A method to calculate cloud-free long-wave irradiance at the surface based on radiative transfer modeling and temperature lapse rate estimates

We demonstrate a method to improve the performance of commonly used parameterizations to calculate the cloud-free down-welling long-wave radiation at the surface. The method uses a monthly climatology of the effective radiating temperature of the atmosphere instead of the instantaneous screen-level temperature. The climatology of the effective radiating temperature can be derived from pyrgeometer measurements and was incorporated into two commonly used schemes. We compared the calculated cloud-free down-welling long-wave irradiances to high-quality pyrgeometer measurements from four Swiss sites. The discrepancies between observations and modified schemes can be reduced by up to 35 %, resulting in a model uncertainty close to 5 W m^?2 which corresponds to the measurement uncertainty of pyrgeometers. Furthermore, we introduce a new long-wave model which is based on radiative transfer calculations in the 8–14- $\upmu $ m wavelength range. In the remaining long-wave spectrum, the radiation is calculated using the Planck function with the effective radiating temperature of the atmosphere. The performance of this new model is consistent with the modified parameterizations.