Radiative Terms in the Thermal Conduction Equation for Planetary Atmospheres

Abstract

Terms in the thermal conduction equation arising from infrared emissions and absorptions by atomic oxygen and carbon monoxide are investigated. The purpose of the investigation is to develop general expressions for the net emission by O and CO taking into account absorption of planetary radiation from below as well as radiation from regions of the mesosphere and thermosphere. These expressions are valid at all optical depths in the thermosphere. An expression for the net emission from a molecular band is also given. The radiative terms are developed under the assumption of local thermodynamic equilibrium. The expressions developed for the radiative terms permit the evaluation of net heating as well as cooling in the O and CO emission lines. The results are compared to the Bates' approximation to the radiative loss terms for a partly dissociated CO2 atmosphere which is optically thick in both O and CO. For this model it is found that, at high altitudes where the atmosphere is optically thin in O and CO, the net emission differs from the Bates' approximation by about 15% due to the effect of absorption. Near unit optical depth the net emission differs by more than an order of magnitude from the Bates' terms.