Analysing Extreme Rainfall via a Geometric Framework

2026-03-18

AI Summary

This study addresses the challenge of predicting the spatial extent and duration of extreme rainfall events in the eastern United States by proposing a geometric extreme value analysis framework that explicitly incorporates spatiotemporal nonstationarity. The approach employs a time-preserving sampling strategy and integrates topographic and seasonal effects to accurately characterize multivariate tail dependence structures, enabling full-tail extrapolation. Diagnostic evaluation using large ensemble climate model data demonstrates superior performance across three key metrics of extreme rainfall, confirming the model’s capacity to reliably capture the spatiotemporal characteristics of extreme events under complex nonstationary conditions.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

Motivated by the EVA 2025 Data Challenge, we address the problem of predicting extreme rainfall in the eastern United States using data from a large ensemble of climate model runs. The challenge focuses on three quantities of interest related to the spatial extent and/or temporal duration of extreme rainfall, each requiring extrapolation. To tackle these questions, we adopt the recently developed geometric framework for extreme-value analysis, offering substantial flexibility for capturing complex extremal dependence structures and enabling extrapolation across the entire multivariate tail. In this work, we focus on the spatial geometric framework for analysing the spatial extent and consider a sampling procedure that retains the temporal information in the data, thereby enabling estimation of the duration of extreme rainfall events. We also account for the non-stationary behaviour, arising from topographical and seasonal effects, that commonly characterises extreme weather events in both space and time. Using diagnostic metrics, we demonstrate that the proposed model is appropriate for inferring extreme events on this dataset and apply it to estimate target quantities of interest.

Problem

• extreme rainfall
• spatial extent
• temporal duration
• extrapolation
• non-stationarity

Innovation

• geometric framework
• extreme-value analysis
• spatial extremal dependence
• non-stationarity
• multivariate tail extrapolation