Dear Prof. Lee

firstly, I'd like to apologise for the long delay in arriving at an editorial decision.

Due to the significance of the comments received during the review of your revised manuscript, I have taken the time to look into it in great detail myself. There are a number of technical corrections that are required to improve terms, symbols and quantity notation used in the manuscript, please see details below.

However, there are also two major areas of inherently scientific nature that you have not addressed satisfactorily yet:
a) inclusion and propagation of uncertainties
b) regression via Miller-Tans and Keeling methods

Please include uncertainties in all source isotope delta end members (delta_F, delta_C, delta_P) and fluxes (F_F and F_C) propagate errors formally, stating the values and uncertainties of each term. A Monte Carlo analysis is not justified because the underlying mass-balance equations are explicit. Disregarding the fact that it is not needed for the propagation of errors, the MC analysis (in l. 459-467) omits the uncertainties in the fluxes F_F and F_C and the isotope deltas delta_S and delta_C. Most importantly, the uncertainty treatment should not be dealt with "as an afterthought", but should be carried out consistenly throughout the mnauscript.

The fact that your Miller-Tans regressions (Fig. 3 and Fig. 4) show non-zero intercepts provides the insight that they are not a suitable method to analyse the data on the annual timescale. You need to provide evidence that the method is suitable on shorter time-scales, in particular, the monthly timescale you are envisaging. A suitable timescale would be one that results in a non-zero intercept. You might find that a monthly timescale is not appropriate either, in which case an even more finely-grained analyses would be required, e.g. diel or even hourly, with subsequent aggregation of the derived source isotope deltas into daily/monthly/annual means. This was already pointed out by Referee #1. Please include a set of figures (Miller-Tans plots) that shows the data aggregated to subannual time-scales (monthly, possibly diel) and state the resulting source isotope deltas and their uncertainties.

I've tried to replicate the slope of -12 ‰ (instead of -24 ‰), which Referee #2 reported in their review posted on 3 October 2016, but have not been able to.

In your response, please address my comments as well as those of the two Referees. I cannot predict whether the paper will be acceptable after these revisions because it is currently unclear whether the analytical framework adequately underpins the results and conclusions of the paper.

Yours sincerely
Jan Kaiser



Specific comments:
l. 33: Why do you restrict "daytime" to 1000-1600 and "nighttime" to 2200-0600, omitting the hours in between?

l. 162: Please describe how the standard gases were calibrated against NBS 19 (no hyphen) and NBS 20 (with space) and report the individual results of these measurements before conversion to the VPDB scale. What δ(13C) values (w.r.t. VPDB) did you use for NBS 20? The standard gases are a long way removed from the atmospheric value and virtually identical. This introduced significant scale uncertainties, see paper by Coplen et al. New guidelines for 13C measurements. Anal. Chem. 78, 2439-2441.

l. 169: What do you mean by removing "40 3-minute data points"? Data over 3-minute intervals on 40 different occasions? Did this apply to all calibration gas runs? Were there only 40 calibration gas runs in the whole dataset? Perhaps your response could include a schematic or figure to illustrate what you have done.

l. 170: Why were these data removed?

l. 204: Where were the Mount Waliguan data obtained? Please give a reference to the data depository and state how the data were measured, by whom and which instrument was used.

The 2015 WLG data are now available, so the analysis should be performed with the actual data rather than some extrapolated version.

What efforts have been made to ensure that the new data are compatible (i.e. on the same scale) as the WLG data. What is the uncertainty of the delta(13C) of the a) WLG data and b) the new data with respect to VPDB?


Technical corrections:
There should always be a space between value and unit, incl. per cent and per mill symbols, e.g. "-8.48 ‰", "13 %", "15 ºC". There is no space before the degree sign if it refers to a geographic coordinate, but there is a space before the compass direction: "33º N". Please correct these errors throughout the manuscript.

Please use SI units for mole fractions, i.e. "µmol mol-1", not ppm, which is ambiguous.

Units and chemical symbols must not be mixed. The name of the quantity should identify the species of interest, i.e. "the CO2 mass flux", and the unit should simply be "mg m-2 s-1" (e.g. l. 254).

Please note that in line with international conventions, indices should be enclosed in brackets after the quantity symbol, including δ values, i.e. the correct notation is "δ(13C)". Unfortunately, in the past, the isotope geochemistry community has ignored this convention, but this is not a good reason to continue this poor practice. Alternatively, you might want to omit the index and just write "δ" because - at least in the context of the present manuscript - only 13C/12C isotope ratios are considered. This makes also for a more concise terminology when you discuss the isotope delta of sources (Eq. 5), which would then be "δ_S" instead of "δ_S(13C)", see comment on line 97 below. As you are not qualifying the mole fraction symbol further in Eq. 1, I suggest you should omit the index "(13C)" entirely.

The language used at a number of places in the manuscript is not as clear as it should be. Please make the following changes to rectify this. Terms like "13C isotope composition", "13C isotopic signature", "highly enriched 13C signal", etc. do not make sense because they must be quantified by reference to the other stable carbon isotope, 12C.

l. 24: This is grammatically wrong. Please change to "Observations of mole fraction and carbon stable isotope composition (expressed as δ(13C)) of CO2 in urban ...".
l. 25: Add "and sinks" after sources.
l. 26: Replace "C" with "carbon". Please make the same change everywhere else in the manuscript as well. Unncessary abbreviations should be avoided for clarity and easier reading.
l. 29 & 30: Please also give the standard deviations of mean mole fraction and delta(13C).
l. 31: Change word order to "highly 13C-enriched". Delete "the" before "Mount Waliguan".
l. 34: Change to "we showed that the δ(13C) of CO2 sources"
l. 43: Change to "unique 13C/12C ratios" or "unique δ(13C) values" or "unique carbon stable isotope signatures".
l. 48: Replace "isotopic signature" with "δ(13C)".
l. 49: Replace "heavier" with "higher".
l. 51: Replace "13C composition" with "δ(13C)".
l. 55: Replace "δ13C" with "carbon stable isotope".
l. 56: "13C signature" - see l. 43.
l. 74, 87, 96, 123, 145: Delete "its" (mole fractions don't have δ(13C) values).
l. 97 & elsewhere: Wrong order of indices - this should be δ_S(13C).
l. 114: Either add the index "(13C)" to the delta symbols on the left hand side of the equation or omit it from the right hand side.
l. 115: "at a background site"
l. 116: Please rephrase. Mole fractions don't have isotopic compositions, and there is no such thing as a "13C isotopic composition", also see comments above.
l. 125: "built-up area"
l. 127: Change to "190 million" and add a space before the compass direction (e.g. "33.41º N"). Replace hyphens with to, e.g. "29.04º to 33.41º N".
l. 129: Rephrase to "The main vegetation types are all C3 species".
l. 150: I find it hard to believe that there was no other anthropogenic CO2 source within a 3 km radius. Are there no houses? No heating system? No humans? No cars?
l. 152: Please delete the "~" (tilde) sign and give an accurate distance instead (rounded and/or with uncertainties, if necessary). In any case, the "~" sign is not the correct symbol to designate approximations (for which "≈" should be used).
l. 162: Please describe
l. 173: Do you mean "high bias" or "high error"? And if bias, do you mean "biased high" (i.e. too large) or "highly biased" (i.e. biased a lot, but unclear in which direction)? How much is the bias (or error)?
l. 181: Do you mean relative humidity? In any case, the symbol "V" before "%" must be omitted.
Use SI units, i.e. 0.66 cmol/mol, or 0.66 x 10^(-2) m^3/m^3, for mole fractions (or volume fractions).
l. 181: Please replace "13C composition" with "13C/12C ratio".
l. 185: Which one is it? A volume fraction? Or a mole fraction? Do you make a correction for the non-ideality of the gases involved?
l. 188: This equation is wrong (or at least inconsistent with the text). The second term on the right hand side should most likely be 0.46 ‰ (H/% - 2.03).
l. 189: Please delete "in percent". Physical quantities are not limited to one specific unit.
l. 190: Please change "isotopic composition" to "isotope delta" (two occurrences).
l. 193: has -> have
l. 253: Replace 13C isotope composition with an adequate term - see comments above.
l. 255: Units and chemical symbols should not be mixed. If you want to specify the species the fluxes refer to, it should be enclosed in brackets, e.g. F_s(CO2), or you could explain in the text that "F" relates to CO2 mass fluxes. The unit should be written as "mg m-2 s-1".
l. 258: "unknowns to be solved for"
l. 264: adapt -> adopt
l. 264: State the value used for delta(13C) of CO2 released during cement production, and its uncertainty. The uncertainty should be propagated through the flux calculation.
l. 264: You should calculate an uncertainty for delta_P and propagate it to your flux calculation.
l. 271: What is the uncertainty of this value?
l. 288-290: What are the standard deviations of these values?
l. 292: Replace "diurnal" with "diel". Diurnal means "during the day"; "diel" means "over 24 hours".
l. 293: Define the winter season - which months?
l. 301: Value and uncertainty must be enclosed in brackets so that the unit symbol applies to both, i.e. (-24.75±0.26) ‰. Please revise this and similar occurrences throughout the manuscript.
l. 301: bound -> limit
l. 307-321: This whole section is missing uncertainties and their propagation through the calculation.
l. 316: The delta differences have been calculated incorrectly. These should be 1.53 ‰ and 0.53 ‰ because the delta scale is not linear.
l. 319: What do you mean by "linear correlation"? Is that the slope? Please give the full result of the regression (slope and intercept) including uncertainties of slope and intercept and state the R^2 value.
Section 3.3: Again uncertainty estimates are missing as well as their propagation.
l. 349, 449, etc.: There should be a space between "m-2" and "s-1".
l. 369: "consistent"
l. 379: What do you by "varied 70% to 80% in winter and about 50% in summer"? In the remainder of the paragraph you use fractional comparison between winter and summer.
l. 421/2: "monthly mean" (x 2)
l. 422: "WLG value"
l. 459-467: This MC analysis omits the uncertainties in the fluxes F_F and F_C and the isotope deltas delta_S and delta_C and should be improved by including them.
l. 493: The correlation coefficient is not a meaningful figure of merit to compare the "goodness of fit" by a Keeling plot regression and by a Miller-Tans regression because they plot different variables on the axes. It would be more useful to state the resulting uncertainties of the source delta values, delta_S(13C).
l. 853: "diel variation"

Figure 1: x-axis label should be x(H2O)/% or y(H2O)/%.
Figure 5: x-axis label.
Figs. 7 & 8: The lack of variability in F_F seems to be implausible. What variability would you expect? Please indicate this on the plot and include it in the uncertainty propagation.

Dear Dr Lee et al.

many thanks for submitting your revised manuscript, which has undergone a further round of reviews. Both referees have identified overlapping and complementary areas of concern (explanation and discussion of Keeling and Miller-Tans methods; uncertainty due to the lack of standards bracketing the sample composition; as well as several others).

If you can address the areas of concern highlighted by the reviewers satisfactorily, I will be happy to reconsider the further revised manuscript for publication.

Sincerely
Jan Kaiser
Co-Editor ACPD

Dear Drs Xu, Lee et al.

many thanks for your revised submission. I am happy to accept it for publication in Atmospheric Chemistry and Physics, subject to minor revisions:

1) Please re-attach the data supplement with the hourly measurement results. It seems to have gone missing during a previous iteration.

2) In line 218, please replace "H2O < 2.03 %" by "C(H2O) < 2.03 %" (or "C(H2O) < 2.03 cmol mol-1", for consistency with the rules of quantity algebra and the symbol for mole fraction adopted elsewhere.

3) Likewise, in line 219, please replace "H2O % - 2.03 %" with "C(H2O) - 2.03 %" or "C(H2O) - 2.03 cmol mol-1").

4) Fig. S3 refers to the wrong dataset. According to the main text, it is supposed to show data from Los Angeles as published in the paper of Newman et al. (2016), but the caption refers to a site in Switzerland, as published by Sturm et al. (2016).

5) The numbering of figures in supplementary information should be made sequential (S4 is used twice). The references to supplementary figures in the main text also need to be updated.

6) Please add a sentence to reflect your response to the reviewer's suggestion of post-calibrating the analyser (i.e. "We could not implement [an isotope delta calibration using standards with delta values bracketing the sample values] because the detector of our analyzer failed at the end of the experiment." or similar).

Yours sincerely
Jan Kaiser

Dear Drs Xu, Lee et al.

many thanks for your revised submission. I am happy to accept it for publication in Atmospheric Chemistry and Physics, subject to a technical correction:

The section "Data availability" needs to be amended to say that the data are contained in the form of an electronic supplement to the paper.

Yours sincerely
Jan Kaiser