Sailing synthetic seas: Stochastic simulation of benchmark sea state time series

Abstract

Coastal and offshore engineering relies on the analysis of sea state parameters, such as significant wave height ( H m 0 ), zero-crossing mean wave period ( T m 02 ), and mean wave direction ( Θ m ). Since observed records of these parameters usually span only a few years, proper uncertainty assessment requires the simulation of unobserved but equally plausible time series. This study suggests a simple stochastic method, named SyntheSeas, to generate synthetic sequences that preserve marginal distributions and power spectra along with power cross-spectra of H m 0 , T m 02 , and Θ m . SyntheSeas is a tailored version of the multivariate Iterative Amplitude Adjusted Fourier Transform (IAAFT) method, and has several desirable properties: (i) it relies on minimal assumptions, (ii) it accounts for the limiting steepness condition that constrains the relationship between H m 0 and T m 02 without using ad hoc parametrisation, and (iii) it accounts for the modelling problems due to the circular behaviour of Θ m with satisfactory approximation. Thanks to its simplicity and transparency, SyntheSeas (i) allows the identification of the key properties required to simulate realistic time series of H m 0 , T m 02 , and Θ m , (ii) provides a benchmark to test parametric models and their components, and (iii) enables quick applications, such as preliminary uncertainty and sensitivity analyses, without requiring advanced expertise in stochastic modelling. As a proof of concept, we discuss an application to data recorded from four wave buoys deployed around the United Kingdom. • Fourier-based simulation of sea state time series at fine temporal scales. • Preserving distributions, power cross-spectra, and limiting steepness condition. • Introducing synthetic sea state time series to validate alternative models’ output.