Atmospheric blocking events are quasi-stationary high-pressure systems that disrupt the typical paths of polar and subtropical air currents, often producing prolonged extreme weather events such as summer heat waves or winter cold spells. Despite their critical role in shaping mid-latitude weather, accurately modeling and analyzing blocking events in long meteorological records remains a significant challenge. To address this challenge, we present anuncertainty visualization framework for detecting and characterizing atmospheric blocking events. First, we introduce a geometry-based detection and tracking method, evaluated on both pre-industrial climate model simulations (UKESM) and reanalysis data (ERA5), which represent historical Earth observations assimilated from satellite and station measurements onto regular numerical grids using weather models. Second, we propose a suite of uncertainty-aware summaries: contour boxplots that capture representative boundaries and their variability, frequency heatmaps that encode occurrences, and 3D temporal stacks that situate these patterns in time. Third, we demonstrate our framework in a case study of the 2003 European heatwave, mapping the spatiotemporal occurrences of blocking events using these summaries. Collectively, these uncertainty visualizations reveal where blocking events are most likely to occur and how their spatial footprints evolve over time. We envision our framework as a valuable tool for climate scientists and meteorologists: by analyzing how blocking frequency, duration, and intensity vary across regions and climate scenarios, it supports both the study of historical blocking events and the assessment of scenario-dependent climate risks associated with changes in extreme weather linked to blocking.

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using high-performance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. We evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the evolution of connected components in the sublevel sets of scalar fields. We present a new technique for modeling and comparing merge trees using tools from partial optimal transport. In particular, we model a merge tree as a measure network, that is, a network equipped with a probability distribution, and define a notion of distance on the space of merge trees inspired by partial optimal transport. Such a distance offers a new and flexible perspective for encoding intrinsic and extrinsic information in the comparative measures of merge trees. More importantly, it gives rise to a partial matching between topological features in time-varying data, thus enabling flexible topology tracking for scientific simulations. Furthermore, such partial matching may be interpreted as probabilistic coupling between features at adjacent time steps, which gives rise to probabilistic tracking graphs. We derive a stability result for our distance and provide numerous experiments indicating the efficacy of our framework in extracting meaningful feature tracks.