An improved and extended parameterization of the CO₂ 15 µm cooling in the middle/upper atmosphere

Abstract. The radiative infrared cooling of CO₂ in the middle atmosphere, where it emits under non-Local Thermodynamic Equilibrium (non-LTE) conditions, is a crucial contribution to the energy balance of this region and hence to establishing its thermal structure. The non-LTE computation is too CPU time-consuming to be fully incorporated in climate models and hence it is parameterized. The most used parameterization of the CO₂ 15 μm cooling for the Earth's middle and upper atmosphere was developed by Fomichev et al. (1998). The valid range of this parameterization with respect to CO₂ volume mixing ratios (VMR) is, however, exceeded by the CO₂ of several scenarios considered in the Coupled Climate Model Intercomparison Projects; in particular, the abrupt-4xCO₂ experiment. Therefore, an extension, as well as an update, of that parameterization is both needed and timely. In this work, we present an update of the parameterization developed by Fomichev et al. (1998), which now covers CO₂ volume mixing ratios in the lower atmosphere from ~0.5 to over 10 times the CO₂ pre-industrial value of 284 ppmv (i.e., 150 ppmv to 3000 ppmv). Furthermore, it is improved by using a more contemporary CO₂ line list and collisional rates that affect the CO₂ cooling rates. Overall, accuracy is improved when tested against reference line-by-line calculations and by using measured global temperature profiles of the middle atmosphere. On average the errors are below 0.5 K day^-1 for the present-day and lower CO₂ VMRs. The errors increase to ~1–2 K day^-1 at altitudes between 100–120 km for CO₂ concentrations of two to three times the preindustrial values. For very high CO₂ concentrations (four to ten times the pre-industrial abundances) the errors are below ~1 K day^-1 for most regions and conditions, except at 110–120 km where the parameterization overestimates them by ~1.5 %. When applied to a large dataset of global (pole-to-pole and four seasons) measured temperature profiles, the errors of the parameterization are generally below 0.5 K day^-1, except between 5⋅10^-3 hPa and 3⋅10^-4 hPa (~85–95 km), where they can reach biases of 1–2 K day^-1. However, for elevated stratopause events, it underestimates the cooling rates by 3–7 K day^-1 (~10 %) at altitudes of 80–100 km and the parameterized cooling rates show a large spread when compared to reference calculations.