A semiparametric method to simulate bivariate space–time extremes

Abstract

Coastal hazards raise many concerns, as their assessment involves extremely high economic and ecological stakes. In particular, studies on rarely observed but damaging events are quite numerous. In order to anticipate upcoming events of this kind, specialists need to extrapolate the results of their studies to events that have not yet occurred. Such events might be more extreme than those already observed and could therefore severely impact the coast. It is therefore paramount to propose methodologies to simulate such extreme conditions. Parametric and nonparametric statistical methods have already been used to assess environmental extreme quantities, from univariate framework to spatial context; however, they do not generally focus on the simulation of extreme environmental scenarios. This study introduces a semiparametric approach based on the Extreme Value Theory (EVT), dedicated to the simulation of extreme space–time processes. In the proposed application context, these processes describe near-shore hydraulic conditions. They nourish coastal impact models to assess hazards along the coast. The benefit of this approach is to be able to characterise coastal hazards on an event scale, meaning we can characterise the impact both in space and through time for a given extreme event. The usefulness of this space–time extreme modelling is illustrated by a risk analysis related to the long-shore impact of extreme wave events in the Gulf of Lions.