diana maps

An Exclusive Directions Magazine Series

In the third part of our series on Communicating with Maps, Diana Sinton discusses the complex and important ideas about the inherent role of uncertainty in the maps we produce. As a means of communication, published maps are trusted by the public well beyond what they may have earned. My theory is that so few people have ever made maps that they have no sense of how the data might have been collected, what decisions could have been made during map design, and how many opportunities for error the whole process provides, that they just accept a published map at face value.

But, if you were to hand someone a blank piece of paper and ask them to draw their hometown, the experience would be revealing. They may recall some topological relationships well — such as the sequence of streets between their home and school, or how to get to a friend’s house — but most people would also experience a tremendous amount of uncertainty. Maybe the results would include locational errors (drawing the school north rather than south of an intersection), or an attribute error (labeling a building a post office when it was really a bank). Just as likely, there would be blank areas in the sketch. Through this experience, the mapmaker would become aware of terra incognita and uncertainty about what was where.

In a similar way, every map contains imperfections. In his iconic book, Mark Monmonier explains how we lie with maps through manipulations and distortions, deliberate or otherwise. Uncertainty, errors, mistakes and omissions are inevitable. The complexity of the natural and social world must necessarily be simplified and generalized to be mapped, and there are necessarily subjective decisions that are made in the map design process. That’s just the way it is, even though few are aware of it.

Meanwhile, maps continue to be the most popular and common form of graphic representations of our natural and social world. They’re used worldwide in decision-making processes every day. That won’t change, but more could be understood about uncertainty and error within the realm of geospatial information.

The analog of statistics

Similar problems exist in the world of numbers. For example, a probability is a derived calculation of the likelihood of an event occurrence. The likelihood of any particular event outcome depends on how many total outcomes are possible. Statisticians use numerical confidence intervals to communicate the idea of how much variability there could be in the outcomes if one were trying to replicate that same measurement, pattern, etc. Graphically, confidence intervals can be represented as error bars depicting the possible variability around a measured value. Probabilities, confidence intervals and error bars are ways that we communicate about the uncertainty of measured, quantitative values in the social and natural world. Recognizing and acknowledging this uncertainty is part of the scientific process, though that can be a difficult message to accept.

There are equally as many ways that uncertainty, and error, are part of the mapping process, and standards exist for how to measure and document it. The National Standard for Spatial Data Accuracy, which in the late 1990s replaced the 1940s National Map Accuracy Standards, applies a root-mean-square-error approach, together with 95% confidence intervals, in determining the positional accuracy of geospatial data. Take a dataset of X and Y point coordinates that fall at the center of two intersecting roads and compare the distance to the same point coordinates already accepted as being true (because they were derived by high accuracy methods or by an independent source, for example). Once the RMSE is calculated between these two datasets, the NSSDA explains that:

"Accuracy reported at the 95% confidence level means that 95% of the positions in the dataset will have an error with respect to true ground position that is equal to or smaller than the reported accuracy value. The reported accuracy value reflects all uncertainties, including those introduced by geodetic control coordinates, compilation, and final computation of ground coordinate values in the product."

Requiring data to meet standards is one approach to managing uncertainty and reducing the probability of errors. Although assessing potential errors in data sets can be a challenge, undertaking such quality control efforts can build trust in an organization. A good example of this is the European Marine Observation and Data Network, which requires anyone contributing data to complete a Confidence Assessment step in the submission process.

Scale

One way to tolerate and mitigate uncertainty is modifying scale. Measurements of sinuous perimeters, such as coastlines, will vary significantly depending on the length of the unit of measurement. There is power in method, and more specific methods are perceived to be more powerful. Modern mapping is filled with situations where our methods don’t align with our measurements, tools or objectives. Our version of measuring with a micrometer, marking with chalk and cutting with an axe could be measuring with a smart phone, marking by heads-up digitizing and clipping with an XY tolerance of inches. Our use of geospatial data at particular scales, resolutions and precisions should be informed by and in alignment with our mapping intent, our acceptance of error and our tolerance for uncertainty. Mike Bostock illustrates this deftly with his explanation of geometric line simplification, and John Nelson reminds us of how absurdly false the decimal-place values of precision can be.

Cartographic solutions

Modifying scale or aggregating data may mask some types of uncertainty, while applying alternative cartographic solutions may be less of a compromise. For decades, cartographers have experimented with map symbols that are fuzzy, indistinct or partially transparent to indicate to the viewer that there is some degree of uncertainty associated with those corresponding data. Essentially these are cartographic versions of statistical box plots, which themselves can also become fuzzy to illustrate variability. Research has shown that certain types of visual variable characteristics, such as color intensity, value or edge crispness, are more effective at communicating uncertainty than assigning different shapes or sizes. Unfortunately, novel cartographic solutions such as manipulating common borders between polygons to suggest an uncertain zone of transition are more readily achieved with drawing than with mapping software at this point.

Choosing how to label values in a map legend can also give evidence as to how confident one is in the values. Select decimal place values that are appropriate for the data in question, and opting for a more vague and relative description, may be the right approach. “Lower” and “Higher” may be just the right way to describe the spectrum of data values being shown, particularly for mapping modeled probabilities such as erosion or wildfire risk.

Concluding thoughts

Sharing news about uncertainty in maps isn’t meant to bring a mapping effort to a grinding halt. Uncertainty within mapping is a given; ignoring it only promotes misuse of maps and undermines the credibility that they do deserve. Instead, expanding awareness may help us develop more effective ways to communicate information to map users and readers. It just goes back to the intent of the map. For example, current research is underway to determine effective techniques for deliberately adding uncertainty and errors to mapped data so that privacy and confidentiality of the data can be maintained while valid patterns are still displayed.

An additional benefit to expanding awareness about uncertainty and errors in maps and mapping processes, is the developing problem of location fraud within the world of location-based services. Or, as this article is quick to point out, the fact that fraud is only one source of location inaccuracy that the business world is realizing it must confront. There is a whole new commercial audience out there that needs to know about minimizing error and uncertainty in the world of mapping and spatial analysis.

Our exclusive series, Communicating with Maps:

Communicating through Maps Part 1: Exploring the challenges and complexities of GIS mapping 

Communicating with Maps Part 2: Discussing the issues with CaGIS President Sarah Battersby

Communicating with Maps Part 3: Considering uncertainty and error

Selected References for Communicating with Maps

An Exclusive Directions Magazine Series

In the second part of our summer series on Communicating with Maps, Diana Sinton discusses issues and advances in mapmaking with cartographer Sarah Battersby, a research scientist at Tableau Software and currently the president of the Cartographic and Geographic Information Society.

Q: What are some of the key developments that you have seen in cartography in the last decade?

A: I think that one of the most exciting cartographic developments in the last decade is the explosion of online mapping and tools for map design. It’s amazing to think about the huge efforts that have gone into making it easy for people to visualize their spatial data, whether as a Google Map mashup, using desktop or online GIS, with d3 or other scripting libraries, etc. The downside to all of this is that I think it is still too easy to make a bad map, and way too easy to distribute that bad map to a wide audience. My cartographic archive of what not to do just keeps growing thanks to all of the great finds on Twitter and Facebook.

On the other hand, there are a lot of people who really care about helping others work with and understand spatial data and there is some great research in cartography, GIScience and in spatial thinking that I think will help shape the next generation of tools that we use to design maps to make them more intuitive, more beautiful and generally more effective for understanding spatial data.   

The growth of the open source geospatial community has also been impressive. It is exciting to see so many people dedicated to improving the world of geospatial data and technology, and to helping the world with geospatial, like the work coordinated by the Humanitarian OpenStreetMap Team.  I think this open source momentum is key in the future of cartography and GIS.

Q: People often bring up the issue that Web Mercator is used as a default projection with web maps. That creates a tension with all of us who were taught in cartography and GIS classes that the Mercator projection is almost always inappropriate for the maps we’re making; it grossly distorts areas toward the poles and is presumed to give people false ideas about the size of countries and even continents. How much of a problem is this really? Can we cross fear-of-Mercator off of our worry list?

A: A few years back I did a bit of “forensic cartography” research on this to try to figure out how Web Mercator became the standard, and I think it is because of the success of Google Maps — the projection is even occasionally referred to as “Google Mercator.” Other online mapping systems changed projection to match. I’m not sure what the logic was behind the original selection of the projection, but it is easier to tile a rectangular projection, and the equations for Mercator are simple.  The conformal property of the projection is also nice for local-scale mapping.  But…is it the only choice? I imagine that any rectangular projection should tile nicely, and I imagine that it won’t be too many years before we have online mapping systems that don’t tie us to a single projection. For instance, Bernie Jenny has done some amazing work with adaptive map projections.

As for the distortion in the Web Mercator projection, I think this is a significant issue for visual analysis.  I’m a big believer in one of Egenhofer and Mark’s principles of Naïve Geography, that “maps are more real than experience.” I have thought of this as the map becoming our source of truth; even if people know that there is distortion in the map I think there are very few people who can successfully compensate for it in reading the map. This is a significant problem for any distance or area-based analyses calculated in Web Mercator coordinates, as well as for the map reader trying to visually make sense of spatial patterns.

I definitely wouldn’t cross Web Mercator off of our list of things to worry about. It is imperative for map designers to be actively thinking about and addressing issues with projection, otherwise their analyses may be hugely incorrect.It is also important for map readers to be cognizant of the distortions in Web Mercator and other projections. I don’t mean that I expect people to be able to identify and calculate distortion, just to maintain a healthy skepticism with their map reading.  

Q: What do you think are the top “gotcha” issues for mapping today, from the perspective of a cartographic software designer? What about from the perspective of John Q. Mapmaker?

A: I think that every cartographer has a set of pet issues that they always look for. For me, I often focus on classification and data normalization. It drives me crazy when I can’t figure out how the mapmaker decided to break up the data into classes. Are those quantiles? Natural breaks? Do the breaks have meaning? Class breaks make such a huge difference in the resulting pattern on the map and it drives me crazy when I see the default 5-class natural breaks map without any explanation. To me this is the sign that the mapmaker doesn’t know much about the data.  

I also see way too many maps that are really just population maps. Should it be a surprise that locations with more people tend to have higher counts of all sorts of other attributes? This is another problem of not thinking enough about the data. If you don’t know your data well, how do you make a map that tells a clear — and appropriate — story? 

Q: You have the perspective of having taught students about mapmaking for many years, and have done much basic research in cartography. Now you are in the position of working with software designers to help them implement good mapmaking principles to help users of commercial software design more effective maps. How is this shift from basic to applied research working? How has it changed how you pose research questions?

A: It is great to focus on specific, applied problems tied to facilitating how people ask and answer spatial questions. There is still much to think about in terms of general cartography, but now that we’re at a time when it is so easy for anyone to take a dataset and turn it into a map, I think about what we can do to help people make better maps faster. My research has always focused on how people understand and use spatial data, so there hasn’t been a change in my research direction, but I have done a lot of stepping back to what I would call the “cartographic primitives.” Lately I’ve been doing a lot of thinking about very basic questions of what information we need to obtain from maps and what characteristics of a map would facilitate finding answers to these questions. I also spend a good bit of time thinking about what makes an interesting pattern on a map and how I can help someone make better choices about their map type, colors or classification to uncover these interesting patterns.

Essentially, I feel like the questions I face now are based on how we can take our collective research and applied knowledge about designing better maps and put it to use helping people that don’t have decades or even semesters of work in cartography. It’s an amazing challenge and hopefully I can do some good to help the world see and understand their spatial data more effectively.

Our exclusive series, Communicating with Maps:

Communicating through Maps Part 1: Exploring the challenges and complexities of GIS mapping 

Communicating with Maps Part 2: Discussing the issues with CaGIS President Sarah Battersby

Communicating with Maps Part 3: Considering uncertainty and error

Selected References for Communicating with Maps