Modelling long-term joint distribution of significant wave height and mean zero-crossing wave period using a copula mixture

Abstract

Ocean waves are a natural combination of wind sea and swell. Considering this physical process, by comparing the magnitudes of splitting wind sea and swell energy, long-term wave climate can be classified into four basic components: pure wind sea, pure swell and two classes of combined seas, wind sea stronger and swell stronger. From one position in the North Atlantic Ocean, across seasonal analysis on the 44-year (1958–2001) hindcast wave data calculated by WAM in the HIPOCAS project, it was found that the four wave components behave distinctly. Hence, in this study, we propose using a mixture of distributions to perform the copula-based statistical modelling of significant wave height and mean zero-crossing wave period. A case study was dedicated to testify the univariate and bivariate capacity of fitting, the results demonstrate that: 1) compared to straightforward fitting a distribution to data, estimating the marginal distribution of the sea state parameter as a mixture of the four components can improve goodness-of-fit; 2) the proposed copula mixture model can provide an outstanding fit to the bivariate wave data, outperforming those constructed by copulas belonging to Symmetric, Khoudraji-Liebscher and Product families, as well as the classical Conditional Modelling Approach.