A contour line (also level set, isopleth, isoline, isogram or isarithm) is 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.
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 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.
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).
Types of contour linesContour 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.
MeteorologyMeteorological 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.
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
Thermodynamic diagrams use multiple overlapping contour sets (including isobars and isotherms) to present a picture the major thermodynamic factors in a weather system.
Barometric pressureAn 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.
An isostere is a line of constant atmospheric density
Temperature and related subjectsAn 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.
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.
Precipitation and air moistureAn 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.
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.
An isoneph is a line indicating equal cloud cover.
An isochalaz is a line of constant frequency of hail storms.
Snow cover is frequently shown as a contour-line map.
WindAn 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.
Freeze and thawAn isopectic line denotes equal dates of ice formation each winter, and an isotac denotes equal dates of thawing.
Physical geography and oceanography
Elevation and depthContours 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.
"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.
MagnetismIn 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.
OceanographyBesides 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.
Environmental scienceIn 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.
Social sciencesIn 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.
Indifference curves are used to show bundles of goods to whoch a person would assign equal utility. In political science an analogous method is used in understanding coalitions (for example the pretty pictures in Laver and Shepsle's work)
Isolines can also be used to delineate qualitative differences. An isogloss, for example, is used in mapping the geographic spread of linguistic features.
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.
Thermodynamics, engineering, and other sciencesVarious 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.
- isochasm: aurora equal occurrence
- isochor: volume
- isodose: radiation intensity
- isophene: biological events occurring with coincidence such as plants flowering
- isophote: illuminance
HistoryThe 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.
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.
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, called automatic label placement.
isoline in Czech: Izolinie
isoline in Danish: Højdekurve
isoline in German: Höhenlinie
isoline in Estonian: Samajoon
isoline in Spanish: Isógrama
isoline in French: Courbe de niveau
isoline in Italian: isocline
isoline in Hungarian: Szintvonal
isoline in Japanese: 等高線
isoline in Norwegian: Kote
isoline in Norwegian Nynorsk: Kote
isoline in Polish: Izolinia
isoline in Portuguese: Curva de nível
isoline in Slovenian: Izo-črte
isoline in Finnish: Isoviiva
isoline in Swedish: Höjdkurva
isoline in Turkish: Eşyükselti eğrisi
isoline in Chinese: 等高线