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.

Abstract We usek‐order Voronoi diagrams to assess the stability ofk‐neighbourhoods in ensembles of 2D point sets, and apply it to analyse the robustness of a dimensionality reduction technique to variations in its input configurations. To measure the stability ofk‐neighbourhoods over the ensemble, we use cells in thek‐order Voronoi diagrams, and consider the smallest coverings of corresponding points in all point sets to identify coherent point subsets with similar neighbourhood relations. We further introduce a pairwise similarity measure for point sets, which is used to select a subset of representative ensemble members via the PageRank algorithm as an indicator of an individual member's value. The stability information is embedded into thek‐order Voronoi diagrams of the representative ensemble members to emphasize coherent point subsets and simultaneously indicate how stable they lie together in all point sets. We use the proposed technique for visualizing the robustness of t‐distributed stochastic neighbour embedding and multi‐dimensional scaling applied to high‐dimensional data in neural network layers and multi‐parameter cloud simulations.

Ensemble sensitivity analysis (ESA) has been established in the atmospheric sciences as a correlation-based approach to determine the sensitivity of a scalar forecast quantity computed by a numerical weather prediction model to changes in another model variable at a different model state. Its applications include determining the origin of forecast errors and placing targeted observations to improve future forecasts. We-a team of visualization scientists and meteorologists-present a visual analysis framework to improve upon current practice of ESA. We support the user in selecting regions to compute a meaningful target forecast quantity by embedding correlation-based grid-point clustering to obtain statistically coherent regions. The evolution of sensitivity features computed via ESA are then traced through time, by integrating a quantitative measure of feature matching into optical-flow-based feature assignment, and displayed by means of a swipe-path showing the geo-spatial evolution of the sensitivities. Visualization of the internal correlation structure of computed features guides the user towards those features robustly predicting a certain weather event. We demonstrate the use of our method by application to real-world 2D and 3D cases that occurred during the 2016 NAWDEX field campaign, showing the interactive generation of hypothesis chains to explore how atmospheric processes sensitive to each other are interrelated.

In meteorology, cluster analysis is frequently used to determine representative trends in ensemble weather predictions in a selected spatio-temporal region, e.g., to reduce a set of ensemble members to simplify and improve their analysis. Identified clusters (i.e., groups of similar members), however, can be very sensitive to small changes of the selected region, so that clustering results can be misleading and bias subsequent analyses. In this article, we - a team of visualization scientists and meteorologists-deliver visual analytics solutions to analyze the sensitivity of clustering results with respect to changes of a selected region. We propose an interactive visual interface that enables simultaneous visualization of a) the variation in composition of identified clusters (i.e., their robustness), b) the variability in cluster membership for individual ensemble members, and c) the uncertainty in the spatial locations of identified trends. We demonstrate that our solution shows meteorologists how representative a clustering result is, and with respect to which changes in the selected region it becomes unstable. Furthermore, our solution helps to identify those ensemble members which stably belong to a given cluster and can thus be considered similar. In a real-world application case we show how our approach is used to analyze the clustering behavior of different regions in a forecast of "Tropical Cyclone Karl", guiding the user towards the cluster robustness information required for subsequent ensemble analysis.