A new wave crest distribution based on modified Box-Cox transformation and Rayleigh distribution. (15th May 2021) - Cai, Z.W.; Liu, X.L.; Chen, W.W.; Sun, Z.; Ding, J.
Abstract: A modified Box-Cox transformed Rayleigh (MBR) distribution for the wave crests is presented in this paper. The basic idea contains two steps: firstly, non-Gaussian elevations are transformed into Gaussian elevations by a modified Box-Cox transformation. Afterwards the crests of the transformed elevations are described by the Rayleigh distribution. Comparison between the MBR and Tayfun distributions shows that these two models are the same if terms smaller than O ( ε 2 ) are ignored, where ε is the elevations' skewness. Finally, verifications and comparisons are presented for two sets of field measurement. Based on the results, the MBR distribution gives better results than the Forristall model for very large wave crests. Moreover, the MBR model matches the observations better than the Tayfun distribution since it obtains larger probabilities for larger crest in addition to smaller probabilities for small crests. Highlights: A wave crest distribution based on the modified Box-Cox transformation and Rayleigh distribution is proposed. A detail comparison between the distribution and distributions proposed by Tayfun and Forristall is given. The MBR model matches the observations better for larger crests.