Dear Dr Gromov

I am happy to accept your paper for publication in Atmospheric Chemistry and Physics, subject to the following minor revisions, which I will oversee myself.

The manuscript appears fragmented due to the number of appendices and supplementary materials. I think the appendices can stay as they are (but see my comments below regarding their contents). However, please merge Figs. S2, S3 and S4 with the main text. Fig. S1 could stay in the supplementary information, but since this would just leave one figure in the supplementary information, you might want to merge it with the main text at an appropriate location as well.

My main concerns the so-called "contamination kinetic framework" in Appendix A. The term is misleading becase it implies some sort of kinetic modelling, which has no taken place. Instead, you appear to have some sort of regression analysis, but is unclear what was regresses against what and you might want to add a figure to illustrate this. The mathematical presentation is completely incomprehensible and the units on the left hand side and right hand side of the equation do not match. The notation using round brackets is not defined. What does ... stand for? What are "stoichiometric factors"? I have only heard of stoichiometric coefficients. Why do these "factors" appear as indices? What do you mean by integral stoichiometric fractors? Maybe integer? What is the value of k_c you refer to. I suggest you rewrite this "framework" as a set of a chemical equations (this can be examples or placeholders) and derive any purported mathematical relationship from the corresponding kinetic rate equations (where applicable).

Consider replacing the ambiguous term "mixing ratio" with the clearer and - by intuition - more easily understandable "mole fraction".

Please spell out "w.r.t." - there is no need to abbreviate this.

Lines 62, 66, 67 87, 102, 154, 289: Please delete the tilde signsand where necessary give the actual uncertainties of the values.
65: Please define STP - 1 bar, 273.15 K? 1.01325 bar, 298.15 K?
71: The delta and R indices not clear. 13C, 18O and 17O are not suitable superscript indices because they lead to a double superscript index; please use delta(18O), R(18O), R_st(18O) etc. instead.
74: You might want to cite my re-evaluated 13C/12C isotope ratio (Kaiser, Geochimica et Cosmochimica Acta 2008, doi:10.1016/j.gca.2007.12.011) ... I am not saying you should.
83: IUPAC has reserved square brackets are reserved for molar concentrations (units of mol dm–3). If you redefine their meaning, please avoid being ambiguous and use for either mole fraction or number density, not both. On p. 12, you use square brackets for number densities.
85: "every 130 s"
88: Add comma after "viz."
93: Replace "ibid., Panel (b)" with "Figure 1 b".
98: "stratospheric influence increases"
110,195: Replace ; with .
119: Replace ibid.
145: use of subscript indices is not ideal because of length of index and space ("in situ")- use bracket index notation instead?: "Delta(WAS–in situ)"
146: There should be brackets around (5.3±0.2) to indicate that the unit "nmol/mol" applies to the value and its uncertainty.
146 & Fig. 3: Define SD (sometimes you use sigma; what's the difference?).
151: "situ" needs to be subscript;
167, 183: There is no advantage of using rho; please stick with [CO]/[O3].
201: stilted language - please replace "It therefore stands to reason to conclude" by "We therefore conclude", you also use active language elsewhere, which tends to make papers usually much mor readable.
202: prior to
213: allows estimating (or allows us to estimate)
227 equation numbering missing; please split into two equations (or substitute Ca = Ct + Cc into the first equation)
227: i is not needed - can refer to any isotope.
232: Eq. (2) does not match description in text below. Please rewrite the equation with delta_a on the left hand side.
delta_a = delta_c + (delta_t - delta_c)*C_t/C_a
Since C_t is fixed and C_a is increasing with increasing C_C this also simplifies your discussion.
255: Please delete "It is noteworthy". Everything in the paper should be noteworthy, otherwise it should be removed.
260-262: Unclear what you mean and the MM "does not ascertain results" - perhaps you are trying to say is that mixing model does provide any significant information on the delta(13C) value of the contamination?
280: Expand MPI-C.
288-290: Unclear what "by conjecturing an inhibition of the formation KIEs proportional to that measured at ~320 K" means.
291: Unclear why this is missing - what does this refer to?
320,321: Add space between value and unit.
324: Merge unit with value, remove s-1.
327: There are no reactions that are this fast. Kinetic limit is about 2 x 10^(-10) cm3 s–1 (depends on the mass of the molecule).
386: Write as m/z 45 (with m and z in italics - m/z this is a symbol, not a physical quantity; otherwise units would be required).
392: Please separate into two equations. What is this tilde/equal sign supposed to mean? Please show explicitly how you calculated the coefficient of 7.2568⋅10−2 in the delta_b equation with all values going into the calculation- the description is not clear.
393: What "remaining parameters"?

Kind regards
Jan Kaiser
Editor Atmospheric Chemistry and Physics

Dear Dr Gromov

many thanks for submitting your revised manuscript and your efforts to clarify the points I found to be unclear.

Perhaps I need to explain myself better with respect to the points on which you had a different opinion so that we can reach some agreement. Upon re-reading the manuscript, I also found a number of aspects that could be expressed more clearly and ambiguities that could be easily resolved. Please also consider these technical corrections when you submit your response and revised manuscript.

1) Contamination kinetic framework: I commend your efforts at trying to explain this "framework", but unfortunately, what you have written ("We infer the functional dependence of the CO contamination strength in the kinetic framework") still suggests that you can a priori derive this functional dependence from kinetic data or modelling. In fact, what you do, is to use a simple linear regression relationship, without any mathematically founded or otherwise referenced kinetic reasoning behind it - at least none that I found possible to follow.

Specifically, I cannot relate the reaction notation, which apparently describes your "framework" (equation A1) to any scientific convention known to me. Even with your additional explanations, I am unable to reconcile the "framework" with the given description or the following equation (A2).

For example, if k1 refers to an initial reaction, the corresponding product (e.g. P1) is missing (note that I have omitted the left superscript index ("O3") here, as one of the reviewers and I suggested before; if an index was required please use conventional index notation using brackets, e.g. k1(O3)).

This reaction appears to have other reactions as a product. This is illogical. A reaction should have a chemical substance as a product, e.g.
O3 -> P1 k1(O3)

Such a reaction could be described by a kinetic rate equation, e.g.
d[O3]/dt = -k1 [O3]
or
d[P1]/dt = + k1 [O3]
since your notation suggests that you consider it to be a first order unimolecular decomposition reaction. However, you contradict yourself here because on l. 358 you suggest that this reaction might also require another substrate, which, if it was an elementary reaction, would make the reaction second (or higher) order.

If this was the only reaction of the mechanism and you were to integrate this equation, you would find P1 = [O3]_0 [1 - exp(-k1*t)], with [O3]_0 being the O3 number density at time t = 0, suggesting a linear dependence of the product number density on the initial O3 number density (rather than quadratic).

You then suggest that P1 may undergo subsequent reactions with either X or another O3 molecule. Perhaps you could give some examples, but regardless of what these are, they are occurring simultaneously (in parallel), suggesting a _sum_ of reaction rates.

However, equation (A2) gives a rate equation involving _products_ of reaction rates:
d[CO]/dt = (k1*k2*...*k_kappa)*[O3]^kappa * (l1*l2*...*l_K)*[X]^K
= k_c * [O3]^kappa l_c * [X]^K
(using k for the O3 rate coefficients and l for the X rate coefficients; with k_c/l_c being the products of the respective rate coefficients).

This suggests an overall reaction order of kappa + K, which is nonsensical.

I should say that I have assumed that you meant to put some brackets around (k_r*[O3]) and (l_r*[X]) so that the product symbol (capital Pi) applies to both terms. Reading your equation in a strict mathematical sentence, the rate equation would actually have the form
d[CO]/dt = [O3]*(k1*k2*...*k_kappa) * [X]*(l1*l2*...*l_K)
= k_c * l_c * [O3] * [X]

In contrast, the _actual_ rate equation based on your "framework" should be something like
d[CO]/dt = (k2+k3+...k_kappa) [P1][O3] + (l1+l2+...l_K) [P1][X]

I am unable to see how you derive a dependence of the CO artefact formation rate on the squared ozone number density.

The "kinetic" framework is further compromised by the injudicious mixing of mole fractions and number densities. You state that the units match on both sides of your equations, but they don't in case of equations (A2) and (A3). E.g., in case of A3, the term [O3]^kappa has units of (cm–3)^(2.06) = cm^(-6.18).

This leaves the empirical regression equation to justify the apparent dependence of the artefact mixing ratio on the (approximate) square of the O3 mixing ratio. However, looking at Fig. 1d, I'd suggest that a linear fit would give almost as good a fit as power fit (to the power of 2.06). In addition, a linear fit could be more directly related to a kinetic mechanism (as suggested above).


2) Please do not deviate unnecessarily from established nomenclature, e.g. "abundance" is not a defined concentration quantity and should not be used as such. It is only defined in terms of isotopic abundances. Please stick with the terms "mixing ratio" (and explain at some point that you understand this to mean "mole fraction") and, if required, "number density". You might find the following paper of interest:
Cvitaš T (1996) Quantities describing compositions of mixtures Metrologia:35 doi:10.1088/0026-1394/33/1/5
To avoid confusion, please use the same symbol for a specific quantity throughout the manuscript. For example, you use both square brackets and "C" for mixing ratios. Please use only one of these two. Also, if you use square brackets to denote mixing ratios, please do not also use this for number densities. Note that the IUPAC Green Book recommends the symbol "y" for mole fractions in gaseous mixtures and the symbol "C" for number densities (http://media.iupac.org/publications/books/gbook/IUPAC-GB3-2ndPrinting-Online-22apr2011.pdf).


3) Please decide on your preferred delta notation and stick with it. If you were to follow IUPAC recommendations, you would have to write delta(18O, O3), delta(18O, CO), etc. However, I acknowledge that, unfortunately, many isotope geochemists have adopted the incorrect notation delta18O(O3) etc., perhaps because they mixed up the physical quantity symbol delta with a mathematical operator (which, however, would also be wrong because a mathematical operator cannot be applied to a chemical symbol).


4) Please remove tilde signs and round values adequately and/or give uncertainties, as appropriate. In any case, the tilde sign should not be used to indicate approximations; the correct symbol is "≈" (two wavy lines one above the other). However, since very few of the values mentioned in the paper are exact, the approximation sign is almost always redundant and would be best omitted. Instead the corresponding value should be given with an appropriate number of significant figures according to its uncertainty.


Technical corrections:
The supplementary material does no longer need to be submitted.
line 2: "in upper troposphere/lowermost stratosphere (UT/LMS) air"
3: "mixing and isotope ratios"
4-6: words after (i), (ii), (iii) should have lower case initials
5: A photochemical nature is not ascertained because no detailed process studies or kinetic modelling has been undertaken. Photochemistry is unlikely in the (largely) dark pipes of the sampling system. Rather, you "suggest that the magnitude of the artefact is proportional to the square of the ozone mixing ratio".
7: Delete "the" after application.
8: Replace "signature" with "delta" and 18O/16O ratios with delta18O. Replace "unambiguously" with "likely".
9: Replace 13C/12C ratios with delta13C.
10: Delete "ample" or replace with "stratospheric ozone in relative excess compared to the trace organic amounts".
12: Replace "18O/16O" ratios with "delta18O(O3) values.
14: Delta needs to be in italics.
16: Replace "Successful" with "Accurate" and "content" with "mixing ratio".
18: "physicochemical"
41: Please change to "In the stratosphere, O3 number densities [or number concentrations] are high" [or perhaps mixing ratios? both would be correct, but the latter perhaps more than the former because of the dependence of the surrounding air number density on pressure/altitude]
42: "low O3 number densities"
51: Change to "an estimate" - "valid" appears to be a weasel word.
63: Change to "of the mixing ratios (i.e. mole fractions) of various trace gases"
64: Replace "abundance" with "number density",
65: Expand STP.
65: This should be 0.4 to 4 amol/mol since the air number density at the chosen temperature and pressure is 2.69 x 10^19 cm-3.
65: Please delete brackets around sentence starting "Hereinafter ..."
67: Change "within" to "over" and "integral" to "number density-weighted average".
72-75: V-SMOW and V-PDB are spelled without hyphen. Please expand both abbreviations. Since delta values and associated calculations are independent of the actual values of these isotope ratios (Kaiser & Röckmann, 2008; Assonov & Brenninkmeijer, 2003), you should remove the corresponding values of these (sometimes called, incorrectly, "absolute") isotope ratios, which in any case do not have the accuracy suggested here.
75: "isotope composition" for consistency.
80: Please expand "PFA". Replace "/" with "or".
84: Please see comment 2 above and decide on a single symbol for mixing ratio and another symbol for number density (= number concentration).
86: "with an uncertainty"
88: "respectively" can be deleted.
89: Replace "abundances" with "mixing ratios".
91: Replace "abundances" with "mixing ratios".
92: "where C2 [CO] values"
93: Add "in situ" after C2 for clarity.
94: Please delete the round brackets.
95: Replace "abundances" with "mixing ratios".
97: Please delete the round brackets.
99: "in NH tropospheric emissions" (otherwise this would be a tautology)
100: "with increasing [O3], [CO] decreases"
102: "in C1 and C2 [CO], for [O3] > 400 nmol/mol the C1 CO mixing ratios [...]"
104: "In the 580-600 nmol/mol [O3] bin"
105: "accommodates and extra 14 nmol/mol"
108: "compared against the number of C2 samples (n > 3 x 10^5)."
108-112: Please delete the round brackets.
113: "Because the CO-O3 distribution cannot have changed"
114: Please delete the round brackets and "by the difference" and change to "[...] over the period in question, we find that an apparent relative excess CO of up to 55 % justifies an investigation into sampling artefacts and calibration issues".
116: Replace "18O/16O" ratios with "delta18O(CO)".
117: Please replace "departures" with "elevations" for clarity and consistency with the previous sentence.
118: Replace "abundances" with "mixing ratios" and add "are" after "and"
119: Change to "Lower delta18O(CO) values are expected based on our knowledge of ..."
120: "Fig. 3"
122: Please change to "The greater the proportion of stratospheric CO, the greater its fraction stemming from methane oxidation with a characteristic delta(18O) of 0 % or lower".
124-127: This is no logical. Even if the CO+OH sink flux was zero, the addition of CO from CH4 oxidation would lead to an increased fraction of CH4-derived CO in the stratosphere. Also, there is no competition between source and sink reactions, so if the sentence can be appropriately amended to make it logical, "outcompetes" should be replaced with "is faster than".
133: Please replace the tilde sign with a "+" to highlight the inverse isotope effect of the reaction.
135: Please replace "It is beyond doubt" with "We hypothesise" or "We suggest" or something similar. There is no absolute certainty in science (see your own Huxley quote). You could perhaps say "We are confident" if you want to use slightly stronger language. But you can never be completely beyond doubt in science. Lawyers have invented the term "beyond reasonable doubt", but they need to define both "reasonable" and "doubt", so I suggest not to use this term either.
136: Replace "heavy oxygen" with "18O"
138: "Fig. 3"
140: Please delete the tilde sign - see comment 4 above.
145: "The average difference between WAS and in situ measured [CO] of Delta{overbar}(WAS–in situ) = (5.3±3.5) nmol/mol (n = 408) is a possible indication that the artefact CO is specific to the WAS data." You use the standard deviation below, and to avoid confusion, I suggest using it here as well. Otherwise, please discuss why you use the standard error in one case, but the standard deviation in the other.
147: "Delta(WAS–in situ) is randomly distributed with respect to CO and O3 mixing ratios. This difference remained after several intercalibrations between both analytical systems and is therefore unlikely to be due to differences in detection methods or calibration standards." [as these sources of error would have been eliminated by the intercalibrations]. "However, the higher WAS CO mixing ratios may be due to short-term CO production in the stainless steel sampling flasks."
157: Please replace "an opposite case" with "in contrast to".
160: Replace "functions" with "influences".
160-162: This sentence duplicates the message of the previous one and can be deleted.
162: "Below we discuss and quantify these influences."
164" Please delete "such as", "the" (after "at") and replace "abundances" with "mixing ratios".
168: Replace "abundances" with "mixing ratios".
171: This ratio appears to be wrong and should be 600:70 based on the values given here.
172: Please move "compared to the typical 24-26 nmol/mol to after "500-600 nmol/mol" and delete the tilde sign before 40.
181: Delete "the" after "for", add "mixing ratios" after "N2O" and delete "similar to that for [CO] vs. [O3] presented in Fig. 1". As it's not shown here, it can't be demonstrated to be similar.
182: Delete "greatly" and change to "for C1 and C2".
184: This sentence does not make sense. [H2O] cannot witness [CO]:[O3] ratios. Please change or delete the entire sentence from l. 183 to 185 as it does not appear to add any information.
188: Please add "air" before "compositions".
190: Delete "much".
192: Add "sampling interval" before "<1 s".
196: Please replace "statistic" with "distribution"
197: Please change "integration" to "averaging intervals", for consistency.
197-200: This sentence is unclear - is this meant to be a contradiction, confirmation, fact, assumption, hypothetical calculation or what?
203: Please change to "reaching the analytical instrumentation and WAS sampling flasks in the container".
206: Replace "abundance" with "mixing ratio" and change "imply" to "suggest". Why photochemical? O3 could reaction in the dark as well?
208: This is most likely not a "kinetic framework" - see comment 1 above.
209: Replace "abundance" with "mixing ratio". Left hand side of equation 1 should be [CO]_c for consistency.
212: Change "conform" to "conforming".
213: Replace "abundance" with "mixing ratio".
214: Change "allows" to "allow".
220: Change to "Since this information is not available, we applied an ad hoc correction approach as described in the following. This approach is capable of determining ..."
223: Please delete "Practically" and change "resort" to "use". The Keeling plot itself does _not_ require an estimate of [CO]_c; however, your data selection criterion (for delta_true) does. Please change this sentence accordingly.
227: Please break this into two equations and number the equations. Indices should not be italics. The symbol C should be replaced with [CO] for consistency (or "y" if you adopt IUPAC symbols; see comment 2 above).
230-231: Please delete the round brackets.
246: Replace "conformably" with "correspondingly".
253: The symbol 13delta_c has not been defined. For consistency, this should be delta13C_c(CO), or, following conventional symbol and index notation, delta_c(13C, CO).
263: Change "appear adequate" to "agree with B96". "Fig. 3", not "Fig. 2".
267: Please delete "in a mixing fashion".
268: Please delete the tilde sign.
271: Change "low 13CO abundances" to "low delta13C(CO) values".
273: Change "unambiguously" to "likely"|
286: Please use SI units and convert from Torr to mbar, i. e. "67 mbar".
291-292: What value in Table 1 is this decrease calculated relative to? The values should not be given with decimals for consistency with the indicated precision of the values in Table 1.
306: Please delete tilde sign.
323: Please delete tilde sign and change "moles" to "mol".
326: The symbol tau stands for a value and a unit (s), so the unit after the brackets should be just "cm3". "molec" is not a unit.
332: Replace "abundance" with "mixing ratio".
348: Add "in combination with an empirical parameterisation of the [CO] artefact in terms of the O3 mixing ratio" after brackets, followed by "to single out ..."
383, 390, 413: Replace "abundance" with "mixing ratio".
Table 1: epsilon needs to be replaced with delta and "O2" should be changed to "Air-O2". Tilde signs are not required before "67" - both values have an adequate number of significant figures to indicate their uncertainty.
Fig. 3: The bottom x-axis label should be "inverse CO mixing ratio" for consistency with the top x-axis label.
Fig. 5: The bottom x-axis label should be "inverse CO mixing ratio"
Fig. 6: The x-axis label should be "MM", not MMA. The legend labels should be delta18O_c(O3) and delta13C_c(O3); also in the caption.
613: "18Odelta_t" should be deleted.

l. 99-100: Please change this to "The LMS data exhibit large [CO] variations for [O3] between 300 and 400 nmol mol-1, which primarily reflect ..."

l. 103: "from ... onwards" has no mathematical meaning. If you don't like mathematical symbols such as "≥", please change this to "for [O3] greater than or equal to 400 nmol/mol" or "for [O3] greater than 400 nmol/mol" (depending on what you mean).

l. 105: This correction has still not been fully implemented. Please change to "In the 570−590 nmol/mol [O3] bin ..."

l. 224: This sentence is still wrong. Please change this to "We use a differential mixing model (MM, originally known as the “Keeling-plot”) in combination with the parameterisation of the artefact CO component (Eq. 1) to derive the isotopic composition of artefact CO component. This approach makes no assumptions on the isotope signatures of CO in the air portions mixed in a given WAS tank."

The Keeling plot does NOT require an estimate of the artefact component mole fraction (cf. Figure 5), only your added data selection criterion does.

l. 228 to 246 : Your "ok" in the Author Response is not reflected by corresponding changes in the manuscript. Please delete the indices "i" from the delta symbols where they occur in this part of the manuscript [as you had already done in version 4 of the manuscript]. Please change delta_a to delta_a(CO), delta_t to delta_t(CO) and delta_c to delta_c(CO) [with _a, _t, _c standing for subscript indices], for consistency with the notation used in the remainder of the manuscript. Please also explain that delta13C(CO) and delta18O(CO) are equal to delta13C_a(CO) and delta18O_a(CO), respectively.

l. 228 etc.: The indices a, c and t should be written in upright (roman) font, not italics. Italic font is reserved for physical quantity symbols.

l. 229: Please change "isotope compositions" to "isotope deltas" or "delta values" or "relative isotope ratio differences".

l. 231 and 236: Please change "composition" to "isotope delta" or "delta value" or "relative isotope ratio difference".

l. 249, 259, 264, 275, 295, 296, 306, 310, 628, 629: Please change to delta18O_c(CO), for consistency with the notation used in the remainder of the manuscript.

l. 250, 255 261, 303, 628 : Please change to delta13C_c(CO), for consistency with the notation used in the remainder of the manuscript.