The small slope approximation (SSA) and the Kirchhoff approach (KA) are applied to the prediction of microwave sea surface backscatter for both Ku and C bands for various wind speeds and incident angles. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally averaged C- and Ku-band radar backscattering data. The KA can be obtained rigorously for a perfectly-conducting surface, whereas for a dielectric surface, either the KA of order one (KA1) or the stationary phase (SP) method can be used. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally C and Ku bands radar backscattering data for incidence angles of interest for remote sensing. Since the SSA and KA formulations are expressed in polar coordinates, the backscattering coefficient is expressed in terms of surface height autocorrelation and its derivatives of one- and second- orders computed from integrating the sea spectrum multiplied by Bessel functions of the first kind. This allows to have for KA and first-order SSA (SSA-1), a single numerical integration over the radial distance instead of four, when the cartesian coordinates is chosen. Moreover, the azimuthal harmonic magnitudes of the backscattering coefficient according to the wind direction can be performed separately. For an isotropic sea surface assumed to be perfectly conducting where the KA is valid, the deviation between SSA and KA models is smaller than the one computed from the SP model for HH polarization. For the VV polarization, the difference is greater, since the polarization term of SSA is given by the small perturbation method, whereas for the KA approach, it is equal to the Fresnel coefficient. For an anisotropic sea surface, the comparison of KA with SSA-1 leads to the same conclusion. The isotropic part and the second azimuthal harmonic of the backscattering coefficient are also compared with empirical backscattering models CMOD2-I3 and SASS-II valid in C and Ku bands, respectively.
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