An event-based approach for extreme joint probabilities of waves and sea levels

A methodology for determining extreme joint probabilities of two metocean variables, in particular wave height and sea level, is presented in the paper. This methodology focuses in particular on the sampling of the time series, which should be based on the notion of event: either the event generating the variables whose joint probabilities are wanted (such as a storm generating waves and surges) or the event that is a result of the combination of these variables (such as a beach erosion event generated by waves at high sea level). A classification is proposed for multivariate analyses in order to help the choice of the sampling method. The dependence between the variables is analysed using tools such as the chi-plot, of which an enhanced presentation is proposed, then is modelled by extreme-value copulas (Gumbel-Hougaard, Galambos and Hüsler-Reiss) estimated by Canonical Maximum Likelihood or by the upper tail dependence coefficient. Joint return periods are then computed. A comparison is made with a simulation from the JOIN-SEA software on a dataset of wave height and sea levels offshore Brest, France. Then the bivariate methodology is extended to a multivariate framework. The distribution of sea level is determined by an indirect approach (extrapolation of extreme surges then convolution with the astronomical tide) and the dependence is analysed between the wave height and the surge component only. A bidimensional convolution between the joint distribution of wave height and surge and the distribution of the astronomical tide yields the joint distribution of wave height and sea level. The application of this method to the dataset of Brest and its comparison with the bivariate approach are finally discussed.