Flood risk estimation via geometric extremal graphical models

2026-07-16

AI Summary

Existing geometric extreme value methods struggle to effectively estimate high-dimensional joint flood risk across more than a dozen gauging stations in river networks. This study addresses this challenge by introducing, for the first time, an extremal graphical model grounded in multivariate geometric extreme value theory to real-world river network flood assessment. The approach leverages a block graph structure to represent river network topology, yielding a sparse yet interpretable high-dimensional model. The work innovatively proposes a structured norming function and marginal probability correction coefficients, thereby overcoming dimensional limitations and enhancing extrapolation capability. Applied to data from ten gauging stations in the Preston region of England, the model demonstrates excellent fit and successfully quantifies the probability of synchronous extreme flooding at four locations.

Abstract

We exploit the new framework of multivariate geometric extreme value theory for the statistical analysis of river flow extremes at multiple locations on a river network. Current methodologies within the geometric framework are limited to a relatively low number of dimensions. This is insufficient for the purposes of flood risk estimation, since the number of gauging stations on a river network is often of the order $10-20+$. In order to create a parsimonious model in higher dimensions, we translate recent theoretical work on geometric extremal graphical models into statistical practice. We define the gauge function, a key object in geometric extremes, in a structured way using block graphs, which are a natural way of expressing the river network. We introduce both simple models, and more complex ones that can accommodate both simultaneous and non-simultaneous flows, and apply them to extreme flows at 10 locations on a river network around Preston, in north-west England. The models are shown to fit well and indicate strong extrapolation performance. We also introduce a correction coefficient for the geometric framework to address potential over- or under-estimation of marginal probabilities. The overall utility of our approach is illustrated through calculation of probabilities of simultaneous flooding at four locations on the network.

Problem

• flood risk estimation
• geometric extremes
• river network
• multivariate extremes
• high-dimensional modeling

Innovation

• geometric extremes
• extremal graphical models
• block graphs
• flood risk estimation
• gauge function