A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations

A systematic development of the delta-four-stream approximation for calculations of radiative fluxes in planetary atmosphere is presented. It is shown that an analytic solution for this approximation can be derived explicitly, with minimum computational effort for flux calculations. Relative accuracy checks for reflection, transmission, and absorption for numerous asymmetry factors, single-scattering albedos, optical depths, and solar zenith angles have been performed with respect to the 'exact' results computed from the adding method for radiative transfer. Overall, results from the delta-four-stream approximation yield relative accuracies within about 5 percent. This approximation is well suited to radiative transfer parameterizations involving flux and heating calculations in aerosol and cloudy atmospheres.