A distinct feature of GNSS-R land reflectometry is that random rough surfaces are superimposed on many levels of elevations. The rms elevations are in tens of meters which are many times larger than the microwave wavelengths at GNSS frequencies. Such multiple elevations were not considered in the coherent model nor the incoherent model. In this paper, we studied the electromagnetic scattering of this new rough surface scattering problem using Kirchhoff integral as first-principle. A numerical Kirchhoff simulator is developed to calculate the electromagnetic scattering and the power ratio in the specular direction. The integration is carried out over a footprint of 10 km by 10 km with the specular point as the center. In integration the surface discretization is as small as 2cm by 2 cm so that a total of 2.5×1011 patches are used. Parallel computing is implemented requiring a moderate amount of computer resources. The results of the power ratio of the numerical Kirchhoff simulator differ from the results of both the coherent model and incoherent model. The results show that the phase of the first Fresnel zone is random, and the power contributed by the first Fresnel zone is a small fraction of that over the 10 km by 10 km. The power ratios of the numerical Kirchhoff simulations are much larger than that of the incoherent model and smaller than the coherent model for small RMS heights. The results show that the multiple elevations in land have large effects on GNSS-R specular reflections.
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