GEOG 486
Cartography and Visualization

Surfaces

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Together with the visual variables (refer back to the Symbolization concept gallery item from Lesson 2), one of the most important choices you will make in designing a thematic map is what type of representation you would like to use for your data. In this course, we will focus on and discuss four common types of maps: choropleth (here in Lesson 4), graduated/proportional symbol (in Lesson 5), dot density (in Lesson 5), and isoline maps (in Lesson 6).

When cartographers create thematic maps, one general goal they often have is to try to help the map reader understand the character of the spatial distribution of the attribute(s) displayed in the map. One useful way of talking about spatial distributions is to use the concept of a cartographic data model, first developed by George Jenks, a professor at the University of Kansas (Jenks, 1967). As Jenks defined it, a cartographic data model is an abstract method for representing the most important characteristics of a particular spatial distribution; this representation could be either mathematical or graphical. Other cartographers further developed this notion by creating a typology of how map types can be related to data models (MacEachren and DiBiase, 1991). They identified two important axes along which the spatial distribution of a variable can vary: from discrete to continuous and from abruptly changing to smoothly changing (see Figure 4.cg.1, below). They also matched the visual characteristics of these data models to the visual characteristics of different map types (see Figure 4.cg.2, further below; you may recognize this matching as an exercise in creating map-signs that best match their real world referents - remember our discussion of semiotics in Lesson 1, Part II: Visual Communication).

In the figure below, one of the axes shows a range from discrete to continuous. Discrete phenomena are those that have space between observations (e.g., mobile phone towers), while continuous phenomena exist throughout space (e.g., temperature - it exists everywhere even if we do not choose to measure at every possible location). The other axis relates to the degree of spatial dependence of a phenomenon. A phenomenon with a low degree of spatial dependence may change abruptly over a short distance (e.g., income tax rates between states), while phenomena with a high degree of spatial dependence change more smoothly. Elevation is generally a good example of a smoothly changing phenomenon, with the rare exceptions of canyons and cliffs, where there is a large, abrupt elevation change. One important point is that the character of a phenomenon may be scale-dependent (both spatially and temporally). For example, the distribution of cars may be generally considered to be abrupt: generally we do not find cars in locations that are not paved, and there is some amount of space between cars. However, at certain times of the day (e.g., rush hour), the distribution of cars (at least in particular locations, such as freeways) may become continuous.

Chart to show surface conceptualizations of geographic phenomena
Figure 4.cg.1 Different ways of conceptualizing distributions of geographic phenomena (i.e., data models) as they occur through space.
Credit: MacEachren, 1992

These different conceptualizations of geographic phenomena lend themselves to certain map types (or representations) better than others. For example, elevation is smooth and continuous and is therefore often represented with isolines, as shown in the lower right corner of Fig 4.cg.2 (and discussed more in Chapter 6). A tax rate, or most any kind of rate (e.g. mortality) is a value for an area (e.g. county) and therefore is abrupt but still continuous. A choropleth map would then best represent rate data as shown in the lower left corner of Fig 4.cg.2. What data model in Fig 4.cg.1 represents counts of people per area? And what kind of map type in Fig 4.cg.2 would work with that kind of geographic data? Depending on the scale of aggregation you may consider such data to be discrete and abrupt (upper left corner of Fig 4.cg.1) and use a proportional circle for each unit of area, or with small areas of aggregation (compared to your extent) you may think of your data as discrete but smooth (e.g. population per census tract but looking at a whole state), and then you may consider a dot density map (more on this in Chapter 5).

A chart of map types based on the conceptualizations shown in Figure 6.cg.1
Figure 4.cg.2 Corresponding map types that match the data models depicted in the figure above.
Credit: MacEachren, 1992

Recommended Readings

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

  • MacEachren, A. M. and D. W. DiBiase. 1991. "Animated maps of aggregate data: Conceptual and practical problems." Cartography and Geographic Information Systems, 18(4): 221-229.
  • MacEachren, Alan M. 1992. "Visualizing uncertain information." Cartographic Perspectives. 13: 10-19.