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.

翻译：极端偏态增水的合理建模对于海岸风险管理至关重要。本研究聚焦于沿法国大西洋沿岸的极端偏态增水建模，特别关注站点间的极端依赖结构。我们采用峰值超阈值框架，当至少一个站点记录到较大值时（尽管不要求所有站点同时出现），即定义为多元极端事件。我们提出了一种确定适当阈值（用以区分观测值是否为极端值）的新方法。研究探索了两种互补路径：首先，利用多元广义帕累托分布建模极端值，通过其属性推导生成模型，基于邻近站点的观测极端值预测目标站点的极端偏态增水；其次，评估了一种新型极端回归框架用于点预测。该回归框架仅利用输入变量的"角度"（即输入变量除以其范数）即可实现精确的点预测。最终目标是重建数据有限站点的历史偏态增水时间序列。这一目标通过整合来自布雷斯特和圣纳泽尔等拥有150余年观测记录站点的极端偏态增水数据得以实现。