Theoretical and Applied Climatology

, Volume 102, Issue 1–2, pp 227–241 | Cite as

Evaluation of atmospheric thermal radiation algorithms for daylight hours

Original Paper


Existing simple but theoretically based clear-sky models for longwave down-welling radiation (LDRc) and cloud impact algorithms transforming them to all-sky radiation (LDR) are checked against locally calibrated empirical algorithms. They are evaluated for daylight hours based on measurements in regionally differing climates of Germany. The Prata clear-sky scheme is additionally tested with adjusted coefficients so that LDRc converges against a realistic emissivity for a completely dry atmosphere. This version is characterised by an improved modelled variance. Compared with locally calibrated schemes, bias and root mean square error (RMSE) of the more theoretical clear-sky schemes do not differ significantly and yield even better results at a mountain site. In contrast, the locally calibrated algorithms yield biases up to 9% and an increase in RMSE between 6% and 67%, if applied for other sites. For daylight hours, the cloud impact on LDR can be calculated via the ratio of observed to clear-sky global irradiation (CMFsol). With CMFsol, the Crawford and Duchon scheme reveals the lowest bias and a decrease in RMSE by 22% against the next best performing algorithms. Compared with synoptic cloud observations as input, the bias is reduced by 9 to 28 W m−2 and the scattering of the residuals decreases by 20% to 30%. Based on published results for also non-European sites, it is inferred that the more theoretically based LDRc schemes and cloud impact evaluated via CMFsol are universally applicable and perform at least in the order of magnitude of locally calibrated empirical algorithms.


Root Mean Square Error Water Vapour Pressure Precipitable Water Adjusted Coefficient Universal Thermal Climate Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This study has been performed in the framework of the COST-Action 730 on “Universal Thermal Climate Index (UTCI)”. The Southwest German sites used for this study were operated within the framework of a regional climate project (REKLIP) funded by the Ministry of Science and Research, Baden-Württemberg, Germany. The German Meteorological Service (DWD) has provided the observations at the northeast German site.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.German Meteorological Service (emeritus)ElzachGermany
  2. 2.Meteorological InstituteAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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