The present paper describes a model for the distribution of maximum wave and crest heights in a given sea state. The standard Rayleigh and Weibull distributions for wave and crest heights are modified using a third order Stokes expansion of the wave envelope. It was validated by fitting the model distributions to North Sea measurement data and provided much better predictions of maximum crest and wave heights than standard models. To make up for the fact that directionality and spectral shape are not taken into account in the model, correction terms (specific to the studied site) are introduced and mainly one of them will give the optimized mean wave number to consider in the model. The proposed model is relatively easy to apply and could be an effective tool to determine extreme wave and crest heights for offshore structure design purposes.
Standard models for the distribution of wave and crest heights are useful for computing maximum wave and crest heights, on the basis of significant wave heights, for the purposes of designing offshore structures. However, there can be differences of 10–20% in the results obtained with different models, which is unsuitable in terms of design criteria. These between-model discrepancies could be explained by the problem of accurately representing wave properties, especially strong and steep waves, in a given sea state. This is mainly due to nonlinearities in the wave kinematics which are not suitably taken into account in the models, nonlinearities which are controlled by directionality, spectral shape and wavelength-to-depth ratio. In the present paper, maximum wave and crest heights computed by several models are compared, followed by a description of an analysis of maximum wave and crest heights measured at the Frigg offshore site in the North Sea.