Visual Analysis of Multi-Parameter Distributions Across Ensembles of 3D Fields

For an ensemble of 3D multi-parameter fields, we present a visual analytics workflow to analyse whether and which parts of a selected multi-parameter distribution is present in all ensemble members. Supported by a parallel coordinate plot, a multi-parameter brush is applied to all ensemble members to select data points with similar multi-parameter distribution. By a combination of spatial sub-division and a covariance analysis of partitioned sub-sets of data points, a tight partition in multi-parameter space with reduced number of selected data points is obtained. To assess the representativeness of the selected multi-parameter distribution across the ensemble, we propose a novel extension of violin plots that can show multiple parameter distributions simultaneously. We investigate the visual design that effectively conveys (dis-)similarities in multi-parameter distributions, and demonstrate that users can quickly comprehend parameter-specific differences regarding distribution shape and representativeness from a side-by-side view of these plots. In a 3D spatial view, users can analyse and compare the spatial distribution of selected data points in different ensemble members via interval-based isosurface raycasting. In two real-world application cases we show how our approach is used to analyse the multi-parameter distributions across an ensemble of 3D fields.

1 Introduction

In many scientific fields like meteorology and computational fluid dynamics, numerical ensemble simulations are carried out with varying magnitudes of initial condition uncertainty, and by introducing uncertainty in the representation of certain physical processes. In such an ensemble, each simulation predicts possible states of physical quantities, aiming at a representative sampling of the physical phenomena that can occur. One of the major goals in ensemble visualization is to visually convey commonalities and differences between the ensemble members and, thus, to reveal the major trends and outliers in the simulation results.