Electromagnetic scattering based on pair distribution functions retrieved from planar snow sections

Electromagnetic wave propagation and scattering in dense media depends on the 3D pair distribution function of particle positions. In the past researchers have assumed a form, such as Percus-Yevick (PY), for the pair function in snow. Recent efforts in the snow community have concentrated on analyzing planar snow sections to obtain 2D stereological data. In this paper the authors calculate the volume 3D pair distribution function from the 2D stereological data by solving Hanisch´s integral equation (1983). They first use Monte Carlo simulations for single and multi-size particles to verify the inversion procedure with good results. Next they apply the procedure to available planar snow sections. A log-normal distribution of particle sizes is assumed for the ice grains in snow with the distribution parameters derived from stereological measurements. The 3D pair function can be expressed as a weighted sum of size specific pair functions which are necessary for scattering calculations. They choose a small number of representative particle sizes and use a least squares non-linear fit to decompose the 3D pair function into pair functions for those particles. The fit procedure is constrained by a set of physically meaningful rules and can only be applied to those sizes with sufficient number densities. Analysis of scattering from log-normally distributed spheres indicates the larger particles contribute strongly to the independent scattering but have relatively small interaction terms. Since the large, sparsely distributed particles are not retrievable from the fit and have relatively small interaction terms the authors include their scattering contribution by using the hole correction approximation. The family of recovered pair distribution functions gives scattering rates comparable to those calculated under the PY approximation