Unified distribution models for met-ocean variables: Application to series of significant wave height

The design of maritime works requires statistical models for several met-ocean variables, such as significant wave height HS that adequately represent the probability of occurrence and the uncertainty for the entire range of values of the variables. In general, the mean climate of HS is modeled empirically or by log-normal or two-parameter Weibull distributions using all available data. Extremal climate studies are conducted separately, usually by means of the peaks-over-threshold (POT) method. The methods used to define the threshold tend to be subjective and generally do not allow for calculation of the associated uncertainty.This paper proposes to use a mixture model for the marginal distribution of HS that includes thresholds between the central regime and minimum and maximum regimes as parameters of the model. The parameters of the model are estimated by maximum likelihood, for which specific recommendations are given. The distribution is able to parametrically model the mean climate of the variable. For calculating extreme values, a simple methodology is described that accounts for the uncertainty stemming from the estimation of the threshold.The implementation of this model using two HS series shows that it provides a better fit for the data than that obtained with parametric distributions such as log-normal or Weibull. Furthermore, this model automatically and objectively determines the threshold necessary to apply the POT method and the uncertainty associated with the threshold. It was observed that the proposed method for the estimation of the threshold is less sensitive to the presence of a potential outliers than other analyzed methods.

► A mixture distribution for the entire range of values of a met-ocean variable.
► An automatic threshold estimation procedure for applying the peak over threshold (POT) method.
► Inclusion of the threshold uncertainty in the calculation of the confidence intervals of high-return period quantiles.