Determination of the hydrodynamic design parameters water level and wave height using Copula models for the design of coastal protection structures on the Baltic Sea of Germany

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 take into account the joint probability of water levels and waves. Bivariate modeling of the probability with Copula models offers an alternative.

Copulas can be used to describe the non-linear dependencies between water level and wave height and to calculate joint probabilities of occurrence. However, the application of this methodology places greater demands on the underlying data. As the data available in the study area does not meet the requirements, statistical methods are used to generate the data. First, various Copulas are adapted to physically consistent combinations of water level and wave height extracted from storm surge events and validated. Next, the Copulas are used to calculate design water levels and wave heights for selected return intervals. 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 dependency structure. The bivariate parameter heights determined with the same return intervals are lower than the parameters determined with the univariate method. The available data only allow a limited application of the Copulas for design issues in the study area. Nevertheless, Copulas have the potential to replace the univariate methods for determining the design parameters.