Contour line

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Image:Topographic map example.png

A contour line (also level set, isopleth, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. A contour map is a map illustrated with contour lines.

The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone. However if contour lines rotate through three or more widths, or if the lines are numerically labelled, then the direction of the gradient can also be determined from the contour lines.

Various types of contour lines are given different names according to the nature of the variable being mapped:


"Iso" can be replaced with "isallo" to specify a contour line connecting points where a variable has changed at the same rate during a given time period.

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Technical construction factors

To maximize readability of contour maps, there are several design choices available to the map creator, principally line weight, line color, line type and method of numerical marking.

Line weight 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 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 topgraphic map above, the even hundred foot elevations are shown in a different weight from the twenty foot intervals.

Line color is the choice of any number of pigments that suit the display. Sometimes a sheen or gloss is used as well as color to set the contour lines apart from the base map.

Line type 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.

Numerical marking is the manner of denoting the arithmetical the values of contour lines. This can be done by placing numbers along some of the contour lines, typically using interpolation for intervening lines. Alternatively a map key can be produced associating the contours with their values.

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Plan view versus profile view

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 are air pollutant concentrations and sound levels. 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 noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. One can see an example of vertical contours in the article on noise barriers. In actuality, both plan and profile view contour maps are used in air pollution and noise pollution studies.

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External links

cs:Vrstevnice es:isógrama ja:等高線 pl:Izolinia sl:Izo-črte sr:Изохипсе fi:Isoviiva

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