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**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**