Joint distribution of significant wave height and zero-up-crossing wave period using mixture copula method

An estimation of the statistical properties of a met-ocean environment is extremely important in the design and risk assessment of marine structures. An adequate description of the joint distribution of met-ocean variables can be utilised for structural reliability analyses. This study focuses on the joint distribution of significant wave height and zero-up-crossing wave period with a mixture copula distribution model for total sea data. Each component of the mixture model is constructed using a Weibull distribution for the significant wave height, a lognormal distribution for the wave period, and a Gaussian copula function. A commonly used conditional model is used for a comparison with the proposed model. Several evaluation strategies are defined for an assessment of the performance of two fitted models utilising simulated bivariate samples. The results suggest that the conditional model is unsuitable for a description of the pattern of the joint distribution, notably by seriously underestimating the return levels. By contrast, the mixture copula is capable of providing an improved performance, and thus provides extremely reliable environmental contours. Furthermore, the effects of seasonality and short-term dependency on the joint behaviour of the spectral parameters are investigated and discussed based on the environmental contours.