Séance Séminaire

Séminaire des Doctorant·e·s

Spatio-temporal modeling of urban extreme rainfall events at high resolution

Precipitation modeling is of great interest for flood risk analysis. We present a framework for modeling the distribution and the spatio-temporal dependence of rainfall measured at high temporal resolution and fine spatial scale by the rain gauge network of the Montpellier urban observatory since 2019. This data is complemented by hourly radar reanalysis data from Meteo-France, available at 1 km resolution on a regular grid and for a longer time period. By applying a neural network downscaling approach from reanalysis to local point scale for the marginal distributions, we aim to obtain a finer resolution dataset, a longer data period and a better spatial coverage by leveraging information from the two data sources. For univariate modeling, at the point level, we use the Extended Generalized Pareto Distribution (EGPD). It allows us to model both moderate and intense rainfall simultaneously without explicit threshold selection, a step that is often challenging in statistics of extremes, and to reduce the complexity of parameter estimation. The spatio-temporal dependence is modeled using an r-Pareto process with an underlying gaussian dependence structure. Unlike max-stable processes, which are often limited by their focus on block maxima approaches, r-Pareto processes offer more flexibility and practicality for environmental applications by using a Peaks Over Threshold (POT) framework. By incorporating a non-separable spatio-temporal variogram with advection, we account for the horizontal movement of precipitation clouds, enabling realistic simulations of spatio-temporal rainfall patterns. A novel composite likelihood approach based on bivariate joint exceedance indicators used for variogram parameter estimation. The model is validated by simulations of the proposed process and is applied to rainfall data from Montpellier. This methodology will be at the core of a stochastic precipitation generator for the Montpellier region, which will be integrated into a mechanistic water flow model for flood risk analysis.