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A three-dimensional (3D) radiative transfer model has been developed to simulate 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, employing Cartesian coordinates. The extinction coefficient, single-scattering albedo, and asymmetry factor are functions of spatial position and wavelength and are parameterized in terms of the ice water content and mean effective ice crystal size. The correlated k-distribution method is employed for incorporation of gaseous absorption in multiple-scattering atmospheres. Delta-function adjustment is used to account for the strong forward-diffraction 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 monochromatic 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 approximation under the homogeneous condition when the cloud horizontal dimension is much larger than the cloud thickness. As the horizontal dimension decreases, clouds produce less infrared warming at the bottom as well as less cooling at the top, while more solar heating is generated within the cloud. For inhomogeneous cases, upwelling and downwelling fluxes display patterns corresponding to the extinction coefficient field. Cloud inhomogeneity also plays an important role in determining both solar and IR heating rate distributions. The radiation parameterization is applied to potential cloud configurations generated from GCMs to investigate broken clouds and cloud-overlapping effects on the domain-averaged heating rates. Clouds with maximum overlap tend to produce less heating than those with random overlap. For the prescribed cloud configurations designed in this paper, broken clouds show more solar heating as well as more IR cooling as compared with a continuous cloud field.

Radiation Parameterization for Three-Dimensional Inhomogeneous Cirrus Clouds: Application to Climate Models