An improved Eddington approximation method for irradiance calculation in a vertical inhomogeneous medium

It is well known that including the delta-scaling in the radiative transfer calculation improves the accuracy of radiative transfer in a cloud layer. An improved scheme is proposed to handle the delta-scaling in the radiative transfer calculation. The improved scheme is able to calculate irradiance of a vertical inhomogeneous cloud layer. The inherent optical properties (IOPs) in a cloud layer vary with height. Linear functions are used to represent the variation of IOPs. Compared to the exponential expression, the linear functions simplified the representation of IOPs. A perturbation method based on Eddington approximation is applied to solve the radiative transfer equation. The accuracy of the proposed scheme is evaluated by comparing reflectance and absorptance to the benchmark Discrete Ordinates Radiative Transfer (DISORT) simulation for two ideal layers and two water cloud cases. Results show that the error limited to 3.4 for reflectance calculation and 7 for absorptance in using the proposed scheme, while the error of the conventional Eddington approximation is > 20 for both reflectance and absorptance. The proposed scheme also improved the accuracy of calculation by considering the vertical inhomogeneity of the IOPs in water cloud cases