OVERVIEW

The paper presents a new routine to calculate the Non-Local Thermodynamic Equilibrium (NLTE) cooling/heating for CO2 isotopes at 15um wavelength in the Mesosphere and Lower Thermosphere (MLT); the routine is called NLTE15umCool-E-v1.0. To sum up, the paper aims to show this routine as a parameterization alternative for General Circulation Models (GCMs) of Earth's atmosphere. The authors claim it is more accurate and faster than the previous parameterization.

GENERAL COMMENTS

The new routine represents a significant innovation and will be an important option for climate models simulating ancient atmospheres or performing projections based on CO2 increase trending. Still, the new routine brings advantages, such as an expanded volume mixing ratio (VMR) range, achieving 4000 ppmv, or even higher accuracy for temperature computed between 80 - 100 km height (non-LTE region).

Despite the valuable scientific significance of the new methodology, the authors submitted the article without proofreading, which substantially affected my review. Overall, the manuscript introduction delivered an unusual approach at the beginning and along the other sections, where some crucial information was missed. In addition, the authors claim that the new combination of techniques (ALI + ODF) significantly reduced the time consumption during the simulations, as shown in Table 2 in the Ttot column. However, the manuscript doesn't provide the data and scripts used to compute each non-LTE technique comparison, making verifying the results impractical. Still, the authors compared the parameterizations KF23 and F98 with a reference model (WACCM6 CESM) but didn't explain why this model was chosen and what non-LTE parameterization is adopted within his source code. Another point is about the NLTE15µmCool-E v1.0 source code, where the users don't have a manual with instructions for users.

Due to the paper presentation demanding a substantial review and improvements, the authors should rewrite the paper to achieve the desired presentation quality and resubmit the manuscript as soon as possible. Anyway, I tried to perform a complete article review because I enjoyed the new routine purpose and intend to use it. Obviously, It's not a proofread, but it will be useful to rewrite the paper. Below, I shared some specific comments. After that, I shared some minor comments. Then, I hope the authors resubmit the revised manuscript to the GMD journal.

SPECIFIC COMMENTS

1) The introduction starts abruptly from the radiative heat rate (h), also called radiative flux divergence (Eq.1).

The introduction is one of the most essential sections of a paper, where the authors bring an informative discussion within the article's scope. However, the current preprint introduction is similar to a subchapter of a book, which can push the readers away due to the need for more context. 

The paper should present some essential information, but I had to get the omitted information by reading other articles. For example, in the review "Infrared Radiation in the Mesosphere and Lower Thermosphere: Energetic Effects and Remote Sensing (Feofilov and Kutepov, 2012)" I found more precise information that is supposed to be present in the submitted preprint. The same in Kutepov et al. (2007) (https://doi.org/10.1029/2007GL032392) and Kutepov et al. (2016) (https://doi.org/10.5194/amt-10-265-2017, 2017).

It's worth mentioning that in section 2, the authors describe the historical progress of some important iteration techniques along the century XX (e.g., Lambda Iteration (LI), Curtis-Matrix (CM), Accelerated Lambda Iteration (ILA), etc.). Thus, this section approaches the main article's subjects using a well-written structure despite minor details. On the other hand, the introduction is one of the preprint's weak points; to get around it, the authors must begin the paper by discussing attractive and interesting topics, considering increasing the article's readability. For instance, the Mars EXpression Mission (MEX) results or citing articles discussing the high levels of CO2 in the primitive atmosphere (4000 ppmv; threshold of the NLTE). After that, the authors would introduce the specific content gradually to present the general article's goals in the penultimate paragraph.

Overall, I recommend moving the introduction (3 first paragraphs) to section 2 and writing more general paragraphs at the initial of the introduction (e.g., astrophysics, ancient atmosphere, SABER, PFS-MEX, etc.). 

2) Presentation and content connections

Please the authors must draw attention to the text's coherence and cohesion; once a well-written manuscript connects all the given information gradually. Another problem is the omitted nomenclature abbreviations, affecting the readability. For instance, the equation to compute the number of operations for the solution of radiating transfer (Nrad) is not declared as an abbreviation in the paper, only in Eq. 5. The same happens with the number of auxiliary operations (Naux). Ultimately, even though some readers can likely be familiar with this technical vocabulary, it's reasonable never to present abbreviations without declaring it properly before in the text, which occurs often in the manuscript (e.g., GCM, MLT, LIMA, ODF, VV, GRANADA, SABER, HITRAN, and others.).

3) GMD journal technical instructions

The document was prepared in disagreement with the technical instructions provided by the Copernicus/GMD journal. I recommend reading the author's guidelines and downloading the manuscript template file (Latex, Word, or R markdown). For example, the citation of Fomichev et al. (1993) is cited as Fomichev, Kutepov, Akmaev, and Shved (1993); it needs to be corrected. For articles with more than two authors, the citation needs to use the Latin acronym "et al". Otherwise, the readers could consider only the last name as a citation. For example, Fomichev et al. (1993) would be Shved (1993).

Another problem is that Tables 1 and 2 disagree with the technical instructions. Therefore, adjusting your tables before submitting the article again is necessary. Note that Table 2 can be combined to become only one.

The authors mention the unit of measurement for cooling rate in the document, sometimes adopting K/day and K/Day, but the correct is K/d. Please fix it.  

4) Figure 1: CO2 vibrational levels diagram …

Figure 1 is based on Feofilov and Kutepov (2012) but is slightly different. The first problem in Figure 1 is the abbreviations FH, SH, TH, and FB. I didn’t find the abbreviation meaning in the document, but in Feofilov and Kutepov (2012) review, each one is declared: First Hot (FH), Second Hot (SH), Third Hot (TH), and Fundamental Band (FB). Another problem is the CO2 isotopes code 626, 627, 628, and 636. The authors should declare explicitly the isotopes just like in Feofilov and Kutepov (2012) in section 2.2.3 (“... The isotopes are marked using the lower digit of the atomic weight: 16O 12C 16O corresponds to 626 …”). Additionally, the authors should declare and distinguish the main isotopes of the minor CO2 isotopes in the text section 2.

I realized that the HITRAN codes (10002 and 02201) are in different positions than Figure 7 in Feofilov and Kutepov (2012). Thus, my question is: does it affect something in the diagram?

Please include the missed unit on the left side of the figure: Energy (cm^-1). 

The Figure 1 caption is identical to Figure 7 in Feofilov and Kutepov (2012). I recommend using other words to avoid plagiarism issues.

5) Figures legends

Figures 4, 5, and 6 must contain a box legend declaring the latitude with your corresponding color, such as Figures 2 and 3. 

6) Model evaluation

The authors present the KF23 and F98 routines errors compared to a reference model (WACCM6 CESM). Only the graphical plots and interval range aren’t enough to validate KF23. I recommend employing the Root Mean Square Error (RMSE) to show that KF23 is more accurate than F98.

Well, I have some important questions:

1) Why did the authors use the WCACCM6 CESM as a reference Model?

2) What is the parameterization adopted within the reference model? Please declare it in the manuscript.

3) What are the advantages and/or disadvantages of the KF23 compared to the parameterization adopted in the reference model?

The manuscript does not mention anything about the WCACCM6 CESM. If possible, request additional information from Dan Marsh.

6) Comments about the NLTE15µmCool-E v1.0 source code

The program can be compiled using a Makefile, but during the first attempt, the compilation fails due to a deprecated GCC flag "g77" (Line 53 of the Makefile). I solved it by updating it to "gfortran", which can recognize all previous GNU Fortran versions (77, 90, 95, etc.). After that, I tested the program, and at a glance, everything worked well. A minor issue is in the file main.f at line 124, where I needed to provide additional space for Pressure (P) and Temperature (T) strings; otherwise, the value number would remain print merged with P and T in the console.

Additionally, I would like to change some parameters to run different simulations, but the code "read_parameters.c" does not provide the parameter CO2 VMR. Thus, Having a namelist to set CO2 values easier would be interesting. For instance, I am setting from 400 to 4000 ppmv.

Another question is about instructions to install the routine and explain some technical aspects of the program, such as the role of the objects and libraries. Otherwise, it might be hard to couple the routine in climate models. I strongly recommend preparing a readme file.  

MINOR COMMENTS

Line 3: Typo, replace  “nigh” with “night”

Line 3: Cooling rate “K/Day -> “K/d” and so on along the text.

Line 13: “… with the opposite sign” replace by “… with the opposite sign:”

Line 17: “… LTE 15 um band cooling” replace by “… LTE 15 um band cooling:”

Line 21: “Declare what is the GCM abbreviation”

Line 22: where (Curtis and Goody, 1956; …) use (e.g., Curtis and Goody, 1956; …). You should do the same in other parenthesis examples along the text.

Line 40-41: The citation format is wrong, change it for Fomichev et al. (1993).

Line 48: Please avoid using terms like “below” and “above” within the document. After the typesetting stage of the manuscript, the final version will modify the position of the paragraphs, equations, tables, and figures.

Line 54: Declare what is MLT.

Line 55: Declare what LIMA is.

Line 63: Such as the Fomichev et al. (1998) parameterization is called F98; it would be reasonable to call the Kutepov and Feofilov (2023) parameterization of KF23. Please consider adopting KF23 instead of KF2023. 

Line 69: ARMS wasn’t declared before in the introduction, therefore, it should be explained in the manuscript as a full nomenclature: Atmospheric Radiation and Molecular Spectra (ARMS).

Line 71: ODF means Opacity Distribution Function, but it wasn’t declared before.

Line 74: Please consider putting the citation (Hubeny and Mihalas, 2015) at the end of the sentence, Line 76.

Line 82: Add a missed comma after “… non-LTE problem …” -> “… non-LTE problem, …”

In the same line, you should change “… that in case …” -> “… that in the case …”.

Line 88: Put the citations in the final of the sentence.

Line 94: Gramma -> Change “However, the convergence of both algorithms depends, strongly on the way the local non-linearity is treated, see next section.” By “However, the convergence of both algorithms depends strongly on how the local non-linearity is treated, see next section.”

Line 99: What is GRANADA? Declare the nomenclature in the sentence.

Line 113: What is VV? Please declare VV as the intermolecular Vibrational-Vibrational.

Line 139: What do you are comparing in “This way of treating the radiative transfer is about 50-100 times than the 140 classic LBL approach”. You mean “…more than the…”, “…faster than then…”. ?

Line 147: Clarify how it can be standard and modified simultaneously.

Line 150: … “ generalized …” : remove the space at the beginning.

Line 152: Put the citation at the final of the sentence.

Line 160: ALI-ARMS should be declared before.

Line 163: What is PFS? Declare it in the text (Planetary Fourier Spectrometer)

Line 164: What is SABER? Declare it in the text (Sounding of The Atmosphere Using Broadband Emission Radiometer)

Line 175: What is VT? Declare it (Vibrational-Translational).

Line 176: in Lopez-Puertas and Taylor (2001), add DOI and ISBN in the references.

Line 179: Please, change “ro-vibrational” to “rotational-vibrational”.

Line 207-209: Consider including 1) time for solving the radiative transfer (Trad) … 2) time for auxiliary (Taux) … 3) time for matrix inversions (Tinv).

Line 210: After (Kutepov et al., 1998) add “:” . Please do the same before other equations.

Line 211: Remove the comma at the final of the equation. Do the same in other equations.

Line 217-218: Please make sure to regard the architecture name of the processor. Usually, x86 is 32-bit, whereas x64 is 64-bit. Do the same in Line 279.

Line 219: declare the gcc compiler nomenclature: gnu compiler collection

Line 226: I suggest changing “Whereas N is …. “ to “Thus, whereas N is defined by the mathematical nature of the problem and the algorithm applied, the coefficient C may depend on many factors, such as the quality of programming, language used, operational system, interpreter, computer architecture and performance, etc.”

Line 237: It is worth remembering NL meaning (number CO2 vibrational levels) once the readers see NL declared only in line 23 on the second page.

Line 245: Change to “…. is approximately N^3” and where is “Therefore,” change to “Thus, we have the following equations:”

Line 253: Include DOI and ISBN of the Book Press et al. (2002).

Line 271: After compared to the nighttime… include a comma.

Line 286: What is the reference model? Please, declare your name as well as justify the reasons to use it. In addition, declare the abbreviation Volume Mixing Ratio (VMR) here; otherwise, this abbreviation will appear suddenly at line 307.

 Line 289: Change the word above to before.

Line 290: What do you mean about “various waves”? If you are talking about gravity waves, declare it explicitly in the paragraph.

Page 13: In Figure 3, there is a typo in the caption: Solis, change to Solid.

Line 319-321: Update the sentence to “For instance, the test for the nighttime for a roughly twice smaller set of bands, which does not include weak first and second hot bands of 626 and 636 isotopes, shows that the maximal cooling rate error for 400 ppmv may increase up to 3 K/d; however, computing time becomes only 10% shorter (see also Table 2).”

Line 333: include a comma after “… absorption and assimilation”

Line 335: You don’t declare before what is VT and VV.

Line 370: The authors say, “… many previous studies (e.g., Lopez-Puertas and Taylor (2001)). I was expecting to cite at least three papers. Add more citations or modify “… many previous studies”.

Line 377-378: Consider changing the sentence to “The accuracy tests of the KF23 routine were performed for a 1 km step grid with the upper boundary of the atmosphere at 130 km.”

Line 380: Add a comma after However

Line 395: Please consider updating the last conclusion paragraph to “The KF23 routine provides accurate cooling calculations in a vast range of k and O(3 395 P) variations. It also works well for very broad variations of CO2, both below and above the current density, up to 4000 ppmv. Consequently, this allows us to use this routine to model the Earth’s ancient atmospheres and the climate changes caused by increasing CO2.”

Line 424: Typo, replace “…. User to switch on an off” with “… User to switch on and off”?

Review report on the scientific article "New Routine NLTE15μmCool-E v1.0 for Calculating the non-LTE CO₂ 15 μm Cooling in GCMs of Earth’s atmosphere" by A. Kutepov and A. Feofilov

The solid knowledge on the spatial-temporal distributions of CO₂ cooling/heating are desirable for modelling of dynamics and temperature in General Circulation Models. A number of parameterisations are used for this purpose. All of them are characterised by either lack of accuracy or high numerical and time costs. This article describes a model that is devoid of these disadvantages.

The research is scientifically valuable. The theoretical part is presented in the paper very convincingly. The methods and approaches are correct. On my opinion this work bring deep insights on modelling of MLT region and new model essential for precise and efficient calculations. On my opinion this work should be accepted in Geoscientific Model Development after minor revision.

Comments.

1. The ODF technique is explained only briefly, the authors refer to their previous works on the implementation of the ODF to the radiative transfer in molecular bands in the planetary atmospheres. But they say no word about the limitation of this technique - is it 100% equivalent to line-by-line in terms of accuracy? If not, what are the errors introduced by this technique? Do these errors depend on the pressure-temperature profile or on CO₂ concentration or both?

2. Additionally, the authors wrote that they apply ODF exceptionally for the band branches. It looks more reasonable to apply it directly to the entire band. May the authors explain why they do not do this?

3. How the final result is sensitive to the completeness of the spectral database used for an input? I understand that the code uses a pre-formatted HITRAN dataset, but does one need to reprocess this dataset for each new version of HITRAN?

4. When authors write that the "accuracy is not sacrificed", when they change their conversion criterion from 1e-4 to 1e-2, what exactly do they mean? Could you, please, be more specific and provide actual numbers and indicate the test conditions?

5. The model is supposed to work in a plane-parallel approach. What are the errors associated with abandoning spherical geometry? Are they different for the nighttime and daytime?