Bow echo alarm system using Topological Data Analysis

Hélène Canot; Philippe Durand; Emmanuel Frénod

doi:10.3934/ammc.2025002

Article Contents

March 2025, Volume 3, 44-63. Doi: 10.3934/ammc.2025002

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Bow echo alarm system using Topological Data Analysis

1.
Université de Bretagne-Sud, UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique, F-56000 Vannes, France
2.
CNAM, Département de Mathématiques et Statistiques, Laboratoire M2N

^*Corresponding author: Hélène Canot
^*Corresponding author: Hélène Canot

Received: October 2024

Revised: February 2025

Early access: March 2025

Published: March 2025

Abstract / Introduction Full Text(HTML) Figure(9) Related Papers Cited by

Abstract

This study examines the extremely severe storm that hit Corsica in the early hours of August 18, 2022. A "derecho" is a powerful storm system known for producing long-lasting and widespread destructive winds. In this case, the storm was driven by a large cluster of thunderstorms that organized into a fast-moving structure, leading to intense wind gusts across the region. The associated radar signatures generally exhibit linear characteristics, often displaying "bow echo" shapes. In this work, we study the formation and evolution of the bow echo that struck the Corsican coast, causing significant damage and multiple fatalities. Bow echoes are notoriously difficult to predict, as they can form quickly and remain quite localized. We propose using Topological Data Analysis (TDA, specifically, persistent homology, to characterize the shape evolution of a bow echo over time. From weather radar images of reflectivity, we generate point clouds corresponding to the most intense precipitation cells and compute their persistence diagrams via Vietoris–Rips filtrations. We compare persistence diagrams using the Bottleneck distance, the Wasserstein distance, and the kernel approach: the Persistence Weighted Gaussian Kernel (PWGK), the Sliced Wasserstein Kernel (SWK) and the Pertinence Fisher Kernel (PFK). We then apply hierarchical clustering, principal component analysis (PCA), and change-point detection to these distances in order to highlight major structural transitions and detect the moment when the bow echo forms. Additionally, we incorporate a curvature-based metric by measuring the ratio between the arc length and the straight length of the arc shape. We show that combining TDA-based distances with curvature measurements provides valuable insight into the storm's evolution. Finally, we introduce a discussion on triggering an alert based on the topological analysis of the bow echo. Our results suggest that TDA-based methods can help identify distinct structural changes in complex meteorological phenomena.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Filtration with increasing values $ \epsilon = 0, 0.1, 0.35, 1.4 $ (top) of the point cloud $ X $, bottom is the corresponding persistent diagram on the right which each point in 1-dimensional represents the holes

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Figure 2. The storm cells on radar imagery are represented by a point cloud which itself is transformed into a persistence diagram. Then constructing Bottleneck, Wasserstein, PWGK, SW and PFK distance matrices. Clustering and change point detection methods were applied

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Figure 3. Visual timestamps of the bow echo. (b)(d) Radar reflectivity of the forming bow echo with (a)(c) corresponding persistence diagrams

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Figure 4. Distribution of $ H_{1} $ structures in the lifetime diagrams

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Figure 5. Heatmap representation of Bottleneck, Wasserstein distance matrices (top), PWGK and SWK distance matrices (middle) and PFK distance matrix (bottom)

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Figure 6. (Left) Dendrogram of Hierarchical Clustering based on the Ward's criterion to distance matrices, (right) Score plot illustrates how clusters were distributed on Principal Components

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Figure 7. Superposition of ACP projections for the different distance metrics (left), the right graphic represents the zoom of the region where the projection overlap

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Figure 8. SVD graphs of the Bottleneck, Wasserstein, PWGK, SWK and PFK distance matrices

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Figure 9. Graph of the evolution of the curvature of the arc

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