Uncertainty-aware Visualization of Regional Time Series Correlation in Spatio-temporal Ensembles

Abstract

Given a time-varying scalar field, the analysis of correlations between different spatial regions, i.e., the linear dependence of time series within these regions, provides insights into the structural properties of the data. In this context, regions are connected components of the spatial domain with high time series correlations. The detection and analysis of such regions is often performed globally, which requires pairwise correlation computations that are quadratic in the number of spatial data samples. Thus, operations based on all pairwise correlations are computationally demanding, especially when dealing with ensembles that model the uncertainty in the spatio-temporal phenomena using multiple simulation runs. We propose a two-step procedure: In a first step, we map the spatial samples to a 3D embedding based on a pairwise correlation matrix computed from the ensemble of time series. The 3D embedding allows for a one-to-one mapping to a 3D color space such that the outcome can be visually investigated by rendering the colors for all samples in the spatial domain. In a second step, we generate a hierarchical image segmentation based on the color images. From then on, we can visually analyze correlations of regions at all levels in the hierarchy within an interactive setting, which includes the uncertainty-aware analysis of the region's time series correlation and respective time lags.