Theoretical Calculations of Sea Surface Elevation Excess Kurtosis

A. V. Garmashov, A. S. Zapevalov*

Marine Hydrophysical Institute of RAS, Sevastopol, Russia

* e-mail: sevzepter@mail.ru

Abstract

The excess kurtosis of sea surface elevation is a predictor of rogue waves. This paper verifies the dependencies of excess kurtosis on wave steepness ε and inverse wave age ζ, obtained for the JONSWAP wave spectrum. For verification, the paper uses data from in situ wave measurements conducted from a stationary oceanographic platform located in the coastal zone of the Black Sea. It is shown that in a real sea wave field, the excess kurtosis changes within significantly wider limits than those described by both model dependencies. The correlation coefficient between λ4E and ε is 0.06, and between λ4E and ζ is 0.05. The model dependence of λ4E on steepness ε is close to the linear regression constructed for wind waves, i. e., it allows describing only its average changes. The model dependence of excess kurtosis on inverse wave age overestimates its average values; the overestimation is approximately 0.1 and depends on ζ. Thus, the dependencies of the excess kurtosis of sea surface elevation on wave steepness and inverse wave age, constructed on the basis of the JONSWAP spectrum, do not allow describing the entire range of excess kurtosis changes in a real wave field. Rogue waves are observed in the sea when λ4E exceeds the threshold level of 0.6–0.7, while the maximum model values of excess kurtosis at the limiting Stokes wave steepness do not exceed the level of 0.3.

Keywords

wind wave modelling, excess kurtosis, surface wave spectrum, wave steepness, inverse wave age, Black Sea, JONSWAP spectrum, rogue waves

Acknowledgments

The work was carried out under state assignment FNNN-2024-0001 “Fundamental research of the processes determining the flows of matter and energy in the marine environment and at its borders, the state and evolution of the physical and biogeochemical structure of marine systems in modern conditions” and FNNN-2024-0014 “Fundamental studies of interaction processes in the sea–air system that form the physical state variability of the marine environment at various spatial and temporal scales”.

For citation

Garmashov, A.V. and Zapevalov, A.S., 2025. Theoretical Calculations of Sea Surface Elevation Excess Kurtosis. Ecological Safety of Coastal and Shelf Zones of Sea, (4), pp. 64–75.

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