Scattering of Electromagnetic Waves from a Dense Medium Consisting of Correlated Mie Scatterers with Size Distributions and Applications to Dry Snow

Abstract

The scattering of a plane electromagnetic wave obliquely incident on a layer of dense medium consisting of dielectric spherical particles of finite sizes and with size distributions is studied. The spherical particles are of sizes comparable to wavelength so that Mie scattering is used to describe the single particle scattering characteristics. The coherent wave is studied with quasicrystalline approximation using the cross pair distribution functions of multiple sizes governed by Percus-Yevick approximation. The incoherent scattered wave is calculated with the distorted Born approximation with the result expressed in terms of a product of the T-matrices of particles of different sizes and permittivities and the Fourier transform of the cross pair distribution functions. The coherent wave effective propagation constants, the attenuation rates and the backscattering coefficients are illustrated numerically, with examples chosen to illustrate microwave and millimeter wave scattering from snow cover in the frequency range of 5 GHz to 95 GHz, and mean grain radius between 0.03 cm to 0.09 cm. Salient features of the numerical results for scattering from snow with size distribution are: 1. Correlated dense medium scattering is less than independent scattering at low frequency, a fact that is consistent with controlled laboratory experiment. 2. Scattering from dense medium of a Rayleigh size distribution with an average radius can be much larger than the case of monodisperse particles of the sizes identical to that average radius. 3. The scattering attenuation rate increases rapidly with frequency at low frequency regime and begins to level off at high frequency regime. 4. The coherent wave scattering attenuation rate is large in snow at frequencies above 15 GHz indicating large optical thickness and the importance of multiple scattering. Comparisons with extinction measurements of dry snow at 18 GHz, 35 GHz, 60 GHz, and 90 GHz are made.