Accounting for Unresolved Clouds in a 1D Infrared Radiative Transfer Model. Part I: Solution for Radiative Transfer, Including Cloud Scattering and Overlap

Various aspects of infrared radiative transfer through clouds are investigated. First, three solutions to the IR radiative transfer equation are presented and assessed, each corresponding to a different approximation for the Planck function. It is shown that the differences in results between solutions with linear and exponential dependence of the Planck source function are small for typical vertical resolutions in climate models. Second, a new perturbation-based approach to solving the IR radiative transfer equation with the inclusion of cloud scattering is presented. This scheme follows the standard perturbation method, and allows one to identify the zeroth-order equation with the absorption approximation and the first-order equation as including IR scattering effects. This enables one solution to accurately treat cloudy layers in which cloud scattering is included, and allows for an improved and consistent treatment of absorbing aerosol layers in the absence of cloud by using the zeroth-order equation. This new scheme is more simple and efficient compared to previous perturbation method work for treating infrared absorption and scattering. Last, a general method is devised for calculating the random, maximum, and slantwise overlap of cloud layers, which conveniently integrates into the two-stream radiative transfer solution in this work. For several random and maximum (or slantwise) overlap cloud cases with a wide variation of cloud fractions, the error in the cooling rate is generally less than 1 K day 21 and the error in the radiative flux is generally less than 3 W m22.