THE VISUALIZATION OF UNCERTAINTY by Kristin Potter A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science School of Computing The University of Utah August 2010 Copyright c Kristin Potter 2010 All Rights Reserved THE UNIVERSITY OF UTAH GRADUATE SCHOOL SUPERVISORY COMMITTEE APPROVAL of a dissertation submitted by Kristin Potter This dissertation has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory. Chair: Richard F. Riesenfeld Chrisopher R. Johnson Elaine Cohen Robert M. Kirby Bruce Gooch ABSTRACT The graphical depiction of uncertainty information is emerging as a problem of great importance in the field of visualization. Scientific data sets are not considered complete without indications of error, accuracy, or levels of confidence, and this information is often presented as charts and tables alongside visual representations of the data. Uncer- tainty measures are often excluded from explicit representation within data visualizations because the increased visual complexity incurred can cause clutter, obscure the data display, and may lead to erroneous conclusions or false predictions. However, uncertainty is an essential component of the data, and its display must be integrated in order for a visualization to be considered a true representation of the data. The growing need for the addition of qualitative information into the visual representation of data, and the challenges associated with that need, command fundamental research on the visualization of uncertainty. This dissertation seeks to advance approaches for uncertainty visualization by explor- ing techniques from scientific and information visualization, creating new visual devices to handle the complexities of uncertainty data, and combining the most effective display methods into the Ensemble-Vis framework for visual data analysis. Many techniques exist for graphical data display. However, their usage on data with uncertainty information is not straightforward. This work begins by first exploring existing methods for data visu- alization and assessing their application to uncertainty. New visual metaphors are then presented for the depiction of salient features of data distributions, including indications of uncertainty. These new methods are inspired by proven visual data analysis techniques, but account for the requirements of large, complex data sets. Finally, Ensemble-Vis is presented, which combines effective uncertainty visualization techniques with interactive selection, linking, and querying to provide a user-driven, component-based framework for data investigation, exploration, and analysis. To Mom and Dad CONTENTS ABSTRACT ................................................... ... iii LIST OF FIGURES ............................................... viii ACKNOWLEDGEMENTS ......................................... xi CHAPTERS 1. INTRODUCTION ............................................. 1 1.1 TypesofUncertainty.............................. ............ 2 1.1.1 Experimental Uncertainty....................... ........... 3 1.1.2 Geometric Uncertainty .......................... .......... 3 1.1.3 Simulation Uncertainty......................... ........... 4 1.1.4 Visualization Uncertainty ...................... ............ 5 1.2 The Need for Uncertainty Visualization . ............. 5 1.3 Contributions ................................... ............ 10 1.4 Overview........................................ ........... 11 2. TECHNICAL BACKGROUND ................................. 13 2.1 EnsembleData .................................... .......... 13 2.2 Probability Density Functions..................... .............. 14 2.3 Descriptive Statistics........................... ............... 15 2.4 Uncertainty ..................................... ............ 17 3. VISUALIZATION OF SUMMARY STATISTICS ................. 19 3.1 Introduction .................................... ............ 19 3.2 RelatedWork ..................................... .......... 20 3.2.1 Statistical Plotting Techniques . ............. 21 3.2.1.1 TheBoxplot .................................. ...... 21 3.2.1.1.1 Origins. .................................. ...... 22 3.2.1.2 Modifications to the Boxplot .................... ....... 23 3.2.1.2.2 Density information. ....................... ....... 24 3.2.1.2.3 Additional descriptive statistics. ........... 26 3.2.1.3 Bivariate Extensions......................... ......... 29 3.3 TheSummaryPlot .................................. ......... 32 3.3.1 The Abbreviated Boxplot ......................... ......... 32 3.3.2 Quartiles and the Histogram...................... .......... 34 3.3.3 Moments....................................... ........ 35 3.3.3.1 Mean and Standard Deviation .................... ...... 36 3.3.3.2 Skew ........................................ ...... 37 3.3.3.3 Kurtosis .................................... ....... 37 3.3.3.4 Tail........................................ ....... 38 3.3.3.5 Moments, Sample Size, and Outliers . ....... 38 3.3.4 DistributionFitting ........................... ........... 39 3.3.5 User Interface for Reduction of Visual Clutter . ............ 40 3.3.6 Comparison of the Box and Summary Plots. ....... 40 3.4 Joint2DSummaries ................................ .......... 50 3.4.1 Joint Mean and Standard Deviation................. ......... 50 3.4.2 JointDensity.................................. .......... 50 3.4.3 Covariance and Skew Variance ..................... ......... 54 3.4.4 Correlation ................................... .......... 56 3.5 Discussion ...................................... ............ 57 3.6 Conclusion...................................... ............ 59 4. THE VISUALIZATION OF MULTIDIMENSIONAL UNCERTAINTY DATA ........................................ 60 4.1 Introduction .................................... ............ 60 4.2 ApplicationData................................. ............ 61 4.3 RelatedWork ..................................... .......... 64 4.4 Two-Dimensional Techniques ....................... ............ 65 4.4.1 Colormapping .................................. ......... 65 4.4.2 BivariateColormaps ............................ .......... 69 4.4.3 Perceptual Considerations...................... ............ 73 4.5 Three-Dimensional Techniques ..................... ............. 75 4.5.1 Displacement Mapping ........................... ......... 75 4.5.2 Volume Rendering and Isosurfacing . .......... 78 4.5.3 Streamlines and Particle Tracing ................. ........... 80 4.6 Conclusion...................................... ............ 82 5. ENSEMBLE-VIS .............................................. 84 5.1 Introduction .................................... ............ 84 5.1.1 Motivation.................................... .......... 85 5.1.2 DrivingProblems ............................... ......... 85 5.1.2.1 Weather Forecasting .......................... ........ 85 5.1.2.2 ClimateModeling ............................. ....... 86 5.1.3 EnsembleDataSets .............................. ........ 86 5.1.3.1 Ensembles and Uncertainty ..................... ....... 87 5.1.3.2 Challenges for Analysis....................... ......... 87 5.2 RelatedWork ..................................... .......... 88 5.2.1 Visualization of Climate and Weather Data . .......... 88 5.2.1.1 Multidimensional Data Visualization . .......... 89 5.2.2 Uncertainty Visualization ...................... ............ 91 5.2.2.1 Comparison Techniques ........................ ....... 91 5.2.2.2 Attribute Modification ........................ ........ 93 5.2.2.3 Glyphs ...................................... ...... 94 5.2.2.4 Image Discontinuity .......................... ........ 95 5.3 The Ensemble-Vis Framework........................ ........... 95 5.3.1 WorkFlow ...................................... ....... 96 5.3.2 DataSources................................... ......... 96 vi 5.3.3 EnsembleOverviews ............................. ......... 97 5.3.3.1 Spatial-Domain Summary Views .................. ...... 97 5.3.3.2 Time Navigation Summary Views .................. ..... 99 5.3.4 TrendCharts................................... ......... 103 5.3.4.1 QuartileCharts.............................. ........ 103 5.3.4.2 PlumeCharts ................................. 103 5.3.5 ConditionQueries.............................. .......... 104 5.3.6 Multivariate Layer Views ........................ .......... 105 5.3.7 SpaghettiPlots ................................ .......... 107 5.3.8 Coordination Between Views ...................... ......... 107 5.3.9 Clustering .................................... .......... 108 5.4 Implementation Details........................... ............. 110 5.4.1 SREFWeatherExplorer........................... ........ 110 5.4.2 ViSUS/CDAT .................................... ....... 113 5.5 Discussion ...................................... ............ 113 5.5.1 DataChallenges ................................ ......... 113 5.5.2 Where Summary Statistics Break Down. ........ 115 5.5.3 Glyphs for Standard Deviation .................... .......... 116 5.6 Conclusion...................................... ............ 116 6. CONCLUSIONS AND FUTURE WORK ........................ 117 6.1 FutureWork ...................................... .......... 117 REFERENCES ..................................................