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

TL;DR

This study tackles reconstructing past extreme skew surges along the French Atlantic coast by exploiting spatial dependence via multivariate extreme value theory. It compares two complementary strategies: a parametric multivariate generalized Pareto (MGP) model that yields full conditional distributions and a nonparametric angular regression approach (ROXANE) that prioritizes point predictions, both built on a novel threshold-determination method. Marginal tails are modelled with an extended GP (EGP) to flexibly fit margins, while dependence is captured either through MGPD on standardized margins or via angular learning. The methods are applied to long-record inputs from Brest and Saint-Nazaire to predict surges at shorter-record outputs (Port Tudy, Concarneau, Le Crouesty) and to reconstruct Port Tudy’s pre-1966 series, demonstrating complementary strengths: MGPRED provides probabilistic reconstructions with confidence intervals, whereas ROXANE delivers sharp extreme-value predictions. Overall, the work extends a practical EVT toolkit for coastal risk assessment and long-range return-period estimation, with potential adaptations to other coastlines and covariates such as wind.

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.

Figures (20)

• Figure 1: Five French tide gauge locations along the French Atlantic coast. Brest and Saint-Nazaire (red dots) have long sea level measurements, while Concarneau, Port Tudy and Le Crouesty (blue dots) have much shorter recordings. The objective of this work is to reconstruct missing surges in the past given extreme values from stations with long historical records (red dots).
• Figure 2: Pairwise skew surge exceedances for all pairs of stations from 01/12/2000 to 31/12/2023. Dark orange (resp. light orange) points represent the observations below (resp. above) the threshold specified in Table \ref{['tab:egpd_tudy']}. The grey dotted lines represent the chosen marginal thresholds via Algorithm \ref{['algo:th_select']} (see Section \ref{['sec:res_marg']}).
• Figure 3: Histograms of skew surge exceedances at the three stations Brest (left), Saint-Nazaire (middle) and Port Tudy (right), from 01/12/2000 to 31/12/2023. The orange curves represent the fitted EGP densities, with parameters specified in Table \ref{['tab:egpd_tudy']}. The dotted vertical grey lines represent the smallest point above which each fitted density is convex, which represent the chosen marginal thresholds via Algorithm \ref{['algo:th_select']} (see Section \ref{['sec:res_marg']}).
• Figure 4: QQ-plots comparing observed skew surge exceedances of the Port Tudy test set (x-axis), ranging from 10/08/1966 to 31/12/1999, to predicted data (y-axis) from the algorithms of Sections \ref{['sec:reg_proc']} and \ref{['sec:mgp_proc']}. The plots show results from the ROXANE procedure with RF regression (left), ROXANE procedure with OLS regression (middle), and MGPRED (right) with bootstrap 0.95 confidence bands (lightorange). The dotted red line represents the identity line $x=y$.
• Figure 5: Predicted skew surge exceedances at Port Tudy station for the years 1989 (left), 1978 (middle), 1977 (right). Red curves represent the true values; purple curves represent the predicted values by the ROXANE procedure with OLS algorithm; orange curves represent the predicted values by MGPRED with bootstrap 0.95 confidence bands (lightorange).