Matrix parameterization of the 15 μm CO2 band cooling in the middle and upper atmosphere for variable CO2 concentration

A matrix parameterization of the 15 mu m CO2 band radiative cooling in the middle and upper terrestrial atmosphere for both local thermodynamic equilibrium (LTE) and non-LTE (NLTE) layers is proposed. For the atmospheric region between similar to 13 and 85 km, matrix coefficients for CO2 concentrations of 150, 360, 540, and 720 ppm have been precalculated using a Line-by-line technique. A method for interpolation of the matrix coefficients for arbitrary CO2 concentration is suggested. In the layer between 85 and 110 km, where strong NLTE effects start to occur, a recurrence formula relating cooling rate values at two neighboring altitude levels is used. To calculate the cooling rate above 110 km, a simple approach accounting for both the absorption of the radiative flux formed below 110 km and the cooling-to-space terms is suggested. The accuracy of the parameterization is examined for different temperature and CO2 profiles as well as for different atomic oxygen concentrations in the NLTE layer.