Evaluation of Skewness and Kurtosis of Wind Waves Parameterized by JONSWAP Spectra

The authors consider the deviations of wave height statistics from Gaussianity, manifested in higher statistical moments of random wind-wave fields, namely, in the nonzero values of the skewness and the kurtosis. These deviations are examined theoretically under the standard set of assumptions used in the established statistical theory of water waves, in particular in the derivation of the Hasselmann kinetic equation. P. Janssen proposed integral representations of the skewness and the kurtosis in terms of multidimensional integrals of wave spectra. However, the use of these representations for broadband wind-wave fields proved to be challenging; it requires substantial computational resources, which is unsuitable for applications. Using specially designed parallel algorithms to evaluate the integrals, the authors provide a comprehensive picture of the behavior of the kurtosis and the skewness of wind waves in the multidimensional parameter space of the most commonly used Joint North Sea Wave Project (JONSWAP) parameterizations of wind-wave spectra. Except for very narrow angular distributions where the overall picture is qualitatively different, the behavior of the higher moments proved to be not sensitive to the particular form of the directional spectrum. On this basis for the broad angular spectra typical of the ocean, the study puts forward simple parameterizations of the skewness and the kurtosis in terms of the JONSWAP peakedness parameter gamma and in terms of the inverse wave age. These parameterizations can be used in operational wave forecasting and other applications.