Snowpack Microstructure Characterization and Partial Coherent and Fully Coherent Forward Scattering Models in Microwave Remote Sensing

In this paper we describe partial coherent model and fully coherent snowpack scattering model based on numerical simulation of Maxwell's equation. In medium characterization, we derive the correlation functions from the pair distribution functions of sticky spheres and multiple-size spheres used in QCA. We show that both the Percus-Yevick pair functions and the bicontinuous model have tails in the correlation functions that are distinctly different from the traditional exponential correlation functions. The methodologies of using ground measurements of grain size distributions and correlation functions to obtain model parameters are addressed. The DMRT theory has been extended to model the backscattering enhancement. We developed the methodology of cyclical corrections beyond first order to all orders of multiple scattering. This enables the physical modeling of combined active and passive microwave remote sensing of snow over the same scene. The bicontinuous /DMRT is applied to compare with data acquired in the NoSREx campaign, and the model results are validated against coincidental active and passive measurements using the same set of physical parameters of snow in all frequency and polarization channels. The DMRT is a partially coherent approach that one accounts for the coherent wave interaction only within few wavelengths as represented by phase matrix. However, the phase information of field is lost in propagating the specific intensity via RT and this hinders the use of DMRT in coherent synthetic aperture radar (SAR) analysis, including InSAR, PolInSAR and Tomo-SAR. One can alternatively calculate the scattering matrix of the terrestrial snowpack above ground by solving the volume integral equations directly with half space Green's function. The scattering matrix of the snowpack is computed for each realization giving rise to the speckle statistics. The resulting bistatic scattering automatically includes the backscattering enhancement effects. Tomograms of the snow pack are constructed and compared using back-projection and frequency and angular correlation functions. The co-pol phase differences of the scattered wave are also computed by modeling the snowpack as densely packed spheroids with distinct orientation preferences within different layers of snow pack.