Visualizing Multimodal Uncertainty in Ensemble Vector Fields
Often times, simulations involve repeated runs where certain parameters, e.g. initial and boundary conditions, or model parameters are varied slightly, in order to capture the variability of the phenomenon being studied. The results are referred to as ensembles. Ensembles are very attractive since they represent both the data values and their uncertainty. Ensembles challenge us to extend traditional visualization assuming that the ensemble represents the distribution of all possible simulation outcomes given an input parameter space. Extending the traditional paradigm is also better suited for complex data associated with ensemble vector fields (EVFs). Derived features of the EVF allow for their summary visual analysis. This approach is related to traditional methods of visualization for crisp fields but require the definition and calculation of additional derived features of interest.
We first focus on a consolidated and extensible representation of EVF. A distinguishing aspect of this dissertation is the treatment of the values at each spatial point of the ensemble field as forming a probability distribution function (PDF) that need not conform to a Gaussian distribution. We present a new method for interpolation of distributions of 2D vector fields, required for handling velocity distributions. We also include velocity probability density information from the EVF in the feature set of streamlines.
Another defining characteristic of this work is considering streamline information content and geometrically based streamline clusters as a derived feature of EVF. We apply a suitable and proven streamline clustering method first introduced to summarize regions of crisp vector fields. Our contribution is redefining this method for use in EVF, both for seed points over the spatial domain and for entire sub-regions of the EVF. We also show correlation between the associated cluster counts and streamline information content at seed points in the EVF.
Our goal is to enable simulation scientists and consumers of ensemble data sets, such as weather forecasters, to visualize areas of predicted flow that are improperly represented by a Gaussian simplification. The potential impact of this work ranges from better representation of current weather prediction forecasts for public consumption to the refinement of computational fluid dynamics (CFD) models.