- Email: [email protected]
Thematic Maps in Geography
Thematic Maps in Geography David Forrest, School of Geographical and Earth Sciences, University of Glasgow, Glasgow, UK Ó 2015 Elsevier Ltd. All rights reserved. This article is a revision of the previous edition article by M. Monmonier, volume 23, pp. 15636–15641, Ó 2001, Elsevier Ltd.
Abstract Thematic maps represent information about a specific topic or about the relationship between topics. Producing effective thematic maps relies on selecting an appropriate base map and an understanding of the nature of the data being mapped. Once the representation method is selected, the individual symbols need to be designed, using variations in the visual or graphic variables. Having introduced these concepts, I go on to discuss basic strategies for representing data using point, line, and area symbols.
Introduction Maps can be divided into three groups: topographic or reference maps; special purpose maps; and special topic or thematic maps. These three groups are closely related to three major types of map-use tasks (Keates, 1996). Topographic or reference maps are used to find out information such as the location of a place and, in theory at least, represent a balanced view of the physical and cultural landscape, including coastlines, roads, rivers, settlements, boundaries, etc. Special purpose maps are mostly associated with wayfinding, some being associated with trained users, such as hydrographic and aeronautical charts, and others with broader user groups, such as road and tourist maps. Sometimes referred to as ‘special topic’ maps, as the name implies, thematic maps emphasize a topic or theme, such as soils or population, and are used where there is a desire to learn about a particular topic. The topic can be relatively broad, such as global population distribution, or very narrowly focused, as for a map showing infant mortality for a specific year by districts within a city. It is also possible to show the relationship between phenomena, for example, a map showing how educational attainment and income levels compare and relate across a region. Comparatively rare at the outset of the nineteenth century, thematic maps as a group have become more numerous, varied, and intellectually richer as data have become available and representation techniques have developed (Robinson, 1982), and the current popularity of map ‘mash-ups’ on the World Wide Web has brought them to a much wider audience. This article examines the distinctive elements of thematic maps, including principal strategies and pitfalls.
Elements of Thematic Mapping Thematic maps have two main components: a base map and the thematic overlay. Typically the base information comes from topographic or general purpose mapping, most likely today in the form of a cartographic database. The special topic information comes from a much wider range of sources. Specific field surveys may have been carried out on features such as geology, or vegetation, or nonmap sources such as government census, and other databases of attribute
260
information that have some spatial reference may be used. In terms of map design, two approaches can be taken. In some cases, an integrated approach is used where reference and topic information is considered together and specific symbols chosen to represent each feature appropriately. Alternatively, in many cases, the base map is used with little or no modification, or perhaps all just reduced to gray, and the special topic information is overlaid on this base, typically using stronger colors. Many examples of the latter approach can be seen today using Google Maps as the base, overlaid by markers of thematic information. Regardless of which approach is taken, the aim of map design is to create a visual hierarchy of information, with the base information less visually prominent than the thematic component, so that the user may focus on the specific distribution or relationship, as shown in Figure 1.
An Appropriate Map Projection is Essential Because the Earth is spherical and most maps are flat, the base map distorts the geometry of boundaries and other reference features (Maling, 1992). The amount of distortion depends in a large measure on the map’s scale, defined as the ratio of distance on the map to distance on the Earth. On a ‘largescale’ map covering a small area, such as a neighborhood or archaeological excavation, distortion will be minimal. By contrast, a ‘small-scale’ map covering a large area, such as a continent, hemisphere, or the entire World, must distort large shapes, distances, and directions, and may also distort angles and areas. By selecting an appropriate projection, the map author can avoid distortions that are likely to mislead readers. At larger scale, certainly at 1:250 000 scale and larger, it is likely that national topographic mapping will be used as the base, without any change of projection. At smaller scales, for most purposes in thematic mapping, an ‘equivalent’ or equal-area projection should be selected, but frequently authors simply use what is available, which can lead to concerns about fair representation of information. Often a distinct disadvantage of using readily available Web mapping (such as Google Maps or Bing Maps) as a basis for thematic maps is that the projections used for display are not equal area.
International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Volume 24
http://dx.doi.org/10.1016/B978-0-08-097086-8.72069-1
Thematic Maps in Geography
261
data. It is also quite likely that boundaries will have altered over time, so care is required to ensure an appropriate set of boundaries is used. For some data sets it may be possible to use postal or zip codes to relate the topic information to a spatial data set. The Internet has greatly increased the availability of suitable base data sets, but beyond nationalor state-level boundaries it may be difficult to find an appropriate data set for many parts of the world, and often there are quite high prices for detailed boundary data.
Base map
Understanding the Data to be Mapped Thematic overlay
New York Los Angeles Mexico City
London Amsterdam Frankfurt Seoul Tokyo Zurich Miami Paris Singapore Madrid São Paulo
Sydney
Thematic map (base map + overlay)
New York Los Angeles Mexico City
London Amsterdam Frankfurt Seoul Tokyo Zurich Miami Paris Singapore Madrid São Paulo
World cities, c.1995 The world’s 15 most important financial and business centers Figure 1 overlay.
Sydney
Global financial center Multinational, regional center Important national center
A thematic map consists of a base map and a thematic
Geocoding In order to map data, there must be a way to plot the data on a base map. Where data have been expressly collected for mapping, this is likely to be straightforward. In other cases the map maker may have to create a link between the topic information and the base map. For census and many other socioeconomic data sets, the data have been gathered based on some form of political or administrative units, such as countries, states, wards, etc., depending on the scale of the data. As long as there is a field (attribute) in the data set that matches one in an appropriate boundary file, then the geocoding process is simply a matter of linking the attribute data to the spatial data (Goldberg, 2008). However, often there can be imprecise definitions of location in thematic data sets which may require manual effort to resolve any nonmatched
The data will likely require some processing and/or classification in order to be in a suitable form for mapping. The author must have an understanding of the nature of the data so that appropriate representation methods and symbols can be specified. First to consider is the spatial nature of the phenomena. Generally speaking, we can identify four types of spatial distribution: phenomena can be found a specific point location, or at least a location considered to be a point at the scale of mapping (such as a city on a very small-scale map); they can be distributed along lines; they can fill an area defined by some form of boundaries; or they can vary continuously over the surface. In most cases, the spatial data we have about the phenomena will be points, lines, or area boundaries. The relationship between the phenomena and the spatial data may not always be simple. For example, people live at specific locations, but typically the data we have is collected for enumeration areas, often to protect individual anonymity. So, although we know the data are about a point phenomenon, what we have for mapping relates to bounded areas. Similarly, it is not possible to collect data for every possible point over a surface, so data may be a sample of points, or lines on the surface. This relationship between the phenomenon and the spatial data is often an indirect one as frequently we are dealing with processed data or secondary sources. In choosing an appropriate mapping technique, it is important to think about what we are trying to map, not just the data we have. The second aspect to consider is the nature of the attribute we are mapping. Often this is discussed in terms of the ‘level of measurement’ of the attribute. Many texts recognize four levels of measurement: nominal, ordinal, interval, and ratio. Nominal or qualitative data are where the distinction between members of the data set is by some form of naming or categorization; such as crop type or ethnic origin. Ordinal data are where there is some ordering or ranking of the data, such as, for settlements: National Capital, State Capital, County town, etc. Interval and ratio measurements are both quantitative and are often considered together, the key difference being the origin of the scale and how appropriate various mathematical operators are on the scale. This simple classification is satisfactory in many cases, but Chrisman (2002) and Forrest (1999) considerably extend the classification to help determine appropriate operations on and representations of the data. For example, it is frequently necessary to distinguish between count data, where the total number present in an area is mapped, and intensity data where the relative density or proportion of a phenomenon is mapped, even though both types are numerical and measured on a ratio measurement scale.
262
Thematic Maps in Geography
Issues relating to this difference between count data and intensity data are well illustrated by Figure 2. All three maps essentially illustrate the same phenomena, infant mortality in the eastern half of the United States. At the left, proportional circles describe differences in the number of infant deaths; a bigger circle unambiguously representing more deaths for that state than a smaller circle. In the center, a gray-tone treatment of the same data yields a potentially misleading map with dark symbols for states with relatively large numbers of deaths and comparatively light shades for states with fewer deaths. The dark tones suggest a health crisis in New York, Florida, and other relatively populous states and comparatively benign conditions in less-populous states such as Alabama and Mississippi. By contrast, the gray tones of the right-hand map offer a far more realistic portrait of the geographic variations in infant mortality which adjusts infant deaths for the number of live births. This recognizes that the size and population of the state will have an impact on our perception of the data. By relating the infant deaths to a more meaningful variable and mapping the proportion, we are in effect normalizing the data and removing the artifact of variable size states. If all states were the same size and population evenly distributed, we would not have to worry about such issues, but this is rarely the case. Once the relationship among phenomenon, spatial data, and attribute measurement is understood, the map maker can choose an appropriate representation method. In many cases there is little choice, but, as we have seen in the example above, in some cases there may be several options (see Section ‘Principle Cartographic Strategies’).
The Visual or Graphic Variables Having chosen the representation method, the individual symbols representing each class of information need to be designed or chosen. These symbols are the language of the
Infant deaths, 1995 (thousands)
map – the way the map maker communicates information to the reader. Jacques Bertin (1983), a French semiologist who proposed a formal theory of graphic language, recognized eight visual variables: the two variables of location in the visual field (x- and y-coordinates) and six ‘retinal’ variables portraying a feature’s character. The six retinal variables described by Bertin are size, shape, orientation, texture, color hue, and color lightness. Other cartographers have since developed Bertin’s theory to include additional variables, such as the generally recognized third variable of color – color saturation, pattern, focus (relating to the sharpness of the symbol), and others (e.g., MacEachren, 1995). To some extent, how much Bertin’s original set of variables should be extended depends on the interpretation of the variables. For example, some authors do not consider shape to be a possible variable for area symbols as the external shape of the area cannot normally change, preferring to introduce the variable ‘pattern’ for variation in the shape of the component elements covering the area, whereas others accept that the use of ‘shape’ refers directly to such components (as Bertin did), making ‘pattern’ unnecessary. More recently, consideration has been given to variables that are possible on interactive computer displays, such as motion, duration, and synchronization which are not possible on paper maps (MacEachren, 1995; Slocum et al., 2009). While such dynamic variables must be viewed over time, their intention is to represent some other variable, not temporal change. Table 1 summarizes the suitability of Bertin’s six retinal variables for representing attributes with different levels of measurement. Generally speaking, it becomes obvious that those variables suitable for representing qualitative data are less suitable for representing quantitative data, and vice versa. If even such basic guidelines were followed by map authors, we would see far fewer maps representing data in inappropriate ways.
Infant mortality rate, 1995 (deaths per 100 000 live births)
Infant deaths, 1995 (thousands)
New York
Rhode Island
Delaware
D.C.
100
38–91
5.2–5.6%
500
143–395
6.4–7.5%
1000
423–642
7.7–8.9%
670–935
9.2–10.4%
Mississippi
Alabama 2000
Florida
1,072–2,084
15.9% U.S. mean = 7.6%
Figure 2 Comparative treatment of count (left and center) and intensity (right) data with symbols varying in size (left) and colour lightness (centre and right). Misuse of intensity symbols for count data on the center map yields a misleading pattern.
Thematic Maps in Geography
Table 1
263
Use of visual variables for different types of attribute measurement
Measurement
Nominal
Ordinal
Interval/Ratio
Visual variable Size Shape
Poor Extensive use
Extensive use Poor
Orientation Texture Color hue
Good Some use Extensive use
Usable Some use, generally combined with size Poor Usable Some use
Color lightness
Poor
Usable
While Bertin’s visual variables have had significant influence on cartographic textbooks, further aspects of his theories of graphics are often overlooked although they do provide a key to what we are often trying to achieve with our symbols. Bertin also discussed the perception of the image and identified four possibilities. In associative perception, the impression is of similarity; we can see there are differences, but association between symbols is emphasized by having relatively low contrast between them. On the other hand, with selective perception we immediately separate the visual field into two (or more) groups, but none is perceived as more important than the other; typically this process involves greater contrast. Ordered perception is where we can see a clear ranking, in that one feature is seen as more important than another. Finally quantitative perception is where we get some impression of the relative numeric value of the phenomena. Figure 3 illustrates these four properties with the examples of point symbols, but this could also be done for lines or areas and use different graphic variables.
Principle Cartographic Strategies Although the range of possible map topics is limitless and interactive graphics has greatly expanded the possible methods for visualizing geospatial data, for static mapping, an examination of printed atlases and cartographic textbooks will confirm
(a)
(b)
(c)
(d)
Figure 3 Bertin’s classification of image perception: (a) associative, (b) selective, (c) ordered, (d) quantitative.
Poor Limited use Limited, but can use spectral ordering Extensive use
that relatively few commonly used cartographic representation methods are in use. These methods (sometimes called different types of maps, rather than methods) are sufficient to portray most combinations of phenomena and mappable data. Although there are different ways to classify them, they will be treated here by way of the point, line, area, and surface representation methods. These representation methods are summarized in Figure 4.
Representations Using Point Symbols Seemingly a simple method, the dot distribution method represents information by a series of small dots, all of the same size and shape. It is possible, but uncommon for each dot to represent one individual; generally each dot represents a number of occurrences of the phenomena. For example, a dot may represent 100 people. Three issues need to be resolved: what is the ratio of features per dot, what size should the dots be, and where should they be placed. The first and second are interrelated. The dots need to be large enough for isolated dots to be noticed, but not too large, because it is the distribution pattern that is important, not the individual dot. Ideally in the densest areas dots should coalesce to become almost solid. Where to place the dots is often the biggest challenge. Although many computer systems can produce ‘dot maps,’ generally they use a random number generator to scatter dots within an enumeration area, which is not effective. Further information, such as a topographic map, is required to decide where the phenomenon most likely occurs. A good dot map is an excellent way of representing distributions, but the effort required to logically place the dots limits their use. A more common way of representing quantitative data by point symbols is the proportional or graduated symbol. Here the size of the symbol varies in relation to the value of the topic, as shown on the left in Figure 2. With proportional symbols, this variation in size is in direct proportion to the value, such as the area of a circle or square increasing in direct relation to the value. Unfortunately, where there is a great data range, it can be impossible to create a scale where the smallest symbols are visible, but the largest are not too big to dominate the map. The solution is to divide the data into classes (much like choropleth maps) and have a fixed size symbols for each class, creating a set of graduated symbols. The most common symbol is the circle, which has a number of advantages, but other shapes are also used. Our perception of the relative size of squares is better than circles, so their use should be
264
Thematic Maps in Geography
Point representation methods
Area representation methods
(a) Dot distribution
(a) Isolated areas
(b) Categorised (b) Unclassed (c) Ranked
(d) Proportional or graduated
(c) Chorochromatic (colour patch)
(e) Subdivided quantitative (d) Graded series (choropleth) 35 50
24
40
(f) Spot values
Line representation methods
(e) Layered colour series not illustrated
(f) Area cartogram (a) Boundaries
Surface representation methods
(b) Linked network
(a) Variable tone surface (c) Tree network
50
(d) Isolines (contours) (b) Shaded surface (eg. hill shading)
(e) Flow lines
(f) Unstructured line symbols
(c) Block diagram
Figure 4 Basic cartographic representation methods (after Forrest, D., 1999. Geographic Information: its nature, classification and cartographic representation. Cartographica 36 (2), 31–53.).
more popular than it is. There is some use of pictographic symbols, particularly in journalistic maps, but our ability to estimate the relative value of more complex shapes is poor, so they are probably best avoided. Where the data for the location can be broken down into components, a number of options are possible, such as pie
charts, or various other graphic devices located at points. These can either be fixed in size, with the focus being on the relative proportions of the components, or varied in size like proportional and graduated symbols to convey both the overall total distribution and the breakdown of components.
Thematic Maps in Geography
For nonnumerical data, we simply show each category by varying the shape and/or hue of the symbol. The key design aspect here is to make the symbols appear different, but equivalent. When appropriate, pictographic symbols can be exploited here as the user can understand the meaning of the symbols without referring to the legend.
Representations Using Line Symbols Boundaries are a common feature represented by lines. Generally the data about these are hierarchical, so the symbols chosen should emphasize the rank of the individual boundary. This could be done by simply varying the thickness of the lines, but most often a combination of thickness and line pattern (dashes) is used, with shorter, thinner dashes for lower-ranked boundaries. Representing quantities by line symbols can either involve a network of lines or flow lines simply connecting pairs of points or areas. This tends to get little coverage in cartographic texts, perhaps because, in the writer’s experience, they are often challenging to both design and produce. The obvious graphic solution is to vary the width of the lines in proportion to the variable being mapped, but there is a limit to the range of data that can be treated in this manner. One problem is that if two lines have the same value, but differ in length, the longer one may give the impression of having greater value. With the flow type of map, crossing lines pose further problems for both design and perception. Another way of representing route information is a linear cartogram, the most famous example being the London Underground map, but a similar style has been used for many metropolitan subway systems, rail and bus networks. Space is distorted for clarity and simplicity purposes, often with the angle of lines limited to a few directions (usually 6 or 8). Scale is varied to allow space in more detailed areas, often city centers, where routes converge and stops are closer. Scale can be reduced where there is less to show, such as in the outer suburbs. Typically each route is shown by a different color. Often there is no other information, but major geographical features, such as the River Thames in London, may be included in simplified form.
Representations Using Area Symbols Many maps represent qualitative data about areas, such as those about geology, soils, and vegetation. There is no generally accepted term for this form of cartographic representation. In some U.K. textbooks, the term ‘chorochromatic’ has been used and some North American texts use terms such as ‘color-patch’ or ‘mosaic’ maps, both of which adequately describe their appearance. Unfortunately some use the term ‘choropleth map’ (see below), but should only be applied to quantitative maps. At larger scales, the design of this type of mapping is often demanding due to the large number of classes and subclasses that can be present. Using many classes requires imaginative use of the graphic variables to ensure that a balanced representation is achieved where no class should appear more important than another. With a classification hierarchy, a major concern is to ensure that subclasses are clearly associated with others within the same overall category and
265
have a greater difference to those in other categories. Often this is solved by using a main color (hue) to distinguish the top-level categories and use of patterns or texture to differentiate subclasses. Probably one of the most widely used techniques for thematic mapping is the choropleth map, as shown on the right of Figure 2. This represents quantitative data for areas, usually some form of administrative unit, such as country, state, wards, census tract, or some other areal unit. They are popular partly because there are enormous amounts of numerical data available for areal units and, assuming the boundary data are available, they are easy to produce using desktop mapping systems and Geographical Information System (GIS). This ease of production has also led to great misuse, typically using data that are affected by the variation in zone sizes as discussed above in terms of representation, but also by poor selection of the area symbols. The typical approach is to represent the data values by light-to-dark series of ordered gray tones or varying the lightness of a single hue, such as shades of green from light to dark. With a single hue, the number of classes that the user can easily identify is generally four or five; if more classes are required, then a part spectral scheme can be adopted, perhaps going from yellow, through oranges, to reds. For showing data such as rates of change where there can be both positive and negative values, two contrasting hues can be used, such as red and blue, becoming darker as the value increases in each direction. Sometimes a neutral color can separate the two scales, representing no, or minimal, change. Such a scheme can also be applied to emphasize variation from the mean, such as divorce rates, where the regional average could be used as the dividing point. In recent times, a ‘traffic light’ color scheme has become popular, using green for good/above average, yellow for neutral, and red for poor/below average, particularly when applied to performance data, or business data such as sales figures. An excellent resource for investigating color choices for choropleth maps (and some other types) is the ColorBrewer Web site (Brewer and Harrower, 2009). Apart from the choice of color scheme, the two key decisions are the number of classes to depict and the choice of class intervals. The fewer the classes the more generalized the representation; too many classes and the user starts to have some difficulty in distinguishing among them. It is also possible, but less common, to produce choropleth maps without classes (see Kennedy, 1994). Because different classifications of the data can produce radically different spatial patterns, the efficiency and effectiveness of a choropleth map depends heavily on its categories (Evans, 1997). Common approaches include equal intervals, where the data range is divided equally, and quantiles, where the same number of zones is included in each class. The choice would not be difficult if data were evenly or normally distributed, but often it is not, and highly skewed data sets present significant difficulties in selection of appropriate classes. Mechanical selection of classes will often result in rather meaningless class boundaries. A wise practice, often ignored, is the use of inherently meaningful category breaks, such as zero on a map of migration rates, or the national mean on a map of per capita income (Monmonier, 1993).
266
Thematic Maps in Geography
Figure 5 Area cartograms adjust the size of areal units according to a transforming variable such as population. Contiguous cartograms (left) may distort shape severely, whereas non-contiguous solutions (right) preserve shape but lose contiguity.
A major disadvantage of choropleth maps is that the boundaries often bear no relation to the actual spatial distribution of the phenomenon. Dasymetric maps appear graphically similar to choropleth maps, in that the data are represented in a similar manner, but in this case the boundaries are drawn to reflect uniform areas in the distribution of the specific phenomenon. Clearly, producing such boundaries requires additional information and effort compared to the choropleth map, which goes a long way to explain their limited use, especially when maps of many variables are to be produced. On an ‘area cartogram,’ the size of the areal units being mapped varies according to population or some other transforming variable. As Figure 5 illustrates, noncontiguous cartograms sacrifice contiguity for shape whereas contiguous area cartograms may require severe distortions of shape in order to retain contiguity. Unless the reader has a good grasp of the original geography, the distorted shapes may make the size differences meaningless. This can effectively be countered by showing both a geographically correct map (typically choropleth) adjacent to the cartogram, so that an easy comparison can be made. Assuming that the reader appreciates the distortion in geography, cartograms make a dramatic demonstration of disparities in aspects such as population, wealth, education, or military spending. An isodemographic map – a populationbased area cartogram – can also provide a useful base map for representation of other socioeconomic data, election outcomes, and public health (Dorling, 1994). Adjusting the base map for population in this way diminishes the exaggerated impact of large areas with small populations and ensures small, densely populated areas are visible. The availability of software to generate effective contiguous cartograms has significantly increased their use.
equal vertical interval between contour lines. In this case, the user can appreciate slopes by variations in the spacing of the contours. In many thematic mapping situations, nonequal intervals are used, so the nature of the ‘surface’ can be harder to visualize. This approach is often adopted because the data values are highly skewed or because the map maker wants to emphasize some particular values. An extension of the isarithmic map is to apply a scale of colors to the zones between isarithms. The choice of colors is similar to that for choropleth maps, but more classes, with smaller color difference is successful here due to the nested nature of adjacent zones. GIS and surface modeling software make extensive use of a chromatic scale with large numbers of classes. Generally the data range is automatically divided by the number of steps in the scale, often resulting in unwieldy values in the legend, rather than selecting a simpler, more rounded interval. Like the surface being represented, there is some value in adopting a representation method that also varies continuously. In terrain mapping, hill shading uses a continuously varying gray tone to represent relief. In its simplest form, the steeper the slope the darker the shading. To give a better impression of the three-dimensional nature of relief, such shading is often modified to have an assumed light source coming from the top left of the map, but this is probably not appropriate for other surfaces. Other techniques of representing continuously varying surfaces depend on a nonorthogonal view of the mapped area. This includes fishnet plots and fully rendered block diagrams.
Conclusions The power of the computer and the development of GIS and scientific visualization software have lead to a significant development of representation methods in recent years. Some of these possibilities have been known for a long time but have been too costly or impractical to carry out manually. Many of the newer methods rely heavily on interactivity and so are beyond the scope of this article. With modern systems, there is more scope to experiment with representation, as a change of color, or even representation method can happen in an instant with the click of a button. Despite these advances, the basic principles of thematic mapping, understanding data to be mapped, and proper use of the visual variables remain as important as ever.
See also: Cartographic Visualization; Cartography; Dynamic Mapping in Geography; Geographic Information Systems; Spatial Data; Tactile Maps in Geography.
Representations of Continually Varying Surfaces Sometimes referred to as contour maps, isarithmic maps refer to maps that represent continuously varying quantities over the surface by lines of equal values. Strictly, the term contour should be used only when the variable mapped is terrain height. Common terms are used for some variables, such as isobars for pressure. Terrain contour maps typically use an
Bibliography Bertin, J., 1983. Semiology of Graphics: Diagrams, Networks, Maps. University of Wisconsin Press, Madison, WI. Reprinted 2010 by ESRI Press, Redland, CA. Brewer, C.A., 2005. Designing Better Maps: A Guide for GIS Users. ESRI Press, Redlands, CA. Brewer, C.A., Harrower, M., 2009. ColorBrewer2. http://colorbrewer2.org/.
Thematic Maps in Geography
Chrisman, N., 2002. Exploring Geographic Information, second ed. Wiley, New York. Dent, B.D., 1999. Cartography: Thematic Map Design, fifth ed. William C. Brown, Boston. Dorling, D., 1994. Cartograms for visualising human geography. In: Hearnshaw, H.M., Unwin, D.J. (Eds.), Visualization in Geographical Information Systems. Wiley, Chichester. Evans, I.S., 1997. The selection of class intervals. Transactions, Institute of British Geographers. New Series 2, 98–124. Forrest, D., 1999. Geographic Information: its nature, classification and cartographic representation. Cartographica 36 (2), 31–53. Goldberg, D.W., 2008. A Geocoding Best Practice Guide. North American Association of Central Cancer Registries, Inc. Keates, J.S., 1996. Understanding Maps. Addison Wesley Longman Ltd, Harlow.
267
Kennedy, S., 1994. Unclassed choropleth maps revisited: some guidelines for the construction of unclassed and classed choropleth maps. Cartographica 31 (1), 16–25. MacEachren, A.M., 1995. How Maps Work: Representation, Visualization, and Design. Guildford, New York. Maling, D.H., 1992. Coordinate Systems and Map Projections, second ed. Pergamon, Oxford. Monmonier, M., 1993. Mapping It Out: Expository Cartography for the Humanities and Social Sciences. University of Chicago Press, Chicago. Robinson, A.H., 1982. Early Thematic Mapping in the History of Cartography. University of Chicago Press, Chicago. Slocum, T.A., McMaster, R.B., Kessler, F.C., Howard, H.H., 2009. Thematic Cartography and Geovisualization, third ed. Pearson Prentice Hall, Upper Saddle River, NJ.
Abstract Thematic maps represent information about a specific topic or about the relationship between topics. Producing effective thematic maps relies on selecting an appropriate base map and an understanding of the nature of the data being mapped. Once the representation method is selected, the individual symbols need to be designed, using variations in the visual or graphic variables. Having introduced these concepts, I go on to discuss basic strategies for representing data using point, line, and area symbols.
Introduction Maps can be divided into three groups: topographic or reference maps; special purpose maps; and special topic or thematic maps. These three groups are closely related to three major types of map-use tasks (Keates, 1996). Topographic or reference maps are used to find out information such as the location of a place and, in theory at least, represent a balanced view of the physical and cultural landscape, including coastlines, roads, rivers, settlements, boundaries, etc. Special purpose maps are mostly associated with wayfinding, some being associated with trained users, such as hydrographic and aeronautical charts, and others with broader user groups, such as road and tourist maps. Sometimes referred to as ‘special topic’ maps, as the name implies, thematic maps emphasize a topic or theme, such as soils or population, and are used where there is a desire to learn about a particular topic. The topic can be relatively broad, such as global population distribution, or very narrowly focused, as for a map showing infant mortality for a specific year by districts within a city. It is also possible to show the relationship between phenomena, for example, a map showing how educational attainment and income levels compare and relate across a region. Comparatively rare at the outset of the nineteenth century, thematic maps as a group have become more numerous, varied, and intellectually richer as data have become available and representation techniques have developed (Robinson, 1982), and the current popularity of map ‘mash-ups’ on the World Wide Web has brought them to a much wider audience. This article examines the distinctive elements of thematic maps, including principal strategies and pitfalls.
Elements of Thematic Mapping Thematic maps have two main components: a base map and the thematic overlay. Typically the base information comes from topographic or general purpose mapping, most likely today in the form of a cartographic database. The special topic information comes from a much wider range of sources. Specific field surveys may have been carried out on features such as geology, or vegetation, or nonmap sources such as government census, and other databases of attribute
260
information that have some spatial reference may be used. In terms of map design, two approaches can be taken. In some cases, an integrated approach is used where reference and topic information is considered together and specific symbols chosen to represent each feature appropriately. Alternatively, in many cases, the base map is used with little or no modification, or perhaps all just reduced to gray, and the special topic information is overlaid on this base, typically using stronger colors. Many examples of the latter approach can be seen today using Google Maps as the base, overlaid by markers of thematic information. Regardless of which approach is taken, the aim of map design is to create a visual hierarchy of information, with the base information less visually prominent than the thematic component, so that the user may focus on the specific distribution or relationship, as shown in Figure 1.
An Appropriate Map Projection is Essential Because the Earth is spherical and most maps are flat, the base map distorts the geometry of boundaries and other reference features (Maling, 1992). The amount of distortion depends in a large measure on the map’s scale, defined as the ratio of distance on the map to distance on the Earth. On a ‘largescale’ map covering a small area, such as a neighborhood or archaeological excavation, distortion will be minimal. By contrast, a ‘small-scale’ map covering a large area, such as a continent, hemisphere, or the entire World, must distort large shapes, distances, and directions, and may also distort angles and areas. By selecting an appropriate projection, the map author can avoid distortions that are likely to mislead readers. At larger scale, certainly at 1:250 000 scale and larger, it is likely that national topographic mapping will be used as the base, without any change of projection. At smaller scales, for most purposes in thematic mapping, an ‘equivalent’ or equal-area projection should be selected, but frequently authors simply use what is available, which can lead to concerns about fair representation of information. Often a distinct disadvantage of using readily available Web mapping (such as Google Maps or Bing Maps) as a basis for thematic maps is that the projections used for display are not equal area.
International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Volume 24
http://dx.doi.org/10.1016/B978-0-08-097086-8.72069-1
Thematic Maps in Geography
261
data. It is also quite likely that boundaries will have altered over time, so care is required to ensure an appropriate set of boundaries is used. For some data sets it may be possible to use postal or zip codes to relate the topic information to a spatial data set. The Internet has greatly increased the availability of suitable base data sets, but beyond nationalor state-level boundaries it may be difficult to find an appropriate data set for many parts of the world, and often there are quite high prices for detailed boundary data.
Base map
Understanding the Data to be Mapped Thematic overlay
New York Los Angeles Mexico City
London Amsterdam Frankfurt Seoul Tokyo Zurich Miami Paris Singapore Madrid São Paulo
Sydney
Thematic map (base map + overlay)
New York Los Angeles Mexico City
London Amsterdam Frankfurt Seoul Tokyo Zurich Miami Paris Singapore Madrid São Paulo
World cities, c.1995 The world’s 15 most important financial and business centers Figure 1 overlay.
Sydney
Global financial center Multinational, regional center Important national center
A thematic map consists of a base map and a thematic
Geocoding In order to map data, there must be a way to plot the data on a base map. Where data have been expressly collected for mapping, this is likely to be straightforward. In other cases the map maker may have to create a link between the topic information and the base map. For census and many other socioeconomic data sets, the data have been gathered based on some form of political or administrative units, such as countries, states, wards, etc., depending on the scale of the data. As long as there is a field (attribute) in the data set that matches one in an appropriate boundary file, then the geocoding process is simply a matter of linking the attribute data to the spatial data (Goldberg, 2008). However, often there can be imprecise definitions of location in thematic data sets which may require manual effort to resolve any nonmatched
The data will likely require some processing and/or classification in order to be in a suitable form for mapping. The author must have an understanding of the nature of the data so that appropriate representation methods and symbols can be specified. First to consider is the spatial nature of the phenomena. Generally speaking, we can identify four types of spatial distribution: phenomena can be found a specific point location, or at least a location considered to be a point at the scale of mapping (such as a city on a very small-scale map); they can be distributed along lines; they can fill an area defined by some form of boundaries; or they can vary continuously over the surface. In most cases, the spatial data we have about the phenomena will be points, lines, or area boundaries. The relationship between the phenomena and the spatial data may not always be simple. For example, people live at specific locations, but typically the data we have is collected for enumeration areas, often to protect individual anonymity. So, although we know the data are about a point phenomenon, what we have for mapping relates to bounded areas. Similarly, it is not possible to collect data for every possible point over a surface, so data may be a sample of points, or lines on the surface. This relationship between the phenomenon and the spatial data is often an indirect one as frequently we are dealing with processed data or secondary sources. In choosing an appropriate mapping technique, it is important to think about what we are trying to map, not just the data we have. The second aspect to consider is the nature of the attribute we are mapping. Often this is discussed in terms of the ‘level of measurement’ of the attribute. Many texts recognize four levels of measurement: nominal, ordinal, interval, and ratio. Nominal or qualitative data are where the distinction between members of the data set is by some form of naming or categorization; such as crop type or ethnic origin. Ordinal data are where there is some ordering or ranking of the data, such as, for settlements: National Capital, State Capital, County town, etc. Interval and ratio measurements are both quantitative and are often considered together, the key difference being the origin of the scale and how appropriate various mathematical operators are on the scale. This simple classification is satisfactory in many cases, but Chrisman (2002) and Forrest (1999) considerably extend the classification to help determine appropriate operations on and representations of the data. For example, it is frequently necessary to distinguish between count data, where the total number present in an area is mapped, and intensity data where the relative density or proportion of a phenomenon is mapped, even though both types are numerical and measured on a ratio measurement scale.
262
Thematic Maps in Geography
Issues relating to this difference between count data and intensity data are well illustrated by Figure 2. All three maps essentially illustrate the same phenomena, infant mortality in the eastern half of the United States. At the left, proportional circles describe differences in the number of infant deaths; a bigger circle unambiguously representing more deaths for that state than a smaller circle. In the center, a gray-tone treatment of the same data yields a potentially misleading map with dark symbols for states with relatively large numbers of deaths and comparatively light shades for states with fewer deaths. The dark tones suggest a health crisis in New York, Florida, and other relatively populous states and comparatively benign conditions in less-populous states such as Alabama and Mississippi. By contrast, the gray tones of the right-hand map offer a far more realistic portrait of the geographic variations in infant mortality which adjusts infant deaths for the number of live births. This recognizes that the size and population of the state will have an impact on our perception of the data. By relating the infant deaths to a more meaningful variable and mapping the proportion, we are in effect normalizing the data and removing the artifact of variable size states. If all states were the same size and population evenly distributed, we would not have to worry about such issues, but this is rarely the case. Once the relationship among phenomenon, spatial data, and attribute measurement is understood, the map maker can choose an appropriate representation method. In many cases there is little choice, but, as we have seen in the example above, in some cases there may be several options (see Section ‘Principle Cartographic Strategies’).
The Visual or Graphic Variables Having chosen the representation method, the individual symbols representing each class of information need to be designed or chosen. These symbols are the language of the
Infant deaths, 1995 (thousands)
map – the way the map maker communicates information to the reader. Jacques Bertin (1983), a French semiologist who proposed a formal theory of graphic language, recognized eight visual variables: the two variables of location in the visual field (x- and y-coordinates) and six ‘retinal’ variables portraying a feature’s character. The six retinal variables described by Bertin are size, shape, orientation, texture, color hue, and color lightness. Other cartographers have since developed Bertin’s theory to include additional variables, such as the generally recognized third variable of color – color saturation, pattern, focus (relating to the sharpness of the symbol), and others (e.g., MacEachren, 1995). To some extent, how much Bertin’s original set of variables should be extended depends on the interpretation of the variables. For example, some authors do not consider shape to be a possible variable for area symbols as the external shape of the area cannot normally change, preferring to introduce the variable ‘pattern’ for variation in the shape of the component elements covering the area, whereas others accept that the use of ‘shape’ refers directly to such components (as Bertin did), making ‘pattern’ unnecessary. More recently, consideration has been given to variables that are possible on interactive computer displays, such as motion, duration, and synchronization which are not possible on paper maps (MacEachren, 1995; Slocum et al., 2009). While such dynamic variables must be viewed over time, their intention is to represent some other variable, not temporal change. Table 1 summarizes the suitability of Bertin’s six retinal variables for representing attributes with different levels of measurement. Generally speaking, it becomes obvious that those variables suitable for representing qualitative data are less suitable for representing quantitative data, and vice versa. If even such basic guidelines were followed by map authors, we would see far fewer maps representing data in inappropriate ways.
Infant mortality rate, 1995 (deaths per 100 000 live births)
Infant deaths, 1995 (thousands)
New York
Rhode Island
Delaware
D.C.
100
38–91
5.2–5.6%
500
143–395
6.4–7.5%
1000
423–642
7.7–8.9%
670–935
9.2–10.4%
Mississippi
Alabama 2000
Florida
1,072–2,084
15.9% U.S. mean = 7.6%
Figure 2 Comparative treatment of count (left and center) and intensity (right) data with symbols varying in size (left) and colour lightness (centre and right). Misuse of intensity symbols for count data on the center map yields a misleading pattern.
Thematic Maps in Geography
Table 1
263
Use of visual variables for different types of attribute measurement
Measurement
Nominal
Ordinal
Interval/Ratio
Visual variable Size Shape
Poor Extensive use
Extensive use Poor
Orientation Texture Color hue
Good Some use Extensive use
Usable Some use, generally combined with size Poor Usable Some use
Color lightness
Poor
Usable
While Bertin’s visual variables have had significant influence on cartographic textbooks, further aspects of his theories of graphics are often overlooked although they do provide a key to what we are often trying to achieve with our symbols. Bertin also discussed the perception of the image and identified four possibilities. In associative perception, the impression is of similarity; we can see there are differences, but association between symbols is emphasized by having relatively low contrast between them. On the other hand, with selective perception we immediately separate the visual field into two (or more) groups, but none is perceived as more important than the other; typically this process involves greater contrast. Ordered perception is where we can see a clear ranking, in that one feature is seen as more important than another. Finally quantitative perception is where we get some impression of the relative numeric value of the phenomena. Figure 3 illustrates these four properties with the examples of point symbols, but this could also be done for lines or areas and use different graphic variables.
Principle Cartographic Strategies Although the range of possible map topics is limitless and interactive graphics has greatly expanded the possible methods for visualizing geospatial data, for static mapping, an examination of printed atlases and cartographic textbooks will confirm
(a)
(b)
(c)
(d)
Figure 3 Bertin’s classification of image perception: (a) associative, (b) selective, (c) ordered, (d) quantitative.
Poor Limited use Limited, but can use spectral ordering Extensive use
that relatively few commonly used cartographic representation methods are in use. These methods (sometimes called different types of maps, rather than methods) are sufficient to portray most combinations of phenomena and mappable data. Although there are different ways to classify them, they will be treated here by way of the point, line, area, and surface representation methods. These representation methods are summarized in Figure 4.
Representations Using Point Symbols Seemingly a simple method, the dot distribution method represents information by a series of small dots, all of the same size and shape. It is possible, but uncommon for each dot to represent one individual; generally each dot represents a number of occurrences of the phenomena. For example, a dot may represent 100 people. Three issues need to be resolved: what is the ratio of features per dot, what size should the dots be, and where should they be placed. The first and second are interrelated. The dots need to be large enough for isolated dots to be noticed, but not too large, because it is the distribution pattern that is important, not the individual dot. Ideally in the densest areas dots should coalesce to become almost solid. Where to place the dots is often the biggest challenge. Although many computer systems can produce ‘dot maps,’ generally they use a random number generator to scatter dots within an enumeration area, which is not effective. Further information, such as a topographic map, is required to decide where the phenomenon most likely occurs. A good dot map is an excellent way of representing distributions, but the effort required to logically place the dots limits their use. A more common way of representing quantitative data by point symbols is the proportional or graduated symbol. Here the size of the symbol varies in relation to the value of the topic, as shown on the left in Figure 2. With proportional symbols, this variation in size is in direct proportion to the value, such as the area of a circle or square increasing in direct relation to the value. Unfortunately, where there is a great data range, it can be impossible to create a scale where the smallest symbols are visible, but the largest are not too big to dominate the map. The solution is to divide the data into classes (much like choropleth maps) and have a fixed size symbols for each class, creating a set of graduated symbols. The most common symbol is the circle, which has a number of advantages, but other shapes are also used. Our perception of the relative size of squares is better than circles, so their use should be
264
Thematic Maps in Geography
Point representation methods
Area representation methods
(a) Dot distribution
(a) Isolated areas
(b) Categorised (b) Unclassed (c) Ranked
(d) Proportional or graduated
(c) Chorochromatic (colour patch)
(e) Subdivided quantitative (d) Graded series (choropleth) 35 50
24
40
(f) Spot values
Line representation methods
(e) Layered colour series not illustrated
(f) Area cartogram (a) Boundaries
Surface representation methods
(b) Linked network
(a) Variable tone surface (c) Tree network
50
(d) Isolines (contours) (b) Shaded surface (eg. hill shading)
(e) Flow lines
(f) Unstructured line symbols
(c) Block diagram
Figure 4 Basic cartographic representation methods (after Forrest, D., 1999. Geographic Information: its nature, classification and cartographic representation. Cartographica 36 (2), 31–53.).
more popular than it is. There is some use of pictographic symbols, particularly in journalistic maps, but our ability to estimate the relative value of more complex shapes is poor, so they are probably best avoided. Where the data for the location can be broken down into components, a number of options are possible, such as pie
charts, or various other graphic devices located at points. These can either be fixed in size, with the focus being on the relative proportions of the components, or varied in size like proportional and graduated symbols to convey both the overall total distribution and the breakdown of components.
Thematic Maps in Geography
For nonnumerical data, we simply show each category by varying the shape and/or hue of the symbol. The key design aspect here is to make the symbols appear different, but equivalent. When appropriate, pictographic symbols can be exploited here as the user can understand the meaning of the symbols without referring to the legend.
Representations Using Line Symbols Boundaries are a common feature represented by lines. Generally the data about these are hierarchical, so the symbols chosen should emphasize the rank of the individual boundary. This could be done by simply varying the thickness of the lines, but most often a combination of thickness and line pattern (dashes) is used, with shorter, thinner dashes for lower-ranked boundaries. Representing quantities by line symbols can either involve a network of lines or flow lines simply connecting pairs of points or areas. This tends to get little coverage in cartographic texts, perhaps because, in the writer’s experience, they are often challenging to both design and produce. The obvious graphic solution is to vary the width of the lines in proportion to the variable being mapped, but there is a limit to the range of data that can be treated in this manner. One problem is that if two lines have the same value, but differ in length, the longer one may give the impression of having greater value. With the flow type of map, crossing lines pose further problems for both design and perception. Another way of representing route information is a linear cartogram, the most famous example being the London Underground map, but a similar style has been used for many metropolitan subway systems, rail and bus networks. Space is distorted for clarity and simplicity purposes, often with the angle of lines limited to a few directions (usually 6 or 8). Scale is varied to allow space in more detailed areas, often city centers, where routes converge and stops are closer. Scale can be reduced where there is less to show, such as in the outer suburbs. Typically each route is shown by a different color. Often there is no other information, but major geographical features, such as the River Thames in London, may be included in simplified form.
Representations Using Area Symbols Many maps represent qualitative data about areas, such as those about geology, soils, and vegetation. There is no generally accepted term for this form of cartographic representation. In some U.K. textbooks, the term ‘chorochromatic’ has been used and some North American texts use terms such as ‘color-patch’ or ‘mosaic’ maps, both of which adequately describe their appearance. Unfortunately some use the term ‘choropleth map’ (see below), but should only be applied to quantitative maps. At larger scales, the design of this type of mapping is often demanding due to the large number of classes and subclasses that can be present. Using many classes requires imaginative use of the graphic variables to ensure that a balanced representation is achieved where no class should appear more important than another. With a classification hierarchy, a major concern is to ensure that subclasses are clearly associated with others within the same overall category and
265
have a greater difference to those in other categories. Often this is solved by using a main color (hue) to distinguish the top-level categories and use of patterns or texture to differentiate subclasses. Probably one of the most widely used techniques for thematic mapping is the choropleth map, as shown on the right of Figure 2. This represents quantitative data for areas, usually some form of administrative unit, such as country, state, wards, census tract, or some other areal unit. They are popular partly because there are enormous amounts of numerical data available for areal units and, assuming the boundary data are available, they are easy to produce using desktop mapping systems and Geographical Information System (GIS). This ease of production has also led to great misuse, typically using data that are affected by the variation in zone sizes as discussed above in terms of representation, but also by poor selection of the area symbols. The typical approach is to represent the data values by light-to-dark series of ordered gray tones or varying the lightness of a single hue, such as shades of green from light to dark. With a single hue, the number of classes that the user can easily identify is generally four or five; if more classes are required, then a part spectral scheme can be adopted, perhaps going from yellow, through oranges, to reds. For showing data such as rates of change where there can be both positive and negative values, two contrasting hues can be used, such as red and blue, becoming darker as the value increases in each direction. Sometimes a neutral color can separate the two scales, representing no, or minimal, change. Such a scheme can also be applied to emphasize variation from the mean, such as divorce rates, where the regional average could be used as the dividing point. In recent times, a ‘traffic light’ color scheme has become popular, using green for good/above average, yellow for neutral, and red for poor/below average, particularly when applied to performance data, or business data such as sales figures. An excellent resource for investigating color choices for choropleth maps (and some other types) is the ColorBrewer Web site (Brewer and Harrower, 2009). Apart from the choice of color scheme, the two key decisions are the number of classes to depict and the choice of class intervals. The fewer the classes the more generalized the representation; too many classes and the user starts to have some difficulty in distinguishing among them. It is also possible, but less common, to produce choropleth maps without classes (see Kennedy, 1994). Because different classifications of the data can produce radically different spatial patterns, the efficiency and effectiveness of a choropleth map depends heavily on its categories (Evans, 1997). Common approaches include equal intervals, where the data range is divided equally, and quantiles, where the same number of zones is included in each class. The choice would not be difficult if data were evenly or normally distributed, but often it is not, and highly skewed data sets present significant difficulties in selection of appropriate classes. Mechanical selection of classes will often result in rather meaningless class boundaries. A wise practice, often ignored, is the use of inherently meaningful category breaks, such as zero on a map of migration rates, or the national mean on a map of per capita income (Monmonier, 1993).
266
Thematic Maps in Geography
Figure 5 Area cartograms adjust the size of areal units according to a transforming variable such as population. Contiguous cartograms (left) may distort shape severely, whereas non-contiguous solutions (right) preserve shape but lose contiguity.
A major disadvantage of choropleth maps is that the boundaries often bear no relation to the actual spatial distribution of the phenomenon. Dasymetric maps appear graphically similar to choropleth maps, in that the data are represented in a similar manner, but in this case the boundaries are drawn to reflect uniform areas in the distribution of the specific phenomenon. Clearly, producing such boundaries requires additional information and effort compared to the choropleth map, which goes a long way to explain their limited use, especially when maps of many variables are to be produced. On an ‘area cartogram,’ the size of the areal units being mapped varies according to population or some other transforming variable. As Figure 5 illustrates, noncontiguous cartograms sacrifice contiguity for shape whereas contiguous area cartograms may require severe distortions of shape in order to retain contiguity. Unless the reader has a good grasp of the original geography, the distorted shapes may make the size differences meaningless. This can effectively be countered by showing both a geographically correct map (typically choropleth) adjacent to the cartogram, so that an easy comparison can be made. Assuming that the reader appreciates the distortion in geography, cartograms make a dramatic demonstration of disparities in aspects such as population, wealth, education, or military spending. An isodemographic map – a populationbased area cartogram – can also provide a useful base map for representation of other socioeconomic data, election outcomes, and public health (Dorling, 1994). Adjusting the base map for population in this way diminishes the exaggerated impact of large areas with small populations and ensures small, densely populated areas are visible. The availability of software to generate effective contiguous cartograms has significantly increased their use.
equal vertical interval between contour lines. In this case, the user can appreciate slopes by variations in the spacing of the contours. In many thematic mapping situations, nonequal intervals are used, so the nature of the ‘surface’ can be harder to visualize. This approach is often adopted because the data values are highly skewed or because the map maker wants to emphasize some particular values. An extension of the isarithmic map is to apply a scale of colors to the zones between isarithms. The choice of colors is similar to that for choropleth maps, but more classes, with smaller color difference is successful here due to the nested nature of adjacent zones. GIS and surface modeling software make extensive use of a chromatic scale with large numbers of classes. Generally the data range is automatically divided by the number of steps in the scale, often resulting in unwieldy values in the legend, rather than selecting a simpler, more rounded interval. Like the surface being represented, there is some value in adopting a representation method that also varies continuously. In terrain mapping, hill shading uses a continuously varying gray tone to represent relief. In its simplest form, the steeper the slope the darker the shading. To give a better impression of the three-dimensional nature of relief, such shading is often modified to have an assumed light source coming from the top left of the map, but this is probably not appropriate for other surfaces. Other techniques of representing continuously varying surfaces depend on a nonorthogonal view of the mapped area. This includes fishnet plots and fully rendered block diagrams.
Conclusions The power of the computer and the development of GIS and scientific visualization software have lead to a significant development of representation methods in recent years. Some of these possibilities have been known for a long time but have been too costly or impractical to carry out manually. Many of the newer methods rely heavily on interactivity and so are beyond the scope of this article. With modern systems, there is more scope to experiment with representation, as a change of color, or even representation method can happen in an instant with the click of a button. Despite these advances, the basic principles of thematic mapping, understanding data to be mapped, and proper use of the visual variables remain as important as ever.
See also: Cartographic Visualization; Cartography; Dynamic Mapping in Geography; Geographic Information Systems; Spatial Data; Tactile Maps in Geography.
Representations of Continually Varying Surfaces Sometimes referred to as contour maps, isarithmic maps refer to maps that represent continuously varying quantities over the surface by lines of equal values. Strictly, the term contour should be used only when the variable mapped is terrain height. Common terms are used for some variables, such as isobars for pressure. Terrain contour maps typically use an
Bibliography Bertin, J., 1983. Semiology of Graphics: Diagrams, Networks, Maps. University of Wisconsin Press, Madison, WI. Reprinted 2010 by ESRI Press, Redland, CA. Brewer, C.A., 2005. Designing Better Maps: A Guide for GIS Users. ESRI Press, Redlands, CA. Brewer, C.A., Harrower, M., 2009. ColorBrewer2. http://colorbrewer2.org/.
Thematic Maps in Geography
Chrisman, N., 2002. Exploring Geographic Information, second ed. Wiley, New York. Dent, B.D., 1999. Cartography: Thematic Map Design, fifth ed. William C. Brown, Boston. Dorling, D., 1994. Cartograms for visualising human geography. In: Hearnshaw, H.M., Unwin, D.J. (Eds.), Visualization in Geographical Information Systems. Wiley, Chichester. Evans, I.S., 1997. The selection of class intervals. Transactions, Institute of British Geographers. New Series 2, 98–124. Forrest, D., 1999. Geographic Information: its nature, classification and cartographic representation. Cartographica 36 (2), 31–53. Goldberg, D.W., 2008. A Geocoding Best Practice Guide. North American Association of Central Cancer Registries, Inc. Keates, J.S., 1996. Understanding Maps. Addison Wesley Longman Ltd, Harlow.
267
Kennedy, S., 1994. Unclassed choropleth maps revisited: some guidelines for the construction of unclassed and classed choropleth maps. Cartographica 31 (1), 16–25. MacEachren, A.M., 1995. How Maps Work: Representation, Visualization, and Design. Guildford, New York. Maling, D.H., 1992. Coordinate Systems and Map Projections, second ed. Pergamon, Oxford. Monmonier, M., 1993. Mapping It Out: Expository Cartography for the Humanities and Social Sciences. University of Chicago Press, Chicago. Robinson, A.H., 1982. Early Thematic Mapping in the History of Cartography. University of Chicago Press, Chicago. Slocum, T.A., McMaster, R.B., Kessler, F.C., Howard, H.H., 2009. Thematic Cartography and Geovisualization, third ed. Pearson Prentice Hall, Upper Saddle River, NJ.