|The revised version of the manuscript entitled "Calculating the vertical column density of O4 from surface values of pressure, temperature and relative humidity" does address most of the reviewers comments or, where the authors disagree, they give arguments for not changing, just as they state in their answer.|
In terms of structure, the manuscript improved and is now easier to follow. Adding references to specific equations and subsections in the appendix also makes it easier to follow.
In terms of validation datasets, two of the three datasets increased greatly in number of measurements compared to the original submission. I also acknowledge the extra section on temperature inversions, however, I think it is misleading to exclude temperature inversions from the analysis and urge the authors to re-include them in the analysis to reflect fairly the ability and shortcomings of the proposed method since temperature inversions cannot be detected from just measuring the surface values of temperature, pressure and relative humidity and hence their results could be unfairly biased to better values when intentionally taking out temperature inversions from the comparisons in Sect 5. Likewise, I urge the authors to use a different day for the ECMWF dataset in Sect.5 than the day which was used for the fit.
I mostly checked the new submission with track changes i.e. document amt-2021-213-author_response-version1.pdf. However, I see now that there are actually differences between that version and what was submitted as a new version, likely exclusively attributable to latex issues with the diff package [and hence nothing the authors could influence]. See for example page 11 (page 32) in the former document, last sentence of Sect. 3.2 "For further details see Appendix B0.1 and B0.1" and compare this with the last sentence of the document which was submitted as new version as amt-2021-213-manuscript-version2.pdf (page 9): "For further details see Appendix B1.2 and B1.3". Please ignore comments that refer to non-existing sections or multiple figure numbers if you find them correct in the not-track changed version. Line numbers below refer to the track changed version.
(1) Since the authors only consider in their validation daytime VCDs (see also Sect. 3, especially lines 209- 212), the title should reflect this limitation. Please add this to the title accordingly.
(2) Regarding following the AMT guidelines:
(a) I disagree with the authors that the use of "quantity/ unit" in axes labels and table headings is only a recommendation. I have also never "noted" that it is only a recommendation either. Please read carefully the AMT author guidelines (https://www.atmospheric-measurement-techniques.net/submission.html#math):
In addition, the SI and IUPAC recommendations should be followed:
IUPAC Green Book, 3rd edition
IUPAC Gold Book
Collins dictionary says about the use of the word "should" (https://www.collinsdictionary.com/dictionary/english/should #2) :
You use should to give someone an order to do something, or to report an official order.
All visitors should register with the British Embassy.
The European Commission ruled that the company should pay back tens of millions of pounds.
Hence, it is more an obligation than a recommendation to follow the guidelines (or recommendations) of the SI brochure and the green/ gold book. The point is that AMT uses "should be followed" not "it is recommended to follow" or "authors are encouraged to follow".
(b) The argument that the authors give " Thus we prefer to provide units in brackets in figure axis, which is also commonly done in most of recently published AMT papers", is not a valid argument for the validity of their choice; it is merely a statement about the state of quality control at AMT regarding their own guidelines.
(c) Even if following the guidelines of the green book and the SI brochure were just a recommendation:
Who will follow these guidelines, if not even the chief editor of the journal which publishes these guidelines/ recommendations follows them? People in power should set good examples and follow (at least their own) recommendations, otherwise recommendations do not make any sense and could be removed all together.
(d) There are good reasons why AMT refers to the SI brochure and the green book. For a motivation for these guidelines, check out the preface of the green book, where it reads on page IX:
"The purpose of this manual is to improve the exchange of scientific information among the readers in different disciplines and across different nations"
Including the unit in round brackets in an axis label (or table heading) is common in some areas (e.g. physical review letters prefers the notation with round brackets is even recommended: https://journals.aps.org/prl/authors/axis-labels-and-scales-on-graphs-h18; but keep in mind that the article in question was not submitted to APS but to AMT; AMT has different style guidelines, as cited above), square brackets are in fact used to give units of a quantity as follows: [quantity] = unit, e.g.: [T] = K. Using square brackets in axis labels around units is simply not correct and should never be used. Using round brackets is accepted, but has certain disadvantages: It can be easily mistaken as a multiplication factor whereas it really should be the denominator of a quotient. Hence, labeling a distance axis as "distance (m)" could be interpreted as "distance <<times>> meters". This is incorrect. What is labeled on the ticks on the x-axis in the graph is "distance <<over>> meters" (a plain number); the notation "distance/ m" does not leave any room for interpretation and will be understood correctly independent on your field or background. A very instructive explication in German (see the original from the BIPM linked on the AMT homepage) can be found in the German version of the SI brochure: "https://www.ptb.de/cms/fileadmin/internet/publikationen/ptb_mitteilungen/mitt2007/Heft2/PTB-Mitteilungen_2007_Heft_2.pdf", as in the original, in Sect. 5.3.1 (especially page 174 [corresponding to page 33 in the pdf]).
(3) Regarding the authors answer about the criticism of the limited datasets:
I acknowledge that the authors increased the number of both ECMWF and WRF and I agree that this is a sufficient coverage now. However, two comments here:
(a) regarding the GRUAN dataset, I would still like to mention that more than 70% of their ~6300 datasets come from 3 stations, and hence, I do not agree that that is a good coverage.
(b) from the authors answer on page 5 from document amt-2021-213-author_response-version1.pdf, I understand that the authors submitted the first version of the manuscript in the middle of the process of creating the validation data set, anticipating the full results based on a subset of just ~15%. This is certainly bad practice and should be avoided in the future. It was highly inconsistent (2 months vs a few days) and confusing in the first version.
line 44: "this study" is ambiguous: does it refer to "the current study" (maybe better refer to the specific Sect. 4.1) or to "Wagner et al." (better use: "that")?
line 51: To which equation does "The final equation" refer to?
Table 1: I think "deviation to" should be "deviation from" (https://www.collinsdictionary.com/dictionary/english/deviation or https://dictionary.cambridge.org/dictionary/english/deviation) (likewise l.195)
line 88: Are the authors sure that they want to refer to Eq. 19 here? This seems to have nothing to do with the derivation here?
line 264: Please check the references here, it currently reads Appendix B0.1 and B0.1 There is not even any B0, Appendix B starts (as it should) with 1. (page 31, page 52 in the document.)
line 284/285: "correlation ... are found". "is"?
Figure 1: The frequency is defined as points in some "square" area made of delta-x time delta-y? Please give more detail here, otherwise the quantitative description in the color bar is not meaningful (of course, the qualitative message still comes across and I think it's a very good idea). Same for Fig. 5. , 10, 11. For most of these figures: The inclusion of the colour bar in either one or all subplots is inconsistent. Consider to include it as a separate axis instead. (Although it is not wrong as it is now since multiple colour bars are included where the colour scale differs between subplots. Still it seems not very pleasing for the eye as it is now. Additionally, e.g. in Fig. 10, the colour bar lacks the top axis while it s present in e.g. Fig. 11).
line 311: "too low" wit respect to what? Why "too low"? They are not "too" low?
Figure 8: Caption refers to "top" and "bottom" in a figure where only left and right are present. Please include horizontal separation lines between the stations. Are the authors serious in including stations with single digit numbers (Beltsville, Darwin, Nauru, LaReunion) here?
line 303: "agreement to"?
Fig. 7: Please choose any of the other 3 days here (or best all) and not the day which was used for fitting the parameters. Using the day used for fitting does not make sense. So replace Fig.7 by Fig. C2. Especially, because your argument of "But there is also a considerable reduction of SD from 1.6% for δΓ to 1.0% for δRH" (line 366) is not that strong any longer if you actually consider days that were not used for the fit, the SD only decreases from 2.0% to 1.8% (Mar), from 1.6% to 1.3% (Sep) and from 1.3% to 1.2% for Dec.
line 495: I acknowledge the footnote here, I was at first a bit puzzled here.
line 513: Maybe better "equation"?
line 614: "Note that the for a"? Remove "the"?
Figure B1: Please increase the space between the map and the x- and y- axis labels. Also: There are four "Fig. B1" (at least in the version with track changes), comment is about the first one.