This paper presents a comprehensive study of interactive rendering techniques for large 3D line sets with transparency. The rendering of transparent lines is widely used for visualizing trajectories of tracer particles in flow fields. Transparency is then used to fade out lines deemed unimportant, based on, for instance, geometric properties or attributes defined along them. Since accurate blending of transparent lines requires rendering the lines in back-to-front or front-to-back order, enforcing this order for 3D line sets with tens or even hundreds of thousands of elements becomes challenging. In this paper, we study CPU and GPU rendering techniques for large transparent 3D line sets. We compare accurate and approximate techniques using optimized implementations and a number of benchmark data sets. We discuss the effects of data size and transparency on quality, performance and memory consumption. Based on our study, we propose two improvements to per-pixel fragment lists and multi-layer alpha blending. The first improves the rendering speed via an improved GPU sorting operation, and the second improves rendering quality via a transparency-based bucketing.

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Visualizing spatial structures in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.

Cloud microphysical processes are highly relevant for cloud and precipitation characteristics, cloud radiative properties and the latent heat release during phase changes of water can interact with atmospheric dynamics. These sub-grid scale processes are typically parameterized in numerical weather prediction models, introducing parametric uncertainty in weather forecasts. The analysis of uncertainties related to these parameterizations imposes multiple challenges: On the one hand, it requires robust quantification of the impact of hundreds of uncertain model parameters. On the other hand, it requires adequate tools to filter, visualize, and understand the parameter impacts. Algorithmic Differentiation (AD) is a tool to efficiently evaluate the magnitude and timing at which a model state is sensitive to a model parameter [1]. We demonstrate the capabilities of AD, focusing on uncertain parameters in a two-moment cloud microphysics scheme along trajectories of a warm conveyor belt, which is the primary cloud- and precipitation-forming airstream in extratropical cyclones. To understand the parameter influence, we here introduce methods to systematically analyze different impacts in different warm conveyor belt ascent scenarios [2]. For example, this includes an objective clustering of trajectories w.r.t to parameter sensitivities. Met.3D, an open-source tool for interactive, three-dimensional visualization of numerical atmospheric model datasets, then provides a visual interface to compare multiple sensitivities on multiple trajectories from each cluster, assess the spatio-temporal relationships between the sensitivities and the trajectories’ shapes and locations, and find similarities in the temporal development of sensitivities along various trajectories’ location and time for ascent.    [1] Hieronymus, M., Baumgartner, M., Miltenberger, A. and Brinkmann, A.: Algorithmic Differentiation for Sensitivity Analysis in Cloud Microphysics, J. Adv. Model Earth Syst. (2022), 10.1029/2021MS002849.  [2] Neuhauser, C., Hieronymus, M., Kern, M., Rautenhaus, M., Oertel, A., and Westermann, R.: Visual analysis of model parameter sensitivities along warm conveyor belt trajectories using Met.3D (1.6.0-multivar0), Geosci. Model Dev. Discuss. [preprint], https://doi.org/10.5194/gmd-2023-27, in review, 2023.