Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models

A physically based snow albedo model (PBSAM), which can be used in a general circulation model, is developed. PBSAM calculates broadband albedos and the solar heating profile in snowpack as functions of snow grain size and concentrations of snow impurities, black carbon and mineral dust, in snow with any layer structure and under any solar illumination condition. The model calculates the visible and near-infrared (NIR) albedos by dividing each broadband spectrum into several spectral subbands to simulate the change in spectral distribution of solar radiation in the broadband spectra at the snow surface and in the snowpack. PBSAM uses (1) the look-up table method for calculations of albedo and transmittance in spectral subbands for a homogeneous snow layer, (2) an "adding" method for calculating the effect of an inhomogeneous snow structure on albedo and transmittance, and (3) spectral weighting of radiative parameters to obtain the broadband values from the subbands. We confirmed that PBSAM can calculate the broadband albedos of single-and two-layer snow models with good accuracy by comparing them with those calculated by a spectrally detailed radiative transfer model (RTM). In addition, we used radiation budget measurements and snow pit data obtained during the two winters from 2007 to 2009 at Sapporo, Hokkaido, Japan, for simulation of the broadband albedos by PBSAM and compared the results with the in situ measurements. A five-layer snow model with one visible subband and three NIR subbands were necessary for accurate simulation. Comparison of solar heating profiles calculated by PBSAM with those calculated by the spectrally detailed RTM showed that PBSAM calculated accurate solar heating profiles when at least three subbands were used in both the visible and NIR bands.