Atmospheric radiation calculations usually assume a Boltzmann distribution of molecules among the vibrational and rotational energy levels. At the low pressures encountered high in the earth’s atmosphere, the collision rate is insufficient to maintain such a distribution. An equation of transfer is derived, for a vibration-rotation band, which does not assume a Boltzmann distribution among the vibrational levels. From this is derived an equation for the heating rate due to the band in a plane-stratified atmosphere. It is shown that the heating rate per unit mass tends to zero with the pressure, because of the departure from a Boltzmann distribution, which becomes serious above about 75 km. A method of solving the equation for the heating rate is described, and is applied to a model of the 15μ carbon dioxide band as an example. The effect of departures from a Boltzmann distribution among the rotational levels is also considered, and it is shown to be unimportant for vibration-rotation bands, but to limit computations on the water-vapour rotation band to heights less than about 90 km.
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Curtis et al. (1956) studied this question.