The spectrum of gravity-capillary waves, the probability density function of ocean surface slopes and their effects on radar backscatter

The microwave radar backscatter at the ocean surface is closely related to the spectrum of gravity-capillary waves and the probability density function (PDF) of ocean surface slopes.; A form of the gravity-capillary wave spectrum is proposed, based on a balance of the wind input, the spectral flux divergence, the viscous dissipation, and the modulation from the wave-drift interaction. A kinematic wave breaking criterion is applied in the calculation of the short-wave dissipation. It is found that this short-wave dissipation, due to wave-drift interactions, has the effect of suppressing the spectrum at higher winds. It is also found that both the fluctuation of average wind stress and the dissipation due to molecular viscosity and eddy viscosity have an important influence on the spectrum. The molecular viscosity plays a significant role at lower winds; the eddy-viscous dissipation dominates at higher wavenumbers. The threshold wind friction velocity is determined by a balance between the wind input with fluctuation and the molecular-viscous dissipation.; Based on Longuet-Higgins's theory, a new PDF of ocean surface slopes is derived. It is found that the peakness of slopes is generated by the coupling between the different wave components with their neighboring frequencies, and the skewness of slopes is generated by the coupling between the background waves and the short waves riding on them. The peakness coefficient n is related to the spectral width of the gravity waves, and the ratio between the gravity wave slope variance and the detectable short wave slope variance. When {dollar}nrightarrowinfty,{dollar} the proposed PDF is very close to the Gaussian distribution. It fits the Gram Charlier distribution, given by Cox and Munk, very well in the range of small slopes, when n equals 10.; Radar backscatter cross sections (RBCS), calculated from Bragg resonance and specular reflection theory using the proposed spectrum and PDF in the range of large slopes, are in keeping with the empirically based ERS-1 C-band scatterometer models.