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

S. Y. Annenkov; V. I. Shrira

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

机译：用JONSWAP光谱参数化评估风波的偏度和峰度

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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 y and in terms of the inverse wave age. These parameterizations can be used in operational wave forecasting and other applications.

机译：作者认为，波高统计与高斯性的偏差表现在随机风波场的较高统计矩中，即偏度和峰度的非零值。理论上，在已建立的水波统计理论中使用的一组标准假设下，特别是在Hasselmann动力学方程的推导中，对这些偏差进行了理论检验。 P. Janssen根据波谱的多维积分提出了偏度和峰度的积分表示。但是，将这些表示用于宽带风波场被证明具有挑战性。它需要大量的计算资源，因此不适合应用程序。使用专门设计的并行算法评估积分，作者提供了最常见的联合北海波计划（JONSWAP）风参数化多维参数空间中峰度和风波偏斜行为的全面描述。波谱。除了整个图像在质量上都非常不同的非常窄的角度分布之外，较高力矩的行为对方向谱的特定形式不敏感。在此基础上，针对海洋典型的广角光谱，研究提出了根据JONSWAP峰值参数y和逆波年龄对偏斜度和峰度的简单参数化。这些参数化可用于运行波预测和其他应用程序。

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《Journal of Physical Oceanography》 |2014年第6期|1582-1594|共13页
作者
S. Y. Annenkov; V. I. Shrira;
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Department of Mathematics, Research Institute for the Environment, Physical Sciences and Applied Mathematics, Keele University, Keele ST5 5BG, United Kingdom;

Department of Mathematics, Research Institute for the Environment, Physical Sciences and Applied Mathematics,Keele University, Keele, United Kingdom;

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8. Generation of time histories with a specified auto spectral density, skewness, and kurtosis [R] . Smallwood, D. O. 1996

机译：生成具有指定自动光谱密度，偏度和峰度的时间历史

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

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