Multivariate extrapolation in the offshore environment

Abstract

We consider the estimation of the extremes of the metocean climate, in particular those of the univariate and joint distributions of wave height, wave period and wind speed. This is of importance in the design of oil rigs and other marine structures which must be able to withstand extreme environmental loadings. Such loadings are often functions of two or more metocean variables and the problem is to estimate the extremes of their joint distribution, typically beyond the range of the observed 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 statistical association between the variables is a fairly recent development. We review and adapt this theory, presenting simpler descriptions and proofs of the key results. We study in detail an application to data collected over a nine-year period at the Alwyn North platform in the northern North Sea. We consider the many problems arising in the analysis of such data, including those of seasonality and short-term dependence, 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 with such estimates and the implications for future data collection and analysis. Finally we review further both the statistical and engineering issues raised by our analysis.