Simulating a multivariate sea storm using Archimedean copulas

Abstract

In order to provide realistic storm simulations and to quantify coastal risks the dependencies between storm parameters such as wave height, wave period and storm duration need to be considered. Copulas provide a means to achieve this by enabling the development of multivariate statistical models of sea storms. Although there are many families of copulas, Archimedean copulas are appealing to engineers because of their mathematical tractability. The dependencies between wave height, wave period, storm duration, water level and storm inter-arrival time (or calm period) were investigated in a case study on the east coast of South Africa using Kendall's tau correlation coefficient as a dependency metric. Three methods of creating multivariate copulas were applied and the results were compared using (1) Kendall's measure; (2) empirical multivariate distributions; and (3) simulations. Only the wave height, wave period and storm duration were found to be significantly associated. Hierarchical copulas provided the best trivariate model for the case study data. The trivariate analysis extends previous bivariate analyses and thereby enables a more detailed description of sea storms to be incorporated in the statistical model. A significant limitation of the current model is that it fails to link wave parameter statistics to physical forcing and physical constraints. Ways of overcoming these and other limitations are discussed.