A Vine-Copula Model for Time Series of Significant Wave Heights and Mean Zero-Crossing Periods in the North Sea

Abstract

Stochastic descriptions and simulations of oceanographic variables are essential for coastal and marine engineering applications. In the past decade, copula-based approaches have become increasingly popular for estimating the multivariate distribution of some variables at the peak of a storm along with its duration. The modeling of the storm shape, which contributes to its impact, is often simplified. This article proposes a vine-copula approach to characterize hourly significant wave heights and corresponding mean zero-crossing periods as a random process in time. The model is applied to a data set in the North Sea, and time series with the duration of an oceanographic winter are simulated. The synthetic wave scenarios emulate storms as well as daily conditions. The results are useful, for example, as input for coastal risk analyses and for planning offshore operations. Nonetheless, selecting a vine structure, finding appropriate copula families, and estimating parameters is not straightforward. The validity of the model, as well as the conclusions that can be drawn from it, are sensitive to these choices. A valuable byproduct of the proposed vine-copula approach is the bivariate distribution of significant wave heights and corresponding mean zero-crossing periods at the given location. Its dependence structure is approximated by the flexible skew-t copula family and preserves the limiting wave steepness condition.