Parameterization of Atmospheric Radiative Transfer. Part I: Validity of Simple Models

Abstract

This paper outlines a radiation parameterization method for deriving broadband fluxes that is currently being implemented in a number of global and regional 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 these models in the context of a novel method of classifying radiative transfer problems that more clearly identifies the types of problems encountered in calculating globally distributed broadband fluxes. The delta-Eddington model (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 relevant to modeling the global atmosphere. These two methods are used to construct a radiation model of broadband solar and IR fluxes based on the k-distribution data of Fu and Liou. When tested against available line-by-line (LBL) and other reference model calculations of broadband fluxes, it is shown 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 absorption parameterization adopted. (ii) The clear- and cloudy-sky solar fluxes and heating rates agree remarkably with a reference doubling?adding multiple scattering model. The rms TOA flux difference under all-sky conditions is approximately 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 bias when neglected that generally exceeds the model-to-model differences presented. Neglect of IR scattering produces a global bias in the calculated outgoing longwave radiation (OLR) of approximately ?8 W m?2 (i.e., the nonscattering 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 between 2 and 5 W m?2. It was also shown how the computational effort required to produce broadband fluxes varies linearly with the number of model layers. This is an important characteristic given the increasing tendency for increasing the vertical resolution of atmospheric models.