Uncertainty Visualization of Transport Variance in a Time-Varying Ensemble Vector Field

Abstract

Uncertainty analysis of a time-varying ensemble vector field is a challenging topic in geoscience. Due to the complex data structure, the uncertainty of a time-varying ensemble vector field is hard to quantify and analyze. Measuring the differences between pathlines is an effective way to compute the uncertainty. However, existing metrics are not accurate enough or are sensitive to outliers; thus, a comprehensive tool for the further analysis of the uncertainty of transport patterns is required. In this paper, we propose a novel framework for quantifying and analyzing the uncertainty of an ensemble vector field. Based on the classical edit distance on real sequence (EDR) method, a robust and accurate metric was proposed to measure the pathline uncertainty. Considering the spatial continuity, we computed the transport variance of the neighborhood of a location, and evaluated the uncertainty correlation between each location and its neighborhood by using the local Moran’s I. Based on the proposed uncertainty measurements, a visual analysis system called UP-Vis (uncertainty pathline visualization) was developed to interactively explore the uncertainty. It provides an overview of the uncertainty and supports detailed exploration of transport patterns at a selected location, and allows for the comparison of transport patterns between a location and its neighborhood. Through pathline clustering, the major trends of the ensemble pathline at a location were extracted. Moreover, a glyph was designed to intuitively display the transport direction and diverging degree of each cluster. For the uncertainty analysis of the neighborhood, a comparison view was designed to compare the transport patterns between a location and its neighborhood in detail. A synthetic data set and weather simulation data set were used in our experiments. The evaluation and case studies demonstrated that the proposed framework can measure the uncertainty effectively and help users to comprehensively explore uncertainty transport patterns.

Exploratory Lagrangian-Based Particle Tracing Using Deep Learning

“…The result highlighted the relation of the trained model's performance and flow features in the domain. The error for each trajectory was measured using the AEDR metric proposed by [46]. We observed reconstruction errors were higher in regions with greater separation in the flow field, i.e., regions with higher FTLE values.…”

“…To measure the accuracy of new particle trajectories inferred by the model, we used a robust and accurate metric called the adaptive edit distance on real sequences (AEDR) proposed by [46] to measure pathline uncertainty. The metric uses the L1 norm divided by a threshold distance to quantify the local error of each interpolated location, accumulates error along the trajectory, and produces an average across all the interpolated locations.…”