Fitting the Long Term Bivariate Distribution of Wave Heights and Periods to a Theoretical Model

The sea state severity is commonly presented in form of bivariate histograms of significant wave height and the mean zero-upcrossing wave period. Since there is no known theoretical basis for choosing any particular distribution, various statistical models have been proposed to characterise the bivariate distribution of these parameters. The adequacy of a statistical model requires some test to evaluate the goodness-of-fit of the model to the sample data. A two-dimensional version of the classical Kolmogorov-Smimov test, which is distribution-free for practical purposes is described in this paper. This method is illustrated by fitting the empirical distribution of significant wave heights and average zero-upcrossing periods of wave data measured in the Norwegian continental shelf to the Plackett model.