Ramaswamy, V., and S. M. Freidenreich, 1992: A study of broadband parameterizations of the solar radiative interactions with water vapor and water drops. Journal of Geophysical Research, 97(D11), 11,487-11,512.

Abstract: Reference radiative transfer solutions in the near-infrared spectrum, which account for the spectral absorption characteristics of the water vapor molecule and the absorbing-scattering features of water drops, are employed to investigate and develop broadband treatments of solar water vapor absorption and cloud radiative effects. The conceptually simple and widely used Lacis-Hansen parameterization for solar water vapor absorption is modified so as to yield excellent agreement in the clear sky heating rates. The problem of single cloud decks over a nonreflecting surface is used to highlight the factors involved in the development of broadband overcast sky parameterizations. Three factors warrant considerable attention: (1) the manner in which the spectrally dependent drop single-scattering values are used to obtain the broadband cloud radiative properties, (2) the effect of the spectral attenuation by the vapor above the cloud on the determination of the broadband drop reflection and transmission, and (3) the broadband treatment of the spectrally dependent absorption due to drops and vapor inside the cloud. The solar flux convergence in clouds is very sensitive to all these considerations. Ignoring effect 2 tends to overestimate the cloud heating, particularly for low clouds, while a poor treatment of effect 3 tends to an underestimate. A new parameterization that accounts for the aforementioned considerations is accurate to within ~ 30% over a wide range of overcast sky conditions, including solar zenith angles and cloud characteristics (altitudes, drop models, optical depths, and geometrical thicknesses), with the largest inaccuracies occurring for geometrically thick, extended cloud systems containing large amounts of vapor. Broadband methods that treat improperly one or more of the above considerations can yield substantially higher errors (>35%) for some overcast sky conditions while having better agreements over limited portions of the parameter range. For example, a technique that considers effect 3 but ignores effect 2 yields a partial compensation of errors of opposite sign, such that the resulting inaccuracy for geometrically thick clouds can be less than 20%. In contrast to the marked sensitivity of the cloud heating rates, the maximum relative errors in the reflected flux at the top of the overcast atmosphere and the transmitted flux at the surface do not vary appreciably under the various broadband treatments; with the new parameterization, the relative errors are less than 15%. In applying the broadband concept to overcast atmospheres and multiple cloud decks, there are cases when the errors can be larger than stated above. Hence a general use of broadband methods in weather prediction and climate models (e.g., general circulation models) should be accompanied by a realization of the potential inaccuracies that can occur for specific overcast sky cases.