see attached file

I would like to start this comment by mentioning the fact that I had declined the first invitation of the editor to review this paper with the motivation that I am not an expert in spectroscopy in general, nor in the Zeeman splitting effect and its implications. However, because this paper is pending revision since quite some time, and somehow failed to find enough reviewers, I am moved to accept the challenge on a second invitation by the editor and try to contribute to the subject. Please consider that some of my comments may be affected by a certain degree of naivety. I hope this opening statement will at least encourage some colleagues to put additional effort into committing to their fair share of review duties.

GENERAL COMMENTS:

This paper explores the effect of Earth's magnetic field on the microwave absorption spectrum around the 60 GHz Oxygen band and the related Zeeman line splitting. It is argued that the proper inclusion of such effects in the RS-LBL model enables the accurate simulation of hyperspectral Brightness Temperature measurement and thus allows to envision the employment of such measurements for the remote sensing of near-space (>20km) atmospheric properties. Unfortunately, I do not consider the study to be of sufficient quality for a publication on the AMT journal.

Throughout the paper, it is implied that the inclusion of the Larsson (2019) Zeeman splitting coefficients in the RS-LBL model is one of the contributions offered by the study. However, after analyzing the RS-LBL code (and its previous versions) it appears to me that this innovation was already implemented in RS-LBL since 2019. Could the authors clarify this point or correct me if I am wrong? Did they contribute to the update? In case RS-LBL was already available I suggest the authors edit the manuscript in a way that does not suggest an original contribution.

The second major contribution offered by the study is the design of a hyperspectral microwave sounder (HMAS) that would enable "super high resolution". It is not clear to me what is intended with this. The ideal HMAS instrument is compared with the existing SSMIS only in terms of weighting function density which is hardly indicative of effective benefits of remote sensing instrument designs. Similar papers (like Aires 2015 from the list of references) developed also ideal instruments but supported their position with an extensive analysis of error sources, effects of noise and channel resolution and information content distributions. All of this is missing from the presented study and makes this section not acceptable according to the AMT standards.

I believe that the authors had a good idea exploring the effect of more accurate simulations due to the updated Zeeman coefficients but failed to construct a solid scientific approach to the idealization of HMAS. One possible approach would have been to try to replicate the study of Aires 2015 with the updated RS-LBL; analyzing the effect of varying magnetic field would allow for very interesting and novel insights. The authors decided to propose an original instrument, but I argue that in this case proper analysis of the potential sources of uncertainty is still fundamental for the presentation of a remote sensing concept. Basic analysis of retrieval performances and/or contribution to data assimilation are also necessary.

ISSUES:

I had quite a hard time understanding the text in subsection 2.1 and honestly, I had to refer to other sources to fill the gaps. Part of my difficulties arise from the fact that the text is unnecessarily convoluted (e.g Line 69-70 "The magnetic quantum number describes the quantum number..."), uncommon concepts like "fine-structure Hamiltonians" are assumed to be common jargon and symbols and quantities are introduced and never used (vic. sigma, deltaM, deltaJ deltaW and so on). Indeed, the authors demonstrate a very solid knowledge of the topic discussed, but the audience would benefit from a more concise and practical explanation of the advantages introduced by the Larsson 2019 update, which I believe would tend to meld the subsection 2.1 with the later section 3. Regardless of the solution the authors will implement, the problem is that subsection 2.1, as it is, is not useful.

Line 101, Delete "Please refer to (Larsson et al., 2019)" or specify for what we need to investigate the source that is not covered in the paragraph

Line 111, Delete "In mathematics"

Figure 1 - please put measuring units on y axis (K)

Line 406, why does the sentence begin with "since"?

Line 409, why does this sentence mention temperature retrievals if there are no retrievals presented in the paper?

The LBL code is mentioned in the Code Availability section, however this section should be devoted to the permanent links (I can recommend Zenodo) to the code (and data) necessary to ensure the reproducibility of the results. At the same time the LBL should be cited in the text as suggested by its authors:: How to cite: Rosenkranz, P.W.: Line-by-line microwave radiative transfer (non-scattering) [software] (version YYYY/MM/DD), http://cetemps.aquila. infn.it/mwrnet/lblmrt_ns.html (last access: DD Month YYYY).