Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networks

TL;DR

This paper introduces a neural network-based simulation approach to model and estimate the spatial dependence of extreme precipitation events, capturing uncertainty and complex dependencies.

Contribution

It presents a novel generative neural network methodology for estimating max-stable process parameters and spatial dependence in extreme precipitation modeling.

Findings

Effective in complex settings where likelihood estimation is intractable

Provides explicit nonparametric estimates of spatial extremal dependence

Demonstrates robustness and good performance in finite sample studies

Abstract

In this work, we propose a simulation-based estimation approach using generative neural networks to determine dependencies of precipitation maxima and their underlying uncertainty in time and space. Within the common framework of max-stable processes for extremes under temporal and spatial dependence, our methodology allows estimating the process parameters and their respective uncertainty, but also delivers an explicit nonparametric estimate of the spatial dependence through the pairwise extremal coefficient function. We illustrate the effectiveness and robustness of our approach in a thorough finite sample study where we obtain good performance in complex settings for which closed-form likelihood estimation becomes intractable. We use the technique for studying monthly rainfall maxima in Western Germany for the period 2021-2023, which is of particular interest since it contains an extreme precipitation and consecutive flooding event in July 2021 that had a massive deadly impact. Beyond the considered setting, the presented methodology and its main generative ideas also have great potential for other applications.