Joint probability distribution of coastal winds and waves using a log-transformed kernel density estimation and mixed copula approach

The planning, designing, and risk assessment of coastal structures heavily rely on realistic statistical analyses of coastal winds and waves (CWW). In this study, we propose a novel bivariate joint probabilistic approach to describe the complex dependence and model the joint probability distribution (JPD) for CWW. A log-transformed kernel density estimation (KDE) is applied to fit the univariate marginal cumulative distribution (MCD) of the CWW measured at ShiDao station. As a connectivity function between the univariate MCD and JPD, a mixed copula is developed using a linear combination of Gumbel, Clayton, and Frank copula. The analytical results indicate that the optimum MCD for the ocean parameters can be effectively obtained using the log-transform KDE when compared with the Kernel-Pareto and GEV. Compared with five commonly used single copulas (i.e., Gaussian, t, Gumbel, Clayton, and Frank copula), the mixed copula is more suitable for describing the bivariate complex dependency structure between the ocean parameters and can yield more realistic JPD estimations. The return period and conditional probability calculated by the mixed copula were discussed and compared with the best fit single copula, which concluded that the log-transformed KDE and mixed copula approach can improve the precision of statistical analyses for CWW.