Radiative transfer models for light scattering from planetary surfaces

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Abstract
New, accurate numerical solutions of the radiative transfer equation are compared with the Hapke [1981, 1984, 1986] analytic approximation, which is widely used in planetary data analyses. The numerical solutions use the Ambartsumian invariance principle as do the well‐known Chandrasekhar [1960] H function solutions. The invariance principle has been reexpressed in a form which allows high order‐accurate numerical integrations without any required interpolations. The new numerical solutions reproduce the Chandrasekhar H function solutions for Legendre phase functions but also allow single‐scattering phase functions of arbitrary form. Accurate numerical solutions of the radiative transfer equation for Henyey‐Greenstein phase functions reveal that the errors in the Hapke model for estimating bidirectional reflectance values range from <2% rms for dark surfaces like the Moon to <7% rms for bright surfaces such as Europa. Further comparisons demonstrate that Hapke model fitting procedures estimate single particle scattering albedo values to within <3% for both dark and bright surfaces.