Mapping the Fourth Dimension

Our 3-dimensional world is the usual subject of 2-dimensional maps; their purpose is to accurately depict geographic extent on a readable/publishable surface, with or without thematic content.  The purpose of adding the 4th dimension of time is somewhat intuitive- maps of the same area through time can give a viewer an understanding of change in some feature.  The problem in depicting the 4th, temporal, dimension on a 2-dimensional surface is remedied by the use of various spatiotemporal visualization techniques, the most effective of which, it could be argued, is the map animation.  The simplest form of this variety of cartographic visualization is the display of two or more maps, adjacent to one another, showing the same geographic area at different times.  The change in the area depicted is evident in the difference(s) between the various maps.  While this method is effective, actual animation on a map is an even more salient method of displaying areal change through time.  

       
The above graphics represent two years- 1790 and 2000- and contain proportional symbols indicating the most populous cities in the U.S. at those times.  The two maps are actually the beginning and ending frames of an animation, which shows the same map for each 10 year period between 1790 and 2000, and thus gives the viewer an idea of where the major centers of population in the U.S. were for each decade.  The ease of doing so with a simple animation, cycling through each decade, is fairly large in comparison to creating and displaying something singular including separate maps, one for each decade.        

Bivariate Maps of the Choropleth Persuasion

The depiction of multiple variables on the same map, displayed to highlight a relationship between the two, is no simple feat of cartography.  The choropleth map, in particular, is best suited for indicating the geographic prevalence of a single, or single incidence of multiple, phenomena.  Mapping with varying color shades to indicate the prevalence of two separate variables- the areas where there is a high prevalence of one and not the other, and areas where there is a high prevalence of both- is an ambitious task by any estimation.  

The use of the bivariate choropleth map may be employed for this depiction of two separate variables, and thus indicates the relationship between the two.  Above is a representation of both rates of obesity and physical inactivity, by U.S. county, with the use of two different hues with separate quantitative color progressions.  The legend in the lower left illustrates these with a 9-square color palette, which varies by hue according to the X- and Y-axes, and by lightness progressing across both.  As the colors progress towards the upper right corner of the cube, the colors are meant to indicate a high prevalence of both variables.  Thus, the viewer is able to use the 9 different colors there to visualize the spatial relationship between the two.  The current version of ArcMap in use, though, doesn't support the automated creation of this variety of legend, and it must be assembled by hand.  Though creating a 9-color legend, which varies in hue and lightness along two axes, is no easy feat, it is unarguably a valuable practical lesson in applied color theory.   

Infographics: a Method for Cartography Display and Presentation

Making maps, to present and display to others, is all well and good, but what of the context for the map's thematic content?  Presenting information to an audience with a comprehensive understanding of the map's content, perhaps in the form of a presentation, can render the map itself a supporting visual aid.  It is when the map stands alone, and is meant to be viewed and interpreted as a stand-alone visual, that the "infographic" can be an indispensable tool.  Infographics add information that can be integral to understanding a thematic map's purpose, and can lend support to the map as an educational or explanatory visual.  Though this information is, by necessity, often simplified and graphically embellished, it's a valuable tool for presentation nonetheless.  

Above is a visual intended to convey the seriousness of the possible link between increasing rates of drug poisoning mortality and rates of uninsured adults.  This is, by no means, extensive or scholarly research, but is rather intended to raise a question of whether this is an issue that may require more investigation.  The maps, on the left, give an abridged picture of what the geographic distribution of the two factors- rates of drug poisoning mortality and percent of uninsured adults- currently looks like. The darker colored counties that are displayed as such in both maps are locations where prevalence of both factors is increased, which, as the other supporting graphics indicate, may be cause for some concern.  The two charts on the right, a scatterplot showing the general relationship between the two variables, and a bar chart of where the five states with the highest percent of uninsured adults fall in relation to drug poisoning mortality average, summarize some of the quantifiable relationships immediately evident in the data.  The graphics in the center give a few statistics that may support the contention that the relationship between the two variables is serious enough to warrant further investigation.  The infographic, as a whole, sometimes tells more of a story than a map, displayed on its own, is capable of. 

Terrain Visualization- 3D Information in a 2D Map

Maps which include 3-dimensional information are ubiquitous, and not just in the form of those that employ stereoscopic effects for the wearer of the right special glasses- 3 dimensions are regularly portrayed on a 2-dimensional surface with the use of contour lines, hillshading, and hypsometric tinting.  The purpose of these techniques is to allow the viewer to more accurately visualize the varied elevations and land formations within the mapped area.

Hillshading, in particular, can provide a great deal of detailed visual information, which is readily apparent to even a map user unfamiliar with the finer points of deciphering contour lines.  Above are two hillshaded images of the same overhead view- the left image is created with shading that imitates a light source located in approximately the sun's position for this area on the 15th of January at 8 am.  The right uses the shading created by a light source in a particular position and elevation, one which is a default within ArcGIS.  Thought these two images use the same color scheme- that is, the same colors in both for high and low elevation values- it's apparent that the visual images given by each are quite disparate.  It could be contended that the image on the right, with the default light source position, gives a more readily interpreted picture.  The depression in the terrain made by the canyon is immediately evident, outlined with the darker red/brown shadows in the mostly yellow terrain.  The left image could easily be misinterpreted to be depicting a series of hills, in yellow, rising out of the terrain shaded in darker red/brown.  Clearly, the light source's position is an important consideration in the creation of a hillshaded image- and is not always best-placed in the "accurate to earth" location.  

Thematic Mapping's Finest: the Choropleth Map

No cartography education or body of knowledge is complete without the (seemingly) ubiquitous choropleth map- that which portrays a derived quantitative measure by some administrative unit.  The map above displays the percent change in population for Georgia's counties, which includes both population gains, with positive percentage values, and population losses, which are shown with negative percentage values.  The classification scheme used to group the counties according to their percent increase and decrease is the Natural Breaks method, slightly modified.  This method gives a decent visual of where the county gains and losses were, without obscuring any patterns or trends, by maximizing the similarity of values within classes, and maximizing the differences between the classes.  The colors chosen for each class use a diverging color ramp, where the lightness and saturation increase with the subsequent relative size of the population increase and decrease, which uses two different hues, in order to distinguish easily between gains and losses.  Thus, the class directly in the middle represents counties with very little to no population change, and is the least saturated and lightest shade on the map.  The legend itself gives indication of the value ranges for each class, with the average percent change at the bottom.  The labels for "increase" and "decrease" are added with vertical orientation to the side of the classes, for an easy visual of the direction of the scale.  The processes of normalizing derived data, evaluating thematic and data content, choosing effective colors and scale, and a plethora of other small decisions are integral to the construction of a functional and aesthetically pleasing choropleth map.  These skills, in particular, form the foundation of an effective cartography skill set.     

Map Symbols & Legends

The symbols and legend included on a finished map are details carefully chosen by the map's designer- they convey the primary meaning of the map, and, if they are unclear in any manner, can arguably obscure the map's intended purpose.  In the case of symbols rendered proportional to the relative size or magnitude of the thematic feature, it is imperative to choose colors and shapes that maximize the viewer's understanding of the phenomena being displayed on the map.

The above thematic map intends to convey the net increase and decrease in jobs for each state in the U.S. for the period between 2007 and 2015.  The circle sizes are proportionate to the magnitude of net loss/gain, and the color indicates whether the number of jobs represents an increase or decrease.  The legend, in the lower left corner, uses hollow circles to represent the relative numbers, as it applies to both the increase and decrease amounts, and indicates the colors red and green represent the net loss and gain.  The increase and decrease amount circles on the map are two feature classes, created by querying and exporting both sets of values from an original layer that contained both positive and negative values in its attribute table.  This was accomplished by adding a field to the feature class containing negative values, and calculating the absolute values of those numbers, as the layer symbology, as a display of proportional symbols, does not support the use of negative values.  Thus, each layer- one representing net increase, and the other net decrease- is symbolized separately, but with the same symbol range, which allows each set of values, both negative and positive, to be symbolized in differently colored circles.    

The Understated Importance of the Cartographic Element of Color

Color, inasmuch as it is used as a cartographic tool, is probably taken for granted by most map viewers- another map element unremarkable the vast majority of the time, except when it is used poorly, and then becomes unmissable.  The color palette chosen by the map maker isn't purely an aesthetic decision either, it is carefully considered, so that the feature being displayed appears in a logical context.  A map with purple water features and blue forest tracts wouldn't be considered seriously by most, save as a piece of art.  Color is also of utmost importance within the context of the choropleth map, which displays some feature, grouped into classed categories, based upon some measurement.  Color variation for different classes is often seen as a change in saturation or lightness, within the same general hue.

Above is a linear color ramp- the darkest and lightest shades vary by a certain amount for the R, G and B values, and the classes/shades between are a linear progression of those values, yet the color remains a constant hue.  

The light/dark progression of one hue is, however, augmented, as in the ramp above, by adjusting the amount of the interval between the R, G and B values between the darkest colors.  The object here, were these colors being used in a choropleth map, would be to retain the same hue for all of the classes, while appreciably varying the lightness and saturation, so that whatever is being symbolized on the map is shaded in colors different enough to tell one apart from the other, based on the value of the hue.

Finally, we have a color ramp produced by Colorbrewer.org, which is an exceedingly useful tool for generating color ramps such as these.  The above ramp uses a slightly different hue for the top, darkest class, and then varies the lightness of the pinker hue in the classes below.  The use of this type of ramp would be invaluable in a map with which one might want to display different areas in different shades, to indicate the amount of some measurable thing- the colors are all in approximately the same hue, and yet vary enough from one another such that one area would be visually distinct from another.

Typography & Making Map Labels (part II)

Of the many small details essential for a well-made map, labels rank among the most likely to be overlooked.  They are a small element that, when done well, warrant no particular notice, but, when executed poorly, have real potential to destroy a map's aesthetic beauty and practical use.  A working knowledge of typography basics is an integral skill in creating functional and visually appealing map labels.

Mapping the City of San Francisco presents a perfect opportunity for practicing skills and various techniques in effective map labeling, and the above map is my submission.  What would be considered a "good" label has a number of characteristics, among them its legibility, and the degree to which it contributes to a harmonious and visually pleasing display.  Thus, there is a balance to be struck between making the label easily readable, but not so ostentatious that it overpowers other, and possibly more important, details within the map.  Another potential challenge is keeping each label, in accordance with general map-making convention, within the boundaries of, or adequately adjacent to, whatever it is intended to be labeling.  Treasure Island in the map above, for example, isn't wide enough to accommodate its label at the appropriate text size, and thus the decision to change its orientation.  Small choices such as these, and a plethora of various others, lead to useful labels and a functional map.     

Coordinate Systems & Projections

Map projections and coordinate systems are at the heart of a map's utility as location and navigational aid.  The principles involved in selecting and/or analyzing a projection or coordinate system for a map are intuitive in nature, but the underlying concepts can become a bit complicated.

This map of Michigan is projected using the Hotine Oblique Mercator Azimuthal projection, which is an intimidatingly lengthy name, but means that this is a cylindrical, oblique version of the Mercator projection.  As such, it is conformal, and displays the state as accurately shaped.  This particular projection is suitable for Michigan because it doesn't divide the state into multiple zones, like a State Plane or UTM grid would, as the state encompasses multiple zones of both.  Also, as this is intended to be used as a general reference map, the projection is well suited because of its conformal nature, which preserves the distinctive mitten shape of the lower peninsula.    

Revisiting the Basics of Cartography & Map Design Principles

Thus begins a new semester, and a welcomed review of cartography basics.  Having learned to make maps the right way in the past year, it is with particular satisfaction that I revisit the novel concepts of good map design once again this week.  Specifically, there are five map design principles accounted for, including legibility, visual contrast, figure-ground relationships, hierarchical organization, and balance.  

The above, ideally, represents all five of the principles of map design.  Legibility is preserved by the simple display font, and the sizes of the various text.  The text is of a size and color that allows for maximum visual contrast of the graphics.  The symbols for the various mapped features are large enough to be seen, but one doesn't obscure all of the others.  Visual contrast is also maximized with the less saturated color hues used for the background of Travis County, and the surrounding area.  The inset map colors are less saturated as well, to preserve their lower position on the visual hierarchy, but still have enough contrast to visually differentiate them from the other map elements and the background.

Figure-ground relationship is represented with the darker color background for Travis County, the map's focus, and the lighter shade of the surrounding area.  This allows the focus county to stand out, as it is highest on the visual hierarchy among the map's graphics.  Further, the most important map symbols, the golf courses and rec. centers, are the most saturated and brightest hues, bringing them forward based on their relative importance to the map's theme.  Hierarchical order is also seen with the relative size of the various elements- the title and subtitle text and the legend text are the largest, as they are meant to be among the most visible elements.  The scale bar, north arrow and inset map are smaller, as they represent ancillary map elements, and the citations at the bottom are the smallest, as they are least central to the map's theme.

Balance is preserved with the position of the various graphic objects on the page.  The mapped area itself is centered, with the title and subtitle text centered above it.  The legend and inset map are positioned on the bottom, left and right justified, with the scale bar and north arrow centered below and between.  Finally, the citation text for the map author and data sources are positioned along the bottom margin, and are justified to the right and left sides of the page as well, which hopefully balances the various graphics and whitespace.  The objective here is to create a harmonic balance on the page, so that nothing looks crowded or out of place, which, when properly executed, creates a finished and professional-looking map.