Multi-layer solar radiative transfer considering the vertical variation of inherent microphysical properties of clouds.

A multi-layer solar radiative transfer (RT) scheme is proposed to deal with the vertical variation of inherent microphysical properties of clouds in this study. The exponential expressions are used to represent the vertical variation of optical properties caused by inhomogeneous microphysical properties. A perturbation method, coupled with the Eddington approximation, is used to solve the RT equation. In order to have a more accurate estimation of reflectance/transmittance for every single layer, the optical properties are adjusted following the theory of delta scaling in the proposed scheme. In addition, a modified adding method based on Chandrasekhar's invariance principle is introduced to solve the multi-layer RT. The accuracy of the proposed scheme is investigated by comparing the reflectance/absorptance to the benchmark for two double-layer cases, and each layer with vertically inhomogeneous optical properties. Results show that the bias related to vertically inhomogeneous optical properties reaches 13.8 % for reflectance and 29.2 % for absorptance while the bias of the proposed scheme is only -0.8 % for reflectance and 1.7 % for absorptance. We also apply the proposed scheme as well as the conventional Eddington approximation to the CanadianClimate Center RT model which handle RT in CanAM4. The calculations are performed in the following four solar wavenumber bands 2500-4200, 4200-8400, 8400-14500 and 14500-50000 cm . The result also shows that the proposed scheme also improved the accuracy in both flux and heating rate calculation by taking the vertical variation of inherent microphysical properties into account. The proposed scheme is approximately three times more computationally expensive compared to the Eddington approximation when we only consider the algorithm itself. The computational time is doubled compared to the Eddington approximation when we take the complete radiative transfer process into account. Due to its accuracy and efficiency, the proposed scheme is suitable to improve the RT calculations regarding the vertical variation of inherent microphysical properties in climate models.