Distribution of Sea Surface Elevations in the Form of a Two-Component Gaussian Mixture

A. S. Zapevalov*, A. S. Knyazkov

Marine Hydrophysical Institute of RAS, Sevastopol, Russia

* e-mail: sevzepter@mail.ru

Abstract

The approximation of the probability density function of sea surface elevations by a two-component Gaussian mixture has been verified. For verification, the data of direct wave measurements obtained on a stationary oceanographic platform, installed in the Black Sea, were used. The approximation correctness criterion is the relative error  of deviation of the model of probability densities function from the experimental function calculated from the measurement data. The average error ⟨ε⟩ over the ensemble of situations is small if |ξ| < 3. The standard deviation δ is minimal if |ξ| ≈ 0 and is equal to 0.12, if |ξ| = 3 then δ ≈ 0.5. It is shown that the error ⟨ε⟩ has a systematic component, which depends on the deviations of the third and fourth statistical moments from the values corresponding to the Gaussian distribution. A semi-empirical relationship has been constructed to take this component into account. It is noted that the approximation accuracy can be increased by 2–3 times by eliminating the systematic component.

Keywords

Gaussian mixture, sea waves, surface elevation, nonlinear waves, statistical moment, Black Sea

Acknowledgments

The work was performed under state assignment of Marine Hydrophysical Institute of RAS on topic FNNN-2021-0004 “Fundamental studies of oceanological processes which determine the state and evolution of the marine environment influenced by natural and anthropogenic factors, based on observation and modeling methods”.

For citation

Zapevalov, A.S., and Knyazkov, A.S., 2024. Distribution of Sea Surface Elevations in the Form of a Two-Component Gaussian Mixture. Ecological Safety of Coastal and Shelf Zones of Sea, (1), pp. 20–30.

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