Comparison of algorithms for incoming atmospheric long-wave radiation

While numerous algorithms exist for predicting incident atmospheric long-wave radiation under clear (L(clr)) and cloudy skies, few comparisons have been published to assess the accuracy of the different algorithms. Virtually no comparisons have been made for both clear and cloudy skies across multiple sites. This study evaluates the accuracy of 13 algorithms for predicting incident long-wave radiation under clear skies, ten cloud correction algorithms, and four algorithms for all-sky conditions using data from 21 sites across North America and China. Data from five research sites were combined with publicly available data from nine sites in the AmeriFlux network for initial evaluation and optimization of cloud cover estimates; seven additional AmeriFlux sites were used as an independent test of the algorithms. Clear-sky algorithms that excelled in predicting L(clr) were the Dilley, Prata, and Ångström algorithms. Root mean square deviation (RMSD) between predicted and measured 30-minute or hourly L(clr) averaged approximately 23 W m-2 for these three algorithms across all sites, while RMSD of daily estimates was as low as 14 W m-2. Cloud-correction algorithms of Kimball, Unsworth, and Crawford described the data best when combined with the Dilley clear-sky algorithm. Average RMSD across all sites for these three cloud corrections was approximately 24 to 25 W m-2 for 30-minute or hourly estimates and approximately 15 to 16 W m-2 for daily estimates. The Kimball and Unsworth cloud corrections require an estimate of cloud cover, while the Crawford algorithm corrects for cloud cover directly from measured solar radiation. Optimum limits in the clearness index, defined as the ratio of observed solar radiation to theoretical terrestrial solar radiation, for complete cloud cover and clear skies were suggested for the Kimball and Unsworth algorithms. Application of the optimized algorithms to seven independent sites yielded similar results. On the basis of the results, the recommended algorithms can be applied with reasonable accuracy for a wide range of climates, elevations, and latitudes.