Approximation of bivariate probability density of individual wave steepness and height with copulas

The bivariate probability density of individual wave steepness and height is fitted with theoretical bivariate densities in the form of copulas. Copula functions approximate only the relation of the dependency between both random variables and marginal densities can be modeled separately. In this study the primary problem is finding a copula function which could faithfully represent the dependency relation between deep water wave height and steepness, so modeling marginal probability densities is a secondary question. A short description of the formulation of copula functions is given, and five different copula functions used in this study are described. These functions have been fit to wave data measured in an offshore basin and comparison with the empirical distribution allowed some conclusions about the adequacy of the various models.