1159:
228:
1383:
965:
27:
43:
1790:
35:
1519:, 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
714:
581:
1071:: 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
622:
1426:
1703:
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
1732:
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
1750:
If the contour lines are not numerically labeled and adjacent lines have the same style (with the same weight, color and type), then the direction of the gradient cannot be determined from the contour lines alone. However, if the contour lines cycle through three or more styles, then the direction
1098:
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
1805:
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
1765:
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
1093:
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.
202:
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 the relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible
600:. 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.
1373:
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.
449:" 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 "'
1308:
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
682:, 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
651:
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
1704:
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
1045:
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.
606:
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.
30:
The bottom part of the diagram shows some contour lines with a straight line running through the location of the maximum value. The curve at the top represents the values along that straight line.
1809:
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
294:. 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,
1806:
nadir, from several directions if possible, making the visual identification of the summit or nadir easy. Contour labels can be oriented so a reader is facing uphill when reading the label.
1081:: 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
332:
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
557:
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
437:
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.
1061:: 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
1778:
on people at different elevations, for example, living on different floor levels of an urban apartment. In actuality, both plan and profile view contour maps are used in
545:
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
2745:
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.
2375:
119:
151:
1094:
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
191:
of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A
1774:. 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
1557:
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.
743:. Therefore, all points through which an isotherm passes have the same or equal temperatures at the time indicated. An isotherm at 0 °C is called the
1132:. Whether crossing an equipotential line represents ascending or descending the potential is inferred from the labels on the charges. In three dimensions,
2087:
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",
1483:
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.
1751:
of the gradient can be determined from the lines. The orientation of the numerical text labels is often used to indicate the direction of the slope.
153:-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.
2613:
613:
use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic factors in a weather system.
211:, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of
426:, 'measure'), also emerged. Despite attempts to select a single standard, all of these alternatives have survived to the present.
2500:
2736:
Imhof, E., "Die
Anordnung der Namen in der Karte," Annuaire International de Cartographie II, Orell-Füssli Verlag, Zürich, 93–129, 1962.
664:, not the surface pressures at the map locations. The distribution of isobars is closely related to the magnitude and direction of the
1693:
To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line
1390:, an indifference map with three indifference curves shown. All points on a particular indifference curve have the same value of the
755:, who as part of his research into the geographical distribution of plants published the first map of isotherms in Paris, in 1817.
2443:
2409:
295:
549:
for variables that could be measured at a point; this distinction has since been followed generally. An example of an isopleth is
282:
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
1113:
is a measure of electrostatic potential in space, often depicted in two dimensions with the electrostatic charges inducing that
1011:
can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through
501:, 'to lean or slope') is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms
1150:
is often used to describe the full collection of points having a particular potential, especially in higher dimensional space.
705:
height on a constant pressure surface chart. Isohypse and isoheight are simply known as lines showing equal pressure on a map.
2383:
1913:
83:
1628:
207:, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface
1234:
use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular,
717:
The 10 °C (50 °F) mean isotherm in July, marked by the red line, is commonly used to define the border of the
479: 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term
71:
2603:. Scale 1:10,560. Contour intervals: 50 feet up to 200, 20 feet from 200 to 300, and 10 feet above 300.
668:
field, and can be used to predict future weather patterns. Isobars are commonly used in television weather reporting.
2439:
2405:
2371:
2310:
2137:
2116:
2001:
894:
is a line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously.
429:
When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are
2784:
2151:
1532:
2569:
2593:
1743:
values of contour lines. This can be done by placing numbers along some of the contour lines, typically using
1470:
an analogous method is used in understanding coalitions (for example the diagram in Laver and
Shepsle's work).
79:
19:
This article is about lines of equal value in maps and diagrams. For more meanings of the word "contour", see
992:
674:
are lines joining points of equal pressure change during a specific time interval. These can be divided into
406:, 'number') had become common in Europe. Additional alternatives, including the Greek-English hybrid
2682:
2014:
1708:
map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals.
2473:
2323:
1767:
1747:
for intervening lines. Alternatively a map key can be produced associating the contours with their values.
1632:
2621:
2573:
1408:
shows lines of equivalent drive time or travel time to a given location and is used in the generation of
1683:
283:
1447:(as shown at left) are used to show bundles of goods to which a person would assign equal utility. An
78:
along which the function has a constant value, so that the curve joins points of equal value. It is a
2015:"Orígenes de la representación topográfica del terreno en algunos mapas hispanoamericanos del s. XVI"
1810:
1167:
1491:
In statistics, isodensity lines or isodensanes are lines that join points with the same value of a
242:
The idea of lines that join points of equal value was rediscovered several times. The oldest known
20:
1500:
291:
1453:(in the image at right) is a curve of equal production quantity for alternative combinations of
1838:
1496:
913:
847:
813:
752:
729:
637:
610:
469:
337:
321:, they were already in general use in European countries. Isobaths were not routinely used on
2504:
1981:
1887:
1802:
1687:
1454:
1314:
204:
89:
2794:
2774:
2534:
2163:
1775:
1771:
1667:
1179:
367:
255:
124:
1402:, contour lines can be used to describe features which vary quantitatively over space. An
286:
by
Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and
8:
2789:
2350:
2096:
2092:
1953:
1760:
1492:
1474:
1443:
1318:
657:
529:. In this case the function whose value is being held constant along a contour line is a
2538:
2451:
2417:
2167:
2719:
2642:
2546:
2272:
2254:
2212:
2181:
1823:
1645:
1572:
1330:
1261:
1129:
1114:
1016:
678:, lines joining points of equal pressure increase during a specific time interval, and
550:
517:
A curve of equidistant points is a set of points all at the same distance from a given
46:
A two-dimensional contour graph of the three-dimensional surface in the above picture.
2596:
2550:
2336:
2306:
2133:
2112:
1997:
1909:
1467:
1463:(also in the image at right) shows alternative usages having equal production costs.
1346:
1334:
1095:
597:
530:
358:
in 1889 for lines indicating equality of some physical condition or quantity, though
180:, which thus shows valleys and hills, and the steepness or gentleness of slopes. The
2723:
1300:(lines of equal thickness) to illustrate variations in thickness of geologic units.
1162:
Isogonic lines for the year 2000. The agonic lines are thicker and labeled with "0".
2711:
2696:
2542:
2284:
2246:
2185:
2171:
2022:
1848:
1660:
1655:
1434:
1391:
1342:
1273:
1109:
1012:
683:
518:
457:" to specify a contour line connecting points where a variable changes at the same
184:
of a contour map is the difference in elevation between successive contour lines.
2779:
2592:, D Survey, Ministry of Defence, Series M 824, Sheet Sark, Edition 4 GSGS, 1965,
1929:
1783:
1281:
1158:
1086:
968:
786:
593:
522:
434:
310:
299:
279:
275:
227:
177:
1441:
Contour lines are also used to display non-geographic information in economics.
298:, used contour lines at the larger scale of 1:500 on a plan of his projects for
262:
used such lines (isogons) on a chart of magnetic variation. The Dutch engineer
195:
is a generalization of a contour line for functions of any number of variables.
1650:
1547:
1516:
972:
744:
562:
355:
322:
287:
263:
165:
2715:
2045:, University of Chicago Press, 1972, revised 1996, page 97; and Jardine, Lisa
1404:
1394:, whose values implicitly come out of the page in the unshown third dimension.
621:
2768:
2681:
Laver, Michael and
Kenneth A. Shepsle (1996) Making and breaking governments
2554:
1779:
1744:
1719:
1595:
1520:
1409:
1382:
1326:
1265:
1140:
1134:
1119:
984:
718:
589:
558:
314:
259:
231:
212:
2288:
1222:
meaning 'power') connects points with the same intensity of magnetic force.
1858:
1843:
1833:
1430:
1429:
A single production isoquant (convex) and a single isocost curve (linear).
1416:
shows equivalent transport costs from the source of a raw material, and an
1354:
1350:
1289:
1285:
1269:
1231:
1198:
702:
603:
554:
246:(contour line of constant depth) is found on a map dated 1584 of the river
1904:
Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013).
964:
2697:"A Generalized Regression Methodology for Bivariate Heteroscedastic Data"
2600:
1705:
1622:
1607:
1425:
1338:
1293:
1072:
1054:
There are several rules to note when interpreting terrain contour lines:
1031:
1023:
740:
739: 'heat') is a line that connects points on a map that have the same
653:
430:
157:
2757:
1190:
refers to a line of constant annual variation of magnetic declination .
2152:"On the Principle and Methods of Assigning Marks for Bodily Efficiency"
2027:
1828:
1740:
1679:
626:
390:, 'amount') was being used by 1911 in the United States, while
208:
160:, a contour line (often just called a "contour") joins points of equal
2525:
Munzar, Jan (1967-09-01). "Alexander Von
Humboldt and His Isotherms".
2258:
2234:
2216:
2200:
215:
affects the reliability of individual isolines and their portrayal of
2176:
1611:
1418:
1399:
1387:
1276:. Contour maps are used to show the below ground surface of geologic
1244:
1147:
996:
980:
865:
690:
661:
192:
161:
2250:
1853:
1723:
1527:
1479:
1449:
1358:
1000:
839:
648:
526:
485:
374:, but it never attained wide usage. During the early 20th century,
303:
198:
Contour lines are curved, straight or a mixture of both lines on a
188:
63:
1510:
1884:
What Is
Mathematics?: An Elementary Approach to Ideas and Methods
1722:
is used as well as color to set the contour lines apart from the
1715:
1504:
1459:
1277:
1257:
1143:
lines at the intersection of the surfaces and the cross-section.
1062:
1027:
1008:
976:
748:
363:
318:
267:
251:
247:
243:
26:
1863:
1584:
1082:
326:
271:
1793:
Contour map labeled aesthetically in an "elevation up" manner.
1357:
can be substantially reduced; this is especially important in
1139:
may be depicted with a two dimensional cross-section, showing
823: 'rain') is a line joining points of equal rainfall on a
2438:
2404:
2370:
1903:
1789:
1694:
1539:
1213:
876:
561:. The idea of an isopleth map can be compared with that of a
445:
Contour lines are often given specific names beginning with "
216:
75:
2474:"Forecasting weather system movement with pressure tendency"
1182:, the variation of magnetic north from geographic north. An
796:
is a line of equal temperature beneath the Earth's surface.
236:
New and
Correct Chart Shewing the Variations of the Compass
42:
34:
2587:
924:
897:
887:
780:
665:
496:
421:
401:
385:
1238:
are lines showing depths of water with equal temperature,
580:
553:, which can be calculated by dividing the population of a
38:
A three-dimensional surface, whose contour graph is below.
2089:
2043:
Maps and Civilization: Cartography in Culture and Society
1186:
is drawn through points of zero magnetic declination. An
1004:
944:
824:
713:
199:
173:
2348:
1726:. Line colour can be varied to show other information.
1321:(where lines of equal sound pressure level are denoted
270:
with lines of equal depth (isobaths) at intervals of 1
2570:"Depression Contours – Getting Into and Out of a Hole"
2047:
Ingenious Pursuits: Building the Scientific Revolution
954:
2669:
Heathlands and related shrublands: Analytical studies
2498:
923: 'fast') is a line joining points with constant
483:
has specific meanings which are described below. An
127:
92:
16:
Curve along which a 3-D surface is at equal elevation
1882:
Courant, Richard, Herbert Robbins, and Ian Stewart.
827:
in a given period. A map with isohyets is called an
2301:T. Slocum, R. McMaster, F. Kessler, and H. Howard,
774:
762:is a line of equal mean winter temperature, and an
708:
490:
415:
395:
379:
278:used them at 10-fathom intervals on a chart of the
509:have specific meanings which are described below.
145:
113:
2704:Communications in Statistics – Theory and Methods
2503:. American Meteorological Society. Archived from
2303:Thematic Cartography and Geographic Visualization
2130:Ordnance Survey: Map Makers to Britain since 1791
900:cover is frequently shown as a contour-line map.
625:Video loop of isallobars showing the motion of a
2766:
2694:
2111:, 1926, republished by David and Charles, 1969,
1754:
785:, 'Sun') is a line of equal or constant
2019:Boletín de la Asociación de Geógrafos Españoles
1511:Thermodynamics, engineering, and other sciences
1313:. Some of the most widespread applications of
647: 'weight') is a line of equal or constant
541:In 1944, John K. Wright proposed that the term
2688:
1978:Plane Surveying; A Text-Book and Pocket Manual
1007:. From these contours, a sense of the general
176:illustrated with contour lines, for example a
2228:
2226:
2012:
1697:, line type and method of numerical marking.
931:refers to a line of constant wind direction.
864: 'heat') is a line of equal or constant
313:started to regularly record contour lines in
2049:, Little, Brown, and Company, 1999, page 31.
1205:is the isoclinic line of magnetic dip zero.
799:
766:is a line of equal mean summer temperature.
2666:
2660:
2480:. Lyndon State College Atmospheric Sciences
1886:. New York: Oxford University Press, 1996.
1022:"Contour line" is the most common usage in
329:from 1834, and those of Britain from 1838.
2223:
2192:
588:Meteorological contour lines are based on
354: 'writing, drawing') was proposed by
2275:(1971). "The genealogy of the isopleth".
2175:
2026:
2271:
2235:"The Terminology of Certain Map Symbols"
2057:
2055:
1906:Calculus : Single and Multivariable
1899:
1897:
1895:
1797:
1788:
1684:Terrain cartography § Contour lines
1424:
1381:
1303:
1242:show lines of equal ocean salinity, and
1157:
979:. The brown contour lines represent the
963:
712:
620:
579:
226:
41:
33:
25:
2567:
2492:
2349:Edward J. Hopkins, Ph.D. (1996-06-10).
1994:Statistics and data analysis in geology
1980:. New York: J. Wiley & Sons, 1907.
1644:finding boundaries of level sets after
1554:is a line of equal radar reflectivity.
2767:
2524:
2232:
2198:
2149:
2109:The Early Years of the Ordnance Survey
1422:shows equivalent cost of travel time.
959:
616:
572:is used for any type of contour line.
164:(height) above a given level, such as
2432:
2398:
2052:
1892:
1260:data are rendered as contour maps in
1248:are surfaces of equal water density.
512:
2499:DataStreme Atmosphere (2008-04-28).
2065:, Oxford, vol. 6, pp. 612–614, 1958.
1718:that suit the display. Sometimes a
2364:
1673:
1606:: biological events occurring with
955:Physical geography and oceanography
886:is a line of constant frequency of
13:
2547:10.1002/j.1477-8696.1967.tb02989.x
2078:, vol. 1, p. 139, quoted by Close.
1688:Topographic map § Conventions
1560:
1495:. Isodensanes are used to display
1433:usage is plotted horizontally and
1377:
934:
693:is a line of constant density. An
14:
2806:
2751:
2440:World Meteorological Organisation
2406:World Meteorological Organisation
2372:World Meteorological Organisation
2335:NOAA's National Weather Service,
2006:
1733:of the contour line is inferred.
1102:
1049:
2478:Chapter 13 – Weather Forecasting
2351:"Surface Weather Analysis Chart"
1317:contour maps involve mapping of
1019:, up to continental-scale maps.
951:denotes equal dates of thawing.
927:speed. In meteorology, the term
709:Temperature and related subjects
592:of the point data received from
2739:
2730:
2675:
2635:
2606:
2580:
2561:
2518:
2466:
2342:
2329:
2316:
2295:
2265:
2143:
2122:
2101:
2081:
2068:
1714:is the choice of any number of
1533:ordinary differential equations
1499:. For example, for a bivariate
1284:surfaces (especially low angle
1225:
838:is a line of constant relative
302:, now in northern Italy, under
203:three-dimensional model of the
2305:, 2nd edition, Pearson, 2005,
2061:R. A. Skelton, "Cartography",
2035:
2013:Morato-Moreno, Manuel (2017).
1986:
1970:
1946:
1922:
1876:
1739:is the manner of denoting the
1146:The general mathematical term
1128:refers to a curve of constant
1038:for elevations are also used.
947:formation each winter, and an
584:Isohyetal map of precipitation
575:
364:word without a repeated letter
140:
128:
108:
96:
1:
2671:. Elsevier. pp. 219–220.
1870:
1755:Plan view versus profile view
1638:
1486:
1178:refers to a line of constant
983:. The contour interval is 20
747:. The term was coined by the
2233:Wright, John K. (Oct 1944).
2201:"Isopleth as a Generic Term"
2199:Wright, John K. (Apr 1930).
1930:"Definition of contour line"
1768:air pollutant concentrations
1437:usage is plotted vertically.
1153:
991:Contours are one of several
943:line denotes equal dates of
781:
536:
497:
461:during a given time period.
422:
402:
386:
7:
2695:Fernández, Antonio (2011).
2574:City University of New York
1954:"Definition of CONTOUR MAP"
1816:
1515:Various types of graphs in
875:is a line indicating equal
604:Meteorological contour maps
10:
2811:
2568:Leveson, David J. (2002).
2501:"Air Temperature Patterns"
1908:(6 ed.). John wiley.
1758:
1677:
1364:
1251:
1214:
775:
751:geographer and naturalist
491:
416:
396:
380:
347: 'equal' and
284:Duchy of Modena and Reggio
266:drew the bed of the river
222:
18:
2759:Forthright's Phrontistery
2716:10.1080/03610920903444011
2618:historicalcharts.noaa.gov
2353:. University of Wisconsin
1811:automatic label placement
1678:For features specific to
1503:the isodensity lines are
1197:connects points of equal
1030:for underwater depths on
800:Rainfall and air moisture
568:In meteorology, the word
309:By around 1843, when the
258:Pieter Bruinsz. In 1701,
72:function of two variables
2150:Galton, Francis (1889).
2128:T. Owen and E. Pilbeam,
857: 'dew' and
453:" can be replaced with "
440:
21:Contour (disambiguation)
2289:10.1179/caj.1971.8.1.49
1501:elliptical distribution
1497:bivariate distributions
903:
292:Schiehallion experiment
84:three-dimensional graph
2785:Multivariable calculus
2620:. 1946. Archived from
1992:Davis, John C., 1986,
1839:Fall line (topography)
1794:
1438:
1395:
1168:Earth's magnetic field
1163:
988:
753:Alexander von Humboldt
721:
701:is a line of constant
629:
611:Thermodynamic diagrams
585:
239:
147:
115:
114:{\displaystyle f(x,y)}
47:
39:
31:
2063:History of Technology
1798:Labeling contour maps
1792:
1629:mobile received power
1428:
1385:
1315:environmental science
1304:Environmental science
1230:Besides ocean depth,
1161:
967:
716:
660:shown are reduced to
624:
583:
230:
148:
146:{\displaystyle (x,y)}
116:
45:
37:
29:
2420:on 24 September 2015
2277:Cartographic Journal
1776:noise health effects
1668:Active contour model
1180:magnetic declination
1166:In the study of the
1089:can be approximated.
1041:In cartography, the
658:barometric pressures
362:can also refer to a
125:
90:
2539:1967Wthr...22..360M
2239:Geographical Review
2205:Geographical Review
2168:1889Natur..40..649.
1761:Topographic profile
1546:is a line of equal
1493:probability density
1475:population dynamics
1444:Indifference curves
1341:contamination. By
1319:environmental noise
1079:Spacing of contours
960:Elevation and depth
617:Barometric pressure
366:. As late as 1944,
2454:on 5 February 2008
2324:Isopleth: Contours
2076:La Carte de France
2074:Colonel Berthaut,
2041:Thrower, N. J. W.
2028:10.21138/bage.2414
1824:Aeronautical chart
1795:
1646:image segmentation
1633:cell coverage area
1627:mobile telephony:
1531:are used to solve
1439:
1396:
1331:soil contamination
1262:structural geology
1164:
1130:electric potential
1115:electric potential
1099:height increases.
1017:bathymetric charts
989:
722:
630:
598:weather satellites
586:
551:population density
513:Equidistant points
240:
219:, pits and peaks.
143:
111:
48:
40:
32:
2667:Specht, Raymond.
1737:Numerical marking
1550:velocity, and an
1468:political science
1347:contour ploughing
1335:thermal pollution
1126:isopotential line
1096:hypsometric tints
531:distance function
290:used them in the
264:Nicholas Cruquius
2802:
2746:
2743:
2737:
2734:
2728:
2727:
2701:
2692:
2686:
2679:
2673:
2672:
2664:
2658:
2657:
2655:
2654:
2639:
2633:
2632:
2630:
2629:
2610:
2604:
2584:
2578:
2577:
2565:
2559:
2558:
2522:
2516:
2515:
2513:
2512:
2496:
2490:
2489:
2487:
2485:
2470:
2464:
2463:
2461:
2459:
2450:. Archived from
2436:
2430:
2429:
2427:
2425:
2416:. Archived from
2402:
2396:
2395:
2393:
2391:
2386:on 16 April 2014
2382:. Archived from
2368:
2362:
2361:
2359:
2358:
2346:
2340:
2333:
2327:
2320:
2314:
2299:
2293:
2292:
2269:
2263:
2262:
2230:
2221:
2220:
2196:
2190:
2189:
2179:
2177:10.1038/040649a0
2147:
2141:
2126:
2120:
2105:
2099:
2085:
2079:
2072:
2066:
2059:
2050:
2039:
2033:
2032:
2030:
2010:
2004:
1990:
1984:
1974:
1968:
1967:
1965:
1964:
1950:
1944:
1943:
1941:
1940:
1926:
1920:
1919:
1915:978-0470-88861-2
1901:
1890:
1880:
1849:Marching squares
1674:Graphical design
1661:Boundary tracing
1656:Level-set method
1575:equal occurrence
1538:In interpreting
1435:physical capital
1392:utility function
1343:contour planting
1274:economic geology
1217:
1216:
1110:isopotential map
1043:contour interval
1013:topographic maps
784:
778:
777:
684:geostrophic wind
594:weather stations
500:
494:
493:
425:
419:
418:
405:
399:
398:
389:
383:
382:
370:still preferred
182:contour interval
152:
150:
149:
144:
121:parallel to the
120:
118:
117:
112:
86:of the function
2810:
2809:
2805:
2804:
2803:
2801:
2800:
2799:
2765:
2764:
2754:
2749:
2744:
2740:
2735:
2731:
2699:
2693:
2689:
2680:
2676:
2665:
2661:
2652:
2650:
2641:
2640:
2636:
2627:
2625:
2614:"isoporic line"
2612:
2611:
2607:
2585:
2581:
2566:
2562:
2523:
2519:
2510:
2508:
2497:
2493:
2483:
2481:
2472:
2471:
2467:
2457:
2455:
2437:
2433:
2423:
2421:
2403:
2399:
2389:
2387:
2369:
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2356:
2354:
2347:
2343:
2334:
2330:
2321:
2317:
2300:
2296:
2270:
2266:
2231:
2224:
2197:
2193:
2148:
2144:
2127:
2123:
2106:
2102:
2091:, vol. 68, pp.
2086:
2082:
2073:
2069:
2060:
2053:
2040:
2036:
2011:
2007:
1991:
1987:
1976:Tracy, John C.
1975:
1971:
1962:
1960:
1958:Merriam-Webster
1952:
1951:
1947:
1938:
1936:
1928:
1927:
1923:
1916:
1902:
1893:
1881:
1877:
1873:
1868:
1819:
1800:
1784:noise pollution
1763:
1757:
1691:
1676:
1641:
1610:such as plants
1563:
1561:Other phenomena
1513:
1489:
1380:
1378:Social sciences
1367:
1306:
1254:
1228:
1210:isodynamic line
1156:
1105:
1087:stream gradient
1052:
995:used to denote
969:Topographic map
962:
957:
937:
935:Freeze and thaw
906:
890:storms, and an
802:
787:solar radiation
711:
619:
578:
555:census district
547:isometric lines
539:
515:
443:
435:noise pollution
325:until those of
323:nautical charts
311:Ordnance Survey
280:English Channel
276:Philippe Buache
225:
178:topographic map
126:
123:
122:
91:
88:
87:
24:
17:
12:
11:
5:
2808:
2798:
2797:
2792:
2787:
2782:
2777:
2763:
2762:
2753:
2752:External links
2750:
2748:
2747:
2738:
2729:
2710:(4): 598–621.
2687:
2674:
2659:
2634:
2605:
2579:
2560:
2533:(9): 360–363.
2517:
2491:
2465:
2431:
2397:
2363:
2341:
2328:
2315:
2294:
2264:
2251:10.2307/210035
2245:(4): 653–654.
2222:
2191:
2142:
2132:, HMSO, 1992,
2121:
2119:, pp. 141–144.
2100:
2080:
2067:
2051:
2034:
2005:
1985:
1969:
1945:
1934:Dictionary.com
1921:
1914:
1891:
1874:
1872:
1869:
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1841:
1836:
1831:
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1815:
1799:
1796:
1756:
1753:
1720:sheen or gloss
1675:
1672:
1671:
1670:
1665:
1664:
1663:
1658:
1653:
1651:Edge detection
1640:
1637:
1636:
1635:
1625:
1614:
1599:
1587:
1576:
1562:
1559:
1521:phase diagrams
1517:thermodynamics
1512:
1509:
1488:
1485:
1410:isochrone maps
1379:
1376:
1366:
1363:
1349:, the rate of
1305:
1302:
1290:unconformities
1253:
1250:
1236:isobathytherms
1232:oceanographers
1227:
1224:
1195:isoclinic line
1155:
1152:
1104:
1103:Electrostatics
1101:
1091:
1090:
1076:
1069:The rule of Os
1066:
1059:The rule of Vs
1051:
1050:Interpretation
1048:
993:common methods
961:
958:
956:
953:
936:
933:
905:
902:
810:isohyetal line
801:
798:
745:freezing level
710:
707:
618:
615:
577:
574:
563:choropleth map
538:
535:
514:
511:
507:isoclinic line
442:
439:
412:isometric line
368:John K. Wright
356:Francis Galton
288:Charles Hutton
224:
221:
166:mean sea level
142:
139:
136:
133:
130:
110:
107:
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98:
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6:
4:
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2705:
2698:
2691:
2684:
2678:
2670:
2663:
2648:
2644:
2638:
2624:on 2015-07-21
2623:
2619:
2615:
2609:
2602:
2598:
2595:
2591:
2589:
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2575:
2571:
2564:
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2548:
2544:
2540:
2536:
2532:
2528:
2521:
2507:on 2008-05-11
2506:
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2419:
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2325:
2319:
2312:
2311:0-13-035123-7
2308:
2304:
2298:
2290:
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2274:
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2256:
2252:
2248:
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2240:
2236:
2229:
2227:
2218:
2214:
2210:
2206:
2202:
2195:
2187:
2183:
2178:
2173:
2169:
2165:
2162:(1044): 651.
2161:
2157:
2153:
2146:
2139:
2138:0-11-701507-5
2135:
2131:
2125:
2118:
2117:0-7153-4477-3
2114:
2110:
2104:
2098:
2094:
2090:
2084:
2077:
2071:
2064:
2058:
2056:
2048:
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2024:
2020:
2016:
2009:
2003:
2002:0-471-08079-9
1999:
1995:
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1814:
1812:
1807:
1804:
1791:
1787:
1785:
1781:
1780:air pollution
1777:
1773:
1769:
1762:
1752:
1748:
1746:
1745:interpolation
1742:
1738:
1734:
1731:
1727:
1725:
1721:
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1707:
1702:
1698:
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1609:
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1600:
1597:
1596:absorbed dose
1593:
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1498:
1494:
1484:
1482:
1481:
1476:
1471:
1469:
1464:
1462:
1461:
1460:isocost curve
1456:
1452:
1451:
1446:
1445:
1436:
1432:
1427:
1423:
1421:
1420:
1415:
1411:
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1401:
1393:
1389:
1384:
1375:
1372:
1362:
1360:
1356:
1352:
1348:
1344:
1340:
1336:
1332:
1328:
1327:air pollution
1324:
1320:
1316:
1312:
1301:
1299:
1295:
1291:
1287:
1286:thrust faults
1283:
1279:
1275:
1271:
1267:
1266:sedimentology
1263:
1259:
1249:
1247:
1246:
1241:
1237:
1233:
1223:
1221:
1211:
1206:
1204:
1200:
1196:
1191:
1189:
1188:isoporic line
1185:
1181:
1177:
1176:isogonic line
1173:
1169:
1160:
1151:
1149:
1144:
1142:
1141:equipotential
1138:
1136:
1135:equipotential
1131:
1127:
1123:
1121:
1120:equipotential
1116:
1112:
1111:
1100:
1097:
1088:
1084:
1080:
1077:
1074:
1070:
1067:
1064:
1060:
1057:
1056:
1055:
1047:
1044:
1039:
1037:
1033:
1029:
1025:
1020:
1018:
1014:
1010:
1006:
1003:and depth on
1002:
998:
994:
986:
982:
978:
974:
970:
966:
952:
950:
946:
942:
932:
930:
926:
922:
918:
915:
914:Ancient Greek
911:
901:
899:
895:
893:
889:
885:
880:
878:
874:
869:
867:
863:
859:
856:
852:
849:
848:Ancient Greek
845:
844:isodrosotherm
841:
837:
832:
830:
829:isohyetal map
826:
822:
818:
815:
814:Ancient Greek
811:
807:
797:
795:
790:
788:
783:
772:
767:
765:
761:
756:
754:
750:
746:
742:
738:
734:
731:
730:Ancient Greek
727:
720:
719:Arctic region
715:
706:
704:
700:
696:
692:
687:
685:
681:
677:
673:
669:
667:
663:
659:
655:
650:
646:
642:
639:
638:Ancient Greek
635:
628:
623:
614:
612:
608:
605:
601:
599:
595:
591:
590:interpolation
582:
573:
571:
566:
564:
560:
559:interpolation
556:
552:
548:
544:
534:
532:
528:
524:
520:
510:
508:
504:
499:
488:
487:
482:
478:
474:
471:
470:Ancient Greek
467:
462:
460:
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452:
448:
438:
436:
432:
427:
424:
413:
409:
404:
393:
388:
377:
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369:
365:
361:
357:
353:
349:
346:
342:
339:
338:Ancient Greek
335:
330:
328:
324:
320:
316:
315:Great Britain
312:
307:
305:
301:
297:
293:
289:
285:
281:
277:
274:in 1727, and
273:
269:
265:
261:
260:Edmond Halley
257:
253:
249:
245:
237:
233:
232:Edmond Halley
229:
220:
218:
214:
213:interpolation
210:
206:
201:
196:
194:
190:
185:
183:
179:
175:
171:
167:
163:
159:
154:
137:
134:
131:
105:
102:
99:
93:
85:
81:
80:plane section
77:
73:
69:
65:
61:
57:
53:
44:
36:
28:
22:
2758:
2741:
2732:
2707:
2703:
2690:
2677:
2668:
2662:
2651:. Retrieved
2649:. 2005-01-05
2646:
2637:
2626:. Retrieved
2622:the original
2617:
2608:
2586:
2582:
2563:
2530:
2526:
2520:
2509:. Retrieved
2505:the original
2494:
2482:. Retrieved
2477:
2468:
2456:. Retrieved
2452:the original
2447:
2444:"Katallobar"
2434:
2422:. Retrieved
2418:the original
2413:
2400:
2388:. Retrieved
2384:the original
2379:
2366:
2355:. Retrieved
2344:
2331:
2318:
2302:
2297:
2280:
2276:
2267:
2242:
2238:
2208:
2204:
2194:
2159:
2155:
2145:
2129:
2124:
2108:
2103:
2088:
2083:
2075:
2070:
2062:
2046:
2042:
2037:
2018:
2008:
1993:
1988:
1977:
1972:
1961:. Retrieved
1957:
1948:
1937:. Retrieved
1933:
1924:
1905:
1883:
1878:
1859:Tensor field
1844:Geologic map
1834:Dymaxion map
1808:
1801:
1772:sound levels
1764:
1749:
1741:arithmetical
1736:
1735:
1729:
1728:
1711:
1710:
1700:
1699:
1692:
1617:
1616:
1602:
1601:
1598:of radiation
1590:
1589:
1579:
1578:
1567:
1566:
1556:
1551:
1543:
1537:
1526:
1525:
1514:
1490:
1478:
1472:
1465:
1458:
1455:input usages
1448:
1442:
1440:
1417:
1413:
1403:
1397:
1370:
1368:
1355:soil erosion
1351:water runoff
1322:
1310:
1307:
1297:
1294:Isopach maps
1270:stratigraphy
1255:
1243:
1239:
1235:
1229:
1226:Oceanography
1219:
1209:
1207:
1203:aclinic line
1202:
1199:magnetic dip
1194:
1192:
1187:
1183:
1175:
1171:
1165:
1145:
1133:
1125:
1118:
1108:
1106:
1092:
1078:
1073:hachure maps
1068:
1058:
1053:
1042:
1040:
1035:
1021:
990:
948:
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920:
917:
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907:
896:
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861:
858:
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851:
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736:
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703:geopotential
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308:
300:Rocca d'Anfo
241:
235:
197:
186:
181:
169:
155:
67:
59:
55:
52:contour line
51:
49:
2795:Relief maps
2775:Cartography
2410:"Anallobar"
2376:"Isallobar"
2273:Robinson AH
1706:topographic
1701:Line weight
1623:illuminance
1608:coincidence
1542:images, an
1339:groundwater
1184:agonic line
1170:, the term
1117:. The term
1032:bathymetric
1024:cartography
842:, while an
794:isogeotherm
741:temperature
680:katallobars
654:meteorology
576:Meteorology
431:air quality
170:contour map
158:cartography
2790:Topography
2769:Categories
2653:2010-04-25
2647:www.sfu.ca
2628:2015-07-20
2511:2010-02-07
2357:2007-05-10
2211:(2): 341.
2107:C. Close,
1963:2022-04-04
1939:2022-04-04
1871:References
1829:Bathymetry
1759:See also:
1712:Line color
1680:topography
1639:Algorithms
1487:Statistics
1258:geological
1245:isopycnals
1240:isohalines
912:(from
846:(from
812:(from
728:(from
676:anallobars
672:Isallobars
636:(from
627:cold front
468:(from
336:(from
209:elevations
2555:1477-8696
2313:, p. 272.
2283:: 49–53.
1786:studies.
1730:Line type
1612:flowering
1528:Isoclines
1457:, and an
1419:isodapane
1405:isochrone
1400:economics
1388:economics
1353:and thus
1201:, and an
1154:Magnetism
1148:level set
1034:maps and
997:elevation
981:elevation
941:isopectic
884:isochalaz
866:dew point
695:isoheight
691:isopycnal
662:sea level
537:Isopleths
193:level set
162:elevation
2724:55887263
2683:pictures
2643:"Isobel"
2601:27636277
2484:12 April
2458:12 April
2448:Eumetcal
2424:12 April
2414:Eumetcal
2390:12 April
2380:Eumetcal
2337:Glossary
2322:ArcGIS,
1996:, Wiley
1854:Planform
1817:See also
1724:base map
1716:pigments
1618:isophote
1603:isophene
1568:isochasm
1505:ellipses
1480:isocline
1450:isoquant
1359:riparian
1311:isoplats
1298:isopachs
1256:Various
1137:surfaces
1036:isohypse
1001:altitude
921:(tachus)
892:isobront
862:(therme)
855:(drosos)
840:humidity
821:(huetos)
764:isothere
760:isocheim
749:Prussian
737:(thermē)
726:isotherm
699:isohypse
649:pressure
570:isopleth
543:isopleth
527:polyline
503:isocline
486:isocline
403:arithmos
392:isarithm
376:isopleth
352:(gramma)
304:Napoleon
256:Dutchman
189:gradient
68:isarithm
64:isoquant
60:isopleth
2590:(Sercq)
2535:Bibcode
2527:Weather
2326:, 2013.
2186:3996216
2164:Bibcode
1982:p. 337.
1888:p. 344.
1591:isodose
1580:isochor
1552:isoecho
1548:Doppler
1371:isoflor
1365:Ecology
1361:zones.
1323:isobels
1252:Geology
1220:dynamis
1215:δύναμις
1063:erosion
1028:isobath
1009:terrain
977:Vermont
910:isotach
879:cover.
873:isoneph
836:isohume
806:isohyet
645:(baros)
498:klinein
492:κλίνειν
477:(gonia)
455:isallo-
408:isoline
397:ἀριθμός
387:plethos
372:isogram
360:isogram
334:isogram
319:Ireland
268:Merwede
252:Haarlem
250:, near
248:Spaarne
244:isobath
223:History
205:surface
82:of the
70:) of a
56:isoline
2780:Curves
2722:
2599:
2553:
2309:
2259:210035
2257:
2217:208890
2215:
2184:
2156:Nature
2136:
2115:
2000:
1912:
1864:TERCOM
1803:Labels
1686:, and
1682:, see
1585:volume
1573:aurora
1544:isodop
1414:isotim
1288:) and
1278:strata
1212:(from
1172:isogon
1085:, the
1083:stream
1026:, but
949:isotac
929:isogon
853:δρόσος
782:helios
771:isohel
656:, the
634:isobar
481:isogon
466:isogon
423:metron
417:μέτρον
381:πλῆθος
350:γράμμα
345:(isos)
327:Russia
272:fathom
238:(1701)
54:(also
2720:S2CID
2700:(PDF)
2255:JSTOR
2213:JSTOR
2182:S2CID
1695:color
1540:radar
1477:, an
1431:Labor
1412:. An
1386:From
1282:fault
973:Stowe
919:ταχύς
916:
877:cloud
860:θέρμη
850:
819:ὑετός
816:
776:ἥλιος
735:θέρμη
732:
643:βάρος
640:
525:, or
519:point
475:γωνία
472:
441:Types
340:
254:, by
217:slope
172:is a
76:curve
74:is a
2597:OCLC
2594:OCLC
2588:Sark
2551:ISSN
2486:2014
2460:2014
2426:2014
2392:2014
2307:ISBN
2134:ISBN
2113:ISBN
1998:ISBN
1910:ISBN
1782:and
1770:and
1766:are
1631:and
1345:and
1337:and
1296:use
1272:and
1122:line
1015:and
1005:maps
985:feet
925:wind
904:Wind
898:Snow
888:hail
666:wind
596:and
523:line
505:and
459:rate
451:iso-
447:iso-
433:and
410:and
343:ἴσος
317:and
296:Haxo
187:The
168:. A
2712:doi
2543:doi
2285:doi
2247:doi
2172:doi
2097:757
2093:756
2023:doi
1473:In
1466:In
1398:In
1369:An
1325:),
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1193:An
1174:or
1124:or
1107:An
999:or
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871:An
834:An
825:map
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804:An
792:An
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