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

The influence of broken clouds on radiative flux has provided a major sourc e of uncertainty in radiative transfer models of the atmosphere because pla ne-parallel approximations are assumed in most of the current atmospheric m odels, where horizontal inhomogeneity cannot be adequately taken into accou nt. In this paper, effects by cloud inhomogeneity on longwave radiation fie lds are investigated, using a simple model of a cloud array that consists o f identical cuboids following some past studies. In contrast to past work t hat adopted simplified formulations of radiative transfer, multistream radi ative transfer is considered to obtain the exact solutions of radiative flu x, 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 significa nt roles for longwave radiation, are often semitransparent to infrared radi ation. The computational results show that the empirical formula previously derive d by Harshvardhan and Weinman systematically underestimates the effective c loud fraction. An alternative formula is proposed for the effective cloud f raction to supply a better fit to the exact solution of radiative flux. Fur thermore, new formulas are derived to approximate the exact solutions inclu ding the dependence on the optical thickness of clouds. They are useful to convert plane-parallel flux to 3D flux passing through broken clouds, eithe r for optically thick or thin clouds.