Dynamics of extreme events and point processes

The climate system, by its complex nature, results from the interaction of many processes operating at various spatiotemporal scales. The scale and diversity of big data from climate observations and simulations continues to grow, thus providing increased possibilities for studying and predicting this system. Fully understanding and modeling the role of major events in this system is of crucial importance for understanding extreme climate events and the risks they pose. This includes in particular the frequency, co-occurrence and recurrence of these events, as well as their magnitude and extent. The analysis of the synchronicity and causality of events at different spatial and temporal scales is of particular importance.

This project aims to merge probabilistic methods for marked point processes, extreme events, and spatial graphs to propose a new framework for better understanding and simulating the spatial and temporal interactions between different types of extreme events in the climate system. Each extreme episode (be it temperature, precipitation, wind speed, atmospheric pressure, etc.) for a specific climate variable and region will be represented by a point indicating the time of its occurrence, as well as by one or more marks describing key features of the episode, such as maximum, spatial extent, duration, accumulation, etc. First- and second-order statistical features of point processes, such as the intensity function and different variants of the pair and mark correlation functions, will be adapted to study the multi-scale structures of all these marked points. We will also develop new classes of marked point process models, defined on a spatial graph representing the geographic proximity between regions, in order to be able to simulate new realizations of all these events.

The applications envisaged include the occurrences of extreme precipitation events occurring in different watersheds. In the fields of agriculture and ecology, we wish to develop models of ruin for plants or species populations, similar to the classical models used in actuarial science, such as the Cramér-Lundberg model based on a point process representing the damage incurred.