Coastal flooding: A copula based approach for estimating the joint probability of water levels and waves

An accurate joint probability assessment of water levels and waves is of primary importance for effective coastal flooding management even in microtidal environments subjected to severe storm surge events. A copula based approach is presented for modeling the joint distribution derived from almost six years of sea levels and waves at a site suffering from coastal flooding. The evaluation of the upper tail dependence coefficient represents an unavoidable step in the copula selection process since it provides indications on extreme dependence that cannot be neglected to reliably estimate the probability of marine inundation. Based on the results of various statistical tests and estimation of the upper tail dependence coefficient, a one-parameter extreme value copula is selected to model the dependence structure of events representing conditions at peak water levels, including wave height, incoming wave direction and season of occurrence. The joint distribution obtained is subsequently used for reliability analysis. A particular simplified application case is described for the Ravenna coast (Italy) and the probability of failure/inundation is estimated through the direct integration method. Since the failure function employed involves the wave runup depending on wave period, the joint distribution of wave height and wave period is also assessed. The study highlights the importance of taking into account all the variables involved in the flooding phenomenon for a reliable flood probability estimate. The presented methodology can be applied to the assessment of flood probability at coastal sites at risk of inundation due to the combined impact of waves and water levels.