Zhu, X., 1990: Carbon dioxide 15-µm band cooling rates in the upper middle atmosphere calculated by Curtis matrix interpolation. Journal of the Atmospheric Sciences, 47(6), 755-774.

Abstract: A new algorithm for calculating CO₂ 15-µm band cooling rate is suggested following a similar idea proposed by Fels and Schwarzkopf in 1981. Since the Curtis matrix is more useful in cooling rate calculations, we show in this paper that it is possible to calculate the Curtis matrix by direct interpolation with precomputed Curtis matrices. The algorithm is applied to the calculation of the CO₂ 15-µm band cooling rate in the upper-middle atmosphere (64-106 km). The stored Curtis matrices are off-line computed by escape functions with an appropriate treatment of the nearby layer calculations. These escape functions are calculated by line-by-line integrations. With precomputed Curtis Matrices an accurate atmospheric cooling rate by CO₂ can be calculated more objectively than with transmission functions. A multi-energy-level model to treat the non-LTE problem in this region is also derived systematically. It is shown that when vibration-vibration (V-V) transitions are neglected cooling rate calculations of the multi-energy-level model could be approximated by the usual two-energy-level model with the revised ratio of relaxation rates. Since the complete solution of the non-LTE problem including V-V transitions requires tremendous amounts of computation time due to nonlinearity, it is suggested that such a two-energy-level model can be used in GCMs to approximate the total cooling rate by the whole band.