Cartographic design and the quality of climate change maps

Climatic Change (2009) 95:219–230 

DOI 10.1007/s10584-008-9519-5 

Cartographic design and the quality 

of climate change maps 

Jean E. McKendry · Gary E. Machlis 

Received: 13 February 2008 / Accepted: 22 September 2008 / Published online: 21 November 2008 

© Springer Science + Business Media B.V. 2008 

Abstract Maps are essential in climate change research and policymaking, and are 

primary tools for communicating climate change information to the public. The 

consequences of cartographic design are potentially significant to understanding 

climate change and effectively informing policymakers. Yet, the cartographic 

design and quality of climate change maps have not been critically assessed nor 

systematically evaluated. We suggest that evaluating the quality of climate change 

maps is both timely and essential, and offer one approach as a demonstration. We use 

cartographic design principles to evaluate a ‘high visibility’ climate change map from 

the 2007 report of the Intergovernmental Panel on Climate Change. Our specific 

goals are to demonstrate the need and value of cartographic critique, describe how 

such evaluation can be accomplished, and make a case for cartographers’ engagement 

with climate change scientists in mapping activities. We suggest a research and 

policy agenda for the cartographic evaluation and design of climate change maps. 

1 Introduction 

Maps are essential to climate change research and policymaking, and their use is 

substantial: Working Group I of the Intergovernmental Panel on Climate Change 

(IPCC) included over 130 maps in its 2007 report (IPCC 2007a). Climate change 

maps are used by the scientific community to display results of general circulation 

models (GCMs), projected sea level rise, temperature change, migration of flora and 

fauna habitat ranges, and more. Policymakers use climate change maps to compare 

J. E. McKendry · G. E. Machlis 

College of Natural Resources, University of Idaho, 

Moscow, ID 83844-1133, USA 

J. E. McKendry (B) 

c/o AAAS, 1200 New York Avenue, NW (Room 637), 

Washington, DC 20005, USA 

e-mail: jeanm@uidaho.edu

220 Climatic Change (2009) 95:219–230 

costs/benefits of adaptive responses, analyze policy options, and develop mitigation 

plans. Maps are also primary tools for communicating climate change information to 

the public. 

Hence, an important question arises for the producers and users of climate change 

maps: what is the quality of cartographic design used in climate change maps? Here 

‘quality’ refers not to the accuracy or reliability of the underlying data but to how 

data are cartographically displayed. The question is relevant because: (1) maps, including 

climate change maps, are increasingly made by individuals not trained in map 

design, (2) poor map design can hinder effective data analysis, understanding, and 

decision-making, and (3) poorly designed maps can distort information and mislead 

users (see Lilley 2007; Cassettari 2007; Carter2004; McKendry 2000; Monmonier 

1996). 

Mapmaking and cartography have been transformed by technology (see Arikawa 

et al. 2007; Gartner et al. 2007; Monmonier 2007; Butler2006; Taylor and Caquard 

2006). These technological developments have made it easier to produce maps. 

Geographic Information Systems (GIS), remote sensing, Global Positioning Systems 

(GPS), interactive web mapping (including ‘mashups’), inexpensive computing 

platforms, and plentiful data and data delivery options have made mapmaking 

a commonplace activity beyond the realm of the trained cartographer. Today’s 

mapmakers often do not have specialized education or training in the principles of 

cartographic design. As a result, maps made by non-cartographers vary in quality 

(as do maps by cartographers, of course), and are often poorly designed (Cassettari 

2007;Plewe2007; Monmonier 2006; Field 2005;WoodandKeller1996). 

The consequences of poor quality map design can be significant. Maps have the 

power to inform or misinform, lead or mislead, clarifyorconfuse through the use 

or misuse of design principles (Lilley 2007;Carter2004; McKendry 2000; Buttenfield 

1996; Monmonier 1995; Buttenfield and Beard 1991; Petchenik 1983). For example, 

Tufte (1990, 1983) analyzes a broad range of information graphics (including charts, 

diagrams, graphs, tables, and maps) and documents the prevalence of ‘graphic 

mediocrity’ (due to lack of skill). Importantly, he describes how the quality of graphic 

design can directly impact decision-making by revealing or obscuring information 

(Tufte 1997). 

Given the urgent challenges created by climate change and the importance of 

maps in climate change research and policymaking, the role of map design deserves 

attention. Surprisingly, the cartographic design and quality of climate change maps 

have not been critically assessed nor systematically evaluated. 

We suggest that evaluating the quality of climate change maps is both timely 

and essential. We offer one approach as a demonstration. First, we select a ‘high 

visibility’ climate change map to evaluate, in this case a map used in the “Summary 

for Policymakers” report issued by Working Group II of the IPCC (IPCC 2007b). 

We then present a brief overview of selected cartographic design principles that 

can be used to evaluate this and other climate change maps. This overview is not 

a comprehensive ‘primer’ on cartographic design; there are many resources available 

to introduce cartographic design (see Section 3 below). The purpose of this overview 

is to provide specific examples of agreed-upon design principles established through 

cartographic research. Next, we systematically apply these cartographic principles 

to the selected climate change map and report the results. We conclude with a 

proposed research and policy agenda for the systematic cartographic evaluation of

Climatic Change (2009) 95:219–230 221 

climate change maps. We acknowledge that this small case study approach is limited. 

However, our specific goals are to demonstrate the need and value of cartographic 

critique, describe how such evaluation can be accomplished, and make a case for 

cartographers’ engagement with climate change scientists in mapping activities. 

Figure SPM.1. Locations of significant changes in data series of physical systems (snow, ice and frozen ground; hydrology; and coastal processes) and 

biological systems (terrestrial, marine, and freshwater biological systems), are shown together with surface air temperature changes over the period 1970-2004. 

A subset of about 29,000 data series was selected from about 80,000 data series from 577 studies. These met the following criteria: (1) ending in 1990 or later; 

(2) spanning a period of at least 20 years; and (3) showing a significant change in either direction, as assessed in individual studies. These data series are from 

about 75 studies (of which about 70 are new since the Third Assessment) and contain about 29,000 data series, of which about 28,000 are from European 

studies.White areas do not contain sufficient observational climate data to estimate a temperature trend. The 2 x 2 boxes show the total number of data series 

with significant changes (top row) and the percentage of those consistent with warming (bottom row) for (i) continental regions: North America (NAM), Latin 

America (LA), Europe (EUR), Africa (AFR), Asia (AS), Australia and New Zealand (ANZ), and Polar Regions (PR) and (ii) global-scale: Terrestrial (TER), Marine 

and Freshwater (MFW), and Global (GLO). The numbers of studies from the seven regional boxes (NAM, …, PR) do not add up to the global (GLO) totals 

because numbers from regions except Polar do not include the numbers related to Marine and Freshwater (MFW) systems. Locations of large-area marine 

changes are not shown on the map. [Working Group II Fourth Assessment F1.8, F1.9; Working Group I Fourth Assessment F3.9b]. 

Fig. 1 Map, legend, and caption of Figure SPM.1., reprinted from IPCC Working Group II 

“Summary for Policymakers” (2007b, p. 10), used with permission


2 Selecting a climate change map to evaluate 

A climate change map from a recent report of the IPCC was selected to demonstrate 

how climate change maps can be cartographically evaluated. Selecting an IPCC 

map is appropriate for several reasons. Since 1988, the IPCC has released four 

comprehensive scientific assessments of climate change. IPCC reports are considered 

by policymakers and the scientific community to be a definitive source of information 

on climate change and its impacts (Kintisch and Kerr 2007). 

The map shown in Fig. 1 was published in the “Summary for Policymakers” 

completed by Working Group II for Climate Change 2007: Impacts, Adaptation and 

Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of 

the Intergovernmental Panel on Climate Change (IPCC 2007b, p.10).Thetitleofthe 

map is “Changes in physical and biological systems and surface temperature 1970– 

2004.” Figure 1 is the only map included in this summary report for policymakers. 

We consider this map appropriate for a case example given that: (1) the IPCC is a 

legitimated source of climate change information, (2) the IPCC’s fourth assessment 

report (AR4) is a major consensus technical effort to summarize current climate 

change knowledge, (3) the policy summary is an important stand-alone document, 

and (4) Fig. 1 is the sole map in the policy summary approved by Working Group II. 

The map published in the report is 184 mm wide by 194 mm tall, accompanied by 

a caption 184 mm wide by 41 mm tall, and printed in color on a page 215 mm wide 

by 279 mm tall. The map was also made available as a separate color graphic (though 

without its title or caption) on the IPCC website (IPCC 2007b). Since its original 

publication, the map has been distributed through other reports of the IPCC and in 

the public media in both its original and modified form. 

The map appears in the draft copy of the “Summary for Policymakers of the 

Synthesis Report of the IPCC Fourth Assessment Report”—the overall summary of 

the IPCC’s work (IPCC 2007c). It was published in modified form in the Washington 

Post (print and online) on 18 November 2007, page A10 with the caption excluded, 

title changed, and legend edited and rearranged (Struck 2007). The map was adapted 

and split into two separate maps by the Organization of Ibero-American States 

(Organización de Estados Iberoamericanos 2007). The resulting two maps were 

posted on the organization’s website with substantial changes made to the legend 

(see http://www.oei.es/decada/presentacioneurop.htm). 

The color version of the map published in the final summary report of Working 

Group II and shown in Fig. 1 is evaluated in this demonstration, downloaded from 

the IPCC website 21 November 2007 (IPCC 2007b, p. 10). 

3 Selected principles of cartography to use in evaluating climate change maps 

Research and practice in the field of cartography have produced a set of fundamental 

principles that are essential to good cartographic design—principles that deal with 

map layout and symbolizing data and features. Cartographic design principles guide 

decisions about how to represent locations on a map and attributes of those locations, 

using graphic symbols such as color, size, shape, typography, and other symbols. 

Principles describe how points, lines, and areas should be symbolized based on 

the underlying data (i.e., attributes of features). For example, the selection of


Table 1 Selected principles for cartographic design and layout with descriptions (adapted from Brewer 2005 and Krygier and Wood 2005) 

Cartographic principle Description of cartographic principle 

Map projection All map projections have distortions (distance, area, direction, and/or shape). An equal-area map projection is a good selection for most 

small-scale maps (e.g., many world maps) and should be used for maps showing data distributions. 

Generalization Small-scale maps should show more area, less detail, and more generalization of features. Large-scale maps should show less area, more 

detail, and less generalization of features. The coastline of a country on a large-scale map is symbolized by a line with more detailed 

curves than the same coastline on a small-scale map. 

Data classification Qualitative data show differences in kind (e.g., forest versus urban land cover). Qualitative data should be grouped so that features in 

the same group are more similar than dissimilar and features in different groups are more dissimilar than similar. 

Quantitative data show differences in amount (e.g., population density). Quantitative data should be grouped by specific external 

criteria (e.g., quantiles) or by the characteristics of the data (e.g., natural breaks). 

Map layouta Focus Map layout should guide readers through the map elements and help them focus on the most important parts of the map. 

Visual variablesb Color hue Color hue (such as red, green, blue) should be used to categorize features that are qualitatively different, such as a river and a road. 

Color value Color value (or lightness of hue) should be used to represent quantitatively different data (either rank-ordered data or numerical 

amounts), such as population density. Value is typically light for low numbers (e.g., light green) and dark for high numbers (e.g., dark 

green) in sequential datasets, such as a dataset of population change from 0% to 100%. For diverging data sets with an important 

midpoint (between negative and positive values), such as population change from −50% to +50%, hue and value can vary to show the 

two directions in the data set. The midpoint from 0% to −50% can be symbolized using a light to dark color hue. The midpoint from 

0% to +50% can be symbolized using a different, complementary light to dark color hue. 

Color saturation Color saturation (or intensity of hue, such as bright red compared with a dull, gray red) can be used for qualitative or quantitative data. 

It is difficult to use on its own to symbolize data. Saturation is typically used to reinforce changes in value for quantitative data or to 

reinforce changes in hue for small areas on a map that are qualitatively different. 

Size Size should be used to represent quantitatively different data (either rank-ordered data or numerical amounts). A larger square 

signifies a greater quantity than a smaller square. 

Shape Shape should be used to categorize features that are qualitatively different. A square is not more or less than a circle, 

but is different in kind. 

Visual hierarchy Visual hierarchy should emphasize the most important map elements. Less important elements should be less noticeable. Visual hierarchy 

should clearly communicate the intellectual hierarchy and purpose(s) of the map. 

aFor Krygier and Wood (2005) ‘focus’ is one element of map layout that also includes map pieces (title, legend, border, etc.), balance (stability), and the grid 

(underlying grid of vertical and horizontal lines that helps with balance). 

bBertin (1981) initially described seven visual variables. Cartographers have adapted and modified this list. Five visual variables are presented here.


appropriate color schemes is determined by whether the attributes are qualitative 

(use different colors to symbolize different ecotypes) or quantitative (use the same 

color with variation from light to dark to symbolize changes in temperature over 

time). Cartographic principles guide decisions about how to group (‘classify’) data 

for representation. For example, a map showing temperature ranges may have 

temperature data assigned to groups using equal intervals (same data range for 

each class) or quantiles (same number of data points in each class). Cartographic 

principles guide decisions about how to arrange all the graphic symbols included on 

a map so that there is clarity in the overall design and layout. Numerous texts review 

and explain cartographic principles (see, for example, Slocum et al. 2005; Kimerling 

et al. 2001; Dent1999; Robinson et al. 1995; MacEachren1994; Monmonier 1993). 

There is strong consensus within the cartographic community about basic principles. 

Contemporary map design also demands understanding the constraints and opportunities 

determined by the media on which a map will be reproduced. For 

example, maps designed for digital display are limited by screen resolution compared 

with maps designed for printing on paper, and ‘endless zoom’ options carry with them 

unique problems of data accuracy and cartographic design (see Lobben and Patton 

2003, for a comparison of design issues for digital and printed maps). 

Table 2 Selected introductory resources on cartographic design 

Books (full citations are listed under references) 

Cynthia Brewer, Designing Better Maps: A Guide for GIS Users 

Borden Dent, Cartography: Thematic Map Design, 5th edition 

Jon Kimerling, Philip Muehrcke, and Juliana Muehrcke, Map Use: Reading, Analysis, and 

Interpretation, 5th edition 

John Krygier and Denis Wood, Making Maps: A Visual Guide to Map Design for GIS 

Alan MacEachren, Some Truth with Maps: A Primer on Symbolization and Design 

Mark Monmonier, How to Lie with Maps, 2nd edition 

Terry Slocum, Robert McMaster, Fritz Kessler, and Hugh Howard, Thematic Cartography 

and Geographic Visualization, 2nd edition 

Journals 

Cartographic Perspectives (Journal of the North American Cartographic Information Society; 

http://www.nacis.org) 

Cartography and Geographic Information Science (Journal of the Cartography and Geographic 

Information Society; http://www.cartogis.org) 

Cartographica (Journal of the Canadian Cartographic Association; http://www.cca-acc.org/) 

The Cartographic Journal (Journal of the British Cartographic Society; 

http://www.cartography.org.uk/) 

Websites 

http://www.colorbrewer.org 

(an interactive online tool designed to assist in selecting good color schemes for maps and 

other graphics) 

http://www.typebrewer.org/ 

(an online tool designed for people who want to learn more about map typography) 

http://www.progonos.com/furuti/MapProj/Normal/CartProp/cartProp.html 

(an introduction to map projections, with examples of distortions, and a discussion of matching 

projection to a map’s purpose) 

http://mappingcenter.esri.com/ 

(a website that focuses on cartographic resources, examples, and assistance for users of ArcGIS)


Table 1 includes selected cartographic principles adapted from two recent books 

that focus on map design (Brewer 2005; Krygier and Wood 2005). Specifically, 

Table 1 describes principles concerning map projections, generalization, data classification, 

map layout, visual variables (such as color), visual hierarchy (important 

information is visually prominent in the map’s design), and more. The sources were 

selected because their focus is on teaching GIS users how to make better maps, and 

can introduce non-cartographers to the basics of good map design. 

The list of principles, though not exhaustive, deals with common design issues 

encountered in mapping. For example, all maps displayed in two dimensions require 

mathematical transformation of spherical coordinates to plane coordinates through 

the use of a map projection. All map projections have distortions of distance, area, 

direction, and/or shape. Such distortions are particularly noticeable on small-scale 

maps, such as maps of the world. A map projection that preserves relative areas 

should be used for maps showing data distributions. While these principles are basic 

and straightforward, their application in the overall design and layout of a map is 

often complex and challenging, can involve design tradeoffs, and is a requirement 

for high quality map design. 

For climate change scientists interested in learning more about cartographic 

design, Table 2 provides a list of selected resources that include numerous examples 

of good and poor map design. 

4 Evaluating the IPCC climate change map: an example approach 

Figure 1 from the IPCC Working Group II summary report for policymakers 

can be evaluated using the selected principles in Table 1. Each principle can be 

systematically applied to the map with the result rated as good, satisfactory, orpoor 

followed by a brief explanation. We applied this method to the IPCC map shown in 

Fig. 1. 

Table 3 includes the rating of the map for each selected principle with its 

explanation. Our preliminary and limited evaluation indicates that the map published 

in the summary report of Working Group II for policymakers ranges from poor to 

satisfactory in its use of selected cartographic principles. For example, we rated map 

layout and focus as poor. The map legend is complex and includes data not even 

displayed on the map, i.e., the number and percentage of significant changes in the 

series of four-celled tables with arrows. The legend is also the same size as the map, 

and they visually compete with each other for importance on the page. Information 

about the white areas on the map is included in the caption but not in the map legend. 

Meaningful relationships between changes in physical and biological systems and 

changes in surface temperature are difficult to see. 

We rated the generalization of features on the map as satisfactory. The map shows 

coastlines and boundaries between nations. The black linework to symbolize coastlines 

and boundaries is more detailed than needed for the scale of this map. The high 

level of detail for the southern tip of Chile means that the black boundaries blend in 

with the point locations (blue circles with black outlines). Table 3 summarizes results 

for each of the selected cartographic principles. 

Overall, our evaluation is that the map does not clearly and effectively display 

information about its intended topic, “changes in physical and biological systems and


Table 3 Results of evaluating map from IPCC working group II summary report using selected principles for cartographic design and layout 

Cartographic principle Rating Explanation 

Map projection Poor The map shows temperature and other statistical information. The projection should be equal-area. Instead, it is a 

cylindrical equidistant projection. Area is distorted as well as shape. The colored squares on the map are equal in size, 

but they do not represent the same area on the earth. 

Generalization Satisfactory The map shows coastlines and boundaries of nations. The generalization of areas (nothing smaller than a country) is 

appropriate. Linework to symbolize the coastlines and boundaries is too detailed for the scale and purpose of the map. 

Argentina, Chile, Antarctica, and Southeast Asia are examples where too much detail interferes with the areas 

and data being shown. 

Data classification Satisfactory The map displays quantitative and qualitative data that are classified. The observation locations for physical systems are 

combined into a single group. Observation locations for biological systems are combined into a single group. They are 

symbolized as qualitatively different groups using different color hues. 

The data on temperature range are classified into five groups, low to high. It is unknown how the class breaks were 

established. The reader can only determine that the data ranges for the classes are not equal in size. It is unclear in the 

legend where class breaks begin and end as a single value is assigned to a break. 

Map layout 

Focus Poor The map lacks focus. The legend is complex (including data not even displayed on the map, i.e., the number and 

percentage of significant changes in the series of four-celled tables with arrows). The legend is the same size as the 

map, and they visually compete with each other for importance on the page. The map is accompanied by a detailed 

caption. The reader must carefully read the caption first to understand the legend and then carefully read the legend in 

order to understand the map. For example, information about the white areas on the map is included in the caption but 

not in the map legend.


Visual variables 

Color hue Satisfactory Point observations for physical and biological systems are distinguished by different color hues. This is appropriate for 

grouping qualitative features. It is unclear why the green circles have white borders on the map (white and black 

borders in the legend), while blue circles have black borders. 

Color value Poor The temperature data are quantitative and displayed using a color sequence that varies by color hue. It appears that a 

detailed spectral or ‘rainbow’ sequence, often used to symbolize many classes in a temperature range, has been 

simplified to five classes. The visual effects produced on the map are changes in color hue. It is challenging to view the 

sequence in this quantitative dataset symbolized by colors that are qualitatively different, e.g., green, blue, yellow. The 

five classes of data should be displayed by varying color value (light to dark) or by using a diverging scheme around the 

zero data point with color hue/color value changes for the two directions (negative and positive) in the data set. 

Color saturation NA Color saturation is not used to symbolize data on the map. 

Size Satisfactory Circle symbols of different sizes are appropriately used (small to big) to represent quantitative data. However, it is 

unclear why the size varies in Europe only. 

Shape NA Shape is not used to symbolize data on the map. 

Visual hierarchy Poor The visual hierarchy of the map is poor. The relationship between observation locations and temperature is difficult to 

understand. Blue circles (physical systems) completely cover green circles (biological systems) in most locations, while 

green circles cover blue ones in a few locations. Circles that only change size in Europe are confusing. Actual changes 

in physical and biological systems (emphasized in the map title and in the legend) are not displayed on the map. Also, 

the color hues of the circles (blue and green) are very close to the blue and green color hues used to show 

temperature range.


surface temperatures 1970–2004.” For the only map published in an IPCC summary 

report for policymakers, the evaluation reveals specific issues of cartographic quality 

with this ‘high-visibility’ map. Our evaluation is of course subjective, and reflects: (1) 

our choice of selected design principles, (2) the evaluation categories, (3) the lack of 

multiple reviewers, and (4) the reviewers’ expertise in applying the design principles 

to the evaluated map. Nevertheless, this kind of cartographic evaluation can provide 

useful insights into the quality of climate change maps. 

5 Toward a research and policy agenda for evaluating climate change maps 

We have demonstrated how a climate change map can be evaluated. Other climate 

change maps are likely to vary in quality and could benefit from such evaluation. 

Poor quality climate change maps have implications for climate change research 

and policymaking. We suggest a modest but important agenda to improve the 

cartographic quality of climate change maps. 

(a) Systematic evaluation of the cartographic design and quality of climate change 

maps should be undertaken to assess and improve climate change maps. 

Our evaluation was a preliminary demonstration. Evaluation methods should be 

refined to include: (a) carefully designed sampling plans to select a population of 

climate change maps to evaluate, (b) expanding the criteria (cartographic principles) 

to apply in the evaluations, including possible weighting of criteria, (c) assembling 

a panel of expert cartographers to assess map design using established evaluation 

techniques, and (d) developing more elaborate and varied evaluation rankings. Such 

evaluations could provide an important inventory of the state of climate change 

map design, identify key examples of good design, educate climate scientists about 

cartographic principles, and help target efforts to improve climate change maps. 

(b) The impact of climate change maps on climate change research and policymaking 

should be researched to better understand their specific role and influence. 

Such research on the impact of climate change maps includes cartography of course, 

but could usefully extend to psychology, sociology, and political science. There are 

several key questions. How do maps influence or direct scientific efforts and research 

priorities? What assumptions do scientists make about the audiences for whom they 

produce the maps, do these assumptions need to change, and if so, how? How 

effective are climate change maps for synthesizing and interpreting climate change 

data for policymakers? How are specific maps being used to guide decision-making? 

What are the implications of inserting inaccurate or misleading maps (purposefully 

or not) into the policymaking process? What are the cumulative effects of maps 

produced by scientific organizations when reprinted and propagated through the 

popular media (unchanged or modified)? How can the cartographic design and 

persuasiveness of climate change maps be improved? Research to address these 

questions can illuminate the role of climate change maps, help identify key traits 

of effective maps, and improve research, policy analysis, and public communication 

related to climate change.


(c) Climate change scientists should encourage cartographers to become more directly 

engaged with climate change research and cartographers should be responsive 

to such engagement. 

Cartographers can and should be more effectively engaged in climate science activities. 

Climate change research teams should include cartographers or personnel 

well-trained in cartography. Climate change scientists and cartographers should work 

collaboratively to actively advocate and implement good quality map layout and 

design. Potential collaborations include (but are not limited to) training of climate 

research teams, regular map critiques, and experimentation with new cartographic 

methods, technologies, and map designs. 

6 Conclusion 

Climate change is the most pervasive environmental challenge facing contemporary 

societies. Its local, regional, and global impacts are (and will increasingly be) extraordinary 

in scope, complexity, and consequence. The scientific community has a wideranging 

and intense research effort underway, focused on climate change dynamics, 

impacts, adaptation, and mitigation alternatives. The results increasingly depend 

on maps as tools of visualization and analysis, instruments of policy and decisionmaking, 

and ways of communicating climate change science to the public. As we have 

suggested, maps have the power to inform or misinform, lead or mislead, clarify or 

confuse through the use or misuse of design principles. Successful application of good 

map design is a necessary step in the development of the climate change sciences. 

Acknowledgements The authors thank the anonymous reviewers for their review and comment on 

earlier drafts of this manuscript. Wayde Morse and Jim Snyder provided valued assistance. An earlier 

version of this paper was presented at the 23rd International Cartographic Conference, Moscow, 

Russian Federation, August 2007. 

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