The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The non-linearity of steep waves is modelled to second order using Sharma and Dean kinematics and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, non-linearity makes extreme crests higher than the corresponding linear ones. The non-linear effects on wave height are relatively small.

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