An Effective Solar Zenith Angle By Account of Atmospheric Spherical Curvature and Refraction

The effects of atmospheric spherical curvature and refraction and their impact on radiative transfer have been studied. It is shown that formulas employed in GCMs for atmospheric curvature and refraction underestimate the effect of effective solar pathlength. A new parameterization for effective solar zenith angle is therefore proposed. It is emphasized that the atmospheric curvature effect on radiative transfer is a localized problem with height dependence. A method corresponding to the local effective pathlength factor is proposed. This rigorous scheme enables variations in both the pathlength and the gaseous amount along a solar direct beam to be accurately evaluated in the radiative transfer process. The results of the rigorous scheme can be used as the benchmark to the proposed parameterizations for the effective pathlength factor. It is found that the new parameterization proposed in this note has better results in flux and heating rates when compared to other parameterizations.