Greenhouse Phenomenon in the Earth’s Atmosphere

Abstract

The “line-by-line” method is used for evaluation of thermal emission of the standard atmosphere toward the Earth. Accounting for thermodynamic equilibrium of the radiation field with air molecules and considering the atmosphere as a weakly nonuniform layer, we reduce emission at a given frequency for this layer that contained molecules of various types to that of a uniform layer which is characterized by a certain radiative temperature $T_\omega$, an optical thickness $u_\omega$ and an opaque factor $g(u_\omega )$. Radiative parameters of molecules are taken from the HITRAN database, and an altitude of cloud location is taken from the requirement of coincidence of the total radiative flux from such evaluation with that followed from the energetic balance of the Earth. As a result of this evaluation for the contemporary atmosphere, we find that the radiative flux due to H$_2$O molecules equals $165\,\mathrm{W}/\mathrm{m}^2$, the flux of $94\,\mathrm{W}/\mathrm{m}^2$ is created by clouds, the radiative flux due to CO$_2$ molecules is $61\,\mathrm{W}/\mathrm{m}^2$, CH$_4$ molecules create a flux of $4\,\mathrm{W}/\mathrm{m}^2$, and the flux $4\,\mathrm{W}/\mathrm{m}^2$ is due to N$_2$O molecules. In addition, approximately 95% of the radiative flux at frequencies below $800\,\mathrm{cm}^{-1}$ is created by H$_2$O and CO$_2$ molecules, while $84\%$ of this flux at frequencies above $800\,\mathrm{cm}^{-1}$ is due to water microdroplets of clouds. It is shown that an increase of the concentration of one component which leads to an increasing radiative flux due to this component causes simultaneously to decreasing radiative flux due to other components because of overlapping of their spectra that corresponds to the Kirchhoff law. In particular, doubling of the concentration of atmospheric carbon dioxide gives an increase of the radiative flux due to this component by $7.2\,\mathrm{W}/\mathrm{m}^2$, whereas radiative fluxes due to water molecules and water microdroplets decrease by $3.0\,\mathrm{W}/\mathrm{m}^2$ and $2.9\,\mathrm{W}/\mathrm{m}^2$ correspondingly, i.e. the change of the total radiative flux is $1.3\,\mathrm{W}/\mathrm{m}^2$. This fact is not taken into account in some climatological models. Interaction of infrared radiation with water microdroplet and its pass through clouds is analyzed on the basis of the Mie model according to which a droplet is characterized by a sharp boundary. It is shown that stratus clouds, rather than cumulus ones, partake mostly in greenhouse phenomena of the Earth’s atmosphere.