The relationship between specific humidity (q) and down-welling long-wave radiation (El↓) was investigated on a daily, monthly and annual basis for 39 widely distributed sites of the Baseline Surface Radiation Network (BSRN) and validated using two additional BSRN sites. A power relationship between El↓ and q was fitted to the data for each site; the constant did not change significantly with time and geographic location. Neither the mean value of q nor the residual value of El↓ changed significantly between 1998 and 2011, suggesting the applicability of the relationship over periods without large changes in the Earth's temperature and/or concentration of H2O. The root mean square error for both the calibration and validation sites was comparable to that reported for both direct measurements and satellite-derived estimates for daily, monthly and annual periods. The power relationships were weaker for three tropical sites located in the Pacific Ocean, where the seasonal variation in q was smaller than at the other sites. For the remaining stations, a common power relationship, El↓ = 212.64 q0.22, enabled monthly values of El↓ to be accurately estimated from widely available measurements of air temperature, humidity and pressure at the Earth's surface.
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