In this paper, we provide updates on our recent work on the theory of microwave remote sensing for applications in remote sensing of soil moisture and snow water equivalent (SWE). The three topics are the following. (i) For the effects of forests and vegetation, we developed the hybrid method of NMM3D full-wave simulations over the vegetation field and forest canopies. In the hybrid method, we combined the use of commercial off-the-shelf software and wave multiple scattering theory (W-MST). The results showed much larger transmission than classical radiative transfer theory. (ii) In signals of opportunity at L-band and P-band, which are radar bistatic scattering in the vicinity of the specular direction, we developed the Analytical Kirchhoff solution (AKS) and Numerical Kirchhoff approach (NKA) in the calculations of coherent waves and incoherent waves. We also took into account of the effects of topographical elevations and slopes which have strong influences. (iii) In rough surface radar backscattering, we used the volume integral equation approach for NMM3D full-wave simulations for soil surfaces with kh up to 15. The simulations were calculated for the X-band and Ku-band and the results showed saturation effects. The simulation results can be applied to microwave remote sensing of SWE at these two frequencies.

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