Quantitative Evaluation of the delta-Eddington, Hapke, and Shkuratov Models for Predicting the Albedo and Inferring the Grain Radius of Ice

Abstract

Determining the physical properties of ices across the solar system is essential for understanding the surface dynamics, volatile transport, and climate evolution on ice-covered planetary bodies. Here, we use well-constrained measurements of snow that has metamorphosed into coarse-grained firn and bubbly glacier ice in East Antarctica to test three commonly-used radiative transfer models: delta-Eddington, Hapke, and Shkuratov. Using the measured optical properties, we find that the delta-Eddington model generally shows the least deviation from the measured albedo, followed by the Shkuratov and Hapke models, respectively. But when the models are used to infer the grain radius using the measured albedo, the Shkuratov model provides closer best-fit grain radii (off by average factor 0.9) than delta-Eddington (0.6), and Hapke (1.8). Despite this, the spectral albedos estimated by the Shkuratov and Hapke models using their respective best-fit grain radii deviate more from the measurements than delta-Eddington. This result is caused by the Hapke and Shkuratov models not accounting for: (1) the increased absorption within dense ice, and (2) specular reflection at the surface of firn and ice. Additionally, all three models do not account for the nonsphericity of bubbles within ice. The combination of these factors leads to model errors generally increasing with increasing grain radius. Based on our quantitative comparison, we recommend using the delta-Eddington model for predicting the albedo and inferring the grain radius of ices across the solar system because it generally produces the least error while using realistic physical parameters.