An improved and extended parameterization of the CO2 15 µm cooling in the middle and upper atmosphere (CO2_cool_fort-1.0) - M. López-Puertas; F. Fabiano; V. Fomichev; V. Fomichev; B. Funke; D. R. Marsh (Geoscientific Model Development, 2024)
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 into climate models, and hence it is parameterized. The most used parameterization of the CO2 15 µm cooling for 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 (VMRs) is, however, exceeded by the CO2 of several scenarios considered in the Coupled Climate Model Intercomparison Projects, in particular the abrupt-4×CO2 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 that parameterization that 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 to 3000 ppmv). Furthermore, it is improved by using a more contemporary CO2 line list and the collisional rates that affect the CO2 cooling rates. Overall, its accuracy is improved when tested for the reference temperature profiles as well as for measured temperature fields covering all expected conditions (latitude and season) of the middle atmosphere. The errors obtained for the reference temperature profiles are below 0.5 K d−1 for the present-day and lower CO2 VMRs. Those errors increase to ∼1–2K d−1 at altitudes between 110 and 120 km for CO2 concentrations of 2 to 3 times the pre-industrial values. For very high CO2 concentrations (4 to 10 times the pre-industrial abundances), those errors are below ∼1 K d−1 for most regions and conditions, except at 107–135 km, where the parameterization overestimates them by ∼1.2 %. These errors are comparable to the deviation of the non-LTE cooling rates with respect to LTE at about 70 km and below, but they are negligible (several times smaller) above that altitude. When applied to a large dataset of global (pole to pole and four seasons) temperature profiles measured by MIPAS (Michelson Interferometer for Passive Atmospheric Spectroscopy) (middle- and upper-atmosphere mode), the errors of the parameterization for the mean cooling rate (bias) are generally below 0.5 K d−1, except between 5×10-3<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="1dd83ccecf12fe52f17e9284fbd0bf43"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00001.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00001.png"/></svg:svg> and 3×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="2fed4c430e973dc650d596a4bfa81e4e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00002.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00002.png"/></svg:svg> hPa (∼85–98 km), where they can reach biases of 1–2 K d−1. For single-temperature profiles, the cooling rate error (estimated by the root mean square – rms – of a statistically significant sample) is about 1–2 K d−1 below 5×10-3<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="53a5fb93ed1b1e9bb1973dd87da65513"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00003.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00003.png"/></svg:svg> hPa (∼85 km) and above 2×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="f12c0cb7149d4fe6e1064ce180f5146b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00004.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00004.png"/></svg:svg> hPa (∼102 km). In the intermediate region, however, it is between 2 and 7 K d−1. For elevated stratopause events, the parameterization underestimates the mean cooling rates by 3–7 K d−1 (∼10 %) at altitudes of 85–95 km and the individual cooling rates show a significant rms (5–15 K d−1). Further, we have also tested the parameterization for the temperature obtained by a high-resolution version of the Whole Atmosphere Community Climate Model (WACCM-X), which shows a large temperature variability and wave structure in the middle atmosphere. In this case, the mean (bias) error of the parameterization is very small, smaller than 0.5 K d−1 for most atmospheric layers, reaching only maximum values of 2 K d−1 near 5×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="ec4dd8c82ceceea8ba75d52b0da9a23c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00005.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00005.png"/></svg:svg> hPa (∼ 96 km). The rms has values of 1–2 K d−1 (∼20 %) below ∼2×10-2<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="217521afbb8391753c339d6d199de550"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00006.svg" width="52pt" height="14pt" src="gmd-17-4401-2024-ie00006.png"/></svg:svg> hPa (∼80 km) and values smaller than 4 K d−1 (∼2 %) above 10−4 hPa (∼105 km). In the intermediate region between ∼5×10-3<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="3497308fe399392a9470b6f4502f85c3"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00007.svg" width="52pt" height="14pt" src="gmd-17-4401-2024-ie00007.png"/></svg:svg> and ∼2×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="9d5649659638909906faddb7b81f7b4b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00008.svg" width="52pt" height="14pt" src="gmd-17-4401-2024-ie00008.png"/></svg:svg> hPa (85–102 km), the rms is in the range of 5–12 K d−1. While these values are significant in percentage at ∼5×10-3<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="ad37ee4cee13fdfbcfadf762760b737c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00009.svg" width="52pt" height="14pt" src="gmd-17-4401-2024-ie00009.png"/></svg:svg>–5×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="d6be64bf1df502cd7d5b033e5df3f785"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00010.svg" width="42pt" height="14pt" src="gmd-17-4401-2024-ie00010.png"/></svg:svg> hPa, they are very small above ∼5×10-4<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="235bad2fe825ec7a4e90820d681e6b27"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00011.svg" width="52pt" height="14pt" src="gmd-17-4401-2024-ie00011.png"/></svg:svg> hPa (96 km). The routine is very fast, taking (1.5–7.5) ×10-5<svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="32pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="1aa3c57ff8125a283954aca51a1d2de2"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-17-4401-2024-ie00012.svg" width="32pt" height="13pt" src="gmd-17-4401-2024-ie00012.png"/></svg:svg> s, depending on the extension of the atmospheric profile, the processor and the Fortran compiler.