Accuracy assessment of snow surface direct beam spectral albedo derived from reciprocity approach through radiative transfer simulation

We recognized that snow surface direct beam spectral albedo over a wide range of solar zenith angles can be derived by reciprocity from surface directional spectral reflectance under overcast conditions if the ground-level sky diffuse light is perfectly isotropic. Whether the method can produce accurate results under typical overcast conditions is the focus of this study. Theoretical analysis indicates that the error in estimation of direct beam spectral albedo by reciprocity should be proportional to the covariance of the zenith-dependent and azimuthally averaged sky diffuse radiation and surface bi-directional reflectance. Consequently, the error would be small when the sky diffuse light varies randomly. For general overcast conditions, therefore, we focused on situations in which sky diffuse light would exhibit a non-random variation. Therefore, we used a multi-layer zenith- and azimuth-dependent radiative transfer model to simulate both direct beam spectral albedo under clear skies and surface directional spectral reflectance under various overcast conditions. We assessed the feasibility of the reciprocity method in practical use through comparing the two sets of simulation results. The comparison indicates that the derived direct beam albedo in the visible wavelength region, the direct beam spectral albedo derived under typical stratus cloud optical thicknesses (τ10-60) are accurate to within ±0.01. for all cases except for extremely large solar zenith angles (>88°). At near infrared to shortwave infrared wavelengths, results are accurate to within 0.01 for all zenith angles smaller than 74° at 862 nm and for all solar zenith angles smaller than 63 ° at 2250 nm. Thus, the reciprocity approach can provide accurate direct beam spectral albedo complemental to those from the traditional method.