Transmission of Solar Radiation by Clouds over Snow and Ice Surfaces: A Parameterization in Terms of Optical Depth, Solar Zenith Angle, and Surface Albedo

Abstract

A multilevel spectral radiative transfer model is used to develop simple but accurate parameterizations for cloud transmittance as a function of cloud optical depth, solar zenith angle, and surface albedo, for use over snow, ice, and water surfaces. The same functional form is used for broadband and spectral transmittances, but with different coefficients for each spectral interval. When the parameterization is applied to measurements of ?raw? cloud transmittance (the ratio of downward irradiance under cloud to downward irradiance measured under clear sky at the same zenith angle), an ?effective? optical depth τ is inferred for the cloud field, which may be inhomogeneous and even patchy. This effective optical depth is only a convenient intermediate quantity, not an end in itself. It can then be used to compute what the transmittance of this same cloud field would be under different conditions of solar illumination and surface albedo, to obtain diurnal and seasonal cycles of cloud radiative forcing. The parameterization faithfully mimics the radiative transfer model, with rms errors of 1%?2%. Lack of knowledge of cloud droplet sizes causes little error in the inference of cloud radiative properties. The parameterization is applied to pyranometer measurements from a ship in the Antarctic sea ice zone; the largest source of error in inference of inherent cloud properties is uncertainty in surface albedo.