Parameterization of a Two-Component Gaussian Mixture for Description of the Sea Surface

A new approach is proposed for calculating the parameters of a two-component Gaussian mixture for modeling the distribution of sea surface elevations. Unknown distribution parameters are calculated from known statistical moments of a random variable. A two-component Gaussian mixture has five parameters and for their calculation it is necessary to know the statistical moments up to and including the fifth order. In oceanological research, only the first four statistical moments are determined, respectively, only four equations can be used. One of the distribution parameters remains free. This leads to some uncertainty in the constructed distributions. A new approach is proposed. Based on wave measurements carried out in the field, it is shown that there is a linear relationship between the third \(\mu_3\) and fifth \(\mu_5\) statistical moments of sea surface elevation. The linear regression equation between these parameters is obtained. The correlation coefficient between \(\mu_3\) and \(\mu_5\) is 0.92. This allows you to use the equation for the fifth statistical moment, setting it based on information about \(\mu_3\) . With this calculation procedure, the uncertainty of the parameters of the distribution of elevations of the sea surface is excluded.