Quasi-Gaussian probability density function of sea wave slopes from near nadir Ku-band radar observations

Abstract

Although in most circumstances, sea wave slope probability density function (PDF) is expressed as Gaussian distribution, there is evidence that it follows quasi-Gaussian distribution, which can be represented by Gram-Charlier series to fourth order. All the statistical parameters of slope PDF have previously been derived by using optical methods in specular conditions, and values and relationships with surface parameters have been presented in the literature. However they may not be relevant at microwave wavelengths due to diffraction effects. Up to now, sea surface slope PDF consistent with ocean microwave remote sensing is not known yet. So it is important to establish the parameter models of quasi-Gaussian slope PDF compatible with radar application. In this paper, based on the backscattering coefficients from the Ku-band space-borne radar Precipitation Radar (PR) data, all the parameters of the quasi-Gaussian slope PDF are inverted using a so-called “GO4” (Boisot et al., 2015) model with a two-dimensional (2-D) non-linear least square fit on the backscattering coefficients. We also establish the empirical formulae relating the statistical parameters of the quasi-Gaussian sea slope PDF with wind speed, which may be used for ocean Ku-band radar application.The proposed empirical formulae are compared to the Cox and Munk (1954) - CM slope parameter model: the results confirm that the slope variance in upwind and crosswind directions as well as the skewness coefficients exhibit intermediate values between the CM slope parameters of clean surface and slick surface cases. The coefficients of peakedness are just in the range of the CM slope peakedness parameter values.The impacts of wave conditions (swell or wind sea) on slope PDF parameters are also studied. The results show that in most wind speed conditions, the presence of swell increases the skewness coefficients, while it decreases the peakedness coefficients.