Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
3
3
2013
PREFACE WORKING WITH UNCERTAINTY WORKSHOP: REPRESENTATION, QUANTIFICATION, PROPAGATION, VISUALIZATION, AND COMMUNICATION OF UNCERTAINTY, PROVIDENCE, RHODE ISLAND, OCTOBER 2011
vii-viii
10.1615/Int.J.UncertaintyQuantification.v3.i3.10
Alex
Pang
Computer Science Department, Jack Baskin School of Engineering, 1156 High Street, University of California, Santa Cruz, California 95060, USA
Chris R.
Johnson
University of Utah, Scientific Computing and Imaging Institute, Salt Lake City,
UT 84112, USA
THE MUTUAL INFORMATION DIAGRAM FOR UNCERTAINTY VISUALIZATION
187-201
10.1615/Int.J.UncertaintyQuantification.2012003959
Carlos D.
Correa
Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, Livermore, California, USA
Peter
Lindstrom
Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, Livermore, California, USA
mutual information
entropy
variation of information
uncertainty visualization
Taylor diagrams
We present a variant of the Taylor diagram, a type of two-dimensional plot that succinctly shows the relationship between two or more random variables based on their variance and correlation. The Taylor diagram has been adopted by the climate and geophysics communities to produce insightful visualizations, e.g., for intercomparison studies. Our variant, which we call the "mutual information diagram," represents the relationship between random variables in terms of their entropy and mutual information, and naturally maps well-known statistical quantities to their information-theoretic counterparts. Our new diagram is able to describe nonlinear relationships where linear correlation may fail; it allows for categorical and multivariate data to be compared; and it incorporates the notion of uncertainty, key in the study of large ensembles of data.
A CONTOUR TREE BASED VISUALIZATION FOR EXPLORING DATA WITH UNCERTAINTY
203-223
10.1615/Int.J.UncertaintyQuantification.2012003956
Keqin
Wu
The GeoSystems Research Institute, Mississippi State University, Starkville, Mississippi 39762, USA
Song
Zhang
The GeoSystems Research Institute, Mississippi State University, Starkville, Mississippi 39762
Uncertainty visualization
contour tree
topology simplification
weather ensemble
volumetric data
Uncertainty is a common and crucial issue in scientific data. The exploration and analysis of three-dimensional (3D) and large two-dimensional (2D) data with uncertainty information demand an effective visualization augmented with both user interaction and relevant context. The contour tree has been exploited as an efficient data structure to guide exploratory visualization. This paper proposes an interactive visualization tool for exploring data with quantitative uncertainty representations. First, we introduce a balanced planar hierarchical contour tree layout integrated with tree view interaction, allowing users to quickly navigate between levels of detail for contours of large data. Further, uncertainty information is attached to a planar contour tree layout to avoid the visual cluttering and occlusion in viewing uncertainty in 3D data or large 2D data. For the first time, the uncertainty information is explored as a combination of the data-level uncertainty which represents the uncertainty concerning the numerical values of the data, the contour variability which quantifies the positional variation of contours, and the topology variability which reveals the topological variation of contour trees. This information provides a new insight into how the uncertainty exists with and relates to the features of the data. The experimental results show that this new visualization facilitates a quick and accurate selection of prominent contours with high or low uncertainty and variability.
PREDICTABILITY-BASED ADAPTIVE MOUSE INTERACTION AND ZOOMING FOR VISUAL FLOW EXPLORATION
225-240
10.1615/Int.J.UncertaintyQuantification.2012003943
Marcel
Hlawatsch
VISUS, University of Stuttgart, Stuttgart, Germany
Filip
Sadlo
VISUS, University of Stuttgart, Stuttgart, Germany
Daniel
Weiskopf
VISUS, University of Stuttgart, Stuttgart, Germany
interactive flow visualization
predictability
finite-time Lyapunov exponent
adaptive mouse speed
adaptive zoom
Flow fields are often investigated by adopting a Lagrangian view, for example, by particle tracing of integral curves such as streamlines and path lines or by computing delocalized quantities. For visual exploration, mouse interaction is predominantly used to define starting points for time-dependent Lagrangian methods. This paper focuses on the uncertainty of mouse input and its impact on the visualization process. In typical cases, the interaction is achieved by mouse motion, exhibiting uncertainty in the range of a screen pixel. From the perspective of dynamical systems theory, an integral curve represents an initial value problem, the uncertainty a perturbation of its initial condition, and the uncertainty of the visualization procedure a predictability problem. Predictability analysis is concerned with the growth of perturbations under the action of flow. In our case, it is not unusual that the perturbations grow from single pixels to substantial deviations. We therefore present an interaction scheme based on the largest finite-time Lyapunov exponent and the flow map gradient, providing accurate, smooth, and easy-to-use flow exploration. This scheme employs data-driven adaptation of mouse speed and direction as well as optional augmentation by an adaptive zoom lens with consistent magnification. We compare our approach to nonadaptive mouse interaction and demonstrate it for several examples of data sets. Furthermore, we present results from a user study with nine domain experts.
SUMMARY VISUALIZATIONS FOR COASTAL SPATIAL-TEMPORAL DYNAMICS
241-253
10.1615/Int.J.UncertaintyQuantification.2012003969
Sidharth
Thakur
Renaissance Computing Institute, Raleigh, NC 27695
Laura
Tateosian
North Caroline State University Center for Earth Observation, Raleigh, NC 27695
Helena
Mitasova
North Caroline State University Department of Marine, Earth, and Atmospheric Sciences, Raleigh, NC 27695
Eric
Hardin
North Caroline State University Department of Physics, Raleigh, NC 27695
Margery
Overton
North Caroline State University Department of Civil, Construction, and Environmental Engineering, Raleigh, NC 27695
uncertainty
visualization
geovisualization
glyph-based visualization
spatial-temporal analysis
space-time cube
coastal terrain
geomorphology
GRASS GIS
Outer Banks
Digital scans of dynamic terrains such as coastal regions are now being gathered at high spatial and temporal resolution. Although standard tools based on geographic information systems (GIS) are indispensable for analyzing geospatial data, they have limited support to display time-dependent changes in data and information such as statistical distributions and uncertainty in data. We present a set of techniques for visually summarizing the dynamics of coastal dunes. We visualize summary statistics of important data attributes and risk or vulnerability indices as functions of both spatial and temporal dimensions in our data and represent uncertainty in the data set. We apply standard techniques, the space time cube and clustering, in novel ways to the domain of geomorphology. We combine surface-mapping and imagery with summary visualizations to retain important geographical context in the visualizations and reduce clutter due to direct plotting of statistical data in displays of geospatial information. We also address some issues pertaining to visualization of summary statistics for geographical regions at varying scales. We demonstrate visualization tools on time series of elevation models from the Outer Banks of North Carolina and observe temporal-spatial trends therein.
UNCERTAINTY IN THE DEVELOPMENT AND USE OF EQUATION OF STATE MODELS
255-270
10.1615/Int.J.UncertaintyQuantification.2012003960
V. Gregory
Weirs
Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico 87185, USA
Nathan
Fabian
Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico 87185, USA
Kristin
Potter
NREL
Laura
McNamara
Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico 87185, USA
Thomas
Otahal
Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico 87185, USA
materials
uncertainty quantification
representation of uncertainty
model validation and verification
continnum mechanics
In this paper we present the results from a series of focus groups on the visualization of uncertainty in equation-of-state (EOS) models. The initial goal was to identify the most effective ways to present EOS uncertainty to analysts, code developers, and material modelers. Four prototype visualizations were developed to present EOS surfaces in a three-dimensional, thermodynamic space. Focus group participants, primarily from Sandia National Laboratories, evaluated particular features of the various techniques for different use cases and discussed their individual workflow processes, experiences with other visualization tools, and the impact of uncertainty on their work. Related to our prototypes, we found the 3D presentations to be helpful for seeing a large amount of information at once and for a big-picture view; however, participants also desired relatively simple, two-dimensional graphics for better quantitative understanding and because these plots are part of the existing visual language for material models. In addition to feedback on the prototypes, several themes and issues emerged that are as compelling as the original goal and will eventually serve as a starting point for further development of visualization and analysis tools. In particular, a distributed workflow centered around material models was identified. Material model stakeholders contribute and extract information at different points in this workflow depending on their role, but encounter various institutional and technical barriers which restrict the flow of information. An effective software tool for this community must be cognizant of this workflow and alleviate the bottlenecks and barriers within it. Uncertainty in EOS models is defined and interpreted differently at the various stages of the workflow. In this context, uncertainty propagation is difficult to reduce to the mathematical problem of estimating the uncertainty of an output from uncertain inputs.