Long‐wave radiation at the ground I. Angular distribution of incoming radiation

The apparent emissivity of the atmosphere ϵ, defined as the ratio of incoming long‐wave radiation to black‐body radiation at screen temperature T a , was measured under clear skies in the English Midlands and in the Sudan. At a zenith angle Z the emissivity was given by ϵ( Z ) = a + b In( usec Z ) where u is the reduced depth of precipitable water (cm). For a set of 46 scans in England, the mean values of a and b were 0·70±0·05 and 0·090 ± 0·002. Systematic deviations about these mean values could be ascribed to: (i) temperature gradients; (ii) aerosol. The Sudan measurements gave a = 0·67 ± 0·03 and b = 0·085 ± 0·002 consistent with the English results and observations already published. There is some evidence that minimum values of a have increased over the past 50 years. Integration over the hemisphere gives the flux density (Wm −2 ) of atmospheric radiation as 1·06 σ T a 4 − 119 ( T in K), where σ is Stefan's constant, or 5·5 T a + 213 ( T in °C). Radiation records by Dines and Dines (1927) for overcast skies are analysed to show that the angular distribution is the same as for cloudless skies; that the mean temperature of cloud base at their site was UK below screen temperature; and that when the mean fraction of cloud cover is c , the apparent emissivity is ϵ a ( c ) = (1 − 0·84 c )ϵ a (0) + 0·84 c .