Ramaswamy, V., and S. M. Freidenreich, 1991: Solar radiative line-by-line determination of water vapor absorption and water cloud extinction in inhomogeneous atmospheres. Journal of Geophysical Research, 96(D5), 9133-9157.

Abstract: The complete available spectral features (line-by-line, or LBL) of the water vapor molecule in the solar spectrum and a precise treatment of particulate scattering are employed to obtain and analyze the solar radiative fluxes and heating rates in plane-parallel, vertically inhomogeneous model atmospheres containing vapor only, water cloud only, and vapor-plus-cloud present simultaneously. These studies are part of the Intercomparison of Radiation Codes in Climate Models (ICRCCM) project and constitute useful benchmark computations against which results from simpler radiation algorithms can be compared. The "exact" solution of the radiative transfer equation for cloudy atmospheres with the cloud in a single model layer consumes an exorbitant amount of computational resources (~ 100 hours on a Cyber 205). Two other techniques that are considerably more economical are also investigated. These techniques, too, are based on the LBL spectral features of the H₂O molecule but consist of an approximation in either the vapor optical depth or in the multiple-scattering process. The technique involving the "binning" of the vapor optical depths yields extremely accurate fluxes and heating rates for both the vapor and vapor-plus-cloud cases; in particular, it is a practical alternative for obtaining benchmark solutions to the solar radiative transfer in overcast atmospheres (3.8 hours). In contrast, the multiple-scattering approximation technique does not yield precise results; however, considering its computational efficiency (0.5 hours), it offers a rapid means to obtain a first-order approximation of the spectrally integrated quantities. The analyses of the alternate techniques suggest their potential use for high spectral resolution sensitivity studies of the radiative effects due to various types of clouds.