Editing Contour line (section)

== Types ==<!-- [[Isogon]] and internal links redirect here -->
Contour lines are often given specific names beginning with "''iso-''" according to the nature of the variable being mapped, although in many usages the phrase "contour line" is most commonly used. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously. The prefix "'''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.

An '''isogon''' ({{ety|grc|''γωνία'' (gonia)|angle}}) is a contour line for a variable which measures direction.  In meteorology and in geomagnetics, the term ''isogon'' has specific meanings which are described below.  An '''[[isocline]]''' ({{langx|grc|κλίνειν|klinein|to lean or slope|label=none}}) is a line joining points with equal slope.  In population dynamics and in geomagnetics, the terms ''isocline'' and ''isoclinic line'' have specific meanings which are described below.

=== Equidistant points ===
A curve of equidistant points is a set of points all at the same distance from a given [[point (geometry)|point]], [[line (geometry)|line]], or [[polyline]]. In this case the function whose value is being held constant along a contour line is a [[distance function]].

=== Isopleths ===<!-- [[Isopleth]] and [[Isopleths]] redirect here -->
In 1944, John K. Wright proposed that the term ''isopleth'' be used for contour lines that depict a variable which cannot be measured at a point, but which instead must be calculated from data collected over an area, as opposed to ''isometric lines'' for variables that could be measured at a point; this distinction has since been followed generally.<ref name="wright1944" /><ref>{{cite journal | vauthors = Robinson AH | author-link = Arthur H. Robinson | year = 1971 | title = The genealogy of the isopleth | journal = Cartographic Journal | volume = 8 | issue = 1 | pages = 49–53 | doi = 10.1179/caj.1971.8.1.49 | bibcode = 1971CartJ...8...49R }}</ref> An example of an isopleth is [[population density]], which can be calculated by dividing the population of a [[census tract|census district]] by the surface area of that district. Each calculated value is presumed to be the value of the variable at the centre of the area, and isopleths can then be drawn by a process of [[interpolation]]. The idea of an isopleth map can be compared with that of a [[choropleth map]].<ref>T. Slocum, R. McMaster, F. Kessler, and H. Howard, ''Thematic Cartography and Geographic Visualization'', 2nd edition, Pearson, 2005, {{ISBN|0-13-035123-7}}, p. 272.</ref><ref>ArcGIS, [http://www.arcgis.com/home/item.html?id=830338fc8ca947c38b8d97f51724f5c9 Isopleth: Contours], 2013.</ref>

In meteorology, the word ''isopleth'' is used for any type of contour line.<ref>NOAA's National Weather Service, [http://w1.weather.gov/glossary/index.php?letter=i Glossary].</ref>

=== Meteorology ===
[[File:Isohyet.png|thumb|upright=1.3|Isohyetal map of precipitation]]

Meteorological contour lines are based on [[interpolation]] of the point data received from [[weather station]]s and [[weather satellite]]s. 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.

[[Weather maps|Meteorological contour 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 of the major thermodynamic factors in a weather system.

==== Barometric pressure ====<!-- [[Isobar (meteorology)]] redirects here -->
[[File:Loop isallobaric tendencies.gif|thumb|Video loop of isallobars showing the motion of a [[cold front]]]]
An '''isobar''' ({{ety|grc|''βάρος'' (baros)|weight}}) is a line of equal or constant [[pressure]] on a graph, plot, or map; an isopleth or contour line of pressure. More accurately, isobars are lines drawn on a map joining places of equal average atmospheric pressure reduced to sea level for a specified period of time. In [[meteorology]], the [[barometric pressure]]s shown are reduced to [[sea level]], not the surface pressures at the map locations.<ref>{{cite web |publisher=University of Wisconsin |author=Edward J. Hopkins, Ph.D. |date=1996-06-10 |url=http://www.meteor.wisc.edu/~hopkins/aos100/sfc-anl.htm |title=Surface Weather Analysis Chart |access-date=2007-05-10}}</ref>  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 weather reporting.

'''Isallobars''' are lines joining points of equal pressure change during a specific time interval.<ref name="OMM">{{cite web | url= http://www.eumetcal.org/resources/ukmeteocal/rapid_cyclo/www/english/glossary/isalloba.htm | title= Isallobar | author= World Meteorological Organisation | author-link= World Meteorological Organisation | work= Eumetcal | access-date= 12 April 2014 | url-status= dead | archive-url= https://web.archive.org/web/20140416031654/http://www.eumetcal.org/resources/ukmeteocal/rapid_cyclo/www/english/glossary/isalloba.htm | archive-date= 16 April 2014 }}</ref> These can be divided into ''anallobars'', lines joining points of equal pressure increase during a specific time interval,<ref name="OMM-1">{{cite web | url= http://www.eumetcal.org/euromet/glossary/analloba.htm | archive-url= https://web.archive.org/web/20150924003018/http://www.eumetcal.org/euromet/glossary/analloba.htm | url-status= dead | archive-date= 24 September 2015 | title= Anallobar | author= World Meteorological Organisation | author-link= World Meteorological Organisation | work= Eumetcal | access-date= 12 April 2014 }}</ref> and ''katallobars'', lines joining points of equal pressure decrease.<ref name="OMM-2">{{cite web | url= http://www.eumetcal.org/euromet/glossary/katallob.htm | archive-url= https://web.archive.org/web/20080205124154/http://www.eumetcal.org/euromet/glossary/katallob.htm | url-status= dead | archive-date= 5 February 2008 | title= Katallobar | author= World Meteorological Organisation | author-link= World Meteorological Organisation | work= Eumetcal | access-date= 12 April 2014 }}</ref> In general, weather systems move along an axis joining high and low isallobaric centers.<ref>{{ cite web | url= http://apollo.lsc.vsc.edu/classes/met130/notes/chapter13/isallobars.html | title= Forecasting weather system movement with pressure tendency | work= Chapter 13 – Weather Forecasting | publisher = Lyndon State College Atmospheric Sciences | access-date = 12 April 2014}}</ref> Isallobaric gradients are important components of the wind as they increase or decrease the [[geostrophic wind]].

An [[isopycnal]] is a line of constant density. An ''isoheight'' or ''isohypse'' is a line of constant [[geopotential]] height on a constant pressure surface chart. Isohypse and isoheight are simply known as lines showing equal pressure on a map.

==== Temperature and related subjects ====
[[Image:arctic.svg|thumb|The {{convert|10|C}} mean isotherm in July, marked by the red line, is commonly used to define the border of the [[Arctic region]]]]

An '''isotherm''' ({{ety|grc|''θέρμη'' (thermē)|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 or equal temperatures at the time indicated.<ref name="DataAir">{{cite web|author=DataStreme Atmosphere|publisher=American Meteorological Society|url=http://www.ametsoc.org/amsedu/dstreme/learn/sample.act.html |title=Air Temperature Patterns|date=2008-04-28|access-date=2010-02-07 |archive-url = https://web.archive.org/web/20080511124504/http://www.ametsoc.org/amsedu/dstreme/learn/sample.act.html |archive-date = 2008-05-11}}</ref><ref name="Hughes"/>  An isotherm at 0&nbsp;°C is called the [[freezing level]]. The term ''lignes isothermes'' (or ''lignes d'égale chaleur)'' was coined by the [[Prussia]]n geographer and naturalist [[Alexander von Humboldt]], who as part of his research into the geographical distribution of plants published the first map of isotherms in Paris, in 1817.<ref>{{ cite book | last=Daum | first=Andreas W.|author-link=Andreas Daum | year=2024 | title=Alexander von Humboldt: A Concise Biography | location=Trans. Robert Savage. Princeton, N.J. | publisher=Princeton University Press |pages=106–107 | isbn=978-0-691-24736-6 }}</ref><ref>{{Cite journal|last=Munzar|first=Jan|date=1967-09-01|title=Alexander Von Humboldt and His Isotherms|journal=Weather|language=en|volume=22|issue=9|pages=360–363|doi=10.1002/j.1477-8696.1967.tb02989.x|issn=1477-8696|bibcode=1967Wthr...22..360M}}</ref> According to Thomas Hankins, the Scottish engineer [[William Playfair]]'s graphical developments greatly influenced Alexander von Humbolt's invention of the isotherm.<ref>{{Cite journal |date=1999 |title=Blood, Dirt, and Nomograms: A Particular History of Graphs |url=https://www.journals.uchicago.edu/doi/10.1086/384241 |journal=Isis |language=en |volume=90 |issue=1 |pages=50–80 |doi=10.1086/384241 |issn=0021-1753}}</ref> Humbolt later used his visualizations and analyses to contradict theories by Kant and other Enlightenment thinkers that non-Europeans were inferior due to their climate.<ref>{{Cite journal |last=Strobl |first=Michael |date=2021 |title=Alexander von Humbolt's Climatological Writings |url=https://onlinelibrary.wiley.com/doi/10.1111/glal.12313 |journal=German Life and Letters |language=en |volume=74 |issue=3 |pages=371–393 |doi=10.1111/glal.12313 |issn=0016-8777}}</ref> 

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

An '''isohel''' ({{langx|grc|ἥλιος|helios|Sun|label=none}}) is a line of equal or constant [[solar radiation]].

An '''isogeotherm''' is a line of equal temperature beneath the Earth's surface.

==== Rainfall and air moisture ====
An '''isohyet''' or '''isohyetal line''' ({{ety|grc|''ὑετός'' (huetos)|rain}}) is a line on a [[map]] joining points of equal rainfall in a given period. A map with isohyets is called an '''isohyetal map'''.

An '''isohume''' is a line of constant relative [[humidity]], while an '''isodrosotherm''' ({{ety|grc|''δρόσος'' (drosos)|dew||''θέρμη'' (therme)|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, and an '''isobront''' is a line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously.

[[Snow]] cover is frequently shown as a contour-line map.

==== Wind ====<!-- [[Isogon (meteorology)]] redirects here -->
An '''isotach''' ({{ety|grc|''ταχύς'' (tachus)|fast}}) is a line joining points with constant [[wind]] speed.
In meteorology, the term '''isogon''' refers to a line of constant wind direction.

==== Freeze and thaw ====
An '''isopectic''' line denotes equal dates of [[ice]] formation each winter, and an '''isotac''' denotes equal dates of thawing.

=== Physical geography and oceanography ===

==== Elevation and depth ====
[[File:Topographic map example.png|thumb|right|[[Topographic map]] of [[Stowe, Vermont|Stowe]], [[Vermont]]. The brown contour lines represent the [[elevation]]. The contour interval is 20 [[foot (length)|feet]].]]

Contours are one of several [[Cartographic relief depiction|common methods]] used to denote [[elevation]] or [[altitude]] and depth on [[map]]s. 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 elevation difference between adjacent contour lines. The contour interval should be the same over a single map. When calculated as a ratio against the map scale, a sense of the hilliness of the terrain can be derived.

===== Interpretation =====

There are several rules to note when interpreting terrain contour lines:
* '''The rule of Vs''': sharp-pointed vees usually are in stream valleys, with the drainage channel passing through the point of the vee, with the vee pointing upstream. This is a consequence of [[erosion]].
* '''The rule of Os''': closed loops are normally uphill on the inside and downhill on the outside, and the innermost loop is the highest area. If a loop instead represents a depression, some maps note this by short lines called hachures which are perpendicular to the contour and point in the direction of the low.<ref>{{cite web|last =Leveson|first= David J.|title = Depression Contours – Getting Into and Out of a Hole |url= http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/depression.html |publisher= [[City University of New York]] |date= 2002}}</ref> (The concept is similar to but distinct from hachures used in [[hachure map]]s.)
* '''Spacing of contours''': close contours indicate a steep slope; distant contours a shallow slope. Two or more contour lines merging indicates a cliff. By counting the number of contours that cross a segment of a [[stream]], the [[stream gradient]] can be approximated.

Of course, to determine differences in elevation between two points, the contour interval, or distance in altitude between two adjacent contour lines, must be known, and this is normally stated in the map key. Usually contour intervals are consistent throughout a map, but there are exceptions. Sometimes intermediate contours are present in flatter areas; these can be dashed or dotted lines at half the noted contour interval. When contours are used with [[hypsometric tints]] on a small-scale map that includes mountains and flatter low-lying areas, it is common to have smaller intervals at lower elevations so that detail is shown in all areas. Conversely, for an island which consists of a plateau surrounded by steep cliffs, it is possible to use smaller intervals as the height increases.<ref>''[[Sark]] (Sercq)'', D Survey, Ministry of Defence, Series M 824, Sheet Sark, Edition 4 GSGS, 1965, [[Online Computer Library Center|OCLC]] {{OCLC|27636277}}. Scale 1:10,560. Contour intervals: 50&nbsp;feet up to 200, 20&nbsp;feet from 200 to 300, and 10&nbsp;feet above 300.</ref>

==== Electrostatics ====
An '''[[isopotential map]]''' is a measure of electrostatic potential in space, often depicted in two dimensions with the electrostatic charges inducing that [[electric potential]]. The term '''[[equipotential]] line''' or '''isopotential line'''  refers to a curve of constant [[electric potential]]. Whether crossing an equipotential line represents ascending or descending the potential is inferred from the labels on the charges. In three dimensions, '''[[equipotential]] surfaces''' may be depicted with a two dimensional cross-section, showing [[equipotential]] lines at the intersection of the surfaces and the cross-section.

The general mathematical term [[level set]] is often used to describe the full collection of points having a particular potential, especially in higher dimensional space.

==== Magnetism ====<!-- [[Isogon (geomagnetism)]], [[Isogonic line]], [[Isogonic lines]], [[Agonic line]], [[Agonic lines]], [[Isoclinic line]], [[Aclinic line]] and [[Isodynamic line]] redirect here -->
[[Image:IGRF 2000 magnetic declination.gif|thumb|left|Isogonic lines for the year 2000. The agonic lines are thicker and labeled with "0".]]
In the study of the [[Earth's magnetic field]], the term '''isogon''' or '''isogonic line''' refers to a 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
.<ref>{{cite web
|url=http://historicalcharts.noaa.gov/historicals/preview/image/3077-00-1946
|access-date=2015-07-20
|title=isoporic line
|website=historicalcharts.noaa.gov
|date=1946
|archive-date=2015-07-21
|archive-url=https://web.archive.org/web/20150721172841/http://historicalcharts.noaa.gov/historicals/preview/image/3077-00-1946
|url-status=dead
}}</ref>

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 {{lang|grc|δύναμις}} or ''dynamis'' meaning 'power') connects points with the same intensity of magnetic force.

==== Oceanography ====
Besides ocean depth, [[oceanography|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, '''isohalines''' show lines of equal ocean salinity, and '''[[isopycnal]]s''' are surfaces of equal water density.

=== Geology ===
Various [[Geology|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 [[stratum|strata]], [[Fault (geology)|fault]] surfaces (especially low angle [[thrust fault]]s) and [[unconformity|unconformities]]. [[Isopach map]]s use '''isopachs''' (lines of equal thickness) to illustrate variations in thickness of geologic units.

=== 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]] (where lines of equal sound pressure level are denoted '''isobels'''<ref>{{cite web |url=https://www.sfu.ca/sonic-studio/handbook/Isobel.html
|access-date=2010-04-25
|title=Isobel
|website=www.sfu.ca
|date=2005-01-05
}}</ref>), [[air pollution]], [[soil contamination]], [[thermal pollution]] and [[groundwater]] contamination.  By [[contour planting]] and [[contour ploughing]], the rate of [[water runoff]] and thus [[soil erosion]] can be substantially reduced; this is especially important in [[riparian]] zones.

=== Ecology ===
An '''isoflor''' is an isopleth contour connecting areas of comparable biological diversity. Usually, the variable is the number of species of a given genus or family that occurs in a region. Isoflor maps are thus used to show distribution patterns and trends such as centres of diversity.<ref name="Specht 1981">{{cite book | author = Specht, Raymond | title = Heathlands and related shrublands: Analytical studies | publisher = Elsevier | pages = 219–220}}</ref>

=== Social sciences ===
[[File:Simple-indifference-curves.svg|thumb|left|From [[economics]], an indifference map with three indifference curves shown. All points on a particular indifference curve have the same value of the [[utility function]], whose values implicitly come out of the page in the unshown third dimension.]]

In [[economics]], contour lines can be used to describe features which vary quantitatively over space. An '''[[wikt:isochrone|isochrone]]''' shows lines of equivalent drive time or travel time to a given location and is used in the generation of [[isochrone map]]s. An '''isotim''' shows equivalent transport costs from the source of a raw material, and an '''[[isodapane]]''' shows equivalent cost of travel time.

[[File:TE-Production-Isoquant.png|thumb|A single production isoquant (convex) and a single isocost curve (linear). [[labor demand|Labor]] usage is plotted horizontally and [[physical capital]] usage is plotted vertically.]]

Contour lines are also used to display non-geographic information in economics. '''[[Indifference curves]]''' (as shown at left) are used to show bundles of goods to which a person would assign equal utility. An '''[[isoquant]]''' (in the image at right) is a curve of equal production quantity for alternative combinations of [[factors of production|input usages]], and an '''[[isocost|isocost curve]]''' (also in the image at right) shows alternative usages having equal production costs.

In [[political science]] an analogous method is used in understanding coalitions (for example the diagram in Laver and Shepsle's work<ref>Laver, Michael and Kenneth A. Shepsle (1996) Making and breaking governments [https://books.google.com/books?id=nFeKE07AUMsC&pg=PA132&lpg=PA132 pictures].</ref>).

In [[population dynamics]], an '''[[isocline]]''' shows the set of population sizes at which the rate of change, or partial derivative, for one population in a pair of interacting populations is zero.

=== Statistics ===
In statistics, isodensity lines <ref name="Fernandez 2011">{{cite journal |vauthors= Fernández, Antonio|date=2011 |title= A Generalized Regression Methodology for Bivariate Heteroscedastic Data|journal= Communications in Statistics – Theory and Methods|volume= 40|issue=4 |pages= 598–621 |doi=10.1080/03610920903444011 |s2cid=55887263 |url= http://oa.upm.es/12253/1/INVE_MEM_2011_92717.pdf}}</ref> or isodensanes are lines that join points with the same value of a [[probability density]]. Isodensanes are used to display [[bivariate distribution]]s. For example, for a bivariate [[elliptical distribution]] the isodensity lines are [[ellipse]]s.

=== Thermodynamics, engineering, and other sciences ===
Various types of graphs in [[thermodynamics]], engineering, and other sciences use isobars (constant pressure), isotherms (constant temperature), isochors (constant specific volume), or other types of isolines, even though these graphs are usually not related to maps.  Such isolines are useful for representing more than two dimensions (or quantities) on two-dimensional graphs.  Common examples in thermodynamics are some types of [[phase diagram]]s.

'''[[Isocline]]s''' are used to solve [[ordinary differential equations]].

In interpreting [[radar]] images, an '''isodop''' is a line of equal [[Doppler effect|Doppler]] velocity, and an '''isoecho''' is a line of equal radar reflectivity.

In the case of hybrid contours, energies of hybrid orbitals and the energies of pure atomic orbitals are plotted. The graph obtained is called hybrid contour.

=== Other phenomena ===
* '''''isochasm''''': [[aurora (astronomy)|aurora]] equal occurrence
* '''''isochor''''': [[volume]]
* '''''isodose''''': [[absorbed dose]] of radiation
* '''''isophene''''': biological events occurring with [[coincidence]] such as plants [[flowering]]
* '''''[[isophote]]''''': [[illuminance]]
* mobile telephony: [[Received signal strength indication|mobile received power]] and [[Coverage (telecommunication)|cell coverage area]]