GEOG 486
Cartography and Visualization

Isolines

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Isolines, which are sometimes also called isarithms, are a type of two-dimensional cartographic symbolization that is commonly used for depicting a three-dimensional statistical surface on a flat piece of paper or a computer screen. This three-dimensional surface may be real (e.g., elevation or air pressure) or conceptual (e.g., crop yields). The location of each isoline depicts all of the places on the surface that have a particular value (i.e., a particular isoline on a contour map shows all of the places that have a particular elevation; see Figure 6.cg.3, below). Over time, we have come to use specialized names for isolines that are used for representing certain types of phenomena (e.g., an isotherm is a line of equal temperature, while an isobar is a line of equal pressure). However, whatever the isolines are called, they are created using a similar procedure.

Graphic drawings to show a line of constant elevation depicted on a surface (left), and on a contour map (right).
Figure 6.cg.3 A line of constant elevation depicted on a surface and on a contour map.

Isoline symbolization is generally appropriate for depicting phenomena that are continuous and smoothly changing (refer back to the section on Surfaces in the Lesson 4 concept gallery for a more detailed discussion of these characteristics of spatial distributions). Until the advent of remote sensing, cartographers were only rarely able to measure a phenomenon at all locations on a surface, so they used methods generally known as interpolation (see the section on Interpolation for more information on these methods) for estimating the values of variables at non-measured locations from measurements made at particular points (see Figure 6.cg.4, below). Even with the availability of remotely sensed data today, there are still many variables for which we cannot obtain measurements at each point on the earth's surface, so these interpolation methods are still very important. After a surface representation of the attribute of interest has been created (usually in the form of either a raster or a triangulated irregular network), the cartographer chooses which isolines s/he wants to represent on the map, and the computer can identify every location where the value of interest occurs and draw a line connecting those locations (i.e., the isoline).

A series of drawings to show the process of creating isolines. Explained further in the figure caption.
Figure 6.cg.4 In order to create isolines, cartographers begin with a set of sample points (top) to create a surface (left). From this surface, they can connect all locations that have equal values at particular values of interest (right).

When communicating data with isolines, there are several design factors to consider. Although isoline maps allow map readers to estimate values at particular locations with reasonably good precision, map readers often have a difficult time forming a mental image of the surface's shape from isolines alone (see figure below, left). Filling contours with some sort of sequential color scheme can help map readers to more easily form an overall impression of where highs and lows exist in the space (see figure below, right).

200m contoursTwo versions of a section of a map: one a black and white image with isolines alone (left), and one with a sequential color scheme in addition to the isolines (right).
Figure 6.cg.5 Isolines alone (above left) do not help map readers form a mental image of the surface's shape as well as they do when filled with some sort of sequential color scheme (above right).

The choice of an appropriate contour interval can sometimes be tricky: if you choose a small contour interval, you may be left with a map that becomes a mass of closely packed lines that make it difficult to effectively read or display any other relevant information; if you choose a larger contour interval, map readers may miss important surface features, particularly in areas of slower attribute change.

Two identical map areas shown with different contour interval lines. The left map shows an example of a small contour interval, and the right map shows a larger contour interval level.Two identical map areas shown with different contour interval lines. The left map shows an example of a small contour interval, and the right map shows a larger contour interval level.
Figure 6.cg.6 Small contour intervals (above left) may coalesce at points and make the map congested; a larger contour interval (right), can obscure some surface features, e.g., the valley bottom in this map.

By altering the base position or starting point for drawing the isolines, there may be features that get hidden or obscured. See Figure 6.cg. 7 below for an example.

Two identical map areas shown with different base positions for the drawing of isolines. See figure caption for more information.visual spaceTwo identical map areas shown with different base positions for the drawing of isolines. See figure caption for more information.
Figure 6.cg.7 In the area mapped above, there is small island that shows up in the upper right corner of the mapped area when the contour base position is changed from 6013 feet (above left) to 6050 feet (above right). In the left hand-map, this island disappears into the area between contours as the elevation of the entire island is between 6013 and 6053 feet.

Isoline maps often include symbolization in addition to the isolines themselves in order to communicate other features or data. It is important to be sure that your isolines stand out as figure against any other features you include in the map.

Two identical map areas shown with different colored contour lines. See figure caption for more information.visual spaceTwo identical map areas shown with different colored contour lines. See figure caption for more information.
Figure 6.cg.8 In the map at left, which uses light grey contours, there is not enough contrast between the green background and the grey lines to see the isolines. In the map at right, however, the black lines appear strongly as figure against all of the different color hues used for symbolizing vegetation community types.

Sometimes it can be helpful to use additional visual variables within the isolines to add supplementary information. For example, using two types of line weights for elevation contours results in index and intermediate contours. The index contours, which are usually symbolized by a thicker line, are at set intervals (usually every fourth or fifth contour) and can help the map reader more quickly identify elevation information. For example, if you had a 20 meter contour interval, you might make index contours at every 100m. An advantage to this approach is that it is only necessary to label the index contours, making label placement easier.

A second type of visual characteristic that can be used for isoline maps is for depressions, or areas of decreasing value that are encircled by areas of increasing value. These are often represented with a line that is hatched towards the interior of the depression to give the map reader the impression that the surface is trending downward within the isolines. See Figure 6.cg.9, at right, for an example.

A map marked with two types of isolines: index contours and supplementary contours.visual spaceDrawing to show contour depression using a line that is hatched toward the interior of the depression.
Figure 6.cg.9 In the map above left, the visual character of the isolines have been changed to communicate different aspects of the variable. A heavier-weight line is used to create index contours, a lighter solid line is used for the intermediate contours, and a dashed line is used for supplementary contours. Supplementary contours can be used to display additional information that would normally be lost between contours. This type of symbol is especially useful in cases where you have both quickly changing and slowly changing areas on a surface, as in this example. In the map above right, a depression is represented with lines that are hatched towards the interior of the depression.

The placement of labels in isoline maps is very important. The result of a computer's default label placement can result in some lines falling directly on top of labels, rendering them illegible without masking; others are placed at angles that make reading them awkward or that make it difficult to tell to which line they refer. Generally, label only the index contours, and only repeat labels in cases where the line is long, or interrupted. Labels should be placed "in-line" with the lines to which they refer, and techniques such as haloing can be used to mask or break the line so that the label is legible (refer back to the Text Effects concept gallery item in Lesson 3 for a refresher on line halos).

Two map areas, one (left) shown with poor isoline label placement, and the other (right) shown with acceptable isoline label placement.visual spaceTwo map areas, one (left) shown with poor isoline label placement, and the other (right) shown with acceptable isoline label placement.
Figure 6.cg.10 At upper left, you can see the result of the computer's default label placement. The map at right is a better example of isoline label placement.