Radiative entropy balance and vertical stability of a gray atmosphere

Abstract

Radiative entropy production and entropy flux are subject to ongoing controversial discussion in the scientific literature. The entropy export of planets such as Earth enables and limits all processes of self-organisation in the atmosphere, hydrosphere and biosphere, and is of fundamental importance for climate studies in the context of the so-called greenhouse effect. In this paper, as tutorial examples, formulas for the entropy balance are derived for two simplified gray atmosphere models, each in radiation balance with a black planetary surface of given temperature and with the cold cosmic background. It is shown that the atmospheric entropy production increases strongly with the absorptivity of the atmosphere, while the stationary surface air temperature is always very close to that of the black surface underneath, even though sensible heat flow is intentionally omitted from the models.