Development of environmental contours using Nataf distribution model

Developing environmental contours requires knowledge of the joint probability distribution of the environmental variables; however, it is commonly the case that only the marginal distributions and the correlation structure of the environmental variables are known based on available statistical data. The Nataf distribution model provides a way to derive joint distribution models consistent with prescribed marginal distributions and a correlation structure. It has been used extensively for multivariate models of metocean variables. In this paper, the development of contours for environmental variables having joint probability density defined by the Nataf distribution model is examined. A formulation is proposed for developing environmental contours in terms of the marginal distributions of the environmental variables and their correlation coefficients. Analytical expressions are derived for the values of the environmental variables in terms of standard normal variates defining the environmental contours. The proposed method is simple to implement and provides a direct way to easily produce contours for more than two environmental variables, thus extending 2-D contours to higher dimension contour surfaces involving a greater number of environmental variables. An example shows its application to characterize multi-variate extreme sea-states using hindcast data for hurricanes and winter storms in the Gulf of Mexico.