Electromagnetic scattering calculated from pair distribution functions retrieved from planar snow sections

Electromagnetic wave scattering in dense media, such as snow, depends on the three-dimensional (3D) pair distribution function of particle positions. In snow, two-dimensional (2D) stereological data can be obtained by analyzing planar sections. In this paper the authors calculate the volume 3D pair distribution functions from the 2D stereological data by solving Hanisch's integral equation. They first use Monte Carlo simulations for multisize particles to verify the procedure. 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. To derive multisize pair functions, a least squares fit is used to recover pair functions for particles with sufficient number density and the hole correction approximation is assumed for the larger particles. A family of 3D pair distribution functions are derived. These are then substituted into dense media scattering theory to calculate scattering. It is found that the computed scattering rates are comparable to those calculated under the Percus-Yevick approximation of pair distribution functions of multiple sizes.