Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast

TL;DR

This study develops new multivariate extreme value models to reconstruct historical skew surge data along the French Atlantic coast, improving coastal risk management.

Contribution

It introduces a novel threshold determination method and a new extreme regression framework for better modeling and prediction of skew surges.

Findings

The multivariate generalized Pareto distribution effectively models extreme skew surges.

The extreme regression framework accurately predicts point estimates using input angles.

Historical surge series are reconstructed using long-term data from Brest and Saint-Nazaire.

Abstract

Appropriate modelling of extreme skew surges is crucial, particularly for coastal risk management. Our study focuses on modelling extreme skew surges along the French Atlantic coast, with a particular emphasis on investigating the extremal dependence structure between stations. We employ the peak-over-threshold framework, where a multivariate extreme event is defined whenever at least one location records a large value, though not necessarily all stations simultaneously. A novel method for determining an appropriate level (threshold) above which observations can be classified as extreme is proposed. Two complementary approaches are explored. First, the multivariate generalized Pareto distribution is employed to model extremes, leveraging its properties to derive a generative model that predicts extreme skew surges at one station based on observed extremes at nearby stations. Second, a novel extreme regression framework is assessed for point predictions. This specific regression framework enables accurate point predictions using only the 'angle' of input variables, i.e., input variables divided by their norms. The ultimate objective is to reconstruct historical skew surge time series at stations with limited data. This is achieved by integrating extreme skew surge data from stations with longer records, such as Brest and Saint-Nazaire, which provide over 150 years of observations.