Long‐wave radiation from clear skies

TLDR

Long‑wave radiation from clear skies correlates almost perfectly (r = 0.99) with black‑body radiation σT⁴, indicating that temperature dominates R and vapor‑pressure effects are negligible. The study re‑examines Brunt and Angström’s relations to demonstrate that their temperature–humidity correlations are largely due to underlying temperature–humidity coupling. The authors argue that the correlation between R/σT⁴ and vapor pressure e depends on the local temperature–humidity regime. New measurements over a wide range of temperatures and humidities confirm a 0.99 correlation between R and σT⁴, yielding regression equations R = –17.195 σT⁴ and R = 5.31 × 10⁻¹⁴ T⁻⁶ that predict R within 0.5 mW cm⁻², and explain regional variations in Brunt–Angström coefficients via local temperature–humidity regimes.

Abstract

Abstract Analysis of the observations of long‐wave radiation from clear skies, R, made by Dines at Benson, yields a correlation coefficient of 0·99 between R and the black‐body radiation at the corresponding screen temperature T . A new series of measurements over wider ranges of temperature and humidity confirms this, with the same value for the correlation between R and σT 4 , the regression equation being: R = −17·195 σT 4 (milliwatt cm − , T °K). An alterlative representation of equals accuracy is R = 5·31.10 −14 T −6 (Milliwatt cm −2 , T°K) The latter formulation is probably better founded physically, and brings out the temperature dependence of the ‘effective emissivity’ ϵ (i.e. R/σT 4 ), which the atmosphere must exhibit. Either expression provides an estimate of R in terms of T with a probable error less than 0·5 mw cm −2 . The present analysis omits any explicit reference to the influence of vapour pressure e on R, and so differs essentially from those due to Brunt and Angström. Re‐appraisal of these latter suggests that the relationships established therein between * and e result basically from a correlation between temperature and humidity. Both the nature and the degree of the correlation between RσT 4 and e for a given locality would then depend on the temperature‐humidity regime occurring there. The wide variations from place to place, both in the values of the coefficients occurring in the Brunt and Angström equations, and in the degree of correlation found between R/σT 4 and the corresponding function of e, are thereby explained.