Radiation parameterization for three-dimensional inhomogeneous cirrus clouds: Application to climate models

A three-dimensional (3D) radiative transfer model has been developed to sim ulate the transfer of solar and thermal infrared radiation in inhomogeneous cirrus clouds. The model utilizes a diffusion approximation approach (four -term expansion in the intensity) for application to inhomogeneous media, e mploying Cartesian coordinates. The extinction coefficient, single-scatteri ng albedo, and asymmetry factor are functions of spatial position and wavel ength and are parameterized in terms of the ice water content and mean effe ctive ice crystal size. The correlated k-distribution method is employed fo r incorporation of gaseous absorption in multiple-scattering atmospheres. D elta-function adjustment is used to account for the strong forward-diffract ion nature in the phase function of ice particles to enhance computational accuracy. Comparisons of the model results with those from plane-parallel ( PP) and other 3D models show reasonable agreement for both broadband and mo nochromatic results. Three-dimensional flux and heating/cooling rate fields are presented for a number of cirrus cases in which the ice water content and ice crystal size are prescribed. The PP method is shown to be a good ap proximation under the homogeneous condition when the cloud horizontal dimen sion is much larger than the cloud thickness. As the horizontal dimension d ecreases, clouds produce less infrared warming at the bottom as well as les s cooling at the top, while more solar heating is generated within the clou d. For inhomogeneous cases, upwelling and downwelling fluxes display patter ns corresponding to the extinction coefficient field. Cloud inhomogeneity a lso plays an important role in determining both solar and IR heating rate d istributions. The radiation parameterization is applied to potential cloud configurations generated from GCMs to investigate broken clouds and cloud-o verlapping effects on the domain-averaged heating rates. Clouds with maximu m overlap tend to produce less heating than those with random overlap. For the prescribed cloud configurations designed in this paper, broken clouds s how more solar heating as well as more IR cooling as compared with a contin uous cloud field.