An Efficient and Accurate Algorithm for Computing Grid-Averaged Solar Fluxes for Horizontally Inhomogeneous Clouds

Abstract

Abstract A computationally efficient method is presented to account for the horizontal cloud inhomogeneity by using a radiatively equivalent plane-parallel homogeneous (PPH) cloud. The algorithm can accurately match the calculations of the reference (rPPH) independent column approximation (ICA) results but uses only the same computational time required for a single plane-parallel computation. The effective optical depth of this synthetic sPPH cloud is derived by exactly matching the direct transmission to that of the inhomogeneous ICA cloud. The effective scattering asymmetry factor is found from a precalculated albedo inverse lookup table that is allowed to vary over the range from −1.0 to 1.0. In the special cases of conservative scattering and total absorption, the synthetic method is exactly equivalent to the ICA, with only a small bias (about 0.2% in flux) relative to ICA resulting from imperfect interpolation in using the lookup tables. In principle, the ICA albedo can be approximated accurately regardless of cloud inhomogeneity. For a more complete comparison, the broadband shortwave albedo and transmission calculated from the synthetic sPPH cloud and averaged over all incident directions have RMS biases of 0.26% and 0.76%, respectively, for inhomogeneous clouds over a wide variation of particle size. The advantages of the synthetic PPH method are that 1) it is not required that all the cloud subcolumns have uniform microphysical characteristic, 2) it is applicable to any 1D radiative transfer scheme, and 3) it can handle arbitrary cloud optical depth distributions and an arbitrary number of cloud subcolumns with uniform computational efficiency.