Transformed Rayleigh distribution of trough depths for stochastic ocean waves

This paper deals with the calculation of wave trough depths exceedance probabilities for stochastic ocean waves, and a Transformed Rayleigh method is proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The detailed mathematical procedures and formulas of the proposed Transformed Rayleigh method are given in this article, and the second order Stokes wave model has been integrated into this Transformed Rayleigh method. The proposed new method has been applied for calculating the wave trough depths exceedance probabilities of two sea states, one with the surface elevation data measured at the coast of Yura in the Japan Sea, and another one with the surface elevation data measured at the North Sea. It is demonstrated that the proposed new method can offer better predictions than those from using the theoretical Rayleigh wave trough depths distribution model. The calculation results from using the proposed new method are further compared with those obtained from using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al. wave trough depths distribution model, and the accuracy of the new method has been once again substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh method can be readily utilized in the process of designing various kinds of ocean engineering structures.