An improved δ-Eddington approximation

Abstract

Based on an accuracy analysis of two-stream approximations, an improved δ-Eddington approximation is developed. The approximation has much better accuracy than all exiting two-stream approximations as the optical depth is less than unity. As the surface reflectance is zero and the optical depth is less than unity, errors in both transmission and reflection calculated by the present approximation are more one time less than those by other two-stream approximations. In the case of aerosol optical depth of < 1, surface reflectance of < 0.6, solar zenith angle of < 78° and aerosol imaginary index of < 0. 05, transmission and reflection errors calculated by the improved δ-Eddington approximation are generally less than 3.5% and 2.6%, respectively. The errors are over 41% and one times less than those by Eddington or δ-Eddington.