Joint stochastic simulation of extreme coastal and offshore significant wave heights

Abstract

The characterisation of future extreme wave events is crucial because of their multiple impacts, covering a broad range of topics such as coastal flood hazard, coastal erosion, reliability of offshore and coastal structures. The main goal of this paper is to propose and study a stochastic simulator that, given offshore conditions (peak direction ${\mathit{D}}_{\mathit{p}}$, peak period ${\mathit{T}}_{\mathit{p}}$ and moderately high significant wave heights ${\mathit{H}}_{\mathit{s}}$), produces jointly offshore and coastal extreme ${\mathit{H}}_{\mathit{s}}$, a quantity measuring the wave severity and which represent a key feature in coastal risk analysis. For this purpose we rely on bivariate Peaks over Threshold, and a nonparametric simulation scheme of bivariate GPD is developed. From this joint simulator, a second generator is derived, allowing for conditional simulations of extreme ${\mathit{H}}_{\mathit{s}}$. Finally, to take into account nonstationarities, the extended generalised Pareto model is also adapted, letting the parameters vary with specific sea-state parameters ${\mathit{T}}_{\mathit{p}}$ and ${\mathit{D}}_{\mathit{p}}$. The performances of the two proposed generators are illustrated on simulated data and then applied to the simulation of new extreme oceanographic conditions close to the French Brittany coast using hindcast sea-state data. Results show that the proposed algorithms successfully simulate future extreme ${\mathit{H}}_{\mathit{s}}$ near the coast in a nonparametric way, jointly or conditionally on sea-state parameters from a coarser model.