Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows

Guo, Hanqi; He, Wenbin; Peterka, Tom; Shen, Han‐Wei; Collis, Scott; Helmus, Jonathan

doi:10.1109/tvcg.2016.2534560

Cited by 42 publications

(29 citation statements)

References 25 publications

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“…Mirzargar et al [MWK14] use 3D box plot visualization for tracing various particles pathlines. Guo et al [GHP∗16] also use 3D flow‐based visualization for analyzing uncertainty in temporal flow fields. Kern et al [KHS∗18a] use 3D core lines for jet stream flow analysis.…”

Section: Taxonomiesmentioning

confidence: 99%

The State of the Art in Visual Analysis Approaches for Ocean and Atmospheric Datasets

Afzal

Hittawe

Ghani

et al. 2019

Computer Graphics Forum

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The analysis of ocean and atmospheric datasets offers a unique set of challenges to scientists working in different application areas. These challenges include dealing with extremely large volumes of multidimensional data, supporting interactive visual analysis, ensembles exploration and visualization, exploring model sensitivities to inputs, mesoscale ocean features analysis, predictive analytics, heterogeneity and complexity of observational data, representing uncertainty, and many more. Researchers across disciplines collaborate to address such challenges, which led to significant research and development advances in ocean and atmospheric sciences, and also in several relevant areas such as visualization and visual analytics, big data analytics, machine learning and statistics. In this report, we perform an extensive survey of research advances in the visual analysis of ocean and atmospheric datasets. First, we survey the task requirements by conducting interviews with researchers, domain experts, and end users working with these datasets on a spectrum of analytics problems in the domain of ocean and atmospheric sciences. We then discuss existing models and frameworks related to data analysis, sense‐making, and knowledge discovery for visual analytics applications. We categorize the techniques, systems, and tools presented in the literature based on the taxonomies of task requirements, interaction methods, visualization techniques, machine learning and statistical methods, evaluation methods, data types, data dimensions and size, spatial scale and application areas. We then evaluate the task requirements identified based on our interviews with domain experts in the context of categorized research based on our taxonomies, and existing models and frameworks of visual analytics to determine the extent to which they fulfill these task requirements, and identify the gaps in current research. In the last part of this report, we summarize the trends, challenges, and opportunities for future research in this area. (see http://www.acm.org/about/class/class/2012)

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Section: Taxonomiesmentioning

confidence: 99%

The State of the Art in Visual Analysis Approaches for Ocean and Atmospheric Datasets

Afzal

Hittawe

Ghani

et al. 2019

Computer Graphics Forum

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“…Finite-time variance analysis (FTVA) [19] is a variance-based, FTLE-like metric that has been proposed to analyze unsteady flow fields. Guo et al [20] introduced three new concepts, including the FTLE of distributions (FTLE-D), the distribution of the FTLE (D-FTLE), and uncertain LCS (U-LCS), which extend the deterministic FTLE and LCS extraction to better understand the transport behaviors in time-varying ensemble vector fields. However, FTLE can have reduced accuracy when strong nonlinear mapping exists.…”

Section: Uncertainty Analysis In Vector Fieldmentioning

confidence: 99%

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

Ren

et al. 2020

IJGI

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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.

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“…The FTLEs at a time t are the finite time averages of the maximum expansion rate for a pair of particles propagated by (2) over the time interval [t, t 1 ] (see, for example, [3] on the computation of FTLEs). Monte Carlo methods for FTLE fields are now emerging as a tool in stochastic situations [18,19,[75][76][77][78][79]. Following these ideas, we seed 200 × 400 particles in the same domain displayed in Fig.…”

Section: Stochastic Sets Respect Exponential Stretching: a Comprmentioning

confidence: 99%

Estimating stable and unstable sets and their role as transport barriers in stochastic flows

Balasuriya

Gottwald

2018

Phys. Rev. E

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We consider the situation of a large-scale stationary flow subjected to small-scale fluctuations. Assuming that the stable and unstable manifolds of the large-scale flow are known, we quantify the mean behavior and stochastic fluctuations of particles close to the unperturbed stable and unstable manifolds and their evolution in time. The mean defines a smooth curve in physical space, while the variance provides a time- and space-dependent quantitative estimate where particles are likely to be found. This allows us to quantify transport properties such as the expected volume of mixing as the result of the stochastic fluctuations of the transport barriers. We corroborate our analytical findings with numerical simulations in both compressible and incompressible flow situations. We moreover demonstrate the intimate connection of our results with finite-time Lyapunov exponent fields, and with spatial mixing regions.

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Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows

Cited by 42 publications

References 25 publications

The State of the Art in Visual Analysis Approaches for Ocean and Atmospheric Datasets

The State of the Art in Visual Analysis Approaches for Ocean and Atmospheric Datasets

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

Estimating stable and unstable sets and their role as transport barriers in stochastic flows

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