Freidenreich, S. M., and V. Ramaswamy, 1993: Solar radiation absorption by CO₂, overlap with H₂O, and a parameterization for general circulation models. Journal of Geophysical Research, 98(D4), 7255-7264.

Abstract: Line-by-line (LBL) solar radiative solutions are obtained for CO₂-only, H₂O-only, and CO₂ + H₂O atmospheres, and the contributions by the major CO₂ and H₂O absorption bands to the heating rates in the stratosphere and troposphere are analyzed. The LBL results are also used to investigate the inaccuracies in the absorption by a CO₂ + H₂O atmosphere, arising due to a multiplication of the individual gas transmissions averaged over specific spectral widths (delta v). Errors in absorption generally increase with the value of delta v chosen. However, even when the interval chosen for averaging the individual gas transmissions is the entire solar spectrum, there is no serious degradation in the accuracy of the atmospheric absorbed flux (error < 3%) and the heating rates (errors < 10%). A broadband parameterization for CO₂ absorption, employed in several weather prediction and climate models, is found to substantially underestimate the LBL heating rates throughout the atmosphere, most notably in the stratosphere (errors > 40%). This parameterization is modified such that the resulting errors are less than 20%. When this modified CO₂ parameterization is combined with a recently modified formulation for H₂O vapor absorption, the resulting errors in the heating rates are also less than 20%. The application of the modified solar absorption parameterizations in a general circulation model (GCM) causes an increase in the simulated clear sky diabatic heating rates, ranging from nonnegligible (middle stratosphere and lower troposphere) to significant (lower stratosphere and upper troposphere) additions. The results here should enable a continued use of the older broadband parameterizations in GCMs, albeit in modified forms.