Copula-Based Bivariate Modelling of Significant Wave Height and Wave Period and the Effects of Climate Change on the Joint Distribution

The joint distribution of several met-ocean variables is required for risk assessment and load and response calculations in marine engineering. For example, a joint description is needed to construct environmental contours for probabilistic structural reliability analyses. Typically, the joint distribution of significant wave height and wave period is required as a minimum. This paper presents a study on various bivariate modelling techniques for the joint distribution of significant wave height and zero-crossing wave period, i.e. a conditional model, a bi-variate log-normal model and several meta-models based on parametric copulas. Each of the models is fitted to data generated from a numerical wave model for the current climate and for two future climates consistent with the RCP 4.5 and RCP 8.5 scenarios. Thus, the objective of this study is twofold. First, the joint models obtained by the various modelling techniques will be compared. Secondly, the potential effect of climate change on the simultaneous distribution of significant wave height and wave period will be explored. The results indicate that straightforward application of many of the most common families of copulas fails to capture the dependence structure in the data, and that the conditional model performs better than these naive approaches. However, if more advanced copula construction techniques are applied, significant improvements can be achieved. The results also suggest that significant wave height and zero-crossing wave period tend to be more correlated in a future climate, at least in the extremes.