Modeling multivariate ocean data using asymmetric copulas

Abstract

Multivariate descriptions of ocean parameters are quite important for the design and risk assessment of offshore engineering applications. A reliable and realistic statistical multivariate model is essential to produce a representative estimate of the sea state for understanding the ocean conditions. Therefore, an advanced modeling of ocean parameters helps towards improving ocean and coastal engineering practices. In this paper, we introduce the concepts of asymmetric copulas for the modeling of multivariate ocean data. In contrast to extensive previous research on the modeling of symmetric ocean data, this study is focused on capturing asymmetric dependencies among the environmental parameters, which are critical for a realistic description of ocean conditions. This involves particular attention to both nonlinear and asymmetrically dependent variates, which are quite common for the ocean variables. Several asymmetric copula functions, capable of modeling both linear and nonlinear asymmetric dependence structures, are examined in detail. Information on tail dependencies and measures of asymmetric dependencies are exploited. To demonstrate the advantages of asymmetric copulas, the asymmetric copula concept is compared with the traditional copula approaches from the literature using actual environmental data. Each of the introduced copula models is fitted to a set of ocean data collected from a buoy at the US coast. The performance of these asymmetric copulas is discussed and compared based on data fitting and tail dependency characterizations. The accuracy of asymmetric copulas in predicting the extreme value contours is discussed.