Optical characterization of multi-scale morphologically complex heterogeneous media – Application to snow with soot impurities

A multi-scale methodology for the radiative transfer analysis of heterogeneous media composed of morphologically-complex components on two distinct scales is presented. The methodology incorporates the exact morphology at the various scales and utilizes volume-averaging approaches with the corresponding effective properties to couple the scales. At the continuum level, the volume-averaged coupled radiative transfer equations are solved utilizing i) effective radiative transport properties obtained by direct Monte Carlo simulations at the pore level, and ii) averaged bulk material properties obtained at particle level by Lorenz-Mie theory or discrete dipole approximation calculations. This model is applied to a soot-contaminated snow layer, and is experimentally validated with reflectance measurements of such layers. A quantitative and decoupled understanding of the morphological effect on the radiative transport is achieved, and a significant influence of the dual-scale morphology on the macroscopic optical behavior is observed. Our results show that with a small amount of soot particles, of the order of 1ppb in volume fraction, the reduction in reflectance of a snow layer with large ice grains can reach up to 77% (at a wavelength of 0.3 μm). Soot impurities modeled as compact agglomerates yield 2-3% lower reduction of the reflectance in a thick show layer compared to snow with soot impurities modeled as chain-like agglomerates. Soot impurities modeled as equivalent spherical particles underestimate the reflectance reduction by 2-8%. This study implies that the morphology of the heterogeneities in a media significantly affects the macroscopic optical behavior and, specifically for the soot-contaminated snow, indicates the non-negligible role of soot on the absorption behavior of snow layers. It can be equally used in technical applications for the assessment and optimization of optical performance in multi-scale media.