Study on joint probability distribution of wave height and wind velocity

This article introduced the method of bivariate joint probability distribution based on the copula function.A major advantage of this method is that marginal distributions of individual variables can be of any form and the variables can be correlated.Some of conclusions were reached by using extreme wave height and wind speed as an example collected in Shanwei sea area as the following:(1) Optimized marginal distributions of wave height and wind velocity can be represented by the Pearson pattern three and generalized extreme value distribution,respectively;(2) Gumbel–Hougaard Copula that belongs to Archimedean copula family was the optimal copula selected by the goodness-of-fit test;(3) The relative differences of the special frequency design values between the marginal distribution of wave height and the joint distribution fall in between 3.1% and 8.1% for the return periods between 5 and 200 years,and the relative differences of wind velocity fall in between 2.8%~6.4%;(4) The encountering probabilities of wave height given wind velocity decrease along with decreasing the frequency of wave height;whereas the encountering probabilitiy increase while the specific wave height frequency is along with decrease of wind velocity frequency.