Evaluation of radiative parameterizations using an explicit cloud microphysical model

Based on the simulations with a 3-D large-eddy simulation model of marine cloud-topped boundary layer that includes explicit cloud physics formulation, we have evaluated the effect of spatial inhomogeneities in cloud macro- and microstructure on the performance of parameterizations of optical depth commonly used in large-scale models. We have shown that an accurate parameterization of the grid average optical depth alone is not sufficient for correct determination of cloud transmittance to solar radiation due to the non-linear dependence between these two variables.The problem can be solved by introducing the “equivalent” value of optical depth that differs from the ordinarily defined mean optical depth by a factor α_t, that depends on the degree of cloud inhomogeneity and ranges from about 2 in the cumulus case to about 1.3 in the stratiform case.The accuracy of cloud optical depth parameterizations commonly employed in largescale models has been evaluated using the data from the explicit microphysical model as a benchmark for comparison. It has been shown that in the cumulus cloud case the parameterized expressions can err by as much as 100%. The error is smaller for more uniform stratiform clouds, where the error for some parameterizations varied in the 10–40% range. The best results are given by parameterizations that account for vertical stratification of parameters on which they are based. However, the error given by a particular parameterization varies and is different at cloud and surface levels. The results show the limitations of the existing simplified parameterizations and illustrate the scope and complexity of the cloud radiation parameterization problem.