Elevation contour map

A contour line (also level set, isopleth, isoline, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. A contour map is a map illustrated with contour lines, for example a topographic map. The prefix iso-, from the Greek prefix ισος ("equal"), is used from descriptive names for map lines that join points of equal value. The Comet Nucleus Tour (CONTOUR) was a Discovery-class space mission. ... The Ford Contour is a North American variant of the European Ford Mondeo sedan previously sold by Ford Motor Company. ... Description: Example of a topographic map with contour intervals Source: Sample taken from the public domain USGS Digital Raster Graphic file o44072d6. ... Description: Example of a topographic map with contour intervals Source: Sample taken from the public domain USGS Digital Raster Graphic file o44072d6. ... Elevation histogram of the surface of the Earth – approximately 71% of the Earths surface is covered with water. ... In mathematics, a level set of a real-valued function f of n variables is a set of the form { (x1,...,xn) | f(x1,...,xn) = c } where c is a constant. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... For other uses, see Map (disambiguation). ... // Topographic maps are a variety of maps characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. ...

Most everyday use of the term is in cartography. A contour map (topographic map) uses contour lines (often just called a "contour") to join points of equal elevation (height) and thus show valleys and hills, and the steepness of slopes.

More generally, a contour line (also level set, isopleth, isoline, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. The prefix iso-, from the Greek prefix ισος ("equal"), is used from descriptive names for map lines that join points of equal value. The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone. However if contour lines rotate through three or more widths, or if the lines are numerically labelled, then the direction of the gradient can also be determined from the contour lines. In mathematics, a level set of a real-valued function f of n variables is a set of the form { (x1,...,xn) | f(x1,...,xn) = c } where c is a constant. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... For other uses, see Gradient (disambiguation). ...

Contour lines are curved or straight lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from estimated surface elevations, as when a computer program threads contours through a network of observation points ot area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks (see Davis, 1986, Statistics and data analysis in geology). For other uses, see Map (disambiguation). ... An open surface with X-, Y-, and Z-contours shown. ... Part of a topographic map of Haleakala (Hawaii), showing elevation. ... Look up Contours in Wiktionary, the free dictionary. ... This article is about the mathematical term. ...

Types of contour lines

Contour lines are often given specific names beginning "iso-" (from Greek ισος (isos), meaning 'equal') according to the nature of the variable being mapped, although in many usages the word "contour line" is most commonly used. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously.

In general, an isogon is a line along which an angle is held constant. "Iso-" can be replaced with "isallo-" to specify a contour line connecting points where a variable changes at the same rate during a given time period.

Meteorology

Isohyetal map

Meteorological contour lines are based on generalization from point data received from weather stations. Weather stations are seldom exactly positioned at a contour line (when they are, this indicates a measurement precisely equal to the value of the contour). Instead, lines are drawn to best approximate the locations of exact values, based on the scattered information points available. Image File history File links Download high resolution version (1050x638, 287 KB) Source: http://www. ... Image File history File links Download high resolution version (1050x638, 287 KB) Source: http://www. ... For the term in the context of mathematical logic, see Generalization (logic). ... A technician examines a weather stations anemometer. ...

Meteorological countour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future A weather map provides a view of weather elements over a specified geographical area at a specified time. ...

Thermodynamic diagrams use multiple overlapping contour sets (including isobars and isotherms) to present a picture the major thermodynamic factors in a weather system. Thermodynamic diagrams are diagrams used by scientists and engineers to represent the thermodynamic states of a material (typically fluid) and the consequences of manipulating this material. ...

Barometric pressure

An isobar (from βαρος or baros, meaning 'weight') is a line of equal or constant pressure on a graph, plot, or map; an isopleth or contour line of pressure. In meteorology, the barometric pressures shown are reduced to sea level, not the surface pressures at the map locations. The distribution of isobars is closely related to the magnitude and direction of the wind field, and can be used to predict future weather patterns. Isobars are commonly used in television news weather reporting, though more commonly in Europe than in the United States. This article is about pressure in the physical sciences. ... // Meteorology (from Greek: μετέωρον, meteoron, high in the sky; and λόγος, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... Atmospheric pressure is the pressure caused by the weight of air above any area in the Earths atmosphere. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... For other uses, see Wind (disambiguation). ...

An isostere is a line of constant atmospheric density

Temperature and related subjects

The 10°C mean isotherm in July, marked by the red line, is commonly used to define the Arctic region border

An isotherm (from θερμη or thermē, meaning 'heat') is a line that connects points on a map that have the same temperature. Therefore, all points through which an isotherm passes have the same temperatures at the time indicated. Generally, isotherms representing 5°C or 10°F temperature differences are used, but any interval may be chosen. Image File history File links Arctic. ... Image File history File links Arctic. ... The red line indicates the 10°C isotherm in July, commonly used to define the Arctic region border The Arctic is the area around the Earths Russia, Alaska, Canada, Iceland, Norway (including Arctic Ocean. ... For other uses, see Temperature (disambiguation). ... For other uses, see Temperature (disambiguation). ... For other uses, see Temperature (disambiguation). ...

An isogeotherm is a line of equal mean annual temperature. An isocheim is a line of equal mean winter temperature, and an isothere is a line of equal mean summer temperature.

An isohel (from έλιος or helios, meaning 'sun') is a line of equal or constant solar radiation. Solar irradiance spectrum at top of atmosphere. ...

Precipitation and air moisture

An isohyet or isohyetal line (from ύετος or huetos, meaning 'rain') is a line joining points of equal precipitation on a map. A map with isohyets is called an isohyetal map. For other uses, see Map (disambiguation). ...

An isohume is a line of constant relative humidity, while a isodrosotherm (from δροσος or drosos, meaning 'dew', and θερμη or therme, meaning 'heat') is a line of equal or constant dew point. Humidity is the amount of water vapor in air. ... The dew point (or dewpoint) is the temperature to which a given parcel of air must be cooled, at constant barometric pressure, for water vapor to condense into water. ...

An isoneph is a line indicating equal cloud cover. For other uses, see Cloud (disambiguation). ...

An isochalaz is a line of constant frequency of hail storms. This article is about the precipitation. ...

Snow cover is frequently shown as a contour-line map. For other uses, see Snow (disambiguation). ...

Wind

An isotach (from ταχ or tach, meaning 'speed') is a line of constant wind speed. In general, an isogon is a line along which an angle is held constant. In meteorology, the term refers to a line of constant wind direction. For other uses, see Wind (disambiguation). ...

Other terms

• isopectic: ice formation location each winter
• isotac: time of thawing

Physical geography and oceanography

Elevation and depth

Topographic map with isohypses of height

Contours are one of several common methods used to denote elevation or altitude and depth. 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 up to continental-scale maps. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Terrain or relief is an essential aspect of physical geography, and as such its portrayal presents a central problem in cartography, and more recently GIS and 3D Visualization. ... Elevation histogram of the surface of the Earth – approximately 71% of the Earths surface is covered with water. ... Altitude is the elevation of an object from a known level or datum. ... Example of a topographic map with contour lines Topographic maps, also called contour maps, topo maps or topo quads (for quadrangles), are maps that show topography, or land contours, by means of contour lines. ...

"Contour line" is the most common usage in cartography, but isobath for underwater depths on bathymetric maps and isohypse for elevations are also used. The process of drawing isohypse contour lines on a map is called isopletion. The seafloor topography near the Puerto Rico Trench Bathymetry is the underwater equivalent to topography. ...

What makes this this. This is sea level der====Magnetism==== In general, an isogon is a line along which an angle is held constant. In geomagnetism, the term refers to a line of constant magnetic declination (variance of magnetic north from geographic north). Isogonic lines are lines connecting those parts where the declination of the Earth's magnetic field is the same in amount. They are similar to isoclinic lines, which are lines connecting points of equal magnetic inclination. The line drawn through the points of zero magnetic declination is called the agonic line. The cause of Earths magnetic field (the surface magnetic field) is not known for certain, but is possibly explained by dynamo theory. ... This is about the geographic meaning of North Pole. ... Line redirects here. ... The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ... Isoclinic lines are lines connecting those parts where the inclination of the Earths magnetic field is the same in amount. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ... The magnetic declination (or magnetic variation) at any point on the earth is a property of the geomagnetic field defined as the angle that must be added or subtracted in converting between two kinds of directional information: the direction of the needle on a magnetic compass located there, and the...

Oceanography

Besides ocean depth, oceanographers use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular, isobathytherms are lines showing depths of water with equal temperature, and isohalines show lines of equal ocean salinity. Thermohaline circulation Oceanography (from Ocean + Greek γράφειν = write), also called oceanology or marine science, is the branch of Earth Sciences that studies the Earths oceans and seas. ...

Environmental science

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 or scales of pollution. Acid precipitation is indicated on maps with isoplats. Some of the most widespread applications of environmental science contour maps involve mapping of environmental noise, air pollution, soil contamination, thermal pollution and groundwater contamination. Environmental Noise, is unwanted sound, which may cause either nuisance or damage to health. ... Air pollution is the modification of the natural characteristics of the atmosphere by a chemical, particulate matter, or biological agent. ... Excavation of leaking underground storage tank causing soil contamination Soil pollution comprises the pollution of soils with materials, mostly chemicals, that are out of place or are present at concentrations higher than normal which may have adverse effects on humans or other organisms. ... Thermal pollution is a temperature change in natural water bodies caused by human influence. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of lithologic formations. ...

Social sciences

In economics, contour lines can be used to describe features which vary quantitatively over space. An isochrone shows lines of equivalent drive time or travel time to a given location. An isotim shows equivalent transport costs from the source of a raw material, and an isodopane shows equivalent cost of travel time. Face-to-face trading interactions on the New York Stock Exchange trading floor. ...

Isolines can also be used to delineate qualitative differences. An isogloss, for example, is used in mapping the geographic spread of linguistic features. Isoglosses on the Faroe Islands An isogloss is the geographical boundary of a certain linguistic feature, e. ...

Contour lines are also used in non-geographic charts in economics. An isoquant is a line of equal production quantity, and an isocost shows equal production costs. An isoquant map where Q3 > Q2 > Q1. ... A set of input bundles each which costs the same amount. ...

Thermodynamics, engineering, and other sciences

Various types of graphs in thermodynamics, engineering, and other sciences use isobars (for showing constant pressure), isotherms (for constant temperature), isochors (for constant specific volume), or other types of iso-lines (or curves), even though these graphs are usually not related to maps. Such iso-lines are useful for representing more than two dimensions (or quantities) on two-dimensional graphs. Common examples in thermodynamics are some types of phase diagrams. Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... In physical chemistry, mineralogy, and materials science, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases. ...

Other phenomena

• isochasm: aurora equal occurrence
• isochor: volume
• isodose: radiation intensity
• isophene: biological events occurring with coincidence such as plants flowering
• isophote: illuminance

History

The idea of lines that join points of equal value was rediscovered several times. 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 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. The use of such lines to describe a land surface (contour lines) was studied theoretically by Ducarla in 1771, and Charles Hutton used them when calculating the volume of a hill in 1777. 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. In 1801, the chief of the Corps of Engineers, Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for Rocca d'Aufo. ^{[1] [2] [3]} // Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Portrait of Edmond Halley Bust of Edmond Halley in the Museum of the Royal Greenwich Observatory Edmond Halley FRS (sometimes Edmund; IPA: ) (November 8, 1656 – January 14, 1742) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist. ... The Merwede (etymology uncertain, possibly derived from the ancient Dutch word meaning wide water) is the name of several interconnected stretches of river in The Netherlands, all part of the Rhine-Meuse-Scheldt delta. ... A fathom is the name of a unit of length in the Imperial system (and the derived U.S. customary units). ... This 1753 map by Philippe Buache locates Fusang (Fou-Sang des Chinois, Fusang of the Chinese) north of the State of California. ... For the Thoroughbred racehorse of the same name, see English Channel (horse). ... Charles Hutton (August 14, 1737 - January 27, 1823) was an English mathematician. ... François Nicolas Benoît, Baron Haxo (June 24, 1774 - June 25, 1838), French general and military engineer, was born at Lunéville, and entered the Engineers in 1793. ...

By around 1843, when the Ordnance Survey started to regularly record contour lines in Great Britain and Ireland, they were already in general use in European countries. Isobaths were not routinely used on nautical charts until those of Russia from 1834, and those of Britain from 1838. ^{[4] [5] [1]} Part of an Ordnance Survey map at 1 inch to the mile scale from 1945 Ordnance Survey (OS) is an executive agency of the United Kingdom government. ... A 1976 United States NOAA chart of part of Puerto Rico A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. ...

When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are air quality and noise pollution contour maps, which first appeared in the USA, in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters. The Air Quality Index (AQI) is a standardized index of the air quality in a given location, given in parts per billion. ... Noise pollution (or environmental noise in technical venues) is displeasing human or machine created sound that disrupts the environment. ...

Technical construction factors

To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line color, line type and method of numerical marking. Color is an important part of the visual arts. ...

Line weight is simply the darkness or thickness of the line used. This choice is made based upon the least intrusive form of contours that enable the reader to decipher the background information in the map itself. If there is little or no content on the base map, the contour lines may be drawn with relatively heavy thickness. Also, for many forms of contours such as topographic maps, it is common to vary the line weight and/or color, so that a different line characteristic occurs for certain numerical values. For example, in the topographic map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals. Topography, a term in geography, has come to refer to the lay of the land, or the physiogeographic characteristics of land in terms of elevation, slope, and orientation. ...

Line color is the choice of any number of pigments that suit the display. Sometimes a sheen or gloss is used as well as color to set the contour lines apart from the base map. Line colour can be varied to show other information; on some Swiss maps, the contour lines are changed from brown to grey to indicate bare rock and scree. Natural Ultramarine pigment in powdered form. ... Sheen is a place in southwest London nearby to Barnes, Roehampton and Putney to the east and Richmond to the west. ... Scree or detritic cone is a term given to broken rock that appears at the bottom of crags, mountain cliffs or valley shoulders. ...

Line type refers to whether the basic contour line is solid, dashed, dotted or broken in some other pattern to create the desired effect. Dotted or dashed lines are often used when the underlying base map conveys very important (or difficult to read) information. Broken line types are used when the location of the contour line is inferred.

Numerical marking is the manner of denoting the arithmetical the values of contour lines. This can be done by placing numbers along some of the contour lines, typically using interpolation for intervening lines. The direction of these text labels is often used to indicate the direction of the slope. Alternatively a map key can be produced associating the contours with their values. Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points. ...

Plan view versus profile view

Most commonly contour lines are drawn in plan view. or as an observer in space would view the earth's surface: ordinary map form. However, some parameters can often be displayed in profile view showing a vertical profile of the parameter mapped. Some of the most common parameters mapped in profile are air pollutant concentrations and sound levels. In each of those cases it may be important to analyze (air pollutant concentrations or sound levels) at varying heights so as to determine the air quality or noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. One can see an example of vertical contours in the article on noise barriers. In actuality, both plan and profile view contour maps are used in air pollution and noise pollution studies. This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Sound pressure level (SPL) or sound level Lp is a logarithmic measure of the energy of a particular noise relative to a reference noise source. ... Roadway noise is the main source of exposure Noise health effects, the collection of health consequences of elevated sound levels, constitute one of the most widespread public health threats in industrialized countries. ... The sound tube in Melbourne, Australia, designed to reduce roadway noise without detracting from the areas aesthetics. ... Air pollution is the modification of the natural characteristics of the atmosphere by a chemical, particulate matter, or biological agent. ... Noise pollution (or environmental noise in technical venues) is displeasing human or machine created sound that disrupts the environment. ...

Labeling contour maps

Contour map labeled aesthetically in an "elevation up" manner.

Labels are a critical component of elevation maps. A properly labeled contour map helps the reader to quickly interpret the shape of the terrain. If numbers are placed close to each other, it means that the terrain is steep. Labels should be placed along a slightly curved line "pointing" to the summit or nadir, from several directions if possible, making the visual identification of the summit or nadir easy.^[6][7] Image File history File links Size of this preview: 800 × 526 pixelsFull resolution‎ (1,035 × 680 pixels, file size: 170 KB, MIME type: image/jpeg) This is a contour map labeled according to accepted cartographic conventions. ... Image File history File links Size of this preview: 800 × 526 pixelsFull resolution‎ (1,035 × 680 pixels, file size: 170 KB, MIME type: image/jpeg) This is a contour map labeled according to accepted cartographic conventions. ...

Manual labeling of contour maps is a time-consuming process, however, there are a few software systems that can do the job automatically and in accordance with cartographic conventions. For more information visit the Wikipedia article on Automatic label placement. The issue of automatic label placement is one of the most difficult problems in GIS, but other kinds of computer_generated graphics _ like charts, graphs etc. ...

References

1. ^ ^{a b} R. A. Skelton, "Cartography", History of Technology, Oxford, vol. 6, pp. 612-614, 1958.
2. ^ Colonel Berthaut, La Carte de France, vol. 1, p. 139, quoted by Close (see below).
3. ^ C. Hutton, "An account of the calculations made from the survey and measures taken at Schehallien, in order to ascertain the mean density of the Earth", Philosophical Transactions of the Royal Society of London, vol. 68, pp. 756-757
4. ^ C. Close, The Early Years of the Ordnance Survey, 1926, republished by David and Charles, 1969, ISBN 0-7153-4477-3, pp. 141-144.
5. ^ T. Owen and E. Pilbeam, Ordnance Survey: Map Makers to Britain since 1791, HMSO, 1992, ISBN 0-11-701507-5.
6. ^ Imhof, E., “Die Anordnung der Namen in der Karte,” Annuaire International de Cartographie II, Orell-Füssli Verlag, Zürich, 93-129, 1962.
7. ^ Freeman, H., “Computer Name Placement,” ch. 29, in Geographical Information Systems, 1, D.J. Maguire, M.F. Goodchild, and D.W. Rhind, John Wiley, New York, 1991, 449-460.

External links

• Drawing Contour Plots. A lesson plan that deals with drawing various isopleths.
• See also Forthright's Phrontistery for many more different types of isopleths.
• National Science Digital Library - Isobar