L2.04: Scale


You hear the word "scale" often when you work around people who produce or use geographic information. If you listen closely, you'll notice that the term has several different meanings, depending on the context in which it is used. You'll hear talk about the scales of geographic phenomena and about the scales at which phenomena are represented on maps and aerial imagery. You may even hear the word used as a verb, as in "scaling a map" or "downscaling." The goal of this section is to help you learn to tell these different meanings apart and to be able to use concepts of scale to help make sense of geographic data.

Scale as Scope

Often "scale" is used as a synonym for "scope" or "extent." For example, the title of an international research project called The Large Scale Biosphere-Atmosphere Experiment in Amazonia (1999) uses the term "large scale" to describe a comprehensive study of environmental systems operating across a large region. This usage is common not only among environmental scientists and activists, but also among economists, politicians, and the press. Those of us who specialize in geographic information usually use the word "scale" differently, however.

Map Scale

When people who work with maps and aerial images use the word "scale," they usually are talking about the sizes of things that appear on a map or aerial photo relative to the actual sizes of those things on the ground.

Map scale is the proportion between a distance on a map (Dm) and a corresponding distance on the ground (Dg): (Dm / Dg).

By convention, the proportion is expressed as a "representative fraction" in which map distance (Dm) is reduced to 1. The proportion, or ratio, is also typically expressed in the form 1 : Dg rather than 1 / Dg.

The representative fraction 1:100,000, for example, means that a section of road that measures 1 unit in length on a map stands for a section of road on the ground that is 100,000 units long.

If we were to change the scale of the map such that the length of the section of road on the map was reduced to, say, 0.1 units in length, we would have created a smaller-scale map whose representative fraction is 0.1:100,000, or 1:1,000,000. When we talk about large- and small-scale maps and geographic data, then, we are talking about the relative sizes and levels of detail of the features represented in the data. In general, the larger the map scale, the more detail is shown. This tendency is illustrated below in Figure 2.5.

Three maps of different scales showing the same location
Figure 2.5: Geographic data are generalized according to scale in these maps of the town of Gorham. (Adapted from Thompson, 1988.)
Source: GEOG 482

One of the defining characteristics of topographic maps is that scale is consistent across each map and within each map series. This isn't true for aerial imagery, however, except for images that have been orthorectified. Large-scale maps are typically derived from aerial imagery. One of the challenges associated with using aerial photos as sources of map data is that the scale of an aerial image varies from place to place as a function of the elevation of the terrain shown in the scene. Assuming that the aircraft carrying the camera maintains a constant flying height (which pilots of such aircraft try very hard to do), the distance between the camera and the ground varies along each flight path. This causes aerial photo scale to be larger where the terrain is higher and smaller where the terrain is lower. An "orthorectified" image is one in which variations in scale caused by variations in terrain elevation (among other effects) have been removed.

You can calculate the average scale of an unrectified aerial photo by solving the equation Sp = f / (H-havg), where f is the focal length of the camera, H is the flying height of the aircraft above mean sea level, and havg is the average elevation of the terrain. You can also calculate aerial photo scale at a particular point by solving the equation Sp = f / (H-h), where f is the focal length of the camera, H is the flying height of the aircraft above mean sea level, and h is the elevation of the terrain at a given point.

Graphic Map Scale

Another way to express map scale is with a graphic (or "bar") scale. Unlike representative fractions, graphic scales remain true when maps are shrunk or magnified.

Example of a bar scale (left) and a variable scale
Figure 2.6: Graphic scales
Source: GEOG 482

If they include a scale at all, most maps include a bar scale like the one shown above left (Figure 2.6). Some also express map scale as a representative fraction. Either way, the implication is that scale is uniform across the map. In fact, except for maps that show only very small areas, scale varies across every map. As you probably know, this follows from the fact that positions on the nearly-spherical Earth must be transformed to positions on two-dimensional sheets of paper. Systematic transformations of this kind are called map projections. As we will discuss in greater depth later in this chapter, all map projections are accompanied by deformation of features in some or all areas of the map. This deformation causes map scale to vary across the map. Representative fractions may, therefore, specify map scale along a line at which deformation is minimal (nominal scale). Bar scales denote only the nominal or average map scale. Variable scales, like the one illustrated above right, show how scale varies, in this case by latitude, due to deformation caused by map projection.

Scale as a Verb

The term "scale" is sometimes used as a verb. To scale a map is to reproduce it at a different size. For instance, if you photographically reduce a 1:100,000-scale map to 50 percent of its original width and height, the result would be one-quarter the area of the original. Obviously, the map scale of the reduction would be smaller too: 1/2 x 1/100,000 = 1/200,000.

Because of the inaccuracies inherent in all geographic data, particularly in small-scale maps, scrupulous geographic information specialists avoid enlarging source maps. To do so is to exaggerate generalizations and errors. The original map used to illustrate areas in Pennsylvania disqualified from consideration for low-level radioactive waste storage shown below (Figure 2.7), for instance, was printed with the statement "Because of map scale and printing considerations, it is not appropriate to enlarge or otherwise enhance the features on this map."

Example of a bar scale and a variable scale
Figure 2.7: Areas (in gray) disqualified as potential sites for a low level radioactive waste storage facility depicted on a small-scale map (original 1:1,500,000) mask small suitable areas large enough to contain the 500-acre facility (Chem-Nuclear Systems, Inc., 1994).
Source: GEOG 482

Some or all of the above content is used with permission from GEOG 482—The Nature of Geographic Information, Penn State's College of Earth and Mineral Sciences and licensed for use under CC BY 3.0.