Effect of ice crystal shape and effective size on snow bidirectional reflectance

We tested the applicability of three rigorous radiative transfer computational approaches, namely, the discrete ordinates radiative transfer (DISORT) method, the adding-doubling approach, and an efficient computational technique based on Ambartsumian's nonlinear integral equation for computing the bidirectional reflectance of a semi-infinite layer. It was found that each of these three models, in a combination with the truncation of the forward peak of the bulk scattering phase functions of ice particles, can be used to simulate the bidirectional reflectance of a semi-infinite snow layer with appropriate accuracy. Furthermore, we investigate the sensitivity of the bidirectional reflectance of a homogeneous and optically infinite snow layer to ice crystal habit and effective particle size. It is shown that the bidirectional reflectance is not sensitive to the particle effective size in the visible spectrum. The sensitivity of the bidirectional reflectance in the near-infrared spectrum to the particle effective size increases with the increase of the incident wavelength. The sensitivity of the bidirectional reflectance to the effective particle size and shape is attributed fundamentally to the sensitivity of the single-scattering properties to particle size and shape. For a specific ice crystal habit, the truncated phase function used in the radiative transfer computations is not sensitive to particle effective size. Thus, the single-scattering albedo is primarily responsible for the sensitivity of the bidirectional reflectance to particle size, particularly, at a near-infrared wavelength.