Examples of thematic maps (continued)
Chapter 2: What Crime Maps Do and How They Do It

Thematic maps using area symbols

When we think of making maps that represent areas, it's the choropleth map that usually comes to mind, with administrative or political areas shaded according to their statistical values, whether they are frequency counts, averages, or other relevant measures. When is a choropleth map appropriate? Strictly speaking, mapping total numbers, such as crime counts, using choropleth mapping is unacceptable owing to the misleading impression given by unequal areas. For example, if the largest and smallest areas have the same frequency, they will be shaded the same on the map, which fosters possible misinterpretations based on per capita or density considerations. However, many departments overcome this by using a regular grid for choropleth mapping. This has the advantage of equalizing areas but the possible disadvantage that the units of the grid may not be "natural" local areas. In other words, the areas exist only on police department maps and may be difficult to interpret in the field.

For places with boundaries following the rectangular land survey, a grid of square miles (sections) or quarter-square miles will be substantially visible in the local street pattern system. This applies to most areas west of the Appalachian Mountains. East of the Appalachians, survey systems were usually based on irregular "metes and bounds" and do not lend themselves to grid-based maps, except where cities have a regular block grid. (See also chapter 4, "Definition in geographic space.") Examples of choropleth maps are shown in figures 2.11 and 2.12.

Choropleth maps are best used for area averages, such as crime rates, population density, and percentages, as well as nominal-scale information such as land use. Care is needed in the interpretation of all maps, and choropleth maps are no exception. Take, for instance, a choropleth map of a crime rate based on population. Map values are expressed in terms of numbers of crimes per population unit. But what population? Normally, the residential population as enumerated in the census is implied. What about downtown business areas with negligible residential populations? They still have crimes and the statistical effect is to inflate the crime rate. Is this realistic?

One could take this scenario to the extreme: If small areas are used for crime rate calculation, we may have areas with crimes but no resident population, producing an infinite crime rate! Bear in mind that the crime rate concept is a loose one and crime rate maps are only an approximation, particularly for smaller areas. Although neither the offenders nor the victims are necessarily residents of the areas where the crimes happen, they would nevertheless be represented in crime rate maps.

 Rule of Thumb Avoid generating choropleth maps of crime rates for small areas like city blocks because spurious results could be produced for areas where there are crimes but no residents.

Experience has shown that it may be helpful to add a disclaimer note on some maps to point out, where appropriate, that some areas with high crime rates have small or zero residential populations. Another form of this disclaimer would note that rates have not been calculated, or have been intentionally omitted, for areas with small or no residential population. This will have to be handled carefully, however, since some readers may conclude that the police department has something to hide if data are manipulated in what appears to be a selective way.

Note that choropleth maps can be produced in a three-dimensional format with the height of each area proportional to its data value.2 The advantage of this type of presentation is visual appeal and vividness. The disadvantages are that it can be difficult to decipher the actual data value, and that a tall column will hide other areas, as is the case in three-dimensional surface maps.

Thematic maps using surfaces

Although crime maps using isolines have been around in some form since the 1960s, they have only recently become widely used.3 This is a result of the availability of algorithms in mapping programs that perform complex calculations at high speed. With the addition of three-dimensional capabilities, surface maps with textured surfaces are now within the reach of most crime analysts. Such maps are tempting as they are visually more appealing than two-dimensional renditions. But the same caveats noted above apply. Just because a surface map or three-dimensional rendition can be produced, it does not necessarily follow that it is the most appropriate or useful form for visualizing the data. For example, it may be difficult to add legible landmark icons or even boundaries to a three-dimensional map, depending on factors such as scale and amplitude, or the degree of peakedness, of the map, as well as the angle of view. (See figure 1.14 and chapters 4 and 6 for other examples of three-dimensional maps.)

Ultimately, deciding whether to use a surface map involves balancing scientific and artistic judgment, and in many cases the decision can be made only through experimentation. Fortunately, maps can be produced rapidly with desktop computers, so experimentation can and should be a routine part of the mapmaking process.

Thematic maps using linear symbols

Flows between points are shown with linear symbols, with their width or thickness generally proportional to the volume of the flow (figure 2.13). Maps of this type had their origins in economic geography, first showing passenger flows on Irish railways in the 1830s and, later, commodity flows among nations (Campbell, 1993, p. 264). These maps can be used in crime mapping, to show, for example:

• Links between where vehicles were stolen, where they were recovered, and suspects' addresses.
• Routes between victims' and offenders' home addresses (e.g., Pyle et al., 1974; Frisbie et al., 1977, p. 88).
• Passes along streets by patrol cars to illustrate patrol density.4
• Traffic density.

Virtually no flow maps have been seen in the recent literature on crime mapping, even though such maps are in use in police departments. Their absence is not due to lack of data. It may be that the apparent lack of this type of map in the literature is due to the absence of readily available flow-mapping algorithms in the GIS programs most popular among crime mappers. While it is unlikely that flow mapping will ever be a major component of crime maps, it will be increasingly used owing to its obvious utility in limited applications.