Distributions of extreme wave, crest and trough heights measured in the North Sea

We present statistical analyses of the most extreme wave, crest and trough heights occurring during 793 h of surface elevation measurements collected during 14 severe storms in the North Sea. This data contains 104 freak waves. It is shown that the statistics of the extremes of crest and trough heights depends strongly on the significant wave height. Fitted statistical models are provided and a procedure presented whereby one may calculate good estimates of the probability distributions, densities, return periods and other statistics of the extremes of crest and trough heights as functions of significant wave height.