Study on the Joint Probability Distribution of Hydrodynamic Conditions in Xiamen Bay Based on Copula Functions

The Xiamen Bay area is frequently impacted by typhoons and is characterized by a complex hydrodynamic environment. The combined action of waves, currents, and storm surges threatens the construction of the Third Eastern Link. Traditional design methods often overlook the correlations among hydrological variables, potentially leading to overestimated design standards. To address this issue, we developed a high-accuracy multi-driver hydrodynamic numerical model for Xiamen Bay. A high-resolution dataset of waves, currents, and storm surges spanning nearly 20 years was established. Based on the Copula function, a trivariate joint probability distribution of wave–current–storm surge was constructed. The results indicate that the Gamma distribution is the most suitable marginal distribution for the individual variables, and the Clayton Copula function best captures the dependence structure among the three variables. For the same return period, the design values of wave height, current velocity, and water level obtained using the Copula method are lower than those derived using traditional standard methods. The research findings can provide a more scientific and economical design basis for the Third Eastern Link project and serve as a reference for multivariate joint probability modeling in similar sea areas.