While univariate maps are both standard and widespread, there are limitations to their uses. Bivariate maps have the potential to reveal spatial relationships and patterns between two variables on a single map more effectively than by using two side-by-side univariate maps. Bivariate maps can make use of a variety of symbol strategies, such as color combinations, shaded proportional symbols, shaded cartograms, split symbols, shaded isolines, or star plots. Though they can represent any pairing of thematic variables, they are typically employed to examine the relationships between socioeconomic variables, such as elderly populations and ethnic minorities, or levels of educational attainment and household income.

Bivariate choropleth mapping is a relatively recent cartographic method, dating to 1974, when the US Census Bureau saw value in combining two data sets into one map by superimposing two choropleth maps. This technique, called the overlay, crisscross, merge, or crossing, combines two maps along with their color schemes to produce a new map with a new set of colors. Although the maps were aesthetically pleasing, they were strongly criticized as difficult to interpret, as cartographers had no literature to guide their interpretations and relied on their own judgment and that of colleagues. More recently, techniques for drawing bivariate choropleth overlays have improved, and studies have demonstrated that effective color schemes can greatly enhance their readability. Nevertheless, they still lack sophistication for the interrogation of data relationships. This research seeks to explore and demonstrate various methods for bivariate and multivariate maps through four papers.

The first paper encourages thoughtfulness on the part of the mapmaker concerning the purpose of the bivariate map. Trumbo noted that effective map design (including color selection) is directly informed by the intended goal or use of the map (i.e., what questions might the map answer), and he identified three common spatial relationships that can be displayed by a bivariate choropleth: inverse relationships, a range of one variable within another, and direct relationships. Each is best suited to answering different map readers’ questions. Trumbo also suggested sample color palettes to focus the map readers attention on pertinent data. In consultation with Trumbo, this dissertation extends his ideas, first by creating focal models that illustrate his three spatial relationships. This dissertation then constructs sample maps to examine each of the focal models, and compares each model by mapping the same two data sets (of obesity and inactivity). The researcher then investigated the visual differences in each of the resulting maps, and asked spatial questions regarding the relationships between obesity and inactivity. This work validates Trumbo’s ideas on bivariate choropleth map design, and aims to guide cartographers towards making color choices by linking their map purpose to the appropriate focal model.

The second paper explores and demonstrates superimposing statistical analytics over a bivariate legend to create a legend that conveys both classification method and the underlying bivariate distributions. Conventional bivariate legends typically show only a generalized graphic revealing theoretical data relationships. Using simple scatterplots statistical indicators of covariance can be plotted as points directly on to the choropleth bivariate legend. This allows map readers to not only compare aggregate magnitudes between the two variables but also visualize disaggregate distributions that may represent statistical normality in the data as well as skewness, and linearity. In addition, the covariance distributions can direct class interval selection, or at least inform the reader of which classes represent data abundance or data sparsity. The legends demonstrated here convey classification method and bivariate distributions to the mapreader more clearly than a traditional bivariate legend.

The third paper demonstrates a bivariate relationship between land use and land cover using a gridded nested symbology. The concepts of land use and land cover convey information about a landscape. Although land use and land cover are different concepts, the terms have become intermingled and often used interchangeably in GIScience, resulting in a simplified one-to-one relationship that can be visualized using univariate mapping techniques. This research posits that the relationships between land use and land cover are complex, many-to-many relationships, and can be represented bivariately. Land cover is determined by the direct observation of the earth’s surface, resulting in categories such as forest, wetland, and development. Land use by contrast is a socioeconomic interpretation of the activities that take place on that surface, with categories such as residential, commercial, and agricultural. Complications arise when these categories overlap. For example, a forested area can be used for recreation, grazing, or timber production. A residential area can be located within a forest, a grazing plain, or a developed area. A bivariate representation can be useful in conveying these overlapping categories.

The fourth paper introduces bivariate and multivariate symbologies to aid visualization of social vulnerability data produced by the Centers for Disease Control and Prevention (CDC). The Social Vulnerability Index was developed to aid planners and emergency responders when identifying vulnerable segments of the population. The index includes an overall social vulnerability ranking as well as four individual themes: socioeconomic, household composition & disability, ethnicity & language, and housing & transportation. This makes the SVI dataset multivariate, but it is typically viewed using just one theme per map. This paper explores a suite of cartographic techniques that can represent the SVI beyond the univariate view. Specifically, three techniques are recommended: i) bivariate mapping to illustrate overall vulnerability and population density, ii) multivariate mapping using cartographic glyphs to disaggregate levels of the four vulnerability themes, and iii) visual analytics using Euler diagrams to overlap the vulnerability themes. The CDC’s SVI, and by extension, vulnerability indices in other countries, can be viewed in a variety of cartographic forms that illustrate the location of vulnerable groups of society. Viewing data from various perspectives can facilitate the understanding and analysis of the growing amount and complexity of data.

Taken together, these four exploratory demonstrations are hoped to stimulate thought and conversation among cartographers as to possibilities for bivariate and multivariate maps, beginning with a clear understanding of the map’s purpose, and expanding to consider bivariate legends that convey classification method and data distribution, and finally including visual analytics that complement spatial data by displaying data relationships and frequencies.

The feature image is from Cartographic Perspectives.