Design and analysis of a one-dimensional sea surface simulator using the sum-of-sinusoids principle

Simulators for sea surface waves are useful for many practical applications, such as the construction of offshore structures and ocean surface animations. This paper studies three methods for the design of one-dimensional sea surface waves simulators with given wave spectra using the sum-of-sinusoids (SOS) principle. The wave spectrum provides insight into important statistical properties of the sea surface waves, such as the autocorrelation function (ACF) of the sea surface waves, significant wave height, and the moments of the spectrum. The sea surface simulator is designed by applying the concept of deterministic channel modelling on two main classical wave spectra, namely the Pierson-Moskowitz (PM) model and JOint North Sea WAve Project (JONSWAP) model. For the parametrization of the sea surface simulator, we adopt three well-known parameter computation methods: the -norm method (LPNM), method of equal distances (MED), and the method of equal areas (MEA). A good match between the given sea surface models and the corresponding simulation model is achieved with respect to the main statistical properties of the sea surface waves. It is shown that for a given number of sinusoids, the LPNM and the MEA have almost the same performance, whereas the MED results in a sea surface waves simulator that suffers from a relatively small period.