Transformed Rayleigh distribution of trough depths for stochastic ocean waves


During the design of various types of ocean engineering structures, such as the Mobile Offshore Drilling Unit, it comes as a necessity to thoroughly describe the wave trough depths and the associated exceedance probabilities as they represent an input for the design and risk assessment for such structures. Furthermore, the wave trough depths distribution is also very important in the process of design and risk assessment of a tension-leg platform as it is used to compute the tether loads imposed on the platform. As such, it is often required that the wave trough distributions obey the Rayleigh probability law in an ideal Gaussian narrow band random sea. However, a shortcoming emerges as the ideal Gaussian sea model is normally linear while as the waves in the real world are nonlinear. This in turn invalidates the application of the Rayleigh distribution to the wave troughs hence the need to develop more suitable methods. Worse off, in current literature, the nonlinear wave trough distribution model is very rare.

Recently, Professor Yingguang Wang from the School of Naval Architecture, Ocean and Civil Engineering at Shanghai Jiao Tong University presented a Transformed Rayleigh method that could be utilized to calculate wave trough distributions of irregular Stokes waves more accurately and efficiently. He hoped that his computational inputs would facilitate better calculation of wave trough depths exceedance probabilities for stochastic ocean waves more efficiently. His work is currently published in the research journal, Coastal Engineering.

In brief, he commenced his research work by selecting a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process, for the proposed Transformed Rayleigh method. Next, he used the method to predict the wave trough exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea and of another sea state observation in the North Sea. Lastly, he analyzed the obtained calculation results and compared them with those obtained from using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al. wave trough depths distribution model.

The author observed that the Arhan and Plaisted model gave poorer predictions in the wave trough region than the Transformed Rayleigh method. Better still, he noted that the method he proposed took less than 2 seconds on a desktop computer to obtain the results of the wave trough exceedance probabilities by applying the Transformed Rayleigh method. Moreover, the accuracy and efficiency of the Transformed Rayleigh method for calculating the wave trough distributions of irregular Stokes waves could thus be validated.

In summary, the work by Professor Yingguang Wang highlighted and elucidated on the detailed mathematical procedures and formulas of a Transformed Rayleigh method for calculating the wave trough distributions of irregular Stokes waves. Additionally, a second order Stokes wave model has been integrated into this Transformed Rayleigh method. It has been observed that the method demonstrated here can offer better predictions than those from using the theoretical and/or empirical wave trough distribution models. Altogether, the research findings gained from this study demonstrate the suitability of utilizing the proposed Transformed Rayleigh method for engineering purposes.


Yingguang Wang. Transformed Rayleigh distribution of trough depths for stochastic ocean waves. Coastal Engineering, volume 133 (2018) page 106–112.

Go To Coastal Engineering

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