The albedo of snow for partially cloudy skies

The albedo of snow for different cloudiness conditions is an important parameter in the Earth's radiation budget analysis and in the study of snowpack's thermal conditions. In this study an efficient approximate method is derived to calculate the incident spectral solar flux and snow-cover albedo in terms of different atmospheric, cloud, and snow parameters. The global flux under partially cloudy skies is expressed in terms of the clear sky flux and a coefficient which models the effect of scattering and absorption by cloud patches and multiple reflections between the cloud base and snowcover. The direct and the diffuse components of the clear sky flux are obtained using the spectral flux outside the atmosphere and the spectral transmission coefficients for absorption and scattering by molecules and aerosols.The spectral snow reflectance model considers both specular surface reflection and volumetric multiple scattering. The surface reflection is calculated by using a crystal-shape-dependent bidirectional reflectance distribution function; the volumetric multiple scattering is calculated by using a crystal-size-dependent approximate solution in the radiative transfer equation. The input parameters to the model are atmospheric precipitable water, ozone content, turbidity, cloud optical thickness, the size and shape of ice crystals of snow and surface pressure. The model yields spectral and integrated solar flux and snow reflectance as a function of solar elevation and fractional cloudcover.The model is illustrated using representative parameters for the Antarctic coastal regions. The albedo for a clear sky depends inversely on the solar elevation. At high elevations the albedo depends primarily upon the grain size; at low elevation the albedo depends on grain size and shape. The gradient of the albedo-elevation curve increases as the grains become larger and faceted. The albedo for a densely overcast sky is a few percent higher than the clear-sky albedo at high elevations. A simple relationship between grain size and the overcast albedo is obtained. For a set of grain size and shape, the albedo as a function of solar elevation and fractional cloud cover is tabulated.