Simulation of extreme functionals in meteoceanic data: Application to surge evolution over tidal cycles

TL;DR

This paper develops a two-stage methodology combining autoregressive modeling and Pareto process techniques to simulate extreme surge scenarios influenced by tidal cycles, validated on Brittany coastal data.

Contribution

It introduces a novel approach to simulate extreme meteoceanic events accounting for temporal dependence and short-tailed behavior, specifically tailored for tidal cycle data.

Findings

Effective simulation of extreme surge scenarios validated against real data.

Method captures dependence structure and extreme behavior accurately.

Applicable to coastal flood risk assessment in tidal regions.

Abstract

We investigate the influence of time-varying meteoceanic conditions on coastal flooding under the prism of rare events. Focusing on conditions observed over half tidal cycles, we observe that such data fall within the framework of functional extreme value theory, but violate standard assumptions due to temporal dependence and short-tailed behavior.a To address this, we propose a two-stage methodology. First, we introduce an autoregressive model to eliminate temporal dependence between cycles. Second, considering the model residuals, we adapt existing techniques based on Pareto processes. This allows us to build a simulator of extreme scenarios, by applying inverse transformations. These simulations depend on an initial time series, which can be randomly selected to tune the desired level of extremes. We validate the simulator performance by comparing simulated times series with observations, through several criteria, based on principal component analysis, extreme value analysis, and classification algorithms. The approach is applied to the surge data, on the G{\^a}vres site, located in southern Brittany, France.