A method to account for surface albedo heterogeneity in single-column radiative transfer calculations under overcast conditions

[1] A simple parameterization to derive the broadband effective albedo over highly reflecting surfaces under overcast conditions is presented. High spatial variability in the surface albedo affects the downwelling solar irradiance in neighboring regions via the multiple reflections of light between the surface and the cloud base. The effective albedo is defined as the albedo of a homogeneous surface that would result in the same downwelling irradiance as observed at the observation point in the presence of a heterogeneous surface. The proposed method parameterizes the effective albedo using the cloud base height and a surface albedo map as inputs. The parameterization is based on the spatial distribution of surface reflections contributing to the downwelling irradiance at the observation site, which is approximated with a gamma distribution. The parameterization was validated against reference values of effective albedo derived from three-dimensional backward Monte Carlo and one-dimensional DISORT radiative transfer calculations for four idealized surface albedo maps and various specifications of cloud properties. It gave values of effective albedo very close to the reference calculations, performing substantially better than any other approach tested, also when applied to the retrieval of cloud optical depth. The method can be implemented into one-dimensional radiative transfer models or used to interpret broadband irradiance measurements in Polar coastal regions, in the marginal sea ice zones, or in patchy terrain with forests and snow-covered fields.