Modeling directional environmental contours using three dimensional vine copulas

Environmental contours are used to characterize multivariate natural hazards for the purpose of structural analysis and design. They specify combinations of environmental variables for finding the maximum system response associated with a given exceedance probability. Appropriate modeling of the multivariate probability distribution of the environmental variables is fundamental for the computation of contours. In this work, a framework using copulas is presented for environmental contours of two linear variables, such as wave height and peak spectral period, conditioned on circular variables, such as wave or wind direction. A formulation using three dimensional vine copulas is discussed and adopted. The advantage of the vine copula approach is the flexibility to model multivariate distributions using combinations of bivariate copulas that model pairwise dependencies between the environmental variables. Directionality effects on the environmental contours are analyzed considering the degree of association for given circular-linear copula models and the dispersion in the circular distributions. The formulation is then used for building directional environmental contours of metocean variables describing extreme sea states. The methodology for the statistical modeling of the metocean variables is described and contours of significant wave height, peak spectral period, and wind speed are obtained, considering wave and wind directionality.