Global Hierarchical Models for Wind and Wave Contours: Physical Interpretations of the Dependence Functions

Applications such as the design of offshore wind turbines requires the estimation of the joint distribution of variables like wind speed, wave height and wave period. The joint distribution can then be used, for example, to define design load cases using the environmental contour method. Often the joint distribution is described using so-called global hierarchical models. In these models, one variable is taken as independent and the other variables are modelled to be conditional on this variable using particular dependence functions. In this paper, we propose to use dependence functions that offer physical interpretation. We define a novel dependence function that describes how the median of the zero-up-crossing period increases with significant wave height and a novel dependence function that describes how the median significant wave height increases with wind speed. These dependence functions allow us to reason about the physical meaning, even when we extrapolate outside the range of a given sample of environmental data. In addition, we can analyze the estimated parameters of the dependence function to speculate which kind of sea dominates at a given site. We fitted statistical models with the proposed dependence functions to six datasets and analyzed the estimated parameters. Then we calculated environmental contours based on these estimated joint distributions. The environmental contours had physically reasonable shapes, even at areas that were outside the datasets that were used to fit the underlying distributions.