GEOG 486
Cartography and Visualization

Visual Representations of Data Uncertainty


Cartographers have become increasingly aware of the importance of providing map users with information about the uncertainty associated with data that are used in thematic maps, as information about the uncertainty or reliability of the data may influence decision-makers' thinking and reasoning about problems (see the Data Uncertainty concept gallery above). Here, we discuss some methods cartographers have developed for representing data uncertainty as well as the results of some user testing that has evaluated how well these representations help map users understand and work with uncertainty data.

You may recall that in the Data Uncertainty concept gallery item, we talked about different types of uncertainty: spatial uncertainty, temporal uncertainty and attribute uncertainty. Most researchers who have been thinking about creating visual representations of data uncertainty have concentrated on attribute uncertainty. However, some groups have recently begun to create visualization applications that can deal with all three types of uncertainty (see Figure, below). You can see from this figure that symbolization design becomes very tricky and highly multivariate once you begin considering multiple types of uncertainty! For the remainder of this concept gallery, we will focus on representations that are mainly concerned with visualizing attribute uncertainty.

A map featuring the display of spatial, attribute, and temporal uncertainty.
Figure This map displays location (i.e., spatial), temporal and dosage (i.e., attribute) uncertainty in an application designed to help decision makers understand the reliability and uncertainty of intelligence about the potential release of a toxic substance.
Credit: MacEachren, et al. 2004

We can classify representations of uncertainty into five basic types: traditional, split map displays, toggled map displays, integrated symbolization on a single map and animations. Traditional representations of uncertainty include verbal statements in a map legend (e.g., "Data from the San Francisco metropolitan area are most certain. Data certainty decreases as the distance from San Francisco increases.") and reliability diagrams, which are also often located in the map margins near the legend (see Figure, below). One of the main drawbacks to these traditional methods is that because they are small and are not located with the main map frame, they are quite easy for the map reader to ignore. Verbal statements may also be difficult for map users to mentally integrate with the mapped attribute data (i.e., to mentally 'overlay' the uncertainty information with the thematic data).

Reliability diagram, explained in text
Figure This figure shows a reliability diagram from one of the U.S. Army Map Service AMS Series U502 (India and Pakistan 1:250,000 Topographic Maps). Notice that the diagram indicates which areas of the map were compiled from different sources, and may thereby have differing levels of reliability or uncertainty associated with them.
Credit: MacEachren, et al. 2004

Split map displays typically depict the attribute data in one map frame alongside a second map frame that depicts the uncertainty data (see Figure, below). Although it may be quite easy for map users to determine the data certainty associated with a particular location from this type of representation, it may be more difficult for them to determine whether there are any correlations between attribute values and the level of uncertainty associated with them.

A split display: two separate maps with data that must be mentally combined by the user.
Figure In this example, a dataset depicting an interpolated minimum temperature surface and an error surface that shows how accurate the interpolated surface is are displayed as separate maps. The user then has to mentally overlay them in his or her mind or compare specific locations to determine how reliable the interpolated surface is.
Credit: MacEachren, et al. 2004

Toggled map displays are similar to the split map displays in that there are two maps, one of the thematic data and one of the uncertainty data, but differ in that only one of the displays is seen by the map user at a particular time (i.e., the user can flip or 'toggle' back and forth between the displays; see Figure, below).

Animation of the above diagram
Figure Move your mouse over the map to toggle to the data uncertainty frame, and remove it to return to the thematic data.
Credit: MacEachren, et al. 2004

Representations that use integrated symbolization use some sort of multivariate representation to combine information on the attributes of interest and their associated uncertainties within one map (see Figure, below). One advantage of an integrated representation is that it is virtually impossible for map users to ignore the uncertainty information. However, it is important to carefully choose combinations of variables so that the uncertainty information clarifies the map rather than clutters it (Leitner and Buttenfield 2000). Researchers have tested various combinations of variables to determine which ones are most effective, and have generally found that visually separable variable combinations are better than visually integral combinations (see the Multivariate Symbols concept gallery item from Lesson 5 for more details on these combinations) because they do not distract the map reader from noticing potentially important patterns in the map (e.g., clusters) as visually integral variable combinations might (MacEachren et al. 1998).

An example of a map using integrated symbolization.
Figure In this case, we used a combination of texture and color hue and value for representing the minimum temperature surface and its uncertainty. This particular symbolization combination was found to be effective by MacEachren et al. (1998). However, MacEachren and his group only used texture to distinguish between reliable and unreliable data, without specifying relative levels of reliability as in this map. Take a look at the diagram and see if you think that you can attend to one data variable at a time with this symbol combination.
Credit: MacEachren, et al. 1998

Researchers have also suggested several new visual variables that might be particularly useful for representing uncertainty: crispness and transparency (see Figure, below.

An example of a map with varying opacity to represent varying levels of uncertainty.
Figure This example uses different levels of transparency to represent different levels of error in an integrated representation of uncertainty. Areas with a larger error are more difficult to "see through.
Credit: MacEachren, et al. 1995

A final method for representing data uncertainty is animation. In this type of representation, the map user is typically shown a series of realizations (i.e., possible versions of the data) that could be 'true' based on the level of uncertainty we have about the data (see movie below).

You must have Quicktime to view the movie.

If the movie does not appear on your screen try following this link to the data uncertainty movie.

This movie depicts both a series of ten possible approximations (i.e., realizations) of an elevation surface based on the uncertainty of a digital elevation model and the least-cost path of moving through that terrain (Ehlschlaeger et al. 1997). You can see the uncertainty in the elevation through the movement of the red contour lines between realizations. The least cost path is symbolized with a white line. Also, notice how the white line moves fairly substantially throughout the movie; this gives you an idea of how data uncertainty can affect the outcome of an analysis and why it is important to try to communicate information about uncertainty to decision makers.

Recommended Readings

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

  • MacEachren, A.M. 1992. "Visualizing uncertain information." Cartographic Perspectives. 13:10-19.
  • MacEachren, A.M. et al. 1998. "Visualizing georeferenced data: representing reliability of health statistics." Environment and Planning A. 30:1547-61.