The reviewed manuscript discusses an update to a well-known parameterization of the CO2 radiative cooling applicable to the middle and upper atmosphere of Earth. Infrared emission in 15-micron CO2 band is the dominant cooling mechanism in the Earth’s mesosphere and lower thermosphere and these layers affect the lower ones through so-called «downward control», so their including to General Circulation Models (GCM) becomes more and more common.

A pivotal challenge in calculating the cooling rate profiles is linked to the fact that the vibrational level populations of second vibrational mode levels of CO2 molecule are not in local thermodynamic equilibrium with the surrounding atmospheric volume (non-LTE). In other words, one cannot take a local temperature and estimate the vibrational level population needed to calculate the cooling rates. Instead, one has to find these populations in the course of the calculations, which involve two-way radiative transfer in the atmosphere and collisional population and depopulation of the said vibrational levels. These calculations are computationally expensive, and different groups working in the field of non-LTE seek the ways to accelerate them without losing the quality.

From the perspective of a GCM modeler, a streamlined routine for promptly and accurately calculating radiative cooling profiles is always welcomed, with any enhancements in accuracy being commendable.

All this said and acknowledging the usefulness of these routines, I see a number of issues with the present manuscript, which must be resolved prior to its publishing in the journal. I explain it in more details in General comments below. The minor comments and technical corrections section should be also addressed in the next version of the manuscript.

General comments:

• In my opinion, the manuscript tries to cover too many topics despite the fact that the title states that this is an update to existing parameterization. Well, it doesn’t hurt to recall the main milestones of the previous work, but the manuscript in its current form is “unfocused”. If it is intended to be a text-book chapter on non-LTE in the CO2 bands, then the same information could be found in the first authors’ book (Lopez-Puertas and Taylor, 2001). If it is supposed to be a technical paper then it should put more stress on technical aspects like the accuracy, interfacing, and so on. In addition, the text is overloaded with figures. I counted more than a hundred (!) of individual panels in the main part that consists of 41 pages. This is definitely an overkill and one can tell the same story in a much more concise way. I suggest the authors to shorten the manuscript and to keep only the essential parts. For example, all the inputs can be gathered on one two-panel plot, where the left-hand side would be occupied by the reference temperatures and the right-hand side would show the profiles of CO2 (only one is needed) and atomic oxygen, which is crucial for the estimate of the cooling rate. The first figure is not informative at all and can be easily omitted. The large number of panels in figures like Fig. 5 does not add much to the understanding of the principle of the radiative cooling or its calculation, and so on. Overall, I would reduce the number of non-essential figures to a minimum and put more efforts to a description of the routine itself, its implementation to a GCM and its limitations.
• Regarding the routine, I did not see any reference or repository for it provided along with the manuscript. As far as I understand, this is now a requirement for EGUsphere journals, so I wonder when and how did the authors plan to publish the routine. Besides a general conformity with the journal’s rules, it would be advisable to get a self-consistent compilable code with the cooling rate parameterization routine called from the main code with some standard atmospheric profile, which could be replaced with a test profile by the user. In the next paragraph, I explain the current problem I see with the accuracy of the updated parameterization, and I guess the GCM-modelers would have liked to test it themselves prior to implementing it to the model. Summarizing this point, the authors must provide a ready-to-use code and provide an instruction for its compiling and running both as a standalone routine and as a part of the test code, that might be useful not only for GCM-modelers, but for other researchers wanting to get a quick estimate of non-LTE cooling profile for a given atmosphere.
• The authors show that the routine works fairly well for the multitude of atmospheric profiles they use in the tests. This is quite impressive given a large variability of CO2 concentrations used in the study. Still, I cannot consider these tests to be fully representative because the real atmospheric temperature profiles are far from those shown in Fig. 2 of the manuscript in terms of vertical variability. Moreover, they are even worse than the ones shown in Fig. 20 because the averaging kernels of MIPAS instrument in the middle atmosphere are broad (e.g. Dinelli et al., 2021) and, therefore, this instrument cannot capture any wave shorter than 5-7 km. In addition, MIPAS is a limb measuring instrument, so it washes out horizontal inhomogeneities and this further reduces its vertical resolution. At the same time, the gravity waves (GWs) are known to be composed of several waves of different wavelengths and their amplitude increases with height up to the top of the “wave-turbopause” layer at 90-110km (e.g. Offerman et al., 2007; Ge et al., 2022), which overlaps with the non-LTE-affected area. I believe, the MIPAS profiles used in the study do not represent a full picture of a gravity-wave perturbed temperature profiles, so the tests performed with them show only a partial truth. Moreover, large RMS values presented in Fig. 24 even for these, partially smoothed, profiles make me think that the real accuracy of the parameterization is far from 1−2 K/day as it is stated in the abstract (I do not consider the specific case of elevated stratopause, which is addressed; I’m talking about the accuracy of “regular” profiles). If the tests I suggest below do not disprove my suspicions, this wouldn’t cancel the suggested parameterization. But, the GCM modelers will have a clear picture of what they will use and act accordingly if their models produce lifelike GW-perturbed temperature profiles.
• Here is the test I believe is necessary to conduct in order to properly estimate the accuracy of the suggested parameterization. Instead of using the MIPAS profiles and showing the averaged effects, I ask the authors to use the individual temperature profile coming from a ground-based lidar (e.g. Spitsbergen (78°N, 15°E), ALOMAR at Andøya (69°N, 16°E), Kühlungsborn (54°N, 12°E), Boulder (40°N, 105°W), Fort Collins (41°N, 105°W), Logan (42°N, 112°W), Arecibo (18°N, 293°E), Cerro Pachon (30°S, 71°W), or McMurdo (78°S, 167°E).) Since these lidars do not cover the whole atmospheric profile, in the lower atmosphere one can take a corresponding smooth profile from the reanalysis or from any other model. Among the profiles provided by the lidar teams, one has to pick up the ones, which clearly show the GW-signature (at least, the wave of +/- 10 K amplitude at 100km), and perform the exact and parameterized calculations of radiative cooling rate for these profiles. It would be also interesting to see how different wavelengths affect the accuracy, because the non-LTE effects are different in the case of a short-and large-scale perturbations. I have to stress here that due to a nonlinear nature of temperature perturbation effects on non-LTE cooling rates, these results cannot be replaced with the ones obtained for averages.

Minor comments and technical corrections

Lines 4 and 41: this statement is too general. In fact, there are ways of including the non-LTE calculations to GCMs. For example, this was done for Martian GCM (Hartogh et al., 2005) and I don’t see why this can’t be done for Earth. The corresponding manuscript is still in discussion in the same journal, so it can’t be referenced, but the authors claim that the same approach works for the Earth’s atmosphere.

Line 11: since the atomic oxygen is a variable component and the reaction 1c is directly linked to it, it would be good to have it as a variable parameter, see the second general comment

Line 17: the measured profiles themselves is not a ground truth because of the vertical resolution, see the third general comment. Moreover, one cannot average the results for individual runs and present this difference as an error, because the GCMs accumulate the error due to non-linearity of the processes.

Line 58: Figure 1 is not informative, see the first general comment

Lines 120-150: I guess, the readers will be confused here. It looks like GRANADA non-LTE code cannot work in LTE mode whereas normally it requires one line or one flag to calculate LTE populations. Could you, please, explain?

Line 125: I didn’t find any mention of line mixing effects here. Are they not important?

Line 135: I didn’t get the phrase about the “oscillations in RFM results”. Could you, please, clarify?

Line 145: And what about the results without this additional iteration?

Line 171: I recall that the difference is about 2-3K, and I wouldn’t call this a small change, so one should not neglect the daytime vs nighttime differences. This is addressed in Sect. 8, so the wording has to be changed here

Lines 200-215: all these descriptions are correct, but I doubt that they add something to the understanding of the routine or its accuracy, see the first general comment on the scope and focus of the manuscript.

Lines 220-225 (see also the comment to lines 437-462): if we assume that the k(CO2-O) used in the models is equal to 3 x 1e-12 cm3 s-1, then this experiment shows the effects of quadrupling the atomic oxygen mixing ratio. In addition, the reader might be misled by switching from atomic oxygen to k(CO2-O) and back. It would be enough to present this numerical experiment as the one performed for doubled (or quadrupled) atomic oxygen.

Lines 248-395: in fact, this deserves a general comment, but I cannot suggest to modify the general approach, it is what it is, and it works for smooth profiles for a current atmosphere. But what if the atmosphere changes some day and the LTE/NLTE1,2,3,4 regions become different? Let’s imagine that a modeler wants to calculate cooling rates for an Earth-like atmosphere, but with a different vertical temperature structure. How can he/she tell the limits of applicability of this parameterization?

Line 304: this is just one of the examples of the problem outlined in the previous comment. The error introduced by this “implicit assumption” depends on the atmospheric profile and is hidden deep in this module. It is small for the current atmospheres, but it is not guaranteed that it will remain small for some unusual temperature profile.

Lines 437-462: this is another potential candidate for a general comment. The problem is that there are three values of this rate coefficient, k(CO2-O): the first one is measured in the lab and is about 1.5−2.0 x 1e-12 cm3 s-1 (e.g. Castle et al., 2012), the second one is about 6.0-9.0 x 1e-12 cm3 s-1 retrieved from space-borne observations of 15-micron CO2 emissions, and the third one, 3.0 x 1e-12 cm3 s-1 was suggested for using in the GCMs. This paradox has not been resolved over the decades of its study, but it shouldn’t matter for the parameterization itself, because it is supposed to calculate cooling rate with any given k(CO2-O). 

Line 455: how do you explain that the errors obtained for a smaller k(CO2-O) are larger? Usually, the larger the quenching rate, the larger the cooling rate, and the magnitude of this error is linked to cooling, as in the case of enhanced CO2.  

Line 462: Fig. 20 is barely readable. Please, provide only a couple of profiles coming from a different source (see general comment 4) and show the errors for the corresponding cooling rate profile on the right-hand side panel.

References used in the text

• Castle, K. J., L. A. Black, M. W. Simione, and J. A. Dodd, Vibrational relaxation of CO2(n2) by O(3P) in the142–490 K temperature range, J. Geophys. Res.,117, A04310, doi:10.1029/2012JA017519, 2012
• Ge, W.; Sheng, Z.; Huang,Y.; He, Y.; Liao, Q.; Chang, S. Different Influences on “Wave Turbopause” Exerted by 6.5 DWs and Gravity Waves. Remote Sens. 2023, 15,800. https://doi.org/10.3390/rs15030800, 2022.
• Hartogh, P., A.S. Medvedev, T. Kuroda, R. Saito, and G. Villanueva; A.G. Feofilov and A.A. Kutepov, U. Berger, "Description and climatology of a new general circulation model of the Martian atmosphere", J. Geophys. Res., 110, (E11), doi: 10.1029/2005 JE002498, 2005.
• López-Puertas, M. and Taylor, F.W., “Non-LTE Radiative Transfer in the Atmosphere”. World Scientific Publishing Co, River Edge, NJ, 504pp, 2001.
• Offermann, D.; Jarisch, M.; Schmidt, H.; Oberheide, J.; Grossmann, K.U.; Gusev, O.; Iii, J.M.R.; Mlynczak, M.G. The “Wave Turbopause”. J. Atmos. Sol. Terr. Phys., 69, 2139–2158, 2007.