GEOG 486
Cartography and Visualization

Dasymetric Maps

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The term 'dasymetric mapping' was first used by Russian geographers who described dasymetric maps as density measuring maps (Wright 1936). Dasymetric maps are similar to choropleth maps in that both types of maps represent data as stepped statistical surfaces. In other words, the data that are within a polygon are assumed to be distributed equally throughout that polygon’s area, and changes in the surface occur abruptly, and only at polygon boundaries.

The main difference between choropleth maps and dasymetric maps is the type of areal unit that is used for collecting data and representing the phenomenon of interest. In choropleth maps, data are typically represented using enumeration units (e.g., census tracts, health service areas, etc.) whose shapes may not be related to the distribution of the geographic phenomenon we are interested in mapping. For this reason, the visual impression that the map gives (i.e., that the phenomenon is evenly distributed throughout the enumeration unit) is usually incorrect. In dasymetric maps, however, the areal units that divide the space are based on the actual character of the data surface, often in combination with enumeration units (see Figure 4.cg.11,below).

A series of dasymetric maps of population density.
Figure 4.cg.11 This example shows a dasymetric map of population density that was created by using an intersection of land cover information with county boundaries. County polygons were split into multiple polygons based on the land uses present in each county, and the population data from each county were then reapportioned into the new polygons. The map at the left shows a dasymetric map of population density, while the maps in the middle and at the right show estimates of error in estimating the population density using the dasymetric method. The error surface was created by comparing the dasymetric results to a population density surface based on larger scale data (census block groups).
Credit: Eicher and Brewer 2001

By now, you might be wondering how we can create dasymetric maps if data are usually collected using unrelated enumeration units rather than areal units that reflect the nature of the data surface. To get around this problem, we can use ancillary data to create a new set of areal units that better represent the data surface. For example, land use is an ancillary data variable that is often used for creating dasymetric maps of population density. Generally, we can use two types of ancillary data variables: limiting variables and related variables. Limiting variables are attributes that can help us eliminate areas where data values could be. For example, a data layer that depicts where water bodies are located may be useful for mapping population density, as it is highly unlikely that there will be any people living in the middle of lakes or rivers. Related variables have some sort of association or predictable relationship with the data variable we are trying to map. In our population density application, an example of a related ancillary attribute might be land cover; we know that fewer people tend to live in areas that have a cropland land cover than a developed (i.e., built up) land cover, so we can require those areas to have a lower density.

note: We will discuss ancillary data in more detail in the Lesson 5 Concept Gallery item called Dot Maps.

A dasymetric map made with a limiting variable.visual spaceA dasymetric map made with a related variable.
Figures 4.cg.12a and 4.cg.12b The figure at the left (a) depicts the process of creating a dasymetric map from a limiting variable (e.g., lakes), while the figure at the right (b) depicts a map created from a related variable. In figure a, at left, we know that people cannot live on 10% of the area in Beltrami County, Minnesota, so we can calculate a new population density figure for the county based on the 90% of the area they can live on (bottom portion of figure). In the figure b, at right, we also know that there are some areas where people will not live (lakes (10%) and bogs and wetlands (dark blue; 35% of the total county area). This leaves 55% of the county where people can reside. We know that people are likely to reside at higher densities in towns and farmlands (yellow; 10% of the total county area) and at lower densities in forested areas (green; 45% of the total county area). If we know that half of all people live in towns or on farmlands and half live in forested areas, we can calculate new population densities by apportioning the total number of people into the new areas that we have calculated for each land use type. We then arrive at new densities of 82 people per square mile in towns and 36 people per square mile in forested areas.

When we are creating this new set of areal units, we are basically performing what is called an areal interpolation. In other words, we are transferring quantities of our phenomenon from one set of areal units to another. One thing that we need to be careful about is that we should preserve what Tobler (1979) called the pycnophylactic property. An easy way of describing this is that if you have 100 people in a county, and you subdivide the county into a larger number of units (e.g., new units based on land cover) and redistribute the population among the new units, the sum of the population in the new units should still add up to 100 people. As Lanford and Unwin (1994, p.24) succinctly phrased it: "People are not destroyed or manufactured during the redistribution process."

Although off-the-shelf GIS software does not have built-in functionality for creating dasymetric maps, in recent years there has been renewed interest in creating automated methods for creating this type of map in both raster and vector format (e.g., Fisher and Langford (1996); Eicher (1999); Mennis (2003)).

Recommended Readings

If you are interested in investigating this subject further, I recommend the following:

  • Mennis, J. 2003. "Generating surface models of population using dasymetric mapping." Professional Geographer. 55(1): 31-2.
  • Tobler, W. 2001. "Pycnophylactic reallocation." CSISS..

    Note that this resource discussed pycnophylactic reallocation within the context of making isoline maps rather than dasymetric maps. The principle is the same, but the nature of the way the surfaces changes (i.e., smoothly or abruptly) is what is different.