Two-step method for calculating normal reflectance of snow under oblique solar illumination

Abstract

The suggested method is developed for weakly absorbing and highly scattering media such as snow in the visible and shortwave infrared ranges. The multiple scattering of solar radiation is favorable for the transport approximation to determine the source function of the radiative transfer equation (RTE). This source function does not depend on angular coordinates, and the resulting RTE can be easily integrated along an arbitrary direction at the second step of the problem solution. The spectral calculations of the normal reflectance of snow cover of different thicknesses under oblique solar illumination are compared with a numerical reference solution. It is shown that the approximate two-step method is sufficiently accurate for use in practical applications. Computational analysis indicates that the reflectance value depends only on the optical properties of the snow surface layer, the thickness of which decreases strongly with increasing radiation wavelength. It is proposed that the equivalent radius of snow grains or another parameter of the optical model of snow be determined from measurements of albedo maxima in the near-infrared.