MULTIVARIATE EXTRAPOLATION IN THE OFFSHORE ENVIRONMENT

We consider the estimation of the extremes of the metocean climate, in particular those of the univariate and joint distributions of wave he ight, wave period and wind speed. This is of importance in the design of oil rigs and other marine structures which must be able to withstan d extreme environmental loadings. Such loadings are often functions of two or more metocean variables and the problem is to estimate the ext remes of their joint distribution, typically beyond the range of the o bserved data. The statistical methodology involves both univariate and multivariate extreme value theory. Multivariate theory which avoids ( often very inappropriate) prior assumptions about the nature of the st atistical association between the variables is a fairly recent develop ment. We review and adapt this theory, presenting simpler descriptions and proofs of the key results. We study in detail an application to d ata collected over a nine-year period at the Alwyn North platform in t he northern North Sea. We consider the many problems arising in the an alysis of such data, including those of seasonality and short-term dep endence, and we show that multivariate extreme value theory may indeed be used to estimate probabilities and return periods associated with extreme events. We consider also the confidence intervals associated w ith such estimates and the implications for future data collection and analysis. Finally we review further both the statistical and engineer ing issues raised by our analysis. (C) 1998 Elsevier Science Ltd. All rights reserved.