Two-stream approximations revisited:: A new improvement and tests with GCM data

Two-stream approximations (TSAs) are employed for multiple-scattering calculations in most solar radiation schemes used in atmospheric general-circulation models (GCMs). Two issues related to TSAs are addressed. First, a simple extension of the two-stream formalism is presented that allows different parametrizations for different factors, such as water clouds, ice clouds and aerosols. A 'tuned two-stream approximation' that uses this extension is then developed. Second, the accuracy of the tuned TSA and selected other TSAs is quantified using a global GCM-generated dataset (nearly 25000 atmospheric columns with clouds, aerosols and absorbing gases). In the tests with the GCM dataset, the Practical Improved Flux Method (PIFM) provided slightly better results than the delta-Eddington approximation. Two recent modifications of delta-Eddington yielded no, or only slight, improvement. For PIFM, the root-mean-square (r.m.s.) errors in top-of-the-atmosphere (TOA) and surface net short-wave fluxes and in total column absorption were 2.22, 3.09 and 2.98 W m(-2), as compared with delta-16-stream discrete-ordinate method results. For the tuned TSA, which was developed using the present dataset, the TOA and surface r.m.s. errors were 33% and 48% smaller than for PIFM, with substantially larger improvements at low solar elevations. The robustness of these results is tested in several sensitivity experiments in which the properties of the GCM dataset are modified systematically. While typical delta-TSAs performed, overall, fairly well, they all had a negative bias in atmospheric absorption and a positive bias in surface net short-wave flux of approximate to1 W m(-2) in the global mean (including, also, night grid points). Furthermore, the absorption errors depended substantially on solar elevation. The reasons for these problems are discussed. The tests with GCM data also confirmed that the delta-four-stream method is considerably more accurate than the TSAs, especially so for atmospheric absorption.