Parameterization of atmospheric radiative transfer. Part I: Validity of simple models

This paper outlines a radiation parameterization method for deriving broadb and fluxes that is currently being implemented in a number of global and re gional atmospheric models. The rationale for the use of the 2-stream method as a way of solving the radiative transfer problem for broadband solar and longwave fluxes is presented. This rationale is based on assessment of the se models in the context of a novel method of classifying radiative transfe r problems that more clearly identifies the types of problems encountered i n calculating globally distributed broadband fluxes. The delta-Eddington mo del (DEM) and the constant-hemispheric 2-stream models (CHMs) are shown to be superior to other 2-stream methods of solution under this classification and also superior to 4-stream solutions for the many classes of problems r elevant to modeling the global atmosphere. These two methods are used to co nstruct a radiation model of broadband solar and IR fluxes based on the k-d istribution data of Fu and Liou. When tested against available line-by-line (LBL) and other reference model calculations of broadband fluxes, it is sh own that (i) comparisons of CHM top-of-atmosphere (TOA) clear-sky longwave fluxes with fluxes obtained from LBL models agree within approximately 1-2 W m(-2). The agreement with LBL clear-sky fluxes at the surface, typically within 5 W m(-2), is compromised by the specific form of continuum absorpti on parameterization adopted. (ii) The clear- and cloudy-sky solar fluxes an d heating rates agree remarkably with a reference doubling-adding multiple scattering model. The rms TOA flux difference under all-sky conditions is a pproximately 6 W m(-2); the layer-mean heating rate difference is 0.1 K day (-1). (iii) The effect of IR scattering by clouds is shown to produce a bia s when neglected that generally exceeds the model-to-model differences pres ented. Neglect of IR scattering produces a global bias in the calculated ou tgoing longwave radiation (OLR) of approximately -8 W m(-2) (i.e., the nons cattering models calculated an OLR that is larger than what the scattering models calculated by this amount). Locally, the TOA bias may approach 20 W m(-2). The associated bias in surface longwave fluxes varies in magnitude b etween 2 and 5 W m(-2). It was also shown how the computational effort requ ired to produce broadband fluxes varies linearly with the number of model l ayers. This is an important characteristic given the increasing tendency fo r increasing the vertical resolution of atmospheric models.