Bicontinuous DMRT model extracted from multi-size QCA with application to terrestrial snowpack

In terrestrial snow, the ice particles are irregular and densely packed together. At microwave frequencies (X-band to Ka-band), there are thousands of ice grains packed within one-wavelength cube. The interaction of the propagation wave and ice particles is coherent. The bicontinuous model is using computer-generated samples to construct the snow microstructures and numerically solve the Maxwell equations to include coherent wave and incoherent wave. There are two input parameters in the model, the scale parameter ζ and the size distribution parameter b. We related those two inputs with the ground measurement by comparing scattering coefficient of the bicontinuous model and multiple size spheres model. In the multi-size sphere model, the modified gamma distribution is used to describe size distribution of the different spheres. The scattering properties of the multi-size models are calculated by quasi-crystalline approximation (QCA). The incoherent wave is calculated with the distorted Born approximation in terms of the T-matrix and Fourier transform of the Percus-Yevick (PY) cross-pair distribution function. The scale parameter is related to the mean size of the ice particles. Therefore we can extract the size distribution parameter b of the bicontinuous model from the multi-size QCA by comparing the scattering coefficients.