A study of the slope probability density function of the ocean waves from radar observations

Radar observations of the sea surface at C-Band and small incidence angles are used to investigate some properties of the surface slope probability density function (pdf). The method is based on the analysis of the variation of the radar cross-section with incidence angle, assuming a backscattering process following the Geometrical Optics theory. First, we assess the limit of this model in our experimental configuration by using simulations of radar cross-sections with a more accurate backscattering model, namely the Physical Optics model. We show that roughness properties with scales larger than 12 cm can be analyzed in our configuration (C-Band, incidence 7 to 16 degrees). The radar data are then analyzed in terms of filtered mean square slope under the assumption of a Gaussian slope pdf. Dependence of the radar-derived mean square slopes (mss) with wind speed is analyzed, thanks to wind estimates obtained by using coincident observations of the same radar at larger incidence (around 32 degrees). Furthermore an analysis of the anisotropy of the mean square slope is proposed. The results are discussed in comparison with those of Cox and Munk (1954a, 1954b), and with the mean square slopes derived from two surface models (Elfouhaily et al., 1997 and Kudryavtsev et al., 2003). We find that the radar-derived values are in good agreement with Cox and Munk results, taking into account the filtering effect on radar-derived values. We also show that the surface model of Elfouhaily et al. yields good agreement for the omni directional mss, but a too large anisotropy of the mss. The model of Kudryavtsev provides a reasonable anisotropy of the mss, but overestimates the mss values in all directions. Finally, we propose an analysis of the radar data under a non-Gaussian assumption for the slope pdf, by applying the compound model suggested by Chapron et al. (2000) to our observations. To our knowledge, it is the first time that peakedness values are explicitly derived from radar observations, and documented as a function of azimuth and wind speed. We show that the peakedness (or kurtosis) of the slope pdf is not zero but weak (peakedness factor reaching about 0.20), and slightly increases with wind speed.