Bow echo alarm system using Topological Data Analysis

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.