Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis

The validity of the lowest order small slope approximation (SSA(1)) and the extended Kirchhoff approach (EKA) (Elfouhaily et al., 1999) has been studied by comparing the Doppler spectra of the backscattered signals predicted by these models to their counterparts from exact integral equation-based numerical simulations. The study is conducted at L and S bands (electromagnetic wavelengths 23 and 10 cm); the rough ocean-like surfaces correspond to the wind speed of 5 m/s and were generated using both linear and nonlinear (Creamer) models. The incidence angle varies from normal to low grazing. Expressions for the two analytical models possess many similarities but contain different incidence/scattering angle-dependent factors. The analysis of the bistatic scattering cross sections predicted by the two models reveals that SSA(1) follows the exact numerical results more closely than the EKA. Moreover, at horizontal polarization the extended Kirchhoff bistatic cross section displays certain anomalies (unlimited growth at grazing scattering angles) that are indicative of the problems with this model. However, in the backscattering direction, the expressions for the two models are identical. Doppler analysis of the backscattered signals shows that in general, the analytical models provide better agreement with the numerical results for smaller incident angles. In addition, the agreement between the models and the exact numerical simulations is always better in the case of vertical polarization for which the analytical models give a satisfactory prediction of the Doppler spectrum for incident angles as large as 85° from the normal for both linear and nonlinear surfaces. For horizontal polarization, the models give increasingly poor predictions of the shape, magnitude, and location of the Doppler spectrum for incident angles in the range from 60° to low grazing. Doppler analysis proves to be a much more precise and sensitive tool in assessing the scattering model´s validity than the usual comparison of cross sections