Environmental contours using copulas: Fid-Bau Portal

Environmental contours using copulas

Montes-Iturrizaga, R. / Heredia-Zavoni, E.

Highlights • Formulation for constructing environmental contours using copula theory. • Procedure for modeling dependence of metocean variables using copulas. • Copula estimation, selection and goodness-of-fit tests are given. • Effect of degree of association on environmental contours is examined. • Significant differences found in environmental contours depending on copula model.

Abstract A procedure is proposed for constructing environmental contours using copula theory. Copulas are functions that define the multivariate probability distribution of a random vector or a set of random variables, and, thus, also determine their dependence structure. Constructing environmental contours requires knowledge of the joint probability distribution of the environmental variables. In many practical applications, the available statistical data is used to estimate the marginal distributions and the linear correlation matrix, and then the Nataf distribution model is employed to obtain the multivariate probability distribution. It turns out that such an approach implies a particular model of dependence structure defined by a Gaussian copula, which might not always be the appropriate one. In this work, some classes of bivariate copulas are considered for modeling the dependence structure of the environmental variables. We examine measures of association, rank-based methods for estimation of copulas, goodness of fit tests for copulas, and copula selection criteria, and apply them to metocean data from hindcasts of tropical storms and extra-tropical events in the Gulf of Mexico. A formulation is proposed for expressing the variates that define the environmental contours as functions of copulas. It is then applied for computing environmental contours of significant wave height, peak spectral period and wind velocity using the estimated copula models.