Analysis and visualization of multi-dimensional atmospheric data using Pareto sets

In climatology and meteorology, simulations play a key role in analyzing atmospheric processes and events. Resulting data sets commonly consist of time-varying, multivariate 2D and 3D fields – properties that aggravate their visualization and analysis. The latter can be advanced through the identification of features, which can, e.g., be defined as areas of common behavior or as areas of disagreement across the simulated scalar fields. These features can be found using the topological approach known as Pareto sets. With Pareto sets, it becomes possible to locally compare a set of scalar fields based on the largest agreement of the respective ascending and descending behavior of the functions they represent. Hence, the approach is independent of the varying range dimensions of the attributes under investigation. In contrast to similar multivariate analysis methods, Pareto sets identify extremal areas and their spatial connectivities, and impose no restrictions to the number of attributes included into the analysis. Based on the IEEE Visualization 2004 Contest Hurricane Isabel data produced by the Weather Research and Forecast (WRF) model (courtesy of NCAR and the U.S. National Science Foundation (NSF), http://vis.computer.org/vis2004contest/data.html), we demonstrate how Pareto sets can be utilized to identify and visualize global features that correspond to common extremal areas in a set of spatially corresponding scalar fields. This set can, e.g., consist of a combination of different variables, but it can also consist of subsequent time steps, so that changing behavior of selected variables can be tracked.