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A new approach for parameterization of the broadband solar and infrared radiative properties of ice clouds has been developed. This parameterization scheme integrates in a coherent manner the δ-four-stream approximation for radiative transfer, the correlated k-distribution method for nongray gaseous absorption, and the scattering and absorption properties of hexagonal ice crystals. A mean effective size is used, representing an area-weighted mean crystal width, to account for the ice crystal size distribution with respect to radiative calculation. Based on physical principles, the basic single-scattering properties of ice crystals, including the extinction coefficient divided by ice water content single-scattering albedo, and expansion coefficients of the phase function, can be parameterized using third-degree polynomials in terms of the mean effective size. In the development of this parameterization the results computed from a light scattering program that includes a Geometric ray-tracing program for size parameters larger than 30 and the exact spheroid solution for size parameters less than 30 are used. The computations are carried out for 11 observed ice crystal size distributions and cover the entire solar and thermal infrared spectra. Parameterization of the single-scattering properties is shown to provide an accuracy within about 1%. Comparisons have been carried out between results computed from the model and those obtained during the 1986 cirrus FIRE IFO. It is shown that the model results can be used to reasonably interpret the observed IR emissivities and solar albedo involving cirrus clouds. The newly developed scheme has been employed to investigate the radiative effects of ice crystal size distributions. For a given ice water path, cirrus clouds with smaller mean effective sizes reflect more solar radiation, trap more infrared radiation, and product stronger cloud-top cooling and cloud-base beating. The latter effect would enhance the in-cloud heating rate gradients. Further, the effects of ice crystal size distribution in the context of IR greenhouse versus solar albedo effects involving cirrus clouds are presented with the aid of the upward flux at the top of the atmosphere. In most cirrus cases, the IR greenhouse effect outweigh the solar albedo effect. One exception occurs when a significant number of small ice crystals are present. The present scheme for radiative transfer in the atmosphere involving cirrus clouds is well suited for incorporation in numerical models to study the climatic effects of cirrus clouds, as well as to investigate interactions and feedbacks between cloud microphysics and radiation.
Fu et al. (Thu,) studied this question.