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

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. 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, given the albedo, the Shkuratov (off by average factor 0.8) and Hapke (1.4) models provide closer, or similar best-fit grain radii than delta-Eddington (0.6), while outputting modelled spectral albedos that deviate more from the measurements. 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.