On the theory of temperature distribution over the Earth’s atmosphere

The steady-state temperature distribution over the Earth’s atmosphere is described in terms of the law of degradation of energy (or the principle of entropy increase). The distribution is in satisfactory agreement with meteorological measurements. Using constructed dissipative function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot Q$$ \end{document}, a nonlinear differential equation is rigorously derived that describes the synergetics of the steady-state temperature distribution over the atmosphere, from troposphere to exosphere. A detailed analysis of solutions of this equation makes it possible to qualitatively explain nontrivial dependence T(z) over an atmospheric area inhomogeneous in chemical composition. This fact substantiates the correctness of formal introduction and necessity to consider interaction between blackbody radiation and convective stream. It is argued that hard gamma quanta far from the violet part of the spectrum are responsible for heat radiation coming from the Sun.