Comparing trivariate models for coastal winds and waves accounting for monthly seasonality

A realistic multivariate model for extreme values of ocean parameters such as wind speed, wave height, and wave period is needed to obtain accurate statistical descriptions of metocean conditions. Here, using seasonally normalized monthly coastal winds and waves (CWW) data, we constructed an empirical cumulative distribution function-Pareto (ECDF-Pareto) method to model the marginal cumulative distributions (MCDs) of ocean parameters and compared them with the log-transformed KDE-Pareto (LTKDE-Pareto) distributions, generalized Pareto distributions (GPD), and generalized extreme value (GEV) distributions. Furthermore, six types of trivariate copula models for joint probability distributions (JPDs) of pre-processed CWW data, i.e., symmetric Archimedean copulas (SACs), asymmetric Archimedean copulas (AACs), mixed SACs, mixed AACs, mixed symmetric-asymmetric Archimedean copulas (SAACs), and C-Vine copulas, were described and compared. The results indicated that the proposed ECDF-Pareto outperformed the LTKDE-Pareto, GPD, and GEV distributions in fitting both the interior portions and upper tails of the MCDs. The constructed mixed SAACs gave the best overall fit for the pre-processed 3-dimensional CWW data. The proposed approach for fitting distributions, which applied the ECDF-Pareto method to fit the MCDs and the mixed SAACs to model the JPDs, was able to reasonably model the statistical characteristics and dependence structures of pre-processed CWW data, and therefore, was suitable for the statistical analysis of trivariate extremes for CWW data.