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Springer Proceedings in Earth and Environmental Sciences

ISSN:2524342

2023

10.1007/978-3-031-25962-3_8

The statistics of waves in situations that are relatively rarely observed at sea are investigated. The probability and conditions of the occurrence of situations in which the ratio of the maximum crest and maximum trough during the measurement period (ratio R) is less than one are analyzed. The condition $$R < 1$$ means that the trough is larger than the crest. The data of direct wave measurements obtained in the coastal zone of the Black Sea (depth ~ 30 m) were used. It is shown that the average probability of occurrence of values for an ensemble of situations is 13%. It is shown that as the wave steepness $$\varepsilon$$ increases, the conditional probability $$P:{\varepsilon } = P\left({R < 1\left| \varepsilon \right.} \right)$$ also increases. The dependence of the conditional probability $$P:{\zeta } = P\left({R < 1\left| \zeta \right.} \right)$$ on the inverse wave age $$\zeta$$ is observed only for developing waves at $$\zeta > 1.5$$, at later stages of the wave field development it is absent. There is also a dependence of the probability of occurrence of values on the cumulants of sea surface elevations of the third $$\lambda:{3}$$ and fourth $$\lambda:{4}$$ orders (skewness and excess kurtosis). When $$\lambda:{3}$$ changing from − 0.1 to 0.3, the conditional probability $$P:{\lambda 3} = P\left({R < 1\left| {\lambda_{3} } \right.} \right)$$ increases by about five times, when $$\lambda:{4}$$ changing from − 0.4 to 0.4, the conditional probability $$P:{\lambda 4} = P\left({R < 1\left| {\lambda_{4} } \right.} \right)$$ increases by about one and a half times. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Altimetry, Brown model, Distribution of surface elevations, Remote sensing, Sea surface

2023-05-05 13:58:23