner subject to real-time weather conditions and the power grid's mix of energy fuel sources. For example, AI model developers may want to train their models during the noon time when solar energy is more abundant [10], but this is also the hottest time of the day that leads to the worst water efficiency [44]. As a result, carbon-efficient scheduling of AI training can even lead to an increase in the water footprint, and reconciling such water-carbon conflicts requires new and holistic approaches to enable truly sustainable AI.
Our Findings and Recommendations
We provide our findings and recommendations to address the water footprint of AI models, making future AI more socially responsible and environmentally sustainable. Figure 4 shows that "when" and "where" to train a large AI model can significantly affect the water footprint. The underlying reason is the spatial-temporal diversity of both on-site and off-site WUE -on-site WUE changes due to variations of outside weather conditions, and off-site WUE changes due to variations of the grid's energy fuel mixes to meet time-varying demands. In fact, WUE varies at a much faster timescale than monthly or seasonably. For example, we show hourly on-site WUE and total WUE for the first week of August 2022 in Figure 5 and Figure 6, respectively. We see that both on-site WUE and total WUE vary significantly over time, and they are not synchronized across different locations. Therefore, by exploiting spatial-temporal diversity of WUE, we can dynamically schedule AI model training and inference to cut the water footprint. For example, if we train a small AI model, we can schedule the training task at midnight and/or in a data center location with better water efficiency. Likewise, some water-conscious users may prefer to use the inference services of AI models during water-efficient hours and/or in water-efficient data centers, which can contribute to the reduction of AI models' lifecycle water footprint. Such demand-side water management, which decides "when" and "where" to train and use AI models by exploiting the spatialtemporal WUE, complements the existing engineering-based on-site water saving approaches that focus on the supply side.
"When" and "Where" Matter!
As a side note, federated learning [51], where multiple users collaboratively train an AI model using their own datasets on their local devices (e.g., personal computers) without consuming on-site water for data center cooling, can also leverage the spatial-temporal diversity of off-site WUE to reduce the total water footprint. Specifically, by integrating water-efficient schedules into local AI model training, we can achieve water footprint reduction for federated learning. Similar practices have been adopted for carbon footprint reduction in real products -Apple has recently integrated clean energy scheduling into its iPhone by selecting low-carbon hours for charging [52], and Microsoft launched carbon-aware Windows Update services by scheduling installations at specific times of the day when the off-site carbon efficiency is better [53].
M o n T u e W e d T H U F R I S A T S U N
More Transparency is Needed.
To exploit the spatial-temporal diversity of WUE, it is crucial to have a better visibility of the runtime WUE and increase transparency by keeping the AI model developers as well as end users informed of the runtime water efficiency.
Modeling the runtime WUE. The complex relations between the on-site WUE and multiple runtime factors (e.g., outside temperature, humidity, water flow rate, among others) would probably mandate a more advanced and sophisticated model than the one we have presented in Section 3.1. To capture the complex relations, we can leverage strong predictive power of a neural network parameterized by θ to estimate the on-site WUE as W U E on = f θ (x) where x represents the input features. Clearly, building such a neural network model requires labeled data provided by data center operators, but such data is still lacking in the public domain.
Increasing transparency. With more transparency, the general public can be better engaged into the global efforts to address the growing water challenges. For example, water-conscious users may prefer to use the inference services of AI models during water-efficient hours, but currently, the lack of transparency about AI models' detailed water efficiency prohibits them from doing so. Additionally, being informed of the data center's runtime water efficiency, AI model developers can better schedule their model training and choose locations for the deployment of trained models. We recommend AI model developers and data center operators be more transparent. For example, what are the runtime (say, hourly) on-site WUE and off-site WUE? When and where are the AI models trained?
What about the AI models trained and/or deployed in third-party colocation data centers or public clouds? Such information will be of great value to the research community and the general public.
"Follow the Sun" or "Unfollow the Sun"?
To cut the carbon footprint, it is preferable to "follow the sun" when solar energy is more abundant. Nonetheless, to cut the water footprint, it is more appealing to "unfollow the sun" to avoid high-temperature hours of a day when (on-site) WUE is high. This conflict can also be reflected by Figure 5 and Figure 6 where we see that the carbon efficiency and WUE do not align very well with each other. Our figures (e.g., Figure 8) in the appendix also demonstrate this point: carbon-efficient hours and water-efficient hours are different. Thus, to judiciously achieve a balance between "follow the sun" for carbon efficiency and "unfollow the sun" for water efficiency, we need to reconcile the water-carbon conflicts by using new and holistic approaches. In other words, only focusing on AI models' carbon footprint alone is far from enough to enable truly sustainable AI.
Conclusion
In this paper, we recognize the enormous water footprint as a critical concern for socially responsible and environmentally sustainable AI, and make the first-of-its-kind efforts to uncover the secret water footprint of AI models. Specifically, we present a principled methodology to estimate the fine-grained water footprint, and show that AI models such as GPT-3 and Google's LaMDA can consume a stunning amount of water in the order of millions of liters. We also show that WUE is varying both spatially and temporally -judiciously deciding "when" and "where" to train a large AI model can significantly cut the water footprint. In addition, we point out the need of increasing transparency of AI models' water footprint, and highlight the necessity of holistically addressing water footprint along with carbon footprint to enable truly sustainable AI.
AI models' water footprint can no longer stay under the radar -water footprint must be addressed as a priority as part of the collective efforts to combat global water challenges. [17] Urs Hölzle. Our commitment to climate-conscious data center cooling, 2022, https://blog.google/outreach-initiatives/sustainability/ our-commitment-to-climate-conscious-data-center-cooling/.
Figure 1 :
1US drought map for August 2, 2022, with 4.47% area under exceptional drought (D4), 18.96% area under extreme drought or worse (D3-D4), and 37.03% area under severe drought or worse (D2-D4) [20].
Figure 1
1shows that 37.03% of the U.S. area can be under severe drought or worse, where thousands of data centers are located
Figure 2 :
2Data center power infrastructure.
Figure 4 :
4Estimated water and carbon footprints of training LaMDA with different starting months in 2022.
Figure 5 :Figure 6 :
56Hourly carbon efficiency and on-site WUE for the first week of August 2022.M o n T u e W e d T H U F R I S A T S Hourly carbon efficiency and total WUE for the first week of August 2022.
[ 16 ]
16Md Abu Bakar Siddik, Arman Shehabi, and Landon Marston. The environmental footprint of data centers in the United States. Environmental Research Letters, 16(6):064017, 2021.
Figure 7 :Figure 8 :Figure 9 :Figure 10 :Figure 11 :Figure 12 :Figure 13 :Figure 14 :
7891011121314Average hourly WUE and carbon efficiency in Loudoun County, Virginia. February 1 to April 30, 2022. Average hourly WUE and carbon efficiency in Henderson, Nevada. February 1 to April 30, 2022. Average hourly WUE and carbon efficiency in The Dalles, Oregon. February 1 to April 30, 2022. Average hourly WUE and carbon efficiency in Midlothian, Texas. February 1 to April 30, 2022. Average hourly WUE and carbon efficiency in Loudoun County, Virginia. September 1 to October 30, 2022. Average hourly WUE and carbon efficiency in Henderson, Nevada. September 1 to October 30, 2022. Average hourly WUE and carbon efficiency in The Dalles, Oregon. September 1 to October 30, 2022. Average hourly WUE and carbon efficiency in Midlothian, Texas. September 1 to October 30, 2022.
Table 1 :
1Estimated EWIF for Common Energy Fuel Types in the U.S.[45].Fuel Type
Coal Nuclear Natural Gas Solar (PV) Wind Other
Hydro
EWIF (L/kWh)
1.7
2.3
1.1
0
0
1.8
68 (0, if excluded)
Since electricity generated by different fuel types cannot be differentiated once entering the grid,[43] uses the weighted average carbon efficiency of different fuel types serving a data center for carbon footprint estimation. This approach essentially considers the actual carbon emission, without accounting for carbon footprint reduction through purchased carbon credits.
AppendixWe present the average hourly WUE (both on-site and total) as well as hourly carbon efficiency over different months for different data center locations. These figures demonstrate that the hourly WUE can vary significantly over time and across different locations. Importantly, WUE and carbon efficiency are not necessarily compatible with each other, calling for new research to reconcile the conflicts and enable truly socially responsible and environmentally sustainable AI.
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| sample_1965 | 0.9807 | arxiv |
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