The non-LTE correction to the vibrational component of the internal partition sum for atmospheric calculations

In this paper, we develop the theoretical basis for the non-local thermodynamic equilibrium (non-LTE) correction to the vibrational component of the internal partition sum Q_v, and we show how this correction enters into the radiative transfer calculation for a limb-viewing radiometer. The importance of the non-LTE correction to Q_v depends, for the most part, on the degree to which the lowest vibrational state of the molecule is in non-LTE for a given altitude, since it is this vibration that contributes most to the partition sum. The affect on high-altitude emission depends on the principle excitation mechanism of the radiating molecule, and we compare CO₂ and O₃. In the case of CO₂, to first order, the high-altitude radiance measured by a limb-viewing radiometer is dependent on the value of the inverse of the partition sum in the region just above the tangent point. We have shown that in the case of the high-altitude temperature sounding channel of the High Resolution Dynamics Limb Sounder (HIRDLS) the non-LTE correction can result in a difference in calculated radiance of some 30% at 130 km. This suggests that the non-LTE correction to Q_v is an important consideration for high-altitude non-LTE radiative transfer models.