The effective cloud fraction of broken clouds obtained by multistream radiative transfer. Part I: Longwave radiation

Abstract

The influence of broken clouds on radiative flux has provided a major source of uncertainty in radiative transfer models of the atmosphere because plane-parallel approximations are assumed in most of the current atmospheric models, where horizontal inhomogeneity cannot be adequately taken into account. In this paper, effects by cloud inhomogeneity on longwave radiation fields are investigated, using a simple model of a cloud array that consists of identical cuboids following some past studies. In contrast to past work that adopted simplified formulations of radiative transfer, multistream radiative transfer is considered to obtain the exact solutions of radiative flux, which enable us to consider semitransparent clouds as well as optically thick clouds in desirable accuracy. Applicability to semitransparent clouds is important because cirrus clouds, which are considered to play significant roles for longwave radiation, are often semitransparent to infrared radiation. The computational results show that the empirical formula previously derived by Harshvardhan and Weinman systematically underestimates the effective cloud fraction. An alternative formula is proposed for the effective cloud fraction to supply a better fit to the exact solution of radiative flux. Furthermore, new formulas are derived to approximate the exact solutions including the dependence on the optical thickness of clouds. They are useful to convert plane-parallel flux to 3D flux passing through broken clouds, either for optically thick or thin clouds.