Abstract
Computational results have been obtained for the spherical albedo, global transmission, and global absorption of plane-parallel layers composed of cloud droplets. These computations, obtained using the doubling method for the entire range of single scattering albedos (0 ≤ ω0 ≤ 1) and for optical depths between 0.1 and 100, are compared with corresponding results obtained using selected multiple scattering approximations. Both the relative and absolute accuracies of asymptotic theory for thick layers, three diffuse two-stream approximations, and two integrated two-stream approximations are presented as a function of optical thickness and single scattering albedo for a scattering phase function representative of cloud droplets at visible wavelengths. The spherical albedo and global absorption computed using asymptotic theory are found to be accurate to better than 5% for all values of the single scattering albedo, provided the optical thickness exceeds about 2. The diffuse two-stream approximations have relative accuracies that are much worse than 5% for the spherical albedo over most of the parameter space, yet are accurate to within 5% in the global absorption when the absorption is significant. The integrated delta-Eddington scheme appears to be the most suitable model over the entire range of variables, generally producing relative errors of less than 5% in both the spherical albedo and global absorption.
