Data ensembles are often used to infer statistics to be used for a summary display of an uncertain prediction. In a spatial context, these summary displays have the drawback that when uncertainty is encoded via a spatial spread, display glyph area increases in size with prediction uncertainty. This increase can be easily confounded with an increase in the size, strength or other attribute of the phenomenon being presented. We argue that by directly displaying a carefully chosen subset of a prediction ensemble, so that uncertainty is conveyed implicitly, such misinterpretations can be avoided. Since such a display does not require uncertainty annotation, an information channel remains available for encoding additional information about the prediction. We demonstrate these points in the context of hurricane prediction visualizations, showing how we avoid occlusion of selected ensemble elements while preserving the spatial statistics of the original ensemble, and how an explicit encoding of uncertainty can also be constructed from such a selection. We conclude with the results of a cognitive experiment demonstrating that the approach can be used to construct storm prediction displays that significantly reduce the confounding of uncertainty with storm size, and thus improve viewers' ability to estimate potential for storm damage.

Many techniques have been proposed for visualizing uncertainty in geospatial data. Previous empirical research on the effectiveness of visualizations of geospatial uncertainty has focused primarily on user intuitions rather than objective measures of performance when reasoning under uncertainty. Framed in the context of Google’s blue dot, we examined the effectiveness of four alternative visualizations for representing positional uncertainty when reasoning about self-location data. Our task presents a mobile mapping scenario in which GPS satellite location readings produce location estimates with varying levels of uncertainty. Given a known location and two smartphone estimates of that known location, participants were asked to judge which smartphone produces the better location reading, taking uncertainty into account. We produced visualizations that vary by glyph type (uniform blue circle with border vs. Gaussian fade) and visibility of a centroid dot (visible vs. not visible) to produce the four visualization formats. Participants viewing the uniform blue circle are most likely to respond in accordance with the actual probability density of points sampled from bivariate normal distributions and additionally respond most rapidly. Participants reported a number of simple heuristics on which they based their judgments, and consistency with these heuristics was highly predictive of their judgments.

Three experiments examined how cognitive abilities and qualities of external visualizations affected performance of a mental visualization task; inferring the cross-section of a complex three-dimensional object. Experiment 1 investigated the effect of animations designed to provide different task-relevant views of the external object. Experiment 2 examined the effects of both stereoscopic and motion-based depth cues. Experiment 3 examined the effects of interactive animations, with and without stereoscopic viewing conditions. In all experiments, spatial and general reasoning abilities were measured. Effects of animation, stereopsis, and interactivity were relatively small and did not reach statistical significance. In contrast, spatial ability was significantly associated with superior performance in all experiments, and this remained true after controlling for general intelligence. The results indicate that difficulties in this task stem more from the cognitive ability to perform the relevant internal spatial transformations, than limited visual information about the three-dimensional structure of the object.