We present techniques to improve the understanding of pattern forming processes in Rayleigh-Bénard-type convective heat transport, through visually guided exploration of convection features in time-averaged turbulent flows. To enable the exploration of roll-like heat transfer pathways and pattern-forming anomalies, we combine feature extraction with interactive visualization of particle trajectories. To robustly determine boundaries between circulation rolls, we propose ridge extraction in a z-averaged temperature field, and in the extracted ridge network we automatically classify topological point defects hinting at pattern forming instabilities. An importance measure based on the circular movement of particles is employed to automatically control the density of 3D trajectories and, thus, enable insights into the heat flow in the interior of rolls. A quantitative analysis of the heat transport within and across cell boundaries, as well as investigations of pattern instabilities in the vicinity of defects, is supported by interactive particle visualization including instant computations of particle density maps. We demonstrate the use of the proposed techniques to explore direct numerical simulations of the 3D Boussinesq equations of convection, giving novel insights into Rayleigh-Bénard-type convective heat transport.

We present a voxel-based rendering pipeline for large 3D line sets that employs GPU ray-casting to achieve scalable rendering including transparency and global illumination effects. Even for opaque lines we demonstrate superior rendering performance compared to GPU rasterization of lines, and when transparency is used we can interactively render amounts of lines that are infeasible to be rendered via rasterization. We propose a direction-preserving encoding of lines into a regular voxel grid, along with the quantization of directions using face-to-face connectivity in this grid. On the regular grid structure, parallel GPU ray-casting is used to determine visible fragments in correct visibility order. To enable interactive rendering of global illumination effects like low-frequency shadows and ambient occlusions, illumination simulation is performed during ray-casting on a level-of-detail (LoD) line representation that considers the number of lines and their lengths per voxel. In this way we can render effects which are very difficult to render via GPU rasterization. A detailed performance and quality evaluation compares our approach to rasterization-based rendering of lines.

We propose a new approach for analyzing the temporal growth of the uncertainty in ensembles of weather forecasts which are started from perturbed but similar initial conditions. As an alternative to traditional approaches in meteorology, which use juxtaposition and animation of spaghetti plots of iso-contours, we make use of contour clustering and provide means to encode forecast dynamics and spread in one single visualization. Based on a given ensemble clustering in a specified time window, we merge clusters in time-reversed order to indicate when and where forecast trajectories start to diverge. We present and compare different visualizations of the resulting time-hierarchical grouping, including space-time surfaces built by connecting cluster representatives over time, and stacked contour variability plots. We demonstrate the effectiveness of our visual encodings with forecast examples of the European Centre for Medium-Range Weather Forecasts, which convey the evolution of specific features in the data as well as the temporally increasing spatial variability.

Abstract For an ensemble of iso‐contours in multi‐dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We first show how to derive a statistical model describing the contour variability, by representing the contours implicitly via signed distance functions and clustering similar functions in a reduced order space. We show that the spatial patterns of the ensemble can then be derived by analytically transforming the boundaries of a confidence interval computed from each cluster into the spatial domain. Furthermore, we introduce a mathematical basis for computing correlations between the occurrences of iso‐contours at different locations. We show that the computation of these correlations can be posed in the reduced order space as an integration problem over a region bounded by four hyper‐planes. To visualize the derived statistical properties we employ a variant of variability plots for streamlines, now including the color coding of probabilities of joint contour occurrences. We demonstrate the use of the proposed techniques for ensemble exploration in a number of 2D and 3D examples, using artificial and meteorological data sets.