Comparative study of joint distributions of wave height and surf parameter for individual waves including spectral bandwidth effects

This paper compares the Myrhaug and Fouques (2012) joint distribution of wave height and surf parameter with the transformed Longuet-Higgins (1983) joint distribution of wave height and wave period; both joint distributions are for individual random waves within a sea state. Effects of the spectral bandwith are discussed, together with giving examples of estimating probabilities of breaking waves on different slopes. The Myrhaug and Fouques (2012) distribution is a parametric model originating from best fit to relatively broad-banded field data, while the Longuet-Higgins (1983) distribution is theoretically based. It is found that the theoretically based distribution is inadequate to describe the features of the parametric model representing the relatively broad-banded data, suggesting that parametric models should be used to describe such data.