Multivariate environmental contours using C-vine copulas

Characterization of some natural hazards requires modeling the joint probability distribution of several random environmental variables. For instance, extreme sea states may be defined in terms of wave height, peak spectral period, wind velocity, current velocity, and wave direction. Building environmental contours of extreme sea-states thus requires the multivariate probability distribution of such variables. The approach based on vine copulas is a way to construct multivariate distributions using bivariate copulas as building blocks. C-vines are particularly appealing for sets of random variables where one of them is considered to be the key one in governing dependence with the other variables. In this work we present a procedure to build multidimensional environmental contours using C-vines. The formulation for the decomposition of multivariate distributions into bivariate copulas and the estimation of parameters for C-vines is discussed. The procedure is illustrated with an example of trivariate environmental contours. It is then applied to build trivariate environmental contours of significant wave height, peak spectral period and wind velocity using storm hindcast data from the Gulf of Mexico. Implications on considerations for customary design criteria are discussed. Comparisons of the environmental contours using C-vines with those obtained from standard multivariate copulas are also discussed.