Bias and Uncertainty in the Estimation of Extreme Wave Heights and Crests

The accurate prediction of extreme wave heights and crests is important to the design of offshore structures. For example, knowledge of the extreme crest elevation is required to set the deck elevation of the topside of a jacket structure. However, methods of extreme value analysis have an inherent bias, and the manner in which they are applied affects this bias. Furthermore, there is uncertainty in the design parameters at the time of design and the possibility that the predictions will change during the life of the structure. This paper is concerned with the accurate prediction of design values that incorporate uncertainty. In the first part of this paper the details of commonly applied extreme value analysis techniques are examined. This is achieved through analysis of simulated data of known distribution. In particular it is the application of least squares minimisation routines that is investigated; however, comparisons are made with maximum likelihood estimation. From this, preferred approaches to the analysis are recommended and their advantages and disadvantages discussed. The methods are applied to the analysis of a North Sea data set and the implications for the design values ascertained. In the second part of the paper Bayesian inference is used to consider the effect of uncertainty in the predicted wave heights and crest elevations. The practical implications are determined by the analysis of a measured North Sea data set.