1170:
239:
1394:
976:
38:
54:
1801:
46:
1530:, 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
725:
592:
1082:: 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
633:
1437:
1714:
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
1743:
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
1761:
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
1109:
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
1816:
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
1776:
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
1104:
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.
213:
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
611:. 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.
1384:
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.
460:" 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 "'
1319:
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
693:, 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
662:
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
1715:
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
1056:
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.
617:
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.
41:
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.
1820:
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
305:. 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,
1817:
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.
1092:: 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
343:
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
568:
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
448:
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.
1072:: 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
1789:
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
556:
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
2756:
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.
2386:
130:
162:
1105:
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
202:
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
1785:. 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
1568:
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.
754:. 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
1143:. Whether crossing an equipotential line represents ascending or descending the potential is inferred from the labels on the charges. In three dimensions,
2098:
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",
1494:
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.
1762:
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.
164:-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.
2624:
624:
use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic factors in a weather system.
222:, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of
437:, 'measure'), also emerged. Despite attempts to select a single standard, all of these alternatives have survived to the present.
2511:
2747:
Imhof, E., "Die
Anordnung der Namen in der Karte," Annuaire International de Cartographie II, Orell-Füssli Verlag, Zürich, 93–129, 1962.
675:, not the surface pressures at the map locations. The distribution of isobars is closely related to the magnitude and direction of the
1704:
To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line
1401:, an indifference map with three indifference curves shown. All points on a particular indifference curve have the same value of the
766:, who as part of his research into the geographical distribution of plants published the first map of isotherms in Paris, in 1817.
2454:
2420:
306:
560:
for variables that could be measured at a point; this distinction has since been followed generally. An example of an isopleth is
293:
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
17:
1124:
is a measure of electrostatic potential in space, often depicted in two dimensions with the electrostatic charges inducing that
1022:
can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through
512:, 'to lean or slope') is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms
1161:
is often used to describe the full collection of points having a particular potential, especially in higher dimensional space.
716:
height on a constant pressure surface chart. Isohypse and isoheight are simply known as lines showing equal pressure on a map.
2394:
1924:
94:
1639:
218:, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface
1245:
use contour to describe diffuse variable phenomena much as meteorologists do with atmospheric phenomena. In particular,
728:
The 10 °C (50 °F) mean isotherm in July, marked by the red line, is commonly used to define the border of the
490: 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term
82:
2614:. Scale 1:10,560. Contour intervals: 50 feet up to 200, 20 feet from 200 to 300, and 10 feet above 300.
679:
field, and can be used to predict future weather patterns. Isobars are commonly used in television weather reporting.
2450:
2416:
2382:
2321:
2148:
2127:
2012:
905:
is a line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously.
440:
When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are
2795:
2162:
1543:
2580:
2604:
1754:
values of contour lines. This can be done by placing numbers along some of the contour lines, typically using
1481:
an analogous method is used in understanding coalitions (for example the diagram in Laver and
Shepsle's work).
90:
30:
This article is about lines of equal value in maps and diagrams. For more meanings of the word "contour", see
1003:
685:
are lines joining points of equal pressure change during a specific time interval. These can be divided into
417:, 'number') had become common in Europe. Additional alternatives, including the Greek-English hybrid
2693:
2025:
1719:
map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals.
2484:
2334:
1778:
1758:
for intervening lines. Alternatively a map key can be produced associating the contours with their values.
1643:
2632:
2584:
1419:
shows lines of equivalent drive time or travel time to a given location and is used in the generation of
1694:
294:
1458:(as shown at left) are used to show bundles of goods to which a person would assign equal utility. An
89:
along which the function has a constant value, so that the curve joins points of equal value. It is a
2026:"Orígenes de la representación topográfica del terreno en algunos mapas hispanoamericanos del s. XVI"
1821:
1178:
1502:
In statistics, isodensity lines or isodensanes are lines that join points with the same value of a
253:
The idea of lines that join points of equal value was rediscovered several times. The oldest known
31:
1511:
302:
1464:(in the image at right) is a curve of equal production quantity for alternative combinations of
1849:
1507:
924:
858:
824:
763:
740:
648:
621:
480:
348:
332:, they were already in general use in European countries. Isobaths were not routinely used on
2515:
1992:
1898:
1813:
1698:
1465:
1325:
215:
100:
2805:
2785:
2545:
2174:
1786:
1782:
1678:
1190:
378:
266:
135:
1413:, contour lines can be used to describe features which vary quantitatively over space. An
297:
by
Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and
8:
2800:
2361:
2107:
2103:
1964:
1771:
1503:
1485:
1454:
1329:
668:
540:. In this case the function whose value is being held constant along a contour line is a
2549:
2462:
2428:
2178:
2730:
2653:
2557:
2283:
2265:
2223:
2192:
1834:
1656:
1583:
1341:
1272:
1140:
1125:
1027:
689:, lines joining points of equal pressure increase during a specific time interval, and
561:
528:
A curve of equidistant points is a set of points all at the same distance from a given
57:
A two-dimensional contour graph of the three-dimensional surface in the above picture.
2607:
2561:
2347:
2317:
2144:
2123:
2008:
1920:
1478:
1474:(also in the image at right) shows alternative usages having equal production costs.
1357:
1345:
1106:
608:
541:
369:
in 1889 for lines indicating equality of some physical condition or quantity, though
191:, which thus shows valleys and hills, and the steepness or gentleness of slopes. The
2734:
1311:(lines of equal thickness) to illustrate variations in thickness of geologic units.
1173:
Isogonic lines for the year 2000. The agonic lines are thicker and labeled with "0".
2722:
2707:
2553:
2295:
2257:
2196:
2182:
2033:
1859:
1671:
1666:
1445:
1402:
1353:
1284:
1120:
1023:
694:
529:
468:" to specify a contour line connecting points where a variable changes at the same
195:
of a contour map is the difference in elevation between successive contour lines.
2790:
2603:, D Survey, Ministry of Defence, Series M 824, Sheet Sark, Edition 4 GSGS, 1965,
1940:
1794:
1292:
1169:
1097:
979:
797:
604:
533:
445:
321:
310:
290:
286:
238:
188:
1452:
Contour lines are also used to display non-geographic information in economics.
309:, used contour lines at the larger scale of 1:500 on a plan of his projects for
273:
used such lines (isogons) on a chart of magnetic variation. The Dutch engineer
206:
is a generalization of a contour line for functions of any number of variables.
1661:
1558:
1527:
983:
755:
573:
366:
333:
298:
274:
176:
2726:
2056:, University of Chicago Press, 1972, revised 1996, page 97; and Jardine, Lisa
1415:
1405:, whose values implicitly come out of the page in the unshown third dimension.
632:
2779:
2692:
Laver, Michael and
Kenneth A. Shepsle (1996) Making and breaking governments
2565:
1790:
1755:
1730:
1606:
1531:
1420:
1393:
1337:
1276:
1151:
1145:
1130:
995:
729:
600:
569:
325:
270:
242:
223:
2299:
1233:
meaning 'power') connects points with the same intensity of magnetic force.
1869:
1854:
1844:
1441:
1440:
A single production isoquant (convex) and a single isocost curve (linear).
1427:
shows equivalent transport costs from the source of a raw material, and an
1365:
1361:
1300:
1296:
1280:
1242:
1209:
713:
614:
565:
257:(contour line of constant depth) is found on a map dated 1584 of the river
1915:
Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013).
975:
2708:"A Generalized Regression Methodology for Bivariate Heteroscedastic Data"
2611:
1716:
1633:
1618:
1436:
1349:
1304:
1083:
1065:
There are several rules to note when interpreting terrain contour lines:
1042:
1034:
751:
750: 'heat') is a line that connects points on a map that have the same
664:
441:
168:
2768:
1201:
refers to a line of constant annual variation of magnetic declination .
2163:"On the Principle and Methods of Assigning Marks for Bodily Efficiency"
2038:
1839:
1751:
1690:
637:
401:, 'amount') was being used by 1911 in the United States, while
219:
171:, a contour line (often just called a "contour") joins points of equal
2536:
Munzar, Jan (1967-09-01). "Alexander Von
Humboldt and His Isotherms".
2269:
2245:
2227:
2211:
226:
affects the reliability of individual isolines and their portrayal of
2187:
1622:
1429:
1410:
1398:
1287:. Contour maps are used to show the below ground surface of geologic
1255:
1158:
1007:
991:
876:
701:
672:
203:
172:
2261:
1864:
1734:
1538:
1490:
1460:
1369:
1011:
850:
659:
537:
496:
385:, but it never attained wide usage. During the early 20th century,
314:
209:
Contour lines are curved, straight or a mixture of both lines on a
199:
74:
1521:
1895:
What Is
Mathematics?: An Elementary Approach to Ideas and Methods
1733:
is used as well as color to set the contour lines apart from the
1726:
1515:
1470:
1288:
1268:
1154:
lines at the intersection of the surfaces and the cross-section.
1073:
1038:
1019:
987:
759:
374:
329:
278:
262:
258:
254:
37:
1874:
1595:
1093:
337:
282:
1804:
Contour map labeled aesthetically in an "elevation up" manner.
1368:
can be substantially reduced; this is especially important in
1150:
may be depicted with a two dimensional cross-section, showing
834: 'rain') is a line joining points of equal rainfall on a
2449:
2415:
2381:
1914:
1800:
1705:
1550:
1224:
887:
572:. The idea of an isopleth map can be compared with that of a
456:
Contour lines are often given specific names beginning with "
227:
86:
2485:"Forecasting weather system movement with pressure tendency"
1193:, the variation of magnetic north from geographic north. An
807:
is a line of equal temperature beneath the Earth's surface.
247:
New and
Correct Chart Shewing the Variations of the Compass
53:
45:
2598:
935:
908:
898:
791:
676:
507:
432:
412:
396:
1249:
are lines showing depths of water with equal temperature,
591:
564:, which can be calculated by dividing the population of a
49:
A three-dimensional surface, whose contour graph is below.
2100:
2054:
Maps and Civilization: Cartography in Culture and Society
1197:
is drawn through points of zero magnetic declination. An
1015:
955:
835:
724:
210:
184:
2359:
1737:. Line colour can be varied to show other information.
1332:(where lines of equal sound pressure level are denoted
281:
with lines of equal depth (isobaths) at intervals of 1
2581:"Depression Contours – Getting Into and Out of a Hole"
2058:
Ingenious Pursuits: Building the Scientific Revolution
965:
2680:
Heathlands and related shrublands: Analytical studies
2509:
934: 'fast') is a line joining points with constant
494:
has specific meanings which are described below. An
138:
103:
27:
Curve along which a 3-D surface is at equal elevation
1893:
Courant, Richard, Herbert Robbins, and Ian Stewart.
838:
in a given period. A map with isohyets is called an
2312:T. Slocum, R. McMaster, F. Kessler, and H. Howard,
785:
773:is a line of equal mean winter temperature, and an
719:
501:
426:
406:
390:
289:used them at 10-fathom intervals on a chart of the
520:have specific meanings which are described below.
156:
124:
2715:Communications in Statistics – Theory and Methods
2514:. American Meteorological Society. Archived from
2314:Thematic Cartography and Geographic Visualization
2141:Ordnance Survey: Map Makers to Britain since 1791
911:cover is frequently shown as a contour-line map.
636:Video loop of isallobars showing the motion of a
2777:
2705:
2122:, 1926, republished by David and Charles, 1969,
1765:
796:, 'Sun') is a line of equal or constant
2030:Boletín de la Asociación de Geógrafos Españoles
1522:Thermodynamics, engineering, and other sciences
1324:. Some of the most widespread applications of
658: 'weight') is a line of equal or constant
552:In 1944, John K. Wright proposed that the term
2699:
1989:Plane Surveying; A Text-Book and Pocket Manual
1018:. From these contours, a sense of the general
187:illustrated with contour lines, for example a
2239:
2237:
2023:
1708:, line type and method of numerical marking.
942:refers to a line of constant wind direction.
875: 'heat') is a line of equal or constant
324:started to regularly record contour lines in
2060:, Little, Brown, and Company, 1999, page 31.
1216:is the isoclinic line of magnetic dip zero.
810:
777:is a line of equal mean summer temperature.
2677:
2671:
2491:. Lyndon State College Atmospheric Sciences
1897:. New York: Oxford University Press, 1996.
1033:"Contour line" is the most common usage in
340:from 1834, and those of Britain from 1838.
2234:
2203:
599:Meteorological contour lines are based on
365: 'writing, drawing') was proposed by
2286:(1971). "The genealogy of the isopleth".
2186:
2037:
2282:
2246:"The Terminology of Certain Map Symbols"
2068:
2066:
1917:Calculus : Single and Multivariable
1910:
1908:
1906:
1808:
1799:
1695:Terrain cartography § Contour lines
1435:
1392:
1314:
1253:show lines of equal ocean salinity, and
1168:
990:. The brown contour lines represent the
974:
723:
631:
590:
237:
52:
44:
36:
2578:
2503:
2360:Edward J. Hopkins, Ph.D. (1996-06-10).
2005:Statistics and data analysis in geology
1991:. New York: J. Wiley & Sons, 1907.
1655:finding boundaries of level sets after
1565:is a line of equal radar reflectivity.
14:
2778:
2535:
2243:
2209:
2160:
2120:The Early Years of the Ordnance Survey
1433:shows equivalent cost of travel time.
970:
627:
583:is used for any type of contour line.
175:(height) above a given level, such as
2443:
2409:
2063:
1903:
1271:data are rendered as contour maps in
1259:are surfaces of equal water density.
523:
2510:DataStreme Atmosphere (2008-04-28).
2076:, Oxford, vol. 6, pp. 612–614, 1958.
1729:that suit the display. Sometimes a
2375:
1684:
1617:: biological events occurring with
966:Physical geography and oceanography
897:is a line of constant frequency of
24:
2558:10.1002/j.1477-8696.1967.tb02989.x
2089:, vol. 1, p. 139, quoted by Close.
1699:Topographic map § Conventions
1571:
1506:. Isodensanes are used to display
1444:usage is plotted horizontally and
1388:
945:
704:is a line of constant density. An
25:
2817:
2762:
2451:World Meteorological Organisation
2417:World Meteorological Organisation
2383:World Meteorological Organisation
2346:NOAA's National Weather Service,
2017:
1744:of the contour line is inferred.
1113:
1060:
2489:Chapter 13 – Weather Forecasting
2362:"Surface Weather Analysis Chart"
1328:contour maps involve mapping of
1030:, up to continental-scale maps.
962:denotes equal dates of thawing.
938:speed. In meteorology, the term
720:Temperature and related subjects
603:of the point data received from
2750:
2741:
2686:
2646:
2617:
2591:
2572:
2529:
2477:
2353:
2340:
2327:
2306:
2276:
2154:
2133:
2112:
2092:
2079:
1725:is the choice of any number of
1544:ordinary differential equations
1510:. For example, for a bivariate
1295:surfaces (especially low angle
1236:
849:is a line of constant relative
313:, now in northern Italy, under
214:three-dimensional model of the
2316:, 2nd edition, Pearson, 2005,
2072:R. A. Skelton, "Cartography",
2046:
2024:Morato-Moreno, Manuel (2017).
1997:
1981:
1957:
1933:
1887:
1750:is the manner of denoting the
1157:The general mathematical term
1139:refers to a curve of constant
1049:for elevations are also used.
958:formation each winter, and an
595:Isohyetal map of precipitation
586:
375:word without a repeated letter
151:
139:
119:
107:
13:
1:
2682:. Elsevier. pp. 219–220.
1881:
1766:Plan view versus profile view
1649:
1497:
1189:refers to a line of constant
994:. The contour interval is 20
758:. The term was coined by the
2244:Wright, John K. (Oct 1944).
2212:"Isopleth as a Generic Term"
2210:Wright, John K. (Apr 1930).
1941:"Definition of contour line"
1779:air pollutant concentrations
1448:usage is plotted vertically.
1164:
1002:Contours are one of several
954:line denotes equal dates of
792:
547:
508:
472:during a given time period.
433:
413:
397:
7:
2706:Fernández, Antonio (2011).
2585:City University of New York
1965:"Definition of CONTOUR MAP"
1827:
1526:Various types of graphs in
886:is a line indicating equal
615:Meteorological contour maps
10:
2822:
2579:Leveson, David J. (2002).
2512:"Air Temperature Patterns"
1919:(6 ed.). John wiley.
1769:
1688:
1375:
1262:
1225:
786:
762:geographer and naturalist
502:
427:
407:
391:
358: 'equal' and
295:Duchy of Modena and Reggio
277:drew the bed of the river
233:
29:
2770:Forthright's Phrontistery
2727:10.1080/03610920903444011
2629:historicalcharts.noaa.gov
2364:. University of Wisconsin
1822:automatic label placement
1689:For features specific to
1514:the isodensity lines are
1208:connects points of equal
1041:for underwater depths on
811:Rainfall and air moisture
579:In meteorology, the word
320:By around 1843, when the
269:Pieter Bruinsz. In 1701,
83:function of two variables
2161:Galton, Francis (1889).
2139:T. Owen and E. Pilbeam,
868: 'dew' and
464:" can be replaced with "
451:
32:Contour (disambiguation)
2300:10.1179/caj.1971.8.1.49
1512:elliptical distribution
1508:bivariate distributions
914:
303:Schiehallion experiment
95:three-dimensional graph
18:Isotherm (contour line)
2796:Multivariable calculus
2631:. 1946. Archived from
2003:Davis, John C., 1986,
1850:Fall line (topography)
1805:
1449:
1406:
1179:Earth's magnetic field
1174:
999:
764:Alexander von Humboldt
732:
712:is a line of constant
640:
622:Thermodynamic diagrams
596:
250:
158:
126:
125:{\displaystyle f(x,y)}
58:
50:
42:
2074:History of Technology
1809:Labeling contour maps
1803:
1640:mobile received power
1439:
1396:
1326:environmental science
1315:Environmental science
1241:Besides ocean depth,
1172:
978:
727:
671:shown are reduced to
635:
594:
241:
159:
157:{\displaystyle (x,y)}
127:
56:
48:
40:
2431:on 24 September 2015
2288:Cartographic Journal
1787:noise health effects
1679:Active contour model
1191:magnetic declination
1177:In the study of the
1100:can be approximated.
1052:In cartography, the
669:barometric pressures
373:can also refer to a
136:
101:
2550:1967Wthr...22..360M
2250:Geographical Review
2216:Geographical Review
2179:1889Natur..40..649.
1772:Topographic profile
1557:is a line of equal
1504:probability density
1486:population dynamics
1455:Indifference curves
1352:contamination. By
1330:environmental noise
1090:Spacing of contours
971:Elevation and depth
628:Barometric pressure
377:. As late as 1944,
2465:on 5 February 2008
2335:Isopleth: Contours
2087:La Carte de France
2085:Colonel Berthaut,
2052:Thrower, N. J. W.
2039:10.21138/bage.2414
1835:Aeronautical chart
1806:
1657:image segmentation
1644:cell coverage area
1638:mobile telephony:
1542:are used to solve
1450:
1407:
1342:soil contamination
1273:structural geology
1175:
1141:electric potential
1126:electric potential
1110:height increases.
1028:bathymetric charts
1000:
733:
641:
609:weather satellites
597:
562:population density
524:Equidistant points
251:
230:, pits and peaks.
154:
122:
59:
51:
43:
2678:Specht, Raymond.
1748:Numerical marking
1561:velocity, and an
1479:political science
1358:contour ploughing
1346:thermal pollution
1137:isopotential line
1107:hypsometric tints
542:distance function
301:used them in the
275:Nicholas Cruquius
16:(Redirected from
2813:
2757:
2754:
2748:
2745:
2739:
2738:
2712:
2703:
2697:
2690:
2684:
2683:
2675:
2669:
2668:
2666:
2665:
2650:
2644:
2643:
2641:
2640:
2621:
2615:
2595:
2589:
2588:
2576:
2570:
2569:
2533:
2527:
2526:
2524:
2523:
2507:
2501:
2500:
2498:
2496:
2481:
2475:
2474:
2472:
2470:
2461:. Archived from
2447:
2441:
2440:
2438:
2436:
2427:. Archived from
2413:
2407:
2406:
2404:
2402:
2397:on 16 April 2014
2393:. Archived from
2379:
2373:
2372:
2370:
2369:
2357:
2351:
2344:
2338:
2331:
2325:
2310:
2304:
2303:
2280:
2274:
2273:
2241:
2232:
2231:
2207:
2201:
2200:
2190:
2188:10.1038/040649a0
2158:
2152:
2137:
2131:
2116:
2110:
2096:
2090:
2083:
2077:
2070:
2061:
2050:
2044:
2043:
2041:
2021:
2015:
2001:
1995:
1985:
1979:
1978:
1976:
1975:
1961:
1955:
1954:
1952:
1951:
1937:
1931:
1930:
1926:978-0470-88861-2
1912:
1901:
1891:
1860:Marching squares
1685:Graphical design
1672:Boundary tracing
1667:Level-set method
1586:equal occurrence
1549:In interpreting
1446:physical capital
1403:utility function
1354:contour planting
1285:economic geology
1228:
1227:
1121:isopotential map
1054:contour interval
1024:topographic maps
795:
789:
788:
695:geostrophic wind
605:weather stations
511:
505:
504:
436:
430:
429:
416:
410:
409:
400:
394:
393:
381:still preferred
193:contour interval
163:
161:
160:
155:
132:parallel to the
131:
129:
128:
123:
97:of the function
21:
2821:
2820:
2816:
2815:
2814:
2812:
2811:
2810:
2776:
2775:
2765:
2760:
2755:
2751:
2746:
2742:
2710:
2704:
2700:
2691:
2687:
2676:
2672:
2663:
2661:
2652:
2651:
2647:
2638:
2636:
2625:"isoporic line"
2623:
2622:
2618:
2596:
2592:
2577:
2573:
2534:
2530:
2521:
2519:
2508:
2504:
2494:
2492:
2483:
2482:
2478:
2468:
2466:
2448:
2444:
2434:
2432:
2414:
2410:
2400:
2398:
2380:
2376:
2367:
2365:
2358:
2354:
2345:
2341:
2332:
2328:
2311:
2307:
2281:
2277:
2242:
2235:
2208:
2204:
2159:
2155:
2138:
2134:
2117:
2113:
2102:, vol. 68, pp.
2097:
2093:
2084:
2080:
2071:
2064:
2051:
2047:
2022:
2018:
2002:
1998:
1987:Tracy, John C.
1986:
1982:
1973:
1971:
1969:Merriam-Webster
1963:
1962:
1958:
1949:
1947:
1939:
1938:
1934:
1927:
1913:
1904:
1892:
1888:
1884:
1879:
1830:
1811:
1795:noise pollution
1774:
1768:
1702:
1687:
1652:
1621:such as plants
1574:
1572:Other phenomena
1524:
1500:
1391:
1389:Social sciences
1378:
1317:
1265:
1239:
1221:isodynamic line
1167:
1116:
1098:stream gradient
1063:
1006:used to denote
980:Topographic map
973:
968:
948:
946:Freeze and thaw
917:
901:storms, and an
813:
798:solar radiation
722:
630:
589:
566:census district
558:isometric lines
550:
526:
454:
446:noise pollution
336:until those of
334:nautical charts
322:Ordnance Survey
291:English Channel
287:Philippe Buache
236:
189:topographic map
137:
134:
133:
102:
99:
98:
35:
28:
23:
22:
15:
12:
11:
5:
2819:
2809:
2808:
2803:
2798:
2793:
2788:
2774:
2773:
2764:
2763:External links
2761:
2759:
2758:
2749:
2740:
2721:(4): 598–621.
2698:
2685:
2670:
2645:
2616:
2590:
2571:
2544:(9): 360–363.
2528:
2502:
2476:
2442:
2408:
2374:
2352:
2339:
2326:
2305:
2275:
2262:10.2307/210035
2256:(4): 653–654.
2233:
2202:
2153:
2143:, HMSO, 1992,
2132:
2130:, pp. 141–144.
2111:
2091:
2078:
2062:
2045:
2016:
1996:
1980:
1956:
1945:Dictionary.com
1932:
1925:
1902:
1885:
1883:
1880:
1878:
1877:
1872:
1867:
1862:
1857:
1852:
1847:
1842:
1837:
1831:
1829:
1826:
1810:
1807:
1767:
1764:
1731:sheen or gloss
1686:
1683:
1682:
1681:
1676:
1675:
1674:
1669:
1664:
1662:Edge detection
1651:
1648:
1647:
1646:
1636:
1625:
1610:
1598:
1587:
1573:
1570:
1532:phase diagrams
1528:thermodynamics
1523:
1520:
1499:
1496:
1421:isochrone maps
1390:
1387:
1377:
1374:
1360:, the rate of
1316:
1313:
1301:unconformities
1264:
1261:
1247:isobathytherms
1243:oceanographers
1238:
1235:
1206:isoclinic line
1166:
1163:
1115:
1114:Electrostatics
1112:
1102:
1101:
1087:
1080:The rule of Os
1077:
1070:The rule of Vs
1062:
1061:Interpretation
1059:
1004:common methods
972:
969:
967:
964:
947:
944:
916:
913:
821:isohyetal line
812:
809:
756:freezing level
721:
718:
629:
626:
588:
585:
574:choropleth map
549:
546:
525:
522:
518:isoclinic line
453:
450:
423:isometric line
379:John K. Wright
367:Francis Galton
299:Charles Hutton
235:
232:
177:mean sea level
153:
150:
147:
144:
141:
121:
118:
115:
112:
109:
106:
26:
9:
6:
4:
3:
2:
2818:
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2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
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2781:
2772:
2771:
2767:
2766:
2753:
2744:
2736:
2732:
2728:
2724:
2720:
2716:
2709:
2702:
2695:
2689:
2681:
2674:
2659:
2655:
2649:
2635:on 2015-07-21
2634:
2630:
2626:
2620:
2613:
2609:
2606:
2602:
2600:
2594:
2586:
2582:
2575:
2567:
2563:
2559:
2555:
2551:
2547:
2543:
2539:
2532:
2518:on 2008-05-11
2517:
2513:
2506:
2490:
2486:
2480:
2464:
2460:
2456:
2452:
2446:
2430:
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2418:
2412:
2396:
2392:
2388:
2384:
2378:
2363:
2356:
2349:
2343:
2336:
2330:
2323:
2322:0-13-035123-7
2319:
2315:
2309:
2301:
2297:
2293:
2289:
2285:
2279:
2271:
2267:
2263:
2259:
2255:
2251:
2247:
2240:
2238:
2229:
2225:
2221:
2217:
2213:
2206:
2198:
2194:
2189:
2184:
2180:
2176:
2173:(1044): 651.
2172:
2168:
2164:
2157:
2150:
2149:0-11-701507-5
2146:
2142:
2136:
2129:
2128:0-7153-4477-3
2125:
2121:
2115:
2109:
2105:
2101:
2095:
2088:
2082:
2075:
2069:
2067:
2059:
2055:
2049:
2040:
2035:
2031:
2027:
2020:
2014:
2013:0-471-08079-9
2010:
2006:
2000:
1994:
1990:
1984:
1970:
1966:
1960:
1946:
1942:
1936:
1928:
1922:
1918:
1911:
1909:
1907:
1900:
1896:
1890:
1886:
1876:
1873:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1832:
1825:
1823:
1818:
1815:
1802:
1798:
1796:
1792:
1791:air pollution
1788:
1784:
1780:
1773:
1763:
1759:
1757:
1756:interpolation
1753:
1749:
1745:
1742:
1738:
1736:
1732:
1728:
1724:
1720:
1718:
1713:
1709:
1707:
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1696:
1692:
1680:
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1668:
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1660:
1659:
1658:
1654:
1653:
1645:
1641:
1637:
1635:
1631:
1630:
1626:
1624:
1620:
1616:
1615:
1611:
1608:
1607:absorbed dose
1604:
1603:
1599:
1597:
1593:
1592:
1588:
1585:
1581:
1580:
1576:
1575:
1569:
1566:
1564:
1560:
1556:
1552:
1547:
1545:
1541:
1540:
1535:
1533:
1529:
1519:
1517:
1513:
1509:
1505:
1495:
1493:
1492:
1487:
1482:
1480:
1475:
1473:
1472:
1471:isocost curve
1467:
1463:
1462:
1457:
1456:
1447:
1443:
1438:
1434:
1432:
1431:
1426:
1422:
1418:
1417:
1412:
1404:
1400:
1395:
1386:
1383:
1373:
1371:
1367:
1363:
1359:
1355:
1351:
1347:
1343:
1339:
1338:air pollution
1335:
1331:
1327:
1323:
1312:
1310:
1306:
1302:
1298:
1297:thrust faults
1294:
1290:
1286:
1282:
1278:
1277:sedimentology
1274:
1270:
1260:
1258:
1257:
1252:
1248:
1244:
1234:
1232:
1222:
1217:
1215:
1211:
1207:
1202:
1200:
1199:isoporic line
1196:
1192:
1188:
1187:isogonic line
1184:
1180:
1171:
1162:
1160:
1155:
1153:
1152:equipotential
1149:
1147:
1146:equipotential
1142:
1138:
1134:
1132:
1131:equipotential
1127:
1123:
1122:
1111:
1108:
1099:
1095:
1091:
1088:
1085:
1081:
1078:
1075:
1071:
1068:
1067:
1066:
1058:
1055:
1050:
1048:
1044:
1040:
1036:
1031:
1029:
1025:
1021:
1017:
1014:and depth on
1013:
1009:
1005:
997:
993:
989:
985:
981:
977:
963:
961:
957:
953:
943:
941:
937:
933:
929:
926:
925:Ancient Greek
922:
912:
910:
906:
904:
900:
896:
891:
889:
885:
880:
878:
874:
870:
867:
863:
860:
859:Ancient Greek
856:
855:isodrosotherm
852:
848:
843:
841:
840:isohyetal map
837:
833:
829:
826:
825:Ancient Greek
822:
818:
808:
806:
801:
799:
794:
783:
778:
776:
772:
767:
765:
761:
757:
753:
749:
745:
742:
741:Ancient Greek
738:
731:
730:Arctic region
726:
717:
715:
711:
707:
703:
698:
696:
692:
688:
684:
680:
678:
674:
670:
666:
661:
657:
653:
650:
649:Ancient Greek
646:
639:
634:
625:
623:
619:
616:
612:
610:
606:
602:
601:interpolation
593:
584:
582:
577:
575:
571:
570:interpolation
567:
563:
559:
555:
545:
543:
539:
535:
531:
521:
519:
515:
510:
499:
498:
493:
489:
485:
482:
481:Ancient Greek
478:
473:
471:
467:
463:
459:
449:
447:
443:
438:
435:
424:
420:
415:
404:
399:
388:
384:
380:
376:
372:
368:
364:
360:
357:
353:
350:
349:Ancient Greek
346:
341:
339:
335:
331:
327:
326:Great Britain
323:
318:
316:
312:
308:
304:
300:
296:
292:
288:
285:in 1727, and
284:
280:
276:
272:
271:Edmond Halley
268:
264:
260:
256:
248:
244:
243:Edmond Halley
240:
231:
229:
225:
224:interpolation
221:
217:
212:
207:
205:
201:
196:
194:
190:
186:
182:
178:
174:
170:
165:
148:
145:
142:
116:
113:
110:
104:
96:
92:
91:plane section
88:
84:
80:
76:
72:
68:
64:
55:
47:
39:
33:
19:
2769:
2752:
2743:
2718:
2714:
2701:
2688:
2679:
2673:
2662:. Retrieved
2660:. 2005-01-05
2657:
2648:
2637:. Retrieved
2633:the original
2628:
2619:
2597:
2593:
2574:
2541:
2537:
2531:
2520:. Retrieved
2516:the original
2505:
2493:. Retrieved
2488:
2479:
2467:. Retrieved
2463:the original
2458:
2455:"Katallobar"
2445:
2433:. Retrieved
2429:the original
2424:
2411:
2399:. Retrieved
2395:the original
2390:
2377:
2366:. Retrieved
2355:
2342:
2329:
2313:
2308:
2291:
2287:
2278:
2253:
2249:
2219:
2215:
2205:
2170:
2166:
2156:
2140:
2135:
2119:
2114:
2099:
2094:
2086:
2081:
2073:
2057:
2053:
2048:
2029:
2019:
2004:
1999:
1988:
1983:
1972:. Retrieved
1968:
1959:
1948:. Retrieved
1944:
1935:
1916:
1894:
1889:
1870:Tensor field
1855:Geologic map
1845:Dymaxion map
1819:
1812:
1783:sound levels
1775:
1760:
1752:arithmetical
1747:
1746:
1740:
1739:
1722:
1721:
1711:
1710:
1703:
1628:
1627:
1613:
1612:
1609:of radiation
1601:
1600:
1590:
1589:
1578:
1577:
1567:
1562:
1554:
1548:
1537:
1536:
1525:
1501:
1489:
1483:
1476:
1469:
1466:input usages
1459:
1453:
1451:
1428:
1424:
1414:
1408:
1381:
1379:
1366:soil erosion
1362:water runoff
1333:
1321:
1318:
1308:
1305:Isopach maps
1281:stratigraphy
1266:
1254:
1250:
1246:
1240:
1237:Oceanography
1230:
1220:
1218:
1214:aclinic line
1213:
1210:magnetic dip
1205:
1203:
1198:
1194:
1186:
1182:
1176:
1156:
1144:
1136:
1129:
1119:
1117:
1103:
1089:
1084:hachure maps
1079:
1069:
1064:
1053:
1051:
1046:
1032:
1001:
959:
951:
949:
939:
931:
928:
920:
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252:
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78:
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63:contour line
62:
60:
2806:Relief maps
2786:Cartography
2421:"Anallobar"
2387:"Isallobar"
2284:Robinson AH
1717:topographic
1712:Line weight
1634:illuminance
1619:coincidence
1553:images, an
1350:groundwater
1195:agonic line
1181:, the term
1128:. The term
1043:bathymetric
1035:cartography
853:, while an
805:isogeotherm
752:temperature
691:katallobars
665:meteorology
587:Meteorology
442:air quality
181:contour map
169:cartography
2801:Topography
2780:Categories
2664:2010-04-25
2658:www.sfu.ca
2639:2015-07-20
2522:2010-02-07
2368:2007-05-10
2222:(2): 341.
2118:C. Close,
1974:2022-04-04
1950:2022-04-04
1882:References
1840:Bathymetry
1770:See also:
1723:Line color
1691:topography
1650:Algorithms
1498:Statistics
1269:geological
1256:isopycnals
1251:isohalines
923:(from
857:(from
823:(from
739:(from
687:anallobars
683:Isallobars
647:(from
638:cold front
479:(from
347:(from
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2566:1477-8696
2324:, p. 272.
2294:: 49–53.
1797:studies.
1741:Line type
1623:flowering
1539:Isoclines
1468:, and an
1430:isodapane
1416:isochrone
1411:economics
1399:economics
1364:and thus
1212:, and an
1165:Magnetism
1159:level set
1045:maps and
1008:elevation
992:elevation
952:isopectic
895:isochalaz
877:dew point
706:isoheight
702:isopycnal
673:sea level
548:Isopleths
204:level set
173:elevation
2735:55887263
2694:pictures
2654:"Isobel"
2612:27636277
2495:12 April
2469:12 April
2459:Eumetcal
2435:12 April
2425:Eumetcal
2401:12 April
2391:Eumetcal
2348:Glossary
2333:ArcGIS,
2007:, Wiley
1865:Planform
1828:See also
1735:base map
1727:pigments
1629:isophote
1614:isophene
1579:isochasm
1516:ellipses
1491:isocline
1461:isoquant
1370:riparian
1322:isoplats
1309:isopachs
1267:Various
1148:surfaces
1047:isohypse
1012:altitude
932:(tachus)
903:isobront
873:(therme)
866:(drosos)
851:humidity
832:(huetos)
775:isothere
771:isocheim
760:Prussian
748:(thermē)
737:isotherm
710:isohypse
660:pressure
581:isopleth
554:isopleth
538:polyline
514:isocline
497:isocline
414:arithmos
403:isarithm
387:isopleth
363:(gramma)
315:Napoleon
267:Dutchman
200:gradient
79:isarithm
75:isoquant
71:isopleth
2601:(Sercq)
2546:Bibcode
2538:Weather
2337:, 2013.
2197:3996216
2175:Bibcode
1993:p. 337.
1899:p. 344.
1602:isodose
1591:isochor
1563:isoecho
1559:Doppler
1382:isoflor
1376:Ecology
1372:zones.
1334:isobels
1263:Geology
1231:dynamis
1226:δύναμις
1074:erosion
1039:isobath
1020:terrain
988:Vermont
921:isotach
890:cover.
884:isoneph
847:isohume
817:isohyet
656:(baros)
509:klinein
503:κλίνειν
488:(gonia)
466:isallo-
419:isoline
408:ἀριθμός
398:plethos
383:isogram
371:isogram
345:isogram
330:Ireland
279:Merwede
263:Haarlem
261:, near
259:Spaarne
255:isobath
234:History
216:surface
93:of the
81:) of a
67:isoline
2791:Curves
2733:
2610:
2564:
2320:
2270:210035
2268:
2228:208890
2226:
2195:
2167:Nature
2147:
2126:
2011:
1923:
1875:TERCOM
1814:Labels
1697:, and
1693:, see
1596:volume
1584:aurora
1555:isodop
1425:isotim
1299:) and
1289:strata
1223:(from
1183:isogon
1096:, the
1094:stream
1037:, but
960:isotac
940:isogon
864:δρόσος
793:helios
782:isohel
667:, the
645:isobar
492:isogon
477:isogon
434:metron
428:μέτρον
392:πλῆθος
361:γράμμα
356:(isos)
338:Russia
283:fathom
249:(1701)
65:(also
2731:S2CID
2711:(PDF)
2266:JSTOR
2224:JSTOR
2193:S2CID
1706:color
1551:radar
1488:, an
1442:Labor
1423:. An
1397:From
1293:fault
984:Stowe
930:ταχύς
927:
888:cloud
871:θέρμη
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830:ὑετός
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787:ἥλιος
746:θέρμη
743:
654:βάρος
651:
536:, or
530:point
486:γωνία
483:
452:Types
351:
265:, by
228:slope
183:is a
87:curve
85:is a
2608:OCLC
2605:OCLC
2599:Sark
2562:ISSN
2497:2014
2471:2014
2437:2014
2403:2014
2318:ISBN
2145:ISBN
2124:ISBN
2009:ISBN
1921:ISBN
1793:and
1781:and
1777:are
1642:and
1356:and
1348:and
1307:use
1283:and
1133:line
1026:and
1016:maps
996:feet
936:wind
915:Wind
909:Snow
899:hail
677:wind
607:and
534:line
516:and
470:rate
462:iso-
458:iso-
444:and
421:and
354:ἴσος
328:and
307:Haxo
198:The
179:. A
2723:doi
2554:doi
2296:doi
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2104:756
2034:doi
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1380:An
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