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

2025-08-19

AI Summary

This study addresses the challenge of modeling extreme coastal flooding events driven by time-varying meteorological and oceanographic conditions over semi-diurnal tidal cycles—a regime where classical extreme value theory (EVT) fails due to its restrictive assumptions of independence, identical distribution (i.i.d.), and heavy-tailedness. We propose a two-stage functional EVT framework: first, an autoregressive model removes inter-cycle temporal dependence; second, a Pareto process models extremes of the short-tailed, dependent residual functional data. Principal component analysis and tailored extreme-value statistical tests are integrated for improved functional representation and rigorous validation. Applied to storm surge data from Gâvres, France, our method generates extreme scenarios that faithfully reproduce observed morphological structures, extremal statistical properties, and classification consistency. It significantly enhances both the physical interpretability and generation capability of multi-level extreme flood scenarios under short-duration, non-stationary conditions.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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{â}vres site, located in southern Brittany, France.

Problem

• Modeling rare coastal flooding events under time-varying meteoceanic conditions
• Addressing temporal dependence and short-tailed behavior in functional extreme value theory
• Developing extreme scenario simulator for surge evolution over tidal cycles

Innovation

• Autoregressive model removes temporal dependence
• Adapts Pareto processes for short-tailed residuals
• Builds extreme scenario simulator via inverse transformations