Determination of Hydrodynamic Design Parameters for Coastal Protection Structures on the German Baltic Sea Using Copula Models

The design of coastal protection structures requires design parameters that accurately represent the hydrodynamic conditions along the coast. Currently, these input variables are based on univariate probability models, which do not consider the joint probability of water level and statistical wave parameters such as significant wave height. Bivariate probability modeling using copula models offers an alternative. Copulas can be used to describe the dependencies between water level and significant wave height and to compute joint probabilities of occurrence. First, various copulas are fitted to samples of physically consistent combinations of water level and significant wave height extracted from storm surge events along the German Baltic Sea coast of Mecklenburg-Western Pomerania. Next, the most appropriate copula model is used to compute design combinations of water level and significant wave height for selected return periods. The bivariate design parameters are compared with the univariate ones in a simplified design example for wave run-up on a dike. The validation of various models shows that the Frank copula best describes the dependence structure. The bivariate design parameters obtained for the same return periods are lower than those determined using the univariate method. The available data only allow a limited application of the copulas for engineering design in the study area. Nevertheless, copulas have the potential to replace univariate methods for determining design parameters and thus contribute to more reliable and cost-efficient coastal protection structure design.