Available theoretical expressions describing the statistical distribution of wave steepness do not compare favorably with empirical data. The observed histograms of wave steepness tend to fit the log-normal probability law. The practical utility of this result in engineering design requires that the mean and root-mean-square values of wave steepness be predicted accurately. Herein, theoretical approximations describing these two key statistics are derived, and the resulting log-normal distribution is compared with observational data, obtaining good agreement.
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