The apparent emissivity of the atmosphere ϵ, defined as the ratio of incoming long-wave radiation to black-body radiation at screen temperature Ta, 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 + bIn(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 σTa4 − 119 (T in K), where σ is Stefan's constant, or 5·5 Ta + 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 ϵa(c) = (1 − 0·84c)ϵa(0) + 0·84c.
[1]
G. D. Robinson.
Notes on the measurement and estimation of atmospheric radiation — 2
,
1947
.
[2]
R. Geiger,et al.
The Climate near the Ground
,
1951
.
[3]
C. Priestley.
The heat balance of sheep standing in the sun.
,
1957
.
[4]
H. E. Bennett,et al.
Distribution of Infrared Radiance over a Clear Sky
,
1960
.
[5]
John L. Monteith,et al.
An empirical method for estimating long‐wave radiation exchanges in the British Isles
,
1961
.
[6]
W. Swinbank.
Long‐wave radiation from clear skies
,
1963
.
[7]
K. I. Kondratʹev.
Radiation in the atmosphere
,
1969
.
[8]
E. Deacon.
The derivation of Swinbank's long‐wave radiation formula
,
1970
.
[9]
J. Monteith,et al.
Aerosol and solar radiation in Britain
,
1972
.
[10]
J. Monteith,et al.
Principles of Environmental Physics
,
2014
.