In this paper, a new retrieval algorithm for temperature and O₂ VER is introduced for the O₂(¹Delta) and O₂(¹Sigma) bands measured by Sciamachy. O₂ VER and temperatures have been derived from these observations before; what is new here is that both are derived simultaneously, and self-absorption is considered in a consistent. The retrieval is applied to one year of data (2010), and temperature data are compared to ACE-FTS and Mipas. The Mipas comparison is particularly useful as Mipas was on the same satellite as Sciamachy, therefore providing close coincidences. The O₂ airglow is highly relevant both for the accuracy of greenhouse gas remote sensing products, and for the energy budget of the mesosphere / lower thermosphere, and the data from this new algorithm provide a large step forward compared to previous publications. The paper is also generally very well written. However, I have some questions e.g., regarding the derivation of the prior error and the comparison to Mipas MA/UA data, as well as a few minor points listed below.

Line 249-250: Doesn't this imply an altitude dependent differently strong weighting, as the self-absorption affects the lower levels exponentially stronger?

Line 251-252: The statement that a prior error of 100 times the prior value leads to a weak to negligible prior constraint seems not correct in the lower altitudes affected by self-absorption: as there the prior profile is too low, and might be orders-of-magnitude too low, so is the prior error actually quite low.  A climatology might be a better estimate of the prior values here, if available.

Line 355: These missing points … are these related to high solar zenith angles? As during daytime the dominating formation mechanism is O₃ absorption, the O₂ airglow varies strongly from daytime to nighttime, and observations with high SZAs would provide very different (lower) values, the signal-to-noise is also low. This should be discussed somewhere, as you don't separate daytime and nighttime observations at high latitudes, and it should also be stressed in discussing your climatology of O₂ airglow: it is a climatology covering a whole year of observations, but at a very specific time of day, about 10:00 local solar time.

Line 437: can you provide some idea why the A band has such a stable cold bias compared to the ¹Delta?

Line 468: “Mipas temperature retrieval in 2010 is only available below ~80 km”: This statement is factually not correct. A) there are the middle atmosphere / upper atmosphere limb modes of MIPAS which scan up to 120 km respectively 170 km every ten days since 2007. These were coordinated with the Sciamachy MLT mode in such a way that corresponding observations are available every 30 days – about once per months. Observations in the MA/UA modes were carried out also in 2010, and temperatures were retrieved from these modes up to at least 120 km, see e.g., Fig 4 in Sinnhuber et al, JGR, 2022 for an example. Data are available on the MIPAS data server at IMK (https://www.imk-asf.kit.edu/english/308.php), and I am sure the Mipas team (e.g. Bernd Funke or Thomas von Clarmann for the MA/UA modes) would be happy to help in accessing and applying the data. If there are coincidence data between Sciamachy and Mipas for 2010 (and there should be at least 12 days) please do the comparison. B) Just as a caution, the nominal limb mode of Mipas scans up to 68 km, so values above ~70 km are probably dominated by the prior profile.

Figure 16: Here Mipas temperatures are used up to nearly 100 km – if they are from the nominal mode as you imply, the large differences above 80 km are to be expected, as the nominal mode scans up to 68 km only. It’s rather surprising that the region 70-80 km seems to agree fairly well in most month.

Minor points:

Abstract: I know they are commonly used, but nevertheless I found the use of the abbreviations (1Δ and A) for the bands slightly irritating. Could you use the full names (O₂(a¹Δ_g), O₂(b¹Σ_g⁺) at least in the abstract?

Line 5: as the nominal mode only scans up to 93 km in 2010, how do you derive O₂(¹Delta) in 93-100 km?

Lines 9 – 11: please add altitude range where temperatures can be retrieved (~40 – 95 km for nominal mode, 65 – 105 km for the MLT mode?).

Line 62: Yang et al, SPECTROSCOPY AND SPECTRAL ANALYSIS, 2021 also used the O₂ airglow to derive temperatures

Line 84: in the nominal limb mode, Sciamachy scanned up to 93 km in 2010. It was slightly higher at the beginning of the Sciamachys operations, but unfortunately this was changed to 93 km already in late 2003.

Line 166: where is the number 1.4387760 cm K coming from?

Line 192: … will also be N. Actually if you formulate it like that, the number should be N-1. It is N in your retrieval because you add an upper bound layer at the top. Can you clarify this?

Line 300-302: “only limited limb views with deeper tangent heights could observe those layers” I am not quite sure I understand this statement. Does it mean only some of the nominal limb scans (which all go down to the surface) provide a good signal-to-noise ratio in these altitudes? This is how I understood this sentence, however I don’t understand how it applies to the discussion of a single limb profile as given here. Please clarify.

Line 303: as supported by comparison to results of the MLT mode retrieval

Lines 311-312: This is by design … due to the self-absorption

Lines 317-318: a) the lowest tangent altitude of the MLT mode is around 51 km; b) why is the upper limit set to below 120 km?

Line 324: erase the would. They do.

Line 371: the maximum abundance

This was a straightforward, well written paper that I enjoyed reading. For the most part, the methodology and results were clearly presented, although clarification is needed in a few spots (as listed below). After properly addressing the following (mostly minor) issues, I'd recommend the paper for publication.

“1Δ” should be “¹Δ” throughout the manuscript

line 8 – I’m not sure I’ve ever heard the term “loading” before in the context of airglow. If this is a common term and I just haven’t been paying attention, then it’s fine, but otherwise I would suggest the word “density” or “concentration” instead.

line 35 – Please briefly explain in the text what is meant by “confounds the retrieval algorithm”

36 – “As an alternative” confused me, as you’ve already talked about the ¹Δ band. I’d suggest you don’t need an introductory remark for this sentence

40-41 – Please be specific about what there is a “lack of assessment” of

42 – I think “chemically” should be “photochemically”

53 – Please specify what is meant by “subject to errors”

70 – Based on your discussion of the results I don’t think “degrees of freedom of signal” is the correct term. As per Rodgers, DOFS is trace(A), which is a single value. It looks to me like what you’re calling DOFS is what is more commonly referred to as the retrieval response, i.e. the sum of the rows of A. Please clear this up.

71 – please specify what is meant by “the formula”

84 – “tangentially” is not needed

87 – file format details are unnecessary

99-104 – I would assume that a proper background correction would be critical in altitude regions far from the emission profile peak, so I think this requires a bit more discussion. It would also be interesting to see a plot of typical or averaged background signals. Whether or not you include a plot of the background signals, I would appreciate at least a brief discussion on the shape of the background signals, and the assumptions/limitations that go in to using a scaled thermospheric signal.

Section 2.2 – MSIS v2 is now the most recent version, https://doi.org/10.1029/2020EA001321. I don’t necessarily think you need to update to this version (although it would definitely strengthen the paper), but, if you don’t, you at least need to discuss the limitations of MSIS-E-00 (especially in polar MLT regions) as is done in some of your references.

118 – “into two high and low altitude regimes” should just be “into two altitude regimes”

Section 2.3 – temperatures from ACE-FTS have been used in multiple comparison studies (easily found at https://ace.scisat.ca/publications/). Please briefly discuss the results of these studies so readers have an idea of the quality of the ACE-FTS temperatures in the upper atmosphere.

Section 2.4 – same as ACE-FTS, please briefly discuss the quality of MIPAS temperature retrievals

132 – You use the line parameters from HITRAN to calculate absorption/emission spectra. Also, please indicate here what version(s) of HITRAN you’re using

142 – should be “coefficients” as they are different for the two bands

142 and after – the "n" in "n[x]" is not necessary as the square brackets already (typically) indicate number density

140-150 – It seems odd that you’re discussing this in terms of density of “emitting” O2 instead of excited O2 in the specific state. The math is fairly straight forward, and all you need to add to the equation is a branching ratio, e.g. the Franck-Condon factor for the A-band.

151 and after – please use the more standard variables λ and ν_bar (nu with a bar over it) to represent wavelength and wavenumber

Figure 1 – could use a dashed vertical line in the middle to indicate the center of the line-of-sight/location of tangent height. Also, the description indicates that the tangent height is in the middle of a layer, whereas here it looks like it is at the bottom of a layer. Please make it consistent.

Section 3.3 – In optimal estimation, the measurement vector is typically represented by y (the retrieval function is typically R), so it’s a bit odd having the measurement vector as r

238 – I would suggest using something like “retrieval system” instead of “forward model” in order to be more encompassing

250 – I would assume that results of the linear inversion would be prone to large, unrealistic oscillations that could lead to convergence issues. Is that the case? And if so, could some type of heavy regularization (smoothing) be applied to the result to get the profiles closer to a realistic estimate?

258 – was it mentioned earlier that this is performed in log space? If not, please explicitly state this prior to here and discuss the trade off of retrieving log values.

265 – why does the xi+1 variable have a “d” in front of it?

280 – The “airglow retrieval” is not attempted

338 – What is meant by “over and above the mesopause region”?

343 – I get what you’re saying about the profile being “W” shaped, but it’s not exactly intuitive what that means. If you want to describe it in that way, I’d say it’s more “ε” shaped, but I’d suggest simply describing it as an inversion layer or a possible double mesopause.

382-383 – The secondary ozone peak has been studied for multiple decades now, so the Li et al. 2020 reference is not appropriate on its own.

393 – a value of 0.5 seems relatively low, as I usually expect ~0.7-0.8 as a cut-off point. Can you please discuss the distribution of “DOFS” values (what I would call “response” values) for the the retrievals (e.g., what percentage of retrievals are rejected if you use 0.5, 0.75, etc., like what is done later in section 5)

409 – Please explain what you mean by “due to horizontal heterogeneity at large SZA”. Are you saying at larger SZAs there is more diurnal variation along the line-of-sight? If so, wouldn’t it be for SZAs closer to 90° (i.e. sunset or sunrise), not necessarily larger?

Figure 13 – please include the 1:1 lines

436 – What is meant by “very consistent”? because that’s not how I would necessarily describe those results.

440 – coincidence criteria

Figure 14 – a color bar is needed to indicate altitude.

478 – please quantify the findings of previous MIPAS temperature comparisons

Figure 16 – Please use either a dashed line or maybe shading to indicate areas where the MIPAS data is from climatology

500 – It’s unclear what is meant by “due to horizontal heterogeneity of airglow”  

Math is not my thing, so I did not check the equations in the appendices. In my opinion, the appendices aren’t necessary, but I’m not opposed to them.