's
New and Correct Chart Shewing the Variations of the Compass (1701) 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 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. In 1801, the chief of the French Corps of Engineers,
Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for
Rocca d'Anfo, now in northern Italy, under
Napoleon. 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. As different uses of the technique were invented independently, cartographers began to recognize a common theme, and debated what to call these "lines of equal value" generally. The word
isogram () was proposed by
Francis Galton in 1889 for lines indicating equality of some physical condition or quantity, though
isogram can also refer to a
word without a repeated letter. As late as 1944,
John K. Wright still preferred
isogram, but it never attained wide usage. During the early 20th century,
isopleth () was being used by 1911 in the United States, while
isarithm () had become common in Europe. Additional alternatives, including the Greek-English hybrid
isoline and
isometric line (), also emerged. Despite attempts to select a single standard, all of these alternatives have survived to the present. 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 United States in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters. == Types == 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 () 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 () 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,
line, or
polyline. In this case the function whose value is being held constant along a contour line is a
distance function.
Isopleths 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. An example of an isopleth is
population density, which can be calculated by dividing the population of a
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. In meteorology, the word
isopleth is used for any type of contour line.
Meteorology Meteorological contour lines are based on
interpolation of the point data received from
weather stations and
weather satellites. 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 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 An
isobar () 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 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 weather reporting.
Isallobars are lines joining points of equal pressure change during a specific time interval. These can be divided into
anallobars, lines joining points of equal pressure increase during a specific time interval, and
katallobars, lines joining points of equal pressure decrease. In general, weather systems move along an axis joining high and low isallobaric centers. 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 An
isotherm () 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. According to Thomas Hankins, the Scottish engineer
William Playfair's graphical developments greatly influenced Alexander von Humbolt's invention of the isotherm. 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. An
isocheim is a line of equal mean winter temperature, and an
isothere is a line of equal mean summer temperature. An
isohel () 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 () 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 () 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 An
isotach () 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 of
Stowe,
Vermont. The brown contour lines represent the
elevation. The contour interval is 20
feet. 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 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. (The concept is similar to but distinct from hachures used in
hachure maps.) •
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.
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 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 . 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.
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,
isohalines show lines of equal ocean salinity, and
isopycnals are surfaces of equal water density.
Geology 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.
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),
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.
Social sciences , 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
isochrone shows lines of equivalent drive time or travel time to a given location and is used in the generation of
isochrone maps. An
isotim shows equivalent transport costs from the source of a raw material, and an
isodapane shows equivalent cost of travel time. 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
input usages, and an
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). 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 or isodensanes are lines that join points with the same value of a
probability density. Isodensanes are used to display
bivariate distributions. For example, for a bivariate
elliptical distribution the isodensity lines are
ellipses.
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 diagrams.
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. 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 equal occurrence •
isochor:
volume •
isodose:
absorbed dose of radiation •
isophene: biological events occurring with
coincidence such as plants
flowering •
isophote:
illuminance • mobile telephony:
mobile received power and
cell coverage area ==Algorithms==