Sea level rise: using copula function to get structure crest level rating from its average overtopping discharge

With the rise in sea level due to climate change, it is necessary to improve calculation methods for determining the crest level of coastal structures from the mean overtopping discharge at a 100-year return period. Achieving this goal requires more accurate estimation of the joint distributions than those provided by the simplified Defra method. So far, applications of copula theory have been mainly limited to hydrology and oceanography, with few examples in coastal engineering. The originality of our work lies in applying copulas to determine the crest level of coastal structures as a function of mean overtopping discharge. The main results highlight significant differences between the various approaches (direct method, Defra, Clayton, Gumbel, Galambos, Joe, Plackett). The use of the Clayton copula allowed us to establish a linear relationship linking the crest level of the structure to the logarithm of the overtopping discharge, applied to the Port of Le Havre (France).