Abstract
Abstract Based on Longuet-Higgins’s theory of the probability distribution of wave amplitude and wave period and on some observations, a new probability density function (PDF) of ocean surface slopes is derived. It is where ζx and ζy are the slope components in upwind and crosswind directions, respectively; σ2u and σ2c are the corresponding mean-square slopes. The peakedness of slopes is generated by nonlinear wave–wave interactions in the range of gravity waves. The skewness of slopes is generated by nonlinear coupling between the short waves and the underlying long waves. The peakedness coefficient n of the detectable surface slopes is determined by both the spectral width of the gravity waves, and the ratio between the gravity wave mean-square slope and the detectable short wave mean-square slope. When n equals 10, the proposed PDF fits the Gram Charlier distribution, given by Cox and Munk, very well in the range of small slopes. When n → ∞, it is very close to the Gaussian distribution. Radar backscat...
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