Stochastic Space-Time Extremes of Wind Sea States: Validation and Modeling

Abstract

Damages and accidents occurred to offshore structures and routing ships raise questions about adequacy of conventional time domain analysis of short-crested sea waves. Indeed, experimental and field evidence showed that during such wave states, typical of storms, the maximum sea surface elevation gathered at a single point in time, i.e. the time extreme, tends to underestimate the actual maximum that occurs over a surrounding area, i.e. the space-time extreme. Recently, stochastic models for the prediction of multidimensional Gaussian random fields maxima, e.g. Piterbarg’s theorem and Adler and Taylor’s approach, have been applied to ocean waves statistics, permitting to extend extreme value analysis from time to space-time domain. In this paper, we present analytical and numerical approaches aimed at supporting applicability of such models, which is limited by the knowledge of directional spectrum parameters. Firstly, we validate stochastic models against stereo-photogrammetric measurements of surface wave fields. Then, we investigate the dependence of space-time extremes upon physical parameters (wind speed, fetch length, current speed) in the context of analytical spectral formulations, i.e. Pierson-Moskowitz and JONSWAP, and by using spectral numerical wave modeling. To this end, we developed two sets of closed formulae and a modified version of the SWAN model to calculate parameters of analytical and arbitrary directional spectra, respectively. Finally, we present preliminary results of a 3 years Mediterranean Sea hindcast as a first step towards operational forecasts of space-time extremes.