This study focuses on the extremely severe storm system swept across Corsica early in the morning of August 18, 2022. A derecho refers to thunderstorm episodes that are distinguished by the production of particularly long-lasting, strong and widespread downbursts, generated by an extratropical mesoscale convective system (MCS). The associated radar signatures generally exhibit linear characteristics, with arcuate portions (bow echo).

This work studies in particular the life cycle of the bow echo that appeared off the coast of Corsica and caused significant damage on the island as well as victims including five deaths. The bow echo is an exceptional phenomenon that is very difficult to predict because it is very localized. Beyond qualitative observations, methods for detecting the shape of a bow echo from radar images have been studied. We present an alternative method for characterising the bow echo shape using a promising tool based on topological data analysis (TDA) and the measurement of the curvature of the cloud. The use of homological persistence from TDA allows to follow the evolution of the bow echo from its initiation to its maturation just before it hits the Corsican coast. Curvature and persistent homology calculation with the stability property of Wasserstein and Bottleneck distances allows us to detect changes between evolutionary phases. The main idea is to exploit TDA on radar images of this bow echo in order to generate an alert. TDA is one of these new mathematical tools that will help characterize the event.