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 2 cm by 2 cm so that a total of 2.5 × 10 11 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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We consider the Global Navigation Satellite System Reflectometry (GNSS-R) for land applications. A distinct feature of land is that the topography has multiple elevations. The rms of elevations is in meters causing random phases between different elevations, which affect the coherent wave that has definite phase and the Fresnel zone effects as shown previously by a Kirchhoff numerical simulator (KA simulator). In this paper, we develop a physical patch model that is computationally efficient. The entire area within the footprint is divided into patches. Each patch is small enough to satisfy the plane wave incidence and is large enough to ignore mutual wave interactions between patches. The bistatic scattering cross section of each patch for the coherent and incoherent field is computed. The bistatic cross section of plane wave incidence is obtained from lookup tables (LUTs) of the numerical 3D solution of Maxwell equations (NMM3D). The SWC represents the summation of weighted coherent fields over patches. The SWICI represents the summation of weighted incoherent intensities over patches. The formula of the received power is the sum of powers from the SWC and SWICI (the SWC/SWICI formula). The weighting factor of each patch is based on the geometry, spherical waves, and the considerations of field amplitudes and phase variations. We also present an alternative formula, the "correlation" formula, using the summation of power from each physical area and correlations of SWCs from areas. The SWC/SWICI formula and the "correlation" formula are shown analytically to be the same. Results are compared with the KA simulator and two common models (the coherent model and the incoherent model). Results of the patch model are consistent with the KA simulator. For the simulation cases, the results fall between the coherent model and the incoherent model. The patch model is much more computationally efficient than the KA simulator and the results are more accurate. In examples of this paper, the patch model results are independent of patch size as long as the patch size smaller than 50 m and much larger than the wavelength of GNSS-R frequency.

The Ultra-Wideband Software defined microwave radiometer (UWBRAD) was developed to probe internal ice sheet temperatures using 0.5-2 GHz microwave radiometry. The airborne brightness temperature data of UWBRAD show a significant reduction due to reflections of surface layering of density fluctuations making difficult the retrieval of subsurface temperature in the kilometer range of depth. Such reflections can be measured by the ultra-wideband radar in the same frequency range suggesting a combined active and passive remote sensing of polar ice sheets. In this paper, we develop a coherent reflectivity model for both ice sheet thermal emission and backscattering. Maxwell equations are used to calculate the coherent reflections from the cap layers, and the WKB approximation is used to calculate the transmission for the slowly varying profile below the cap layers. Results are then shown to demonstrate the use of radar measurements to compensate reflection effects on brightness temperatures. It is shown that the reflections corrected brightness temperature is directly related to the physical temperature and absorption profile making possible the retrieval of subsurface temperature profile with multi-frequency measurements.