Ecological Safety of Coastal and Shelf Zones of Sea Ecological Safety of Coastal and Shelf Zones of Sea 2413-5577 20240102 Research Article Distribution of Sea Surface Elevations in the Form of a Two-Component Gaussian Mixture Zapevalov A. S.
Russian Federation
sevzepter@mail.ru Knyazkov A. S.
Russian Federation
fizfak83@yandex.ru Marine Hydrophysical Institute of RAS Sevastopol Russian Federation 25 03 2024 2024 1 20 30 06 07 2023 27 12 2023 03 09 2023 Copyright © 2024, A. S. Zapevalov, A. S. Knyazkov 2024 A. S. Zapevalov, A. S. Knyazkov https://creativecommons.org/licenses/by-nc/4.0/ https://ecological-safety.ru/en/repository/issues/2024/01/02/

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 ε 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.

 Gaussian mixture sea waves surface elevation nonlinear waves statistical moment Black Sea 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".

About the authors:

Aleksandr S. Zapevalov, Chief Research Associate, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), Dr.Sci. (Phys.-Math.), Scopus Author ID: 7004433476, ResearcherID: V-7880-2017, ORCID: 0000-0001-9942-2796, sevzepter@mail.ru

Aleksandr S. Knyazkov, Leading Engineer, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), ORCID: 0000-0003-1119-1757, fizfak83@yandex.ru

Contribution of the authors:

Aleksandr S. Zapevalov – task statement, review of literature on the study topic, article preparation

Aleksandr S. Knyazkov – algorithm development and calculation performance, critical analysis of the calculations

The authors have read and approved the final manuscript.

Article text not included.

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