Communication of climate change (CC) risks is challenging, in particular if global-scale spatially resolved quantitative information is to be conveyed. Typically, visualization of CC risks, which arise from the combination of hazard, exposure and vulnerability, is confined to showing only the hazards in the form of global thematic maps. This paper explores the potential of contiguous value-by-area cartograms, that is, distorted density-equalizing maps, for improving communication of CC risks and the countries' differentiated responsibilities for CC. Two global-scale cartogram sets visualize, as an example, groundwater-related CC risks in 0.5° grid cells, another one the correlation of (cumulative) fossil-fuel carbon dioxide emissions with the countries' population and gross domestic product. Viewers of the latter set visually recognize the lack of global equity and that the countries' wealth has been built on harmful emissions. I recommend that CC risks are communicated by bivariate gridded cartograms showing the hazard in color and population, or a combination of population and a vulnerability indicator, by distortion of grid cells. Gridded cartograms are also appropriate for visualizing the availability of natural resources to humans. For communicating complex information, sets of cartograms should be carefully designed instead of presenting single cartograms. Inclusion of a conventionally distorted map enhances the viewers' capability to take up the information represented by distortion. Empirical studies about the capability of global cartograms to convey complex information and to trigger moral emotions should be conducted, with a special focus on risk communication.

Key Points

Cartograms are distorted thematic maps that convey information by changing the relative sizes of spatial units according to some attribute
Cartograms visualize climate change risk by showing hazard by color and exposure by distortion of grid cells according to population
Sets of cartograms are most informative, for example, visualizing the correlation between the countries' wealth and their cumulative CO₂ emissions

Plain Language Summary

With ongoing climate change (CC), policymakers, stakeholders and the public want to know about related risks all around the world. A traditional way of informing about, for example, how CC may alter the world's water resources are global thematic maps; they show the projected change of the amount of water resources until some period in the future by different colors. A new way of visualizing data is cartograms. Cartograms are distorted maps where the areas of spatial map units are changed according to an attribute, for example, the number of people living in the spatial unit. Different from traditional maps, cartograms cannot only show the CC hazard (e.g., the potential water resources decrease) but also the exposure to the hazard (how many people will be affected). The paper presents three sets of global cartograms, two about CC risks and one that shows that the countries' wealth has been built on harmful emissions since the 19th century. I recommend that cartogram sets are used to visualize CC risks and the availability of natural resources to humans. It should be investigated to what extent cartograms can convey complex information and trigger moral emotions, thus supporting the Earth's sustainable development.

1 Introduction

Information about climate change (CC) and about its potential impacts is often provided in the form of thematic maps. Maps do not simply represent spatial data but are communication tools that may be used to make arguments (Mühlenhaus, 2013). Communication about CC should convey factual information but also trigger moral emotions to motivate people to lead a more sustainable lifestyle (Roeser, 2012). It has been increasingly recognized that maps that visualize CC risks should be designed skillfully as maps play a key role in shaping people's beliefs about the world. To produce the Working Group II contribution of the Fifth IPCC Assessment report (IPCC, 2014), for example, a graphic designer helped researchers with the design of figures including maps.

Distortion—in area, shape, distance or angle—is a common feature of all maps as maps represent locations on the curved surface of the Earth on flat surfaces. There are no global map projections that preserve distances or shapes everywhere (Slocum et al., 2009). Many projections preserve either angular relationships (conformal projections) or areas (equal-area projections). The best-known conformal projection, the traditional Mercator projection, was originally devised for navigational purposes and preserves angles but strongly distorts areas: Spatial units closer to the poles are drawn much larger than those further away such that Africa and Greenland appear to be of almost equal size even though Africa is 14 times larger than Greenland. The equal-area Peters projection, where areas of spatial units are shown in correct proportions, was welcomed in the 1970s as a fairer representation of developing countries but remains controversial as it strongly distorts the shapes of spatial units such as continents (Crampton, 1994). Less shape-contorting in the lower latitudes is the similar equal-area Behrmann projection that preserves distances along the standard parallels at 30°N and S. Today, compromise projections that do not preserve any of the four aspects, such as the Robinson projection, are most popular for global maps (e.g., IPCC, 2014).

While distortion is an undesirable characteristic of traditional thematic maps, it serves to convey information in cartograms. In value-by-area cartograms, map polygons representing spatial units on the Earth's surface are modified in a way that the units' polygon areas on the map are proportional to a quantitative attribute of the spatial units (Tobler, 2004). In case of contiguous cartograms, the most popular cartogram type, polygon shapes have to be distorted to achieve proportionality with respect to an attribute while keeping the polygons contiguous. Examples of attributes that can be used as distorter variables are population in administrative units (Dorling, 1996), the number of tractors in U.S. states (Harris & McDowell, 1955) or the area with organic agriculture in the countries of the world (Paull & Hennig, 2016). Cartograms are beneficial if the issue to be visualized is not directly related to area, such as unemployment rate in municipalities, in which case population between 15 and 65 years of age could be used as distorter variable (Burgdorf & Huter, 2009). The distorter variable must be an extensive property, that is, if a certain spatial unit would be copied, the variable value would double. For example, water volume and population are extensive properties, temperature, and per-capita CO₂ emissions are not. Equal-area projections can be regarded as cartograms in which the distorter variable is the land area.

Cartograms enable the representation of one or two attributes of spatial units. Figure 1 provides a schematic that shows how data for two attributes of spatial units (i.e., polygons, here grid cells) can be visualized by bivariate cartograms. While thematic map A represents only variable 1 (e.g., per-cap CO₂ emissions) by different colors of the polygons, the bivariate cartogram B additionally represents variable 2 (e.g., population) by distorting the grid cell polygons of map A such that the density of variable 2 on the map, for example, the population per cartogram area, is the same in all distorted polygons. If the original map polygons are all of the same size, as is the case in map A, polygons with a distorter variable value larger than average increase in size in the cartogram (grid cells 1, 2, and 4), while the others decrease, with the sum of all polygon areas on the map remaining the same. Depending on the spatial heterogeneity of the distorter variable and the topology of the original polygons, it may be impossible to equalize the density, that is, achieve proportionality between the area on the cartogram and the distorter variable, and to keep the spatial units contiguous at the same time. If the density of the distorter variable is very heterogeneous, proportionality can only be achieved in an approximate manner (Tobler, 2004), and distortion accuracy is low (see Section 5.1).

Details are in the caption following the image — **Figure 1**
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Schematic for representing information about spatial units by univariate thematic maps (map A) and bivariate cartograms (map B). While both maps represent variable 1 (e.g., per-cap CO₂ emissions) by different colors, the bivariate cartogram additionally represents variable 2 by distorting the polygons of map A such that density of the distorter variable 2 (e.g., population per cartogram area) is the same in all distorted polygons.

While cartograms were first constructed manually (e.g., Harris & McDowell, 1955), a number of computer algorithms for cartogram construction were developed since the late 1960s (Gastner & Newman, 2004; Tobler, 2004). The efficient diffusion-based algorithm of Gastner and Newman (2004) results in cartograms without topological errors and has been implemented in various cartogram tools. It enabled the development of hundreds of global cartograms in the framework of the Worldmapper project (www.worldmapper.org), which aimed at supporting the achievement of the Millenium Development Goals by showing cartograms that visualize the uneven social conditions and distribution of resources among the Earth's nations (Barford & Dorling, 2006). In the Worldmapper cartograms, which were published extensively in popular media (see references at www.worldmapper.org), country outlines are distorted according to, for example, the number of people in each country living in absolute poverty, the number of hospital beds or the ecological footprint. Also utilizing the Gastner and Newman algorithm, Hennig (2013) introduced grid-based cartograms where regular grid cell polygons are distorted instead of country polygons (www.viewsoftheworld.net). His univariate world population cartogram, where grid cell polygons are distorted according to high-resolution gridded population data, represents the heterogeneous population distribution within countries. However, the stronger distortion of country shapes may render this grid-based cartogram somewhat more difficult to read than is the case when country polygons are directly distorted, like in the Worldmapper project. Hennig also generated a bivariate grid-based cartogram where gridded population is used as a distorter while colors indicate mean annual precipitation (“Precipitation Patterns: Rainfall from a People's Perspective”, in Dorling & Lee, 2016 and at www.viewsoftheworld.net 2016).

This paper explores the potential of global cartograms for the communication of both risks of and responsibilities for CC. Three sets of cartograms are presented. The first two sets aim at communicating CC risks. CC risks are a function of physical hazards caused by CC (e.g., altered renewable groundwater resources) as well as of exposure (e.g., population) and vulnerability (IPCC, 2014). However, most thematic maps only provide information on the spatial distribution of CC hazards. Bivariate cartograms additionally allow visualizing exposure (or a combination of exposure and vulnerability) by distortion. Cartogram set “Components of risk” shows how global-scale gridded data on hazard, exposure and vulnerability can be visualized by bivariate cartograms. Cartogram set “Natural resources under stress” also combines bivariate gridded cartograms to show the risk of CC and population change for the availability of natural resources to humans. As an example, both sets consider risks related to renewable groundwater resources and present results of the global hydrological model WaterGAP (Döll et al., 2003; Müller Schmied et al., 2014). Simulated renewable groundwater resources for historic conditions and for scenarios of future CC are available at a spatial resolution of 0.5° × 0.5°, the typical resolution of climate impact models (Portmann et al., 2013). Cartogram set “CC responsibilities” visualizes that current wealth of countries strongly correlates with the countries' cumulative fossil-fuel CO₂ emissions since preindustrial time, underlining that countries have built their wealth on CO₂ emissions and thus degradation of the Earth system. It consists of cartograms in which country polygons are distorted according to their population, gross domestic product (GDP), and fossil-fuel CO₂ emissions.

2 Methods and Data

2.1 Cartogram Generation

Cartograms were generated with the GIS software ESRI ArcGIS, using the ArcScript Cartogram Geoprocessing Tool version 2 by Tom Gross (http://www.arcgis.com/home/item.html?id=d348614c97264ae19b0311019a5f2276). This tool implements the algorithm of Gastner and Newman (2004). As input of the tool, shapefiles with polygons that are to be distorted and the distorter variable for each of the polygons are required. In case of bivariate cartograms, the shapefile also contains the variable that is shown in color on the cartogram. Besides, the tool allows to distort other shapefiles such as country outlines accordingly. In the diffusion algorithm implemented by the cartogram tool, equally spaced particles located on a mesh are moved to achieve an equal density of the distorter variable. The default mesh size is 512 × 512 particles are located within the map space. Larger mesh sizes lead to more accurate results, that is, cartograms with a higher correlation between polygon area on the cartogram and distorter variable (Brunsdon & Charlton, 2015). In case of a strong heterogeneity of the density of the distorter variable, the algorithm converges too slowly toward an equal density. Then, the tool fails to execute, and a Gaussian blur must be applied that smooths the density differences between adjacent polygons. The default and theoretically best blur factor is 1, that is, no blurring occurs.

Optimum values for mesh size and blur factor for grid- and country-based cartograms were determined by selecting the combination that achieved the highest distortion accuracy, that is, the highest proportionality between the values of the distorter variable and the area of the distorted polygons (see also Section 5.1). In case of the grid-based cartograms, for which almost 67,000 0.5° cell polygons were mostly distorted according to the strongly varying population numbers in these polygons, a mesh size of 1024 × 1024 and a blur factor of 3 was used. The program failed to execute using a blur factor of 1 for all mesh sizes. In case of larger mesh sizes, the program required even higher blur factors to execute. A mesh size of 2048 × 2048 and a blur factor of 1 was used to generate the cartograms with country polygons.

Cartograms are affected by the projection of the initial shapes to be distorted as the diffusion algorithm attempts to resize polygons with minimal distortion of their initial shapes (Dorling et al., 2006). In all cases, unprojected shapefiles with geographical coordinates (degree latitude by degree longitude) were used as input to the cartogram tool, and the resulting cartograms are shown unprojected, too. Any projection of the cartogram would result in a decreased proportionality of distorter values and polygon area on the map. If, for example, population in each of the 0.5° × 0.5° grid cells were the same, the cartogram with population as distorter should look exactly like a global map with unprojected, quadratic 0.5° × 0.5° grid cells as then the population per map area would be the same everywhere. In case of a map projection, this would not no longer apply. Below, the data used in this study are described, first the data for the grid-based CC risk cartograms and then the data for the country-based CC responsibilities cartograms.

2.2 Data for Bivariate Grid-Based Cartograms of Cartogram Sets “Components of Risk” and “Natural Resources Under Stress”

Data for cartogram generation encompass estimates of current and future renewable groundwater resources as computed by the global hydrological model WaterGAP, a gridded data set of population in 2010, a population scenario and an index of vulnerability of humans to decreased groundwater recharge. All data were either computed at or assigned to 0.5° × 0.5° grid cell polygons as defined by the WATCH-CRU land mask used by WaterGAP (Müller Schmied et al., 2014). This land mask with 66,896 grid cells covers all continents of the Earth except Antarctica.

2.2.1 Renewable Groundwater Resources

The global hydrological model WaterGAP computes the dynamics of water flows and water storage on all continents with a spatial resolution of 0.5° using time series of daily climate variables (Döll et al., 2003; Müller Schmied et al., 2014). One of those flows is diffuse groundwater recharge (Döll & Fiedler, 2008), and long-term averages of groundwater recharge are considered to constitute the renewable groundwater resources in each grid cell. The potential impact of CC on renewable groundwater resources was computed by driving WaterGAP with the bias-adjusted output of five different climate models for four different greenhouse gas emissions scenarios (Portmann et al., 2013). Groundwater recharge during 1971–2000 and 2070–2099 was compared to quantify the CC hazard related to renewable groundwater resources. For the production of the cartograms, ensemble means of the groundwater recharge values computed with the five climate scenarios for the high-emissions scenario RCP8.5 were used, or, for maps of percent change of renewable groundwater resources, the ensemble mean of the climate model-specific changes of groundwater recharge.

2.2.2 Population

Population estimates served to quantify exposure to CC hazards in both cartogram sets, as distorter variables, and to compute per-capita availability of renewable groundwater resources in cartogram set “Natural resources under stress”. To obtain population in 0.5° grid cells in 2010, the 2010 GPWv3 gridded population estimate for the year 2010 (Center for International Earth Science Information Network (CIESIN), 2010) was aggregated from its original resolution of 2.5 arc-minutes to the WaterGAP 0.5° grid cells. Population in 2085, the mid-point of the period 2070–2099 used for computing future groundwater resources, was computed by selecting the “Middle of the Road” scenario SSP2 (SSP Database at https://tntcat.iiasa.ac.at, O'Neill, 2012). Gridded population 2085 was produced by scaling with the SSP country totals, neglecting changes in population distribution within countries. To quantify groundwater availability under “current” conditions, per-capita renewable groundwater resources were calculated by dividing renewable groundwater resources in 1971–2000 by population in 2010. For future groundwater availability, population in 2085 was combined with average groundwater resources during 2070–2099.

2.2.3 Indicator of Vulnerability to Decreasing Groundwater Resources

Vulnerability to decreasing groundwater resources was quantified by an indicator that combines a cell-specific water scarcity indicator, a cell-specific indicator for the dependence of water supply on groundwater and the country-specific Human Development Index (Döll, 2009). The vulnerability indicator ranges from 1 to 5, with 5 indicating the highest vulnerability due to high water scarcity and dependence on groundwater for water supply, and a low Human Development Index. To allow an easier visual perception of vulnerability differences, an alternative vulnerability indicator was produced by simply mapping the vulnerability to the larger range between 1 and 21.

2.3 Data for Univariate Country-Based Cartograms of Cartogram Set “CC Responsibilities”

Country-specific data encompass data on fossil-fuel CO₂ emissions in 2010, cumulative fossil-fuel CO₂ emissions from preindustrial time until 2010, GDP and population. These data were assigned to polygons representing countries and/or territories and used as distorter variables. Country polygons were obtained as shapefile TM_WORLD_BORDERS-0.3.zip from http://thematicmapping.org/downloads/world_borders.php. The originally 246 polygons were reduced to 204 polygons by deleting Antarctica and small islands without emissions data, and by merging polygons belonging to one country.

2.3.1 Fossil-Fuel CO₂ Emissions

“Fossil-fuel CO₂ emissions” encompass emissions from fossil-fuel burning, cement manufacture and gas flaring. Annual emissions data for individual countries from 1751 (at the earliest) until 2010 were compiled by Boden et al. (2013). I used these data to calculate cumulative fossil-fuel CO₂ emissions from preindustrial time until 2010 for the 204 country polygons by adding up the annual values. A complication was that the identity of countries may vary over the years. Data for Germany, for example, are provided only until 1945 and starting again in 1991, while for the years in between, individual data for the then existing two German countries are given. In cases of (re-)unification, such as in case of Germany and Vietnam, the values of the predecessor countries were simply added. In case of a breaking up of countries, as happened to the Soviet Union, Yugoslavia, Czechoslovakia and Pakistan, the emissions during times of unity were added to the countries existing in 2010 in proportion to the emissions after breakup. Values available for selected smaller administrative units were added to the values of the country they belong to. For example, values for Hong Kong and Macao were added to the value of mainland China.

2.3.2 Population and GDP in 2010

Data on population and GDP of countries in 2010 were predominantly provided by the World Bank (http://data.worldbank.org/data-catalog/world-development-indicators). GDP was computed as GDP in 2005 United States dollars (USD) at a constant exchange rates in 2000. GDP values for seven countries without World Bank data but from other sources are listed in the Appendix A. No information was available for some of the polygons representing small islands and countries (such as Liechtenstein) that are anyhow not well visible on the cartograms. Regarding population, only the data for French Guiana and Falkland Islands were not available from World Bank and were taken from Wikipedia.

3 Cartograms for Visualizing CC Risks

3.1 Visualizing the Components of CC Risks: Hazard, Exposure and Vulnerability

Cartograms can visualize risks of CC by showing hazard in color and exposure and/or vulnerability by distortion. Cartogram set “Components of risk” (Figure 2) provides an example for the visualizations of risk components by bivariate cartograms, showing the risk for humans by a decrease of renewable groundwater resources due to CC. The hazard, that is, the percent decrease in renewable groundwater resources under RCP8.5 until the end of the 21st century, is shown in color using three classes. It is represented in Figure 2a by a choropleth map with an equal-area Behrmann projection. Exposure to the hazard of decreased groundwater resources is visualized in Figure 2b by distorting the 0.5° grid cells by their population in 2010. Comparison of Figures 2a and 2b shows that at least for humans, decreases in South America and Australia are not so important, while decreases in densely populated Europe, the southern rim of the Mediterranean, the Near East and China affect many people. According to the presented simulation results, the large Indian population will not suffer from a decrease of groundwater resources.

The third dimension of risk, vulnerability, cannot be represented as a distorter by itself because it is not an extensive quantity. However, the vulnerability indicator can be multiplied by population to achieve that in case of two grid cells with the same population, the grid cell with a higher vulnerability becomes larger than the grid cell with the lower vulnerability. Vulnerability indicators are only relative, and therefore the numerical range of the indicator values can be freely selected. If the vulnerability indicator (a function of water scarcity, dependence on groundwater supply and the Human Development Index) is set to range between 1 and 5 (Figure 2c), the differences between Figure 2b, with just population as distorter, and Figure 2c are hardly visible. In case of a range between 1 and 21 (Figure 2d), however, the higher vulnerability of the population on the southern rim of the Mediterranean and the Near East as compared to the European population is clearly recognizable, in particular in the zooms shown in Figure 2e. If the vulnerability indicator would be given an even larger range, the distortion would be more and more dominated by the vulnerability differences and the visual focus would be more on the vulnerable regions.

3.2 Visualizing the Impact of Climate and Population Change on the Availability of Natural Resources to Humans

Cartograms can visualize the impacts of climate and population change on the availability of natural resources to humans. Cartogram set “Natural resources under stress” (Figure 3) visualizes, as an example, the availability of renewable groundwater to humans, that is, per-capita renewable groundwater resources, for both current and future conditions, using the simulation results already presented in Figure 2. If groundwater availability in 2010 (computed using groundwater resources 1971–2000 and population in 2010) is represented as a cartogram with population in 2010 as distorter (Figure 3b), the world appears to be more water scarce than on the equal-area thematic map (Figure 3a). While Figure 3a draws the attention of the eye to large areas with high values of per-capita groundwater resources that are mainly caused by very low population densities (Arctic, Amazon, and Australia), densely populated areas where many people suffer from low water availability (or not) become the focus of the eye in Figure 3b. The conventionally projected map in Figure 3a visualizes groundwater availability on areas, the cartogram in Figure 3b groundwater availability for humans. The cartogram communicates clearly that a very large part of the global population suffers from low groundwater availability, while this information is not provided by the traditional thematic map.

The cartogram in Figure 3c shows the groundwater availability situation in 2085 as affected by climate and population change (groundwater resources 2070–2099 and population in 2085), using a population scenario for 2085 as distorter variable. Due to the large range of groundwater availability values, from almost 0 m³/(cap yr), to more than 20.000 m³/(cap yr), availability classes represented by different colors must be large, too, and the change of groundwater availability between 2010 and 2085 is not well recognizable when comparing the cartogram for 2010 (Figure 3b) with the cartogram for 2085 (Figure 3c). However, the change in exposure, which is visible by the different distortion, is visualized well by the two cartograms. The projected increase of global population between 2010 and 2085 from 6.6 to 9.9 billion is visualized in Figure 3c by increasing the total land area shown in Figure 3b in proportion to the global population increase. This also ensures that population per map area is the same in Figures 3b and 3c. Without increasing the total land area represented in Figure 3c, countries with a smaller than average population increase would be smaller in Figure 3c than in Figure 3b, which may be confusing. Due to the large projected population increases, Sub-Sahara Africa increases strongly in size, while many European countries, China, and Japan become smaller than on the cartogram for 2010 due to population decreases.

As even large temporal changes of groundwater availability may not be visible because the future value is likely to remain in the same color class, a cartogram showing percent changes in groundwater availability is best to visualize changes in groundwater availability between current and future conditions (Figure 3d). To understand the differential impacts of CC versus population change, this cartogram can be compared to the cartogram in Figure 3e that represents the change in groundwater availability due to CC only (equivalent to the change in renewable groundwater resources due to CC). The comparison shows that even large percent increases in groundwater resources due to CC can become decreases in groundwater availability, for example, in India and Africa. In most areas of the globe, CC-induced decreases in groundwater resources are exacerbated by projected population increase, except in some countries including China and Japan.

4 Cartograms for Visualizing the Countries' Responsibility for CC

Responsibility for greenhouse gas emissions and thus CC risks can be visualized by univariate cartograms in which the amount of greenhouse gas emissions serves as the distorter variable. In cartogram set “CC responsibilities” (Figure 4), country polygons are distorted in proportion to the countries' emissions, population, and GDP as data for greenhouse gas emissions are mainly available for countries and not for grid cells. Due to data availability, the cartograms generated in this study are restricted to fossil-fuel CO₂ emissions.

Contrasting a cartogram where the country polygons are distorted according to the population of the country in 2010 (Figure 4a) with a cartogram with the countries' fossil-fuel CO₂ emissions in 2010 (Figure 4b), the differences between per-capita emissions among countries become obvious. The very small per-capita emissions in Sub-Sahara Africa with the exception of South Africa are particularly prominent, as are the very high emissions in the United States and Europe. If the countries' per-capita emissions had been the same in 2010, the cartograms would be identical.

However, the responsibility for CC does not stem from greenhouse gas emissions in any year but from the sum of emissions caused by humans over time as CC is caused by an increase of greenhouse gases in the atmosphere as compared to natural conditions. Therefore, the countries' responsibilities for CC can be visualized by a cartogram in which the country polygons are distorted according to the fossil-fuel CO₂ emissions cumulated from preindustrial time until 2010 (Figure 4c). If two countries have the same size in this cartogram, they have the same responsibility for CC. Obviously, the old industrial countries including Great Britain, Germany, Russia, and the United States have a particularly large share of global cumulative emissions and their size in this cartogram is much larger than in the cartogram with emissions in 2010 as distorter (Figure 4b).

The similarity between a cartogram in which country polygons are distorted according to the countries' GDP in 2010 (Figure 4d) and the cartogram with cumulative emissions until 2010 as distorter (Figure 4c) is striking. The similarity between the GDP-distorted cartogram and the cartograms with population or emissions in 2010 is much smaller. With exceptions that can mostly be explained well, the country shapes in both cartograms are rather similar, for example the United States, China, Europe as a whole and many individual European countries such as Great Britain and Germany. Countries with relatively smaller shares of cumulative emissions as compared to GDP include countries with significant hydropower production such as Norway and Brazil but also countries that became industrialized after World War II such as Japan and South Korea. Countries with a recent decline in economic development such as Russia and South Africa appear larger in the cumulative emissions cartogram than in the GDP 2010 cartogram. Still, the overall similarity between both cartograms visualizes that the current wealth of countries is in most cases built on detrimental fossil-fuel emissions.

Please note that a cartogram with total greenhouse gas emissions as distorter would be less similar to the GDP 2010 cartogram than the depicted cartogram with fossil-fuel CO₂ emissions. Matthews et al. (2014) computed national contributions to CC until 2005 by not only considering fossil-fuel CO₂ emissions (from Boden et al., 2013, as in our study) but by estimating national CO₂ emissions due to land use, land cover change and forestry (based on the decline of forested area since 1805) as well as emissions of other greenhouse gases. They pointed out that their ranking of countries should not be considered as definitive due to both the rather high uncertainty of the non-fossil-fuel emissions and how they contribute to global warming. According to Matthews et al. (2014), Brazil and India have contributed to CC about one third of the United States (instead of one thirtieth and one tenth, respectively, as shown in Figure 4c), and Indonesia should be one tenth the size of the United States instead one fortieth. In addition, the relative sizes of Thailand, Columbia, and Argentina would increase considerably. On the other hand, the size of Japan would decrease from 15% of the size of the United States to 9%, while the relative sizes of Germany and the UK would not change appreciably.

5 Discussion

Design of visualizations to communicate knowledge about CC was reviewed and discussed by Stephens et al. (2012) and Harold et al. (2016). Lorenz et al. (2015) and McMahon et al. (2016) concluded from empirical studies on the perception of CC visualizations that (1) no clear design recommendations can be given and (2) ideal solutions for tailored communication of climate data for decision making on adaptation may not be found due to a lack of within-group homogeneity and the disconnect between actual and individually perceived comprehension by viewers. The visualizations considered in the above studies, however, did not include cartograms. In the following sections, I discuss visualization by cartograms with respect to distortion accuracy, conveying of complex information and triggering of moral emotions.

5.1 Distortion Accuracy

In the case of global cartograms, it is impossible to achieve a perfect density equalization for the distorter variable if polygons are to remain contiguous. The higher the spatial heterogeneity of the distorter variable is, the less likely it is that density of the distorter variable is even approximately equal everywhere on the cartogram. Distorting municipality polygons in Lower Saxony and Bremen (Germany) according to their population, Burgdorf and Huter (2009) calculated deviations from the map area that would be proportional to population of up to 35%, with an average of 0.04%. I evaluated distortion accuracy by plotting the areas of the distorted shapes (0.5° grid cells or country polygons) against the distorter variable and then estimating a linear regression equation with an intercept of zero (cartogram area = k · population). In case of the 204 country polygons and the distorter variable population in 2010 (Figure 4a), the coefficient of determination r² is 0.997, but this high value hides significant deviations in particular for low population countries. Often, densely populated countries such as Singapore are not enlarged enough, and the size of countries with a low population density such as Greenland and Australia is not reduced enough. Among the 30 countries with the largest population, k varies between 344 and 546, with 16 countries having a k between 430 and 470. The coefficient of determination decreases with decreasing mesh size, decreasing from 0.997 in case of a mesh size of 2048 to 0.982 in case of a mesh size of 512. If a blur factor is applied (not recommended or necessary here), r² decreases, and more strongly in case of smaller mesh sizes. With a mesh size of 2048, r² is also 0.997 for the distorter cumulative CO₂ emissions (Figure 4c) and 0.994 for the distorter GDP (Figure 4d).

Distortion accuracy for the 0.5° grid cells is much lower, with an r² of 0.406 only for the distorter population in 2010. This can be explained by the higher spatial heterogeneity of population density (population per land area) among grid cells as compared to population density in countries. Population in the 204 countries varies between 3.000 (Falkland Islands) and 1.35 billion (China), population in the 66,896 0.5° grid cells between 0 and 19 million inhabitants. While population densities in countries approximately range from 4 to 500/km² (not taking into account 20 very small countries with higher population densities as well as the low density countries Greenland and Falkland Islands), population density in the grid cells approximately ranges from 0.0005 to 8000/km² (not taking into account the 20 grid cells with the highest population and the approximately 7500 grid cells with a population of less than 1). As population density among grid cells varies by a factor of 10⁷ and not only by a factor of 10², distortion accuracy is low at the level of individual grid cells. As an example, densely populated grid cells along the Egyptian Nile and its delta are bordered by grid cells with nearly zero population in the surrounding desert, which makes it impossible to distort grid cells according to population if they are to remain contiguous.

What are advantages and disadvantages of population cartogram that are either grid-based (Figure 3b) or country-based (Figure 4a)? Even though the grid cell-specific distortion accuracy is very low, the sizes of larger spatial units in Figure 3b are rather similar to those in the high-accuracy cartogram in Figure 4a, such that for spatial units that are well recognizable at the global scale, distortion in gridded cartograms appears to be reasonably accurate. An advantage of gridded global cartograms is that scarcely populated parts of countries such as Alaska (United States), the Amazon region (Brazil) and Tibet and Xinjiang (China) are shown in accordance with their low population density and not in accordance with the much higher average population density of the whole country. This could, however, also be regarded as a disadvantage, as the original shape of countries, which is familiar to many people, becomes more distorted in grid-based cartogram, and the country is therefore less easily recognizable.

5.2 Can Cartograms Convey Complex Information?

Complex thematic maps that visualize more than one attribute for spatial units are usually composed of several layers, for example, one variable as fill color of a polygon and a second or more variables as hatching or stippling pattern or proportional symbols. In case of global thematic maps where the variables have a high spatial heterogeneity, that is, only small contiguous areas with the attribute to be shown being in the same class, it is necessary to employ simpler graphics. In order to make attributes of small spatial units, for example 0.5° grid cells, discernable, it is possible to visualize two attributes by color, one by color hue and the other by saturation. The disadvantage is that only four to five classes can be differentiated on these maps (e.g., Figure 1 of Schewe et al., 2014 and Figure 5 in Döll, 2009). In cartograms, distortion is used as another means to convey information. Therefore, bivariate cartograms can convey more information than traditional thematic maps. In the particular case of conveying global-scale information about resource availability and the risks of climate and population change (Figures 2 and 3), the bivariate grid-based cartograms allow conveying information about human exposure with high spatial resolution, which would not be possible with conventional thematic mapping methods.

In case of country-based univariate cartograms that are to convey a much smaller amount of information than grid-based cartograms, with about 200 versus about 67,000 spatial units, x-y graphs showing, for example, the countries' emissions as a function of the GDP are alternatives to cartogram set “CC responsibilities” (Figure 4). These alternatives would present the magnitude of the distorter variables in a more accurate way. Thus, sets country-based cartograms convey more complex information than such graphs only in the sense that they additionally inform about location and adjacency of countries.

In their empirical research of cartogram recognition, Dent (1975) and Griffin (1983) found that distortion can convey information only if a conventionally projected map is visible together with the cartogram. This agrees with my experience with different types of cartograms that I have shown in oral presentations. Alternatively, the undistorted map can be shown with the same size or as a smaller inset, or as a background map. The disadvantage of the background map is that depending on the distortion, large parts of the, for example, gray undistorted background map is covered by the cartogram such that the degree of distortion is not recognizable anymore (compare Figure 3 in Matthews et al., 2014).

The more unfamiliar cartograms can be as effective and efficient as traditional statistical mapping techniques, including choropleth maps and graduated circle diagrams (Kaspar et al., 2011). Han et al. (2017) empirically investigated the usability of univariate global country-based cartograms to show the area of certain land-cover types as compared to a global map with proportional symbols, and did not identify relevant differences. Aschwanden (1998) found that participants are able to comprehend a complex theme well when it was displayed in more than one cartogram. To overcome recognition difficulties, Tobler (2004) suggested adding to cartograms additional geographic information for orientation such as the country outlines in Figures 2 and 3. In the context of data mining and knowledge discovery, Vellido et al. (2013) proposed to use cartograms for the visualization and interpretation of non-geographic multivariate data. These findings support that sets of carefully selected cartograms like those shown in Figures 2-4 can be used to convey complex information.

5.3 Can and Should Cartograms Trigger Moral Emotions?

Using the terminology of Mühlenhaus (2013), cartograms are certainly “scientific” as they aim at representing data in a clear, accurate, and efficient way, and their production is reproducible. They are not “persuasive” maps, that is, maps that aim at promoting particular beliefs while neglecting to represent the underlying data well (Mühlenhaus, 2013). Still, the cartogram sets shown in this paper were generated with the hope that they make the viewers see (and feel?) where on Earth humans (and not land areas) are impacted by CC risks and water availability (Figures 2 and 3) and to what extent current wealth of countries is built on historical emissions of harmful greenhouse gases (Figure 4). By showing not only the hazard but also, by distortion, human exposure (or a combination of exposure and vulnerability, Figure 2d) to the hazards, a more holistic representation of risks of climate and population change is achieved in Figures 2 and 3. Visualization of human exposure may be expected to lead to emotions such as compassion for those that are shown to be affected by potential negative impacts. By putting humans in the picture (in case of cartograms with population as distorter), “cartograms (…) produce a more socially just form of mapping, by giving people more equitable representation in an image of the world” (Dorling, 1996, p. 4).

Regarding responsibilities for CC, visual comparison of Figure 4a with Figure 4b or 4c allows the viewers to easily recognize and acknowledge the inequity among the countries regarding harmful emissions, which could trigger moral emotions as equity is considered to be morally good by many people. Comparison of Figures 4c and 4d may induce emotions of responsibility in viewers living in wealthy countries. While triggering of emotions may be considered to be inappropriate for providing scientific information, “emotions are necessary for understanding the moral impact of the risks of CC, and they also paradigmatically provide for motivation” (Roeser, 2012, p. 1033).

Given the experience of myself and other cartogram producers, cartograms do trigger at least some type of emotions, increase the attention of the viewer and may therefore enhance knowledge transfer. Barford (2017) confronted school teachers from three countries with two cartograms in which country polygons where distorted according to population living either on less than USD 2 per day or on more than USD 200 per day. Not finding Kenya on the latter map as Sub-Sahara Africa (except South Africa) was reduced to a black line, Kenyan school teachers reacted with humor and chuckled or laughed while describing the map. Dorling and Barford (2006, p. 39) write: “WE LOVE our maps. At first glance, people are shocked by them: the shapes look familiar, yet everything is absurdly distorted. Without even thinking, they have learned something about the world they live in. (…) It would be hard to provoke any excitement by confronting someone with spreadsheets filled with numbers. But you just can't help looking at these pictures. After all, a new view of the world, rather like the famous Earthrise photo taken by Apollo astronauts, is a compelling sight.” Webb (2006, p. 800) stated about density-equalizing methods that “the potential of such techniques for producing startling representations that challenge our preconceptions seems — unlike world maps — unbounded.”

6 Conclusions

Cartograms have not yet been used for visualizing risks of CC. Regarding responsibility for CC, Matthews et al. (2014) showed a cartogram that was distorted by national contributions to CC but they did not relate these contributions to population or GDP to visualize aspects of equity and the relation to wealth. In this paper, I have explored the potential of global cartograms for communicating risks of CC, also in relation to the impact of population change, as well as the potential of cartograms for communicating responsibilities for CC.

Risks of CC arise from the combination of hazard, exposure, and vulnerability. As grid-based cartograms with population as distorter allow visualizing both the hazard and the exposure to the hazard, they visualize risks in a more comprehensive manner than traditional thematic maps that in many cases can only convey information on hazards. If population weighted by a vulnerability index is used as distorter, even all three risk components are represented in one cartogram. A caveat regarding the distortion of grid cells according to population is that due to the high spatial heterogeneity of population in 0.5° grid cells it is not possible to achieve a perfectly equal population density in all distorted grid cells while keeping the cells contiguous. Overall distortion of larger groups of grid cells, however, is approximately proportional to population. Thus, the presented cartograms appear to be suitable for visualizing population distribution, taking into account that some departure from density equalizing can be tolerated as humans' visual estimates of area are not very accurate (Tobler, 2004).

Therefore, I recommend to visualize CC risks by bivariate grid-based cartograms that show the CC hazard in color and exposure (and vulnerability) by distorting grid cells according to population or a combination of population and a vulnerability indicator. In case of risks for humans, the distorter would be human population and vulnerability, but in case of vulnerability of other biota, their population numbers and vulnerabilities could be visualized by distortion. Bivariate gridded cartograms have the potential to lead to an improved integration of the risks of CC into the management of natural resources, for example, water resources (Döll et al., 2015), and can be used in participatory CC risk management processes (Döll & Romero-Lankao, 2017). Gridded cartograms distorted by population are also more appropriate than traditional thematic maps for showing the availability of natural resources to humans (Figures 3a and b).

An important result of this study is that for conveying information by cartograms it is not optimal to show just one cartogram alone. Instead, carefully designed sets of cartograms such as those presented in Figures 2-4 enhance the capability of the viewer to perceive the information provided by distortion. In most cases, these sets should include a conventionally projected map, preferably an equal-area map, for reference. In cartogram sets that visualize a situation at different points in time and use population as distorter, such as in set “Natural resources under stress” (Figure 3), increasing global population is best visualized by increasing the total land area represented in the cartogram in proportion to the global population increase. By combining, in Figure 4, cartograms that are distorted according to four different attributes of countries (population in 2010, fossil-fuel CO₂ emissions in 2010, cumulative fossil-fuel CO₂ emissions until 2010 and GDP in 2010), direct visual correlation among these attributes becomes possible. Viewers of this set of cartograms get a visual impression of the lack of global equity and they see that the countries' wealth has been built on harmful emissions from which a responsibility of wealthy countries for CC mitigation and financial support for climate adaptation elsewhere may be deduced.

I can only suspect that the presented cartograms trigger moral emotions by either showing who is exposed to the hazards of CC where or by showing inequity and the correlation between wealth and harmful emissions. I recommend that empirical studies about the capability of grid-based and polygon-based global cartograms to convey complex information and to trigger moral emotions are conducted in the future, with a special focus on risk communication.

Acknowledgments

The author thanks Hans-Peter Rulhof-Döll for data processing and generation of the cartograms as well as Irene Marzolff for her valuable comments on the first draft. The reviewer Anna Barlow helped to improve the manuscript. Data used for Figures 2 3 and 4 can be downloaded at http://www.uni-frankfurt.de/45217892/datensaetze

Appendix A A

For seven countries, GDP data were not obtained from World Bank but other sources (Table A1). GDP (“at official exchange rates”) of Greenland, Falkland Islands, North Korea, Somalia and Syria was obtained from the CIA World Factbook (https://www.cia.gov/library/publications/resources/the-world-factbook) for years between 2007 and 2014, and roughly adapted to 2010 using provided growth rates. GDP of Myanmar for 2010 was provided by Trading Economics (https://tradingeconomics.com/myanmar/gdp), GDP of French Guiana by Wikipedia (https://en.wikipedia.org/wiki/French_Guiana).

Table A1. GDP around 2010 derived from sources other than World Bank (used in Figure 4d)

Country	GDP in billion USD	Source
Greenland	2.2	CIA World Factbook
Falkland Islands	0.2	CIA World Factbook
North Korea	28	CIA World Factbook
Somalia	5.8	CIA World Factbook
Syria	35a	CIA World Factbook
French Guiana	4.9	English language Wikipedia
Myanmar	50	Trading Economics

a Very rough pre-war estimate.

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Citing Literature

Volume5, Issue12

December 2017

Pages 1182-1195

This article also appears in:

Cartograms Facilitate Communication of Climate Change Risks and Responsibilities

Abstract

Key Points

Plain Language Summary

1 Introduction