"equal dates of ice formation each winter, and an isotac denotes equal dates of thawing. Contours are one of several common methods used to denote elevation or altitude and depth on maps. From these contours, a sense of the general terrain can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through topographic maps and bathymetric charts, up to continental-scale maps. ""Contour line"" is the most common usage in cartography, but isobath for underwater depths on bathymetric maps and isohypse for elevations are also used. In cartography, the contour interval is the"
"Isoclines are used to solve ordinary differential equations. In interpreting radar images, an isodop is a line of equal Doppler velocity, and an isoecho is a line of equal radar reflectivity. The idea of lines that join points of equal value was rediscovered several times. The oldest known isobath (contour line of constant depth) is found on a map dated 1584 of the river Spaarne, near Haarlem, by Dutchman Pieter Bruinsz. In 1701, Edmond Halley used such lines (isogons) on a chart of magnetic variation. The Dutch engineer Nicholas Cruquius drew the bed of the river Merwede with lines of"
"depths of water with equal temperature, isohalines show lines of equal ocean salinity, and Isopycnals are surfaces of equal water density. Various geological data are rendered as contour maps in structural geology, sedimentology, stratigraphy and economic geology. Contour maps are used to show the below ground surface of geologic strata, fault surfaces (especially low angle thrust faults) and unconformities. Isopach maps use isopachs (lines of equal thickness) to illustrate variations in thickness of geologic units. In discussing pollution, density maps can be very useful in indicating sources and areas of greatest contamination. Contour maps are especially useful for diffuse forms"
"equal depth (isobaths) at intervals of 1 fathom in 1727, and Philippe Buache used them at 10-fathom intervals on a chart of the English Channel that was prepared in 1737 and published in 1752. Such lines were used to describe a land surface (contour lines) in a map of the Duchy of Modena and Reggio by Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and Charles Hutton used them in the Schiehallion experiment. In 1791, a map of France by J. L. Dupain-Triel used contour lines at 20-metre intervals, hachures, spot-heights and a vertical section."
"moves the boat along this line is computed by the tidal speed, and this gives an ""estimated position"" or EP (traditionally marked with a dot in a triangle). Nautical charts display the water's ""charted depth"" at specific locations with ""soundings"" and the use of bathymetric contour lines to depict the submerged surface's shape. These depths are relative to a ""chart datum"", which is typically the water level at the lowest possible astronomical tide (although other datums are commonly used, especially historically, and tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during"
"Bathymetric chart A bathymetric chart is the submerged equivalent of an above-water topographic map. Bathymetric charts are designed to present accurate, measurable description and visual presentation of the submerged terrain. In an ideal case, the joining of a bathymetric chart and topographic map of the same scale and projection of the same geographic area would be seamless. The only difference would be that the values begin increasing after crossing the zero at the designated sea level datum. Thus the topographic map's mountains have the greatest values while the bathymetric chart's greatest depths have the greatest values. Simply put, the bathymetric"
"are also commonly called ""contour maps"" or ""topo maps"". In the United States, where the primary national series is organized by a strict 7.5-minute grid, they are often called ""topo quads"" or quadrangles. Topographic maps conventionally show topography, or land contours, by means of contour lines. Contour lines are curves that connect contiguous points of the same altitude (isohypse). In other words, every point on the marked line of 100 m elevation is 100 m above mean sea level. These maps usually show not only the contours, but also any significant streams or other bodies of water, forest cover, built-up"
"Contour line A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function ""f""(""x"", ""y"") parallel to the ""x"", ""y"" plane. In cartography, a contour line (often just called a ""contour"") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys"
"ocean floor, and the study of underwater earthquakes or volcanoes. The taking and analysis of bathymetric measurements is one of the core areas of modern hydrography, and a fundamental component in ensuring the safe transport of goods worldwide. Bathymetry Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The name comes from Greek βαθύς (""bathus""), ""deep"", and μέτρον (""metron""), ""measure"". Bathymetric (or hydrographic) charts are typically produced to support safety of surface or sub-surface navigation, and usually show seafloor relief or terrain as contour lines"
"an impeller log, to pacing off the distance along the bottom with the arms. Skilled underwater navigators use techniques from both of these categories in a seamless combination, using the compass to navigate between landmarks over longer distances and in poor visibility, while making use of the generic oceanographic indicators to help stay on course and as a check that there is no mistake with the bearing, and then recognising landmarks and using them with the remembered topography of a familiar site to confirm position. Guidelines, also known as cave lines, distance lines, penetration lines and jackstays are permanent or"
"Submersion (mathematics) In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept in differential topology. The notion of a submersion is dual to the notion of an immersion. Let ""M"" and ""N"" be differentiable manifolds and ""f"" : ""M"" → ""N"" be a differentiable map between them. The map ""f"" is a submersion at a point ""p"" ∈ ""M"" if its differential is a surjective linear map. In this case ""p"" is called a regular point of the map ""f"", otherwise, ""p"" is a critical point. A point ""q"""
"Isochrone map An isochrone map (or chart/diagram) in geography and urban planning is a map showing areas related to isochrones between different points. An isochrone is defined as ""a line drawn on a map connecting points at which something occurs or arrives at the same time"". Such a map is sometimes termed simply an isochrone (iso = equal, chrone = time). In hydrology and transportation planning isochrone maps are commonly used to depict areas of equal travel time. The term is also used in cardiology as a tool to visually detect abnormalities using body surface distribution. Isochrone maps have been"
"1,330 million km (320 million mi) with a mean depth of and maximum depth of . Fish that live in the pelagic zone are called pelagic fish. Pelagic life decreases with increasing depth. It is affected by light intensity, pressure, temperature, salinity, the supply of dissolved oxygen and nutrients, and the submarine topography, which is called bathymetry. In deep water, the pelagic zone is sometimes called the open-ocean zone and can be contrasted with water that is near the coast or on the continental shelf. In other contexts, coastal water not near the bottom is still said to be in"
"or ""projection"" of certain navigational maps. A rhumb line appears as a straight line on a Mercator projection map. The name is derived from Old French or Spanish respectively: """"rumb"""" or ""rumbo"", a line on the chart which intersects all meridians at the same angle. On a plane surface this would be the shortest distance between two points. Over the Earth's surface at low latitudes or over short distances it can be used for plotting the course of a vehicle, aircraft or ship. Over longer distances and/or at higher latitudes the great circle route is significantly shorter than the rhumb"
"used as a synonym for relief itself. When relief is described underwater, the term bathymetry is used. In cartography, many different techniques are used to describe relief, including contour lines and TIN (Triangulated irregular network). Elementary landforms (segments, facets, relief units) are the smallest homogeneous divisions of the land surface, at the given scale/resolution. These are areas with relatively homogeneous morphometric properties, bounded by lines of discontinuity. A plateau or a hill can be observed at various scales ranging from few hundred meters to hundreds of kilometers. Hence, the spatial distribution of landforms is often scale-dependent as is the case"
"waters and on rivers. At sea, in order to avoid repeatedly hauling in and measuring the wet line by stretching it out with one's arms, it is common practice to tie marks at intervals along the line. These marks are made of leather, calico, serge and other materials, and so shaped and attached that it is possible to ""read"" them by eye during the day or by feel at night. Traditionally the marks were at every second or third fathom: at 2, 3, 5, 7, 10, 13, 15, 17, and 20 fathoms. The ""leadsman"" called out the depth as he"
"shape of Earth’s surface by using contour lines, the lines on the map that join points of equal elevation. They are among the most well-known symbols on modern maps as they are self-explanatory and accurately represent their phenomena. They make it possible to the depict height, depth, and even slope. Contour lines will be closer together or spaced apart to show the steepness of the area. If the line is spaced closer together, it means that there is a steeper slope. If they are farther apart, the area has a low slope. An area of low slope generally uses contour"
"Hadal zone The hadal zone (named after the realm of Hades, the underworld in Greek mythology), also known as the hadopelagic zone, is the deepest region of the ocean lying within oceanic trenches. The hadal zone is found from a depth of around to the bottom of the ocean, and exists in long but narrow topographic V-shaped depressions. The cumulative area occupied by the 46 individual hadal habitats worldwide is less than 0.25 percent of the world's seafloor, yet trenches account for over 40 percent of the ocean's depth range. Most hadal habitat is found in the Pacific Ocean. Historically"
"drops down to the deep sea floor. The deep-sea floor is called the abyssal plain and is usually about 4,000 meters deep. The ocean floor is not all flat but has submarine ridges and deep ocean trenches known as the hadal zone. For comparison, the pelagic zone is the descriptive term for the ecological region above the benthos, including the water-column up to the surface. Depending on the water-body, the benthic zone may include areas that are only a few inches below water, such as a stream or shallow pond; at the other end of the spectrum, benthos of the"
"line of constant magnetic declination, the variation of magnetic north from geographic north. An agonic line is drawn through points of zero magnetic declination. An isoporic line refers to a line of constant annual variation of magnetic declination An isoclinic line connects points of equal magnetic dip, and an aclinic line is the isoclinic line of magnetic dip zero. An isodynamic line (from or ""dynamis"" meaning 'power') connects points with the same intensity of magnetic force. Besides ocean depth, oceanographers use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular, isobathytherms are lines showing"
"Seafloor mapping Seafloor mapping, also called seabed imaging, is the measurement of water depth of a given body of water. Bathymetric measurements are conducted with various different methods, ranging from sonar and Lidar techniques to buoys and satellite altimetry. Various methods have advantages and disadvantages and the specific method used depends upon the scale of the area under study, financial means, desired measurement accuracy, and additional variables. Despite modern computer-based research, the ocean seabed in many locations is less measured than the topography of Mars. At the beginning of the twentieth century mapping the seafloor was a very difficult task."
"that relative angles at each point of the map are correct, and the local scale (although varying throughout the map) in every direction around any one point is constant. These are some conformal projections: Equal-area maps preserve area measure, generally distorting shapes in order to do that. Equal-area maps are also called ""equivalent"" or ""authalic"". These are some projections that preserve area: These are some projections that preserve distance from some standard point or line: Great circles are displayed as straight lines: Direction to a fixed location B (the bearing at the starting location A of the shortest route) corresponds"
"(e.g., through tunnels) under the land. Technically, an ""equipotential surface"" of the true geopotential, chosen to coincide (on average) with mean sea level. As mean sea level is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible ""near-geoids"" will result, with differences of several decimetres to over one metre between them, due to the dynamic sea surface topography. These are referred to as ""vertical"" or ""height datums"". For every point on Earth, the local direction of gravity or vertical direction, materialized with the plumb line, is ""perpendicular"" to the"
"Underwater Underwater refers to the region below the surface of water where the water exists in a swimming pool or a natural feature (called a body of water) such as an ocean, sea, lake, pond, or river. Three quarters of the planet Earth is covered by water. A majority of the planet's solid surface is abyssal plain, at depths between below the surface of the oceans. The solid surface location on the planet closest to the centre of the orb is the Challenger Deep, located in the Mariana Trench at a depth of . Although a number of human activities"
"Rhumb line In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north. The effect of following a rhumb line course on the surface of a globe was first discussed by the Portuguese mathematician Pedro Nunes in 1537, in his ""Treatise in Defense of the Marine Chart"", with further mathematical development by Thomas Harriot in the 1590s. A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two"
"Hypsometric tints <onlyinclude>Hypsometric tints (also called layer tinting, elevation tinting, elevation coloring, or hysometric coloring) are colors placed between contour lines to indicate elevation. These tints are shown as bands of color in a graduated scheme or as a color ramp applied to contour lines themselves. A typical scheme progresses from dark greens for lower elevations, up through yellows/browns and on to grays and white at the highest elevations. Hypsometric tinting of maps and globes is often accompanied by a similar method of bathymetric tinting to convey depth of oceans; lighter shades of blue represent shallower water such as the"
"follows bottom topography, allowing for the idealized flow of water over features such as seamounts. In both the vertical and horizontal directions, the default equations use centered, second-order finite difference schemes on staggered grids. Higher order schemes are available if desired, for example using parabolic spline reconstruction. Boundaries such as coastlines can be specified for a given region using land- and sea-masking. The top vertical boundary, the air-sea interface, uses an interaction scheme developed by Fairall et al. (1996). The bottom vertical boundary, the sediment-water interface, uses a bottom stress or bottom-boundary-layer scheme developed by Styles and Glenn (2000). ROMS"
"distances whose determination requires more sophisticated calculations. Mercator projection The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (making it a conformal map projection), the Mercator projection distorts the size of objects as"
"the numbers shown on the chart. Depths on charts published in most parts of the world use metres. Older charts, as well as those published by the United States government, may use feet or fathoms. Depth contour lines show the shape of underwater relief. Coloured areas of the sea emphasise shallow water and dangerous underwater obstructions. Depths are measured from the chart datum, which is related to the local sea level. The chart datum varies according to the standard used by each national Hydrographic Office. In general, the move is towards using lowest astronomical tide (LAT), the lowest tide predicted"
"Abyssal plain An abyssal plain is an underwater plain on the deep ocean floor, usually found at depths between and . Lying generally between the foot of a continental rise and a mid-ocean ridge, abyssal plains cover more than 50% of the Earth’s surface. They are among the flattest, smoothest, and least explored regions on Earth. Abyssal plains are key geologic elements of oceanic basins (the other elements being an elevated mid-ocean ridge and flanking abyssal hills). The creation of the abyssal plain is the result of the spreading of the seafloor (plate tectonics) and the melting of the lower"
"below the horizontal). Trend and plunge are used for linear features, and their symbol is a single arrow on the map. The arrow is oriented in the downgoing direction of the linear feature (the ""trend"") and at the end of the arrow, the number of degrees that the feature lies below the horizontal (the ""plunge"") is noted. Trend and plunge are often notated as PLUNGE → TREND (for example: 34 → 86 indicates a feature that is angled at 34 degrees below the horizontal at an angle that is just East of true South). The oldest preserved geologic map is"
"(trademark). The record made by such a device is a fathogram. A fathom line or fathom curve, a usually sinuous line on a nautical chart, joins all points having the same depth of water, thereby indicating the contour of the ocean floor. The components of a commercial fisherman's setline were measured in fathoms. The rope called a ""groundline"", used to form the main line of a setline, was usually provided in bundles of 300 fathoms. A single 50-fathom skein () of this rope was referred to as a ""line"". Especially in Pacific coast fisheries the setline was composed of units"
"travel through fishing areas of the Baltic Sea, as well as area where chemical weapons from World War II had been discarded. Submarine pipeline A submarine pipeline (also known as marine, subsea or offshore pipeline) is a pipeline that is laid on the seabed or below it inside a trench. In some cases, the pipeline is mostly on-land but in places it crosses water expanses, such as small seas, straits and rivers. Submarine pipelines are used primarily to carry oil or gas, but transportation of water is also important. A distinction is sometimes made between a ""flowline"" and a pipeline."