The paper "Ozone Profile Retrieval from nadir TROPOMI measurements in the UV range" by Nora Mettig et al. provides a nice characterisation of the TOPAS algorithm, and its sensitivities to SZA, VZA, different retrieval scenarios, and shows a calibration correction.

Comments:

- Line 42: With the last S5 launched planned in 2038, and an expected lifetime of 7 years, the nadir mission runs into the 2040s if my information is correct. https://www.eumetsat.int/metop-sg

- Line 120+121: Is the ratio between earth- and solar-spectrum actually stable enough to assume that the effects cancel out? Did you check, or is this an assumption?

- Lines 126 and 127: the values '15' and '32' are not insightful to the reader. Do they refer to specific named flags, or is it a confidence scale (and if so, what is the upper limit)? 

- Line 166: 24 hours time difference is areally a long time for locations with gradients (i.e. winter hemispheres and the spring season in the Southern Hemisphere). At a surface wind speed of 5m/s = 432km distance in 24 hours. Wind at higher levels is much stronger. This means that you are potentially looking at a retrieval from an air mass that is not comparable to the air at the time of the sonde or lider measurement. The air masses sampled may even be outside of your distance criterium. Can you address this issue? 

- Line 215: Why subtract a polynomial? This is not motivated in the text (up to now).

- Line 223: To get an estimate of the potential error you introduce with scaling: is there any indication how this WFDOAS method performs with TROPOMI data in terms of accuracy? Or is this explained in Weber (2018)?

- Line 253: It's not clear to me what the purpose of the third pseudo-absorber is. You mention that it is wavelength independent, but Irrad is not constant across the spectral range. Please clarify.

- Line 256: The subtraction of a polynomial is still not motivated. Why is this needed, and what is its effect? How are the factors of the curve established? (Or did I miss something?)

- Line 277: "Within one iterative step": Maybe you mean: "In the first iterative step..."?

- Line 390: Somewhat more of what? Somewhat more of the shape than just the total ozone content?

- Figure 5: The discontinuity at 300nm is quite profound. Is this due to a different binning factor, or just an inconsistent channel transition? Is the variability for wavelengths > 300nm time dependent degradation, air mass type mis-match? Please discuss. 

- Figure 5: Soft corrections based on differences between expected/simulated and measured spectra have been done before, but I think that those corrections were based on more than just one orbit in a day. Have you considered taking a full day of data to get corrections per cross track position? I think it would stabilise the effect of potential mis-matches between the simulated spectrum based on input ozone and the measured spectrum based on the real ozone distribution. 

- Figure 5 & Line 420: The calibration error of 20% for small wavelengths could (in part) be caused by a lack of Rayleight scattered light in your RTM. You may need to extend your model to 0.01hPa as Top Of Atmosphere to catch those photons in your simulation. You now seem to stop at 60km / 0.2hPa according to the conversion table in https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html. I don't think that is high enough. Would it be possible to check with one (subset of an) orbit to check whether this helps to reduce the bias? If you choose to do the test and it does not change the bias curve, then just mention that in your response to my comments. If it does change the curve significantly, then act accordingly.

- Line 421: The +40% you mention, is that related to a spectral range where magnesium has absorption lines? 

- Line 431: is this a fourth pseudo absorber, on top of the 3 already mentioned earlier? What is the distribution of this scaling factor for retrievals across the Earth? Have you plotted it on a map? Does this show an expected pattern? The point I want to make is this: Using a fitted multiplication factor to explain some bias away is risky when it happens unsupervised. 

- Line 455: "The differences vanish in the altitude range where the retrieval is less sensitive". Please be more specific. In some the altitude ranges where the retrieval is less sensitive, like the lower troposphere, the difference increases. Or is something else meant?

- Line 460: About the +40%: With a 1000 km colocation distance and 24h time difference, the difference in observed and reference profile can be large, especially in the UTLS. Can you tighten up those spatial and temporal colocation windows and still have a statistically relevant result, or is the dataset too limited for that?

- Line 465: Would be good to re-iterate that you refer to the raw comparison, not to the AK smoothed comparison (which goes out of the 10% range).

- Figure 9: Why do Lauder and OHP stop near 45km? No data provided above that altitude?

- Line 506: "Low ozone levels are related to cloud coverage": Are these for strictly completely cloud covered pixels? For partially covered pixels is there info below the cloud top? 

- Line 518: Please explain what you mean with the words 'and without jumps'. 

- Line 554: "From this... regions". How can you derive the benefit value of the TOPAS retrieval from a comparison of an a-priori (climatology) with MLS and OMPS? Whether or not you use the same a-priori climatology for TOPAS or not, if no TOPAS retrievals are used in plots I and J, then I do not see the basis for the statement in the paper. Please explain. Maybe I am missing a step in the logic.

Textual comments:

- Line 26: remove comma after '1980s'

- Line 35: remove space before 'launched'

- Line 74: "The main objective of this study..." I think this could be the start of a new paragraph.

- Line 88: LIDAR is an acronym. There are more occurances in the paper.

- Line 220: double periods after a-priori

- Line 220: mention of P and T profile without mentioning its source, and then at line 225 a repeat with origin from ERA-5. Please mention only once. 

- Line 225: period after '(Hersbach et al., 2020)'

- Line 257: has been proved --> has been proven? (To prove, has proved, has been proven? Please check with a native English speaker).

- Line 293: 'is run then' --> 'is then run', or 'then runs'

- Line 383: 'an degrading' --> a degrading

- Line 428: remove 'the': with time 

- Line 489: positiv needs an extra e

Purely for consideration:

- Line 21: the use of the word 'toxic'. Maybe it is a philosophical question: is ozone toxic or just very harmful when it comes into contact with other material? Personally, I would use the word toxic for substance that can cause death by ingestion into the cell material. Ozone primarily affects the surface of the skin / lungs as a reactive molecule. Since we are often not talking about internal effects of ozone inside the human cell (or plant cells), I would consider the use of the word harmful instead. I see that you have native English speakers as authors that can speak out about this. It may be that my knowledge of English nuances is too limited. I leave it up to the authors to decide.

General comments:

With this work on “Ozone Profile Retrieval from nadir TROPOMI measurements in the UV range” Mettig et al. provide an extensive first account of a Tikhonov-type retrieval of TROPOMI nadir ozone profiles and its overall performance. The research is presented clearly and exhaustively, and is of high interest to AMT. Only minor corrections and clarifications are requested, together with some improvements on internal and external referencing.

Specific comments:

Line 5, 142, 159, 439: Using “accuracy” as a synonym for a quantifiable total or systematic uncertainty (to be clarified by the authors) is misleading. Rather use one of the latter.

Line 52: Rather use “space-borne” than “at the top of the atmosphere” because the latter means different things in different applications (e.g. about 100 km for atmospheric modelling)

Line 81: “In the future, an operational TROPOMI Ozone Profile L2 product will also be provided.” Please specify by whom and/or provide a reference.

Lines 126-127: Provide a reference and possibly some interpretation of the numbers for the statement that “For the ozone profile retrieval, all ground pixels are used which do not have an error flag above 15 for "measurement_quality" or a "ground_pixel_quality" flag greater than 32.”

Line 143: Please be more specific on “Version 4.23” Does this refer to the L2 product or processor? Which L1 version does this correspond to?

Line 167: Please be somewhat more specific on the collocation criteria: “100 km maximum distance and 24 hours time difference” Are all pixels within these criteria considered, or only the ‘closest’ or the one with some best retrieval parameters? As TROPOMI has daily global coverage, why not take the single pixel that spatially overlaps with the sonde launch site at the day of the sonde flight, or with (the majority of) the sonde trajectory?

Lines 180-181: The term ‘matching’ is rather vague. It is recommended to stick to the ‘collocation’ terminology throughout the text.

Eq. (3) and following: x_a should be explained upon first use, as well as its replacement of x_0

Table 1. The “Tikhonov 0th order parameter: 11.11” is not explained in the text.

Lines 236-237: “These errors are largely mitigated if the forward model is run by using the angles (viewing, solar zenith and azimuth) at the surface rather than those at the top of the atmosphere” Is this the case in this work then? Please clarify.

Lines 240-241: “These spectra are then convolved with the TROPOMI instrument response function (ISRF).” Please provide a reference for this.

Line 244: Would you have a reference for the “shift and squeeze correction”?

Line 255: “the Tikhonov regularisation has been proved.” This statement is rather brief and hence not very clear.

Lines 325-326: “Consequently, the retrieval seems to be nearly independent by the a-priori.” This is a quite strong statement that does not straightforwardly follow from the previous sentence. It should be quantized either here or with reference to the later analysis.

Lines 347-350 and Figure 3 middle panel (C): The authors mix the use of ‘averaging kernel’ and ‘averaging kernel matrix’ and of their abbreviation. Line 367 introduces “AK” as the abbreviation of “averaging kernel matrix” but later “AK” is used to indicate the individual averaging kernels. Please clearly distinguish between both for clarity, and use separate abbreviations, e.g. AK and AKM, respectively. What is shown in Figure 3 panel (C) are individual averaging kernels and not the averaging kernel matrix as a whole, so please correct the label of the horizontal axis.

Lines 362-363: “The noise retrieval error calculated in the linear approximation by using the Rodgers formalism” Please provide a formula of reference with formula number.

Figure 2: Why do the second and third rows of plots not have green shaded areas showing dispersion, as the top row for the profiles has?

Line 380: “The best vertical resolution is obtained at the smallest angles (blue).” Please briefly explain why this is the case.

Line 384: “A measure for the mean vertical resolution…” Possibly, briefly note whether this indeed corresponds to the vertical averaging of the previous (or not exactly)?

Lines 430-431: And what about latitudes beyond 50° north or south? These are shown e.g. in Figure 11, but not mentioned here.

Figure 6, caption: Please describe the meaning of the grey area in the right plot.

Line 451: “convolved with the TOPAS averaging kernels” Possibly refer to Eq. (9) for clarity?

Lines 452-453: “The differences vanish in the altitude range where the retrieval is less sensitive.” This may sound counterintuitive, so please clarify.

Figure 8, 10, 11: Add note on different (colour) scales.

Lines 517-519: “For most of the altitude layers, an across-track variation of the retrieved ozone number density is noticeable at some locations with higher values on the east side of the swath and lower values on the west side. This issue shall be a part of future investigations.” This is not clear for all latitudes in Figure 11. Depending on the location within the orbit (especially within 40° north to south), one could say that ozone values often look artificially constant within each swath, resulting in stepwise meridian behaviour between orbits, especially for plots (B) to (D), so possibly somewhat extend this discussion.

Line 538: “as the precision of MLS data significantly decreases” Please provide reference.

Line 576: A resolution of 9 km is mentioned in the main text (line 387).

Lines 600-603: Refer to MLS drift / degradation studies to assess how the TROPOMI soft calibration would be affected.

Line 605: TROPOMI L1b, WOUDC, and SHADOZ data are obtained from third parties and should be mentioned separately.

Technical corrections:

Throughout: “ozonesonde(s)” can be written in one word.

Line 51: “stratosphere” instead of “stratospheric”

Lines 108-109: Mention abbreviation of “signal-to-noise ratio” upon first use.

Line 133: Replace “by” by “using”

Line 173: “laser” instead of “lasers”

Line 217: The reference to Eq. (8) should be Eq. (7)?

Line 220: Double period.

Line 298: Add comma after closing bracket for readability.

Table 2: Remove double ‘with’ in “European background with with polluted boundary layer”

Line 342: Add comma after “Figure 2”

Line 464: Double ‘the’

Line 486: “positive”

Line 595: Replace “small” by “smaller”

This paper presents a new TROPOMI ozone profile retrieval from UV (UV-1 and UV-2) measurements using the Tikhonov regularization based TOPAS algorithm. A sensitivity study is presented to show the retrieval quality from synthetic data. Systematic biases in TROPOMI data are shown by comparing simulation using MLS+MERRA-2 ozone profiles with observation, and soft calibration is derived and applied to the retrievals. The retrievals are validated with ozonesonde and lidar measurements as well as MLS, and OMPS satellite measurements. Examples of global distribution of ozone at different altitude ranges are shown. The scope of this study is well suited for AMT. This paper is generally well organized and methodology is generally good. However, some of the important retrieval details are not described and some places require clarification. Overall, I think that this paper can be published after addressing the specific comments below.

Specific comments:

1. L38, SAGE-III on ISS was launched in 2017, not 2006. Suggest changing to “launched in 2001 on Meteor-3M and in 2017 on ISS”
2. L77, I think that it should be “in-flight analyses”
3. L81-84, it would be useful to describe a little more about ozone profile retrievals by Zhao here in addition to the spectral range: for example, using the optimal estimation method, also derive and apply soft calibration. Band 3 is used due to larger systematic radiance differences in band 1 and larger fitting residuals in band 2, and larger biases in total ozone and ozone profile with relative to other correlative measurements.
4. L113, should the spatial resolution of retrievals at nadir be 28.8 x 45 km2 due to coadding of 8 UV2 across-the-track and 8 pixels along the track?
5. L130, according to how SNR is calculated in the L1b (mostly Poisson noise), I think that the binned error should be 1/SQRT(n) * SUM(SNR_i). If n=1, according to your equation, SNR_binned = 1/SQRT(2) * SNR rather than SNR.
6. L150, please check the reference as Flynn et al. (2014) does not talk about LP retrievals. A better reference the LP measurements may be Jaross et al. (2014): https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2013JD020482
7. L167, for the temporal collocation criterion, it says “24 hours time differences”, as it is a fixed time difference here, suggest changing to “within 24 hours” or “24 hours maximum time differences”. Also, I guess most of the time differences are within 12 hours. You may tighten this criterion.
8. L184, the full name of TOPAS has been mentioned earlier in the introduction, so you do not need to mention here again.
9. Table 1 is not referenced in the text. You may mention Table 1 at the beginning of Sect. 3.2 before describing the retrieval in more details.
10. L215, you mad add “base on LUT” after “A polarization correction” and add “ and will be described later in this section”
11. L216, based on the text below, offset is also fitted. So you add it to this sentence. Why is a 1^st order polynomial subtracted? L256 also does not mention why and what kind of 1^st order polynomial is subtracted. Is the 1^st order polynomial pre-determined?
12. In table 1, it is not clear about how and why Tikhonov 0^th order parameter of 11.11 is set. According to equation (4), the 0^th Tikhonov term is just Sa^-1.
13. L255, what do you mean “represented by the inverse solar spectrum”? Are you fitting a scaling factor to the solar spectrum? Please clarify it.
14. L264, you may change to “in generally good agreement on altitude average” as the actual variance changes a lot.
15. L268, the gamma value is fixed to 0.007 for all the retrievals here. In the Tikhonov method, the regularization parameter (i.e., gamma here) is often determined dynamically, for example, using the L-curve method. Have you tried to derive it dynamically?
16. L272-273, has the noise in the solar irradiance been included in the calculation of SNR?
17. L277-278, it is not clear about how “no cross-talk between these two parameters is considered while both are retrieved in one iterative step. I guess that the covariance terms in Sa are 0 between ozone and surface albedo parameters. Do you also set the Jacobians for effective surface albedo to 0 below 310 nm?
18. In Fig. 2, do the green curves on middle and bottom panels show the mean differences between retrievals and convolved true profiles? Or do they show the differences between the mean retrievals (orange with circles) and convolved true profiles? It is not clear from the figure caption.
19. In Fig. 3 caption, the total retrieval error (black) is not seen and also not shown on the legend of panel (e). Should the layer legends on Fig. 3c be 0.5, 5.5, … 59.5 km. From the text, the retrievals are done at 60 layers, but on Figs. 2 and 3, the results are plotted at 61 levels from 0 to 60 km. Please clarify this.
20. L360, based on the definition of vertical resolution as the inverted main diagonal (i.e., layer degree of freedom for signal), the vertical resolution becomes smaller if the retrieval is done at a coarse grid (e.g., every 5 km). Does this definition require the retrieval to be done at every 1 km or require the normalization to layer thickness?
21. L365 and Fig. 3e, the noise errors and standard deviations of retrieval results seem to be too small to be true especially in the lower stratosphere and troposphere. Please check them. What are the binned SNRs at different wavelengths for this specific spectrum?
22. L375-376, it cannot be seen from Fig. 4 that the vertical resolution improves for the bottom layer as the values become much larger for the bottom layer.
23. L383-385, based on Fig. 4, the sentence “At larger SZA, … with increasing VA below 17 km” is true for relative azimuthal angle of 180, but opposite for relative azimuthal angle of 0. Can you please explain why the vertical resolution depends so greatly on VA for large SZA and the dependence is on the opposite? The troposphere becomes invisible at SZA of 85 except for VZA 50/54 and relative azimuthal angle of 0, right? Why the vertical resolution significantly increases for VZ 50/54? Is this real or due to some kind of anomaly in the averaging kernels?
24. L392-394, how and how much do the additional independent variables generally change the DOF?
25. L466-499, the first sentence say “the increased vertical resolution found in this altitude range, see Fig. 4.” But according to Fig. 4., the values at few bottom layers increase (compared to 3-5 km?) and thus the vertical resolution become worse. Also for some of the larger SZAs or high latitude, the vertical resolution decreases in this altitude range and the retrieval sensitivity is very limited in 0-5 km. So I think that this statement is not accurate. Also to show the retrieval improvement over the a priori, I think that it is equally important to show the improvement of standard deviation of the differences. So at what altitude/latitude ranges are the standard deviations of the differences between retrievals and ozonesonde better than those between a priori and ozonesonde?
26. L470-476, it is also useful to discuss about the slope and whether the retrievals improve over the a priori.
27. Figure 9 legend, “num. sondes” should be “num. Lidar”
28. L496-497, it is likely due to reduce retrieval sensitivity for these altitudes? What are the precision for lidar measurements at these altitude ranges.
29. L506, are you getting a priori ozone between scene pressure and surface pressure? Or do you retrieve ozone only above scene pressure?
30. L503-506, it is worth to add that the 0-8 km sub-columns show high wave one pattern in the tropics, with high ozone in the South Atlantic and low ozone in the tropics, and generally higher ozone at mid-latitudes as these features are generally consistent with the tropospheric ozone distribution.
31. L510 and L534, I suggest changing to “no vertical information” as there is still useful information for the sub-columns.
32. L562-563, this seems to suggest that the TOPAS total ozone at high latitudes is less accurate compared to WFDOAS total ozone. I think that WFDOAS retrievals might be more sensitive to a priori ozone as no vertical ozone information is retrieved.

Technical comments:

1. Title: Some words (not prep. or adv.) are not capitalized: nadir, measurements, range. You may remove “nadir” as TROPOMI is a nadir-viewing only instrument.
2. In abstract, it might be useful to show the unabbreviated name of “TOPAS” algorithm at its first occurrence.
3. In abstract, you may show full name of “TROPOMI” as “Tropospheric Monitoring Instrument (TROPOMI)”, “MLS” as “Microwave Limb Sounder (MLS) on the Aura satellite”, and of “OMPS-LP” as “Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP)” at their first occurrences
4. L51, change to “higher” and use subscript for 3 in O3
5. In equation (6), S_R should be S_r for consistency.
6. L220, there is an extra “.” after “a priori”
7. L225, miss an “.” Before “The effective”
8. L228, good to specify the unabbreviated names of OCRA and ROCINN.
9. L271, “y” in “Sy” should be in subscript
10. Figure 2 caption, add ‘s” to “difference”
11. 10 L328, change to “independent of”
12. L422, there is an extra “)”
13. L427, suggest changing to “and tends to be negative” and “A closer look at” or “A closer look into”
14. L540, change to “i.e.”