Earth's Radiative Equilibrium in the Solar Irradiance

Abstract

The average equilibrium temperature for all the Earth's entities involved in its radiative balance with the Sun and Space, is given by:

T (e) [K] = 278.9 [(1 - α) / ɛ]

The controlling factor is the ratio of the absorptivity, a = (1 - α), to the emissivity, ɛ. The quantity α is the Earth's albedo. It is shown that relatively modest changes of only a few percent in α, brought about by variations in cloudiness, are sufficient to account for the observed 20^th Century variations in Earth's measured temperature, provided that such variations in cloudiness can cause an imbalance in the ratio (1 - α) / ɛ. The analysis suggests that in the long run, the absorptivity to emissivity ratio is near unity, as required by Kirchhoff's radiation law, which ensures a moderate average temperature of about 5.7 C for the Earth's surface entities. That calculated temperature is in fair agreement with the observed average temperature of those entities, whose mass average is dominated by the mass of the oceans. Except for the influence of clouds on the albedo, no assumptions are needed regarding the detailed composition of the atmosphere in order to explain the observed small fluctuations in the 20^th Century temperatures or the larger, longer-term variations of Glacial Coolings and Interglacial Warmings.