Pete D. Akers

General comments

In this paper, the authors use both field observations and modelling to examine the controls on temporal variability of oxygen isotopes in atmospheric nitrate. They find that the seasonal changes in nitrate isotopes are related to the formation chemistry pathways. Using oxygen isotopes as a tracer of past chemical origin has been studied some before for Δ¹⁷O but less so for d¹⁸O in nitrate, so it is interesting to see their investigation with d¹⁸O added here. They find evidence from the oxygen isotopes that formation pathways are more different than expected for HNO3 vs pNO3. They investigate this further with their modeled results.

Overall, my comments are minor. I found that the paper is generally written well and is methodologically sound. The authors do a good job explaining their methods in details and providing plenty of statistical values to support their results and discussion. The amount of work and effort put into producing the data and considering its interpretation is clearly evident. The writing and discussion can be rather dense at times, particularly when discussing model results and comparing isotopic values. This isn’t necessarily a bad thing, as it is providing valuable information for people concerned with atmospheric chemistry modeling and nitrogen oxide dynamics. However, it could improve the readability to a broader audience if the dense sections of the discussion were supplemented with some broader summarizing or restating statements that make sure the main point is made clear and understood.

Specific comments

This perhaps goes toward my primary suggestion, which is that it is not entirely evident what the broader impact and implications of the findings are to a non-specialist. Do these findings change our prior understanding of how nitrate is being formed? What do they lead us to think differently about atmospheric chemistry and nitrate going forward? Does the dominance of specific pathways tell us any new information about the local atmospheric chemistry? Are these results just specific to the local area, or is there reason to think that they have broader significance? Anything that can link the dense results into more easily graspable concepts would help the reader (particularly those outside of the nitrogen oxide chemistry community) better understand why these are interesting and intriguing findings. This would be a nice wrap up paragraph or small section of the discussion before the conclusion, just to give kind of a “greatest hits of the discussion” all presented in one place clearly.

The bulk of my comments are focused on the figures. While most of the plots are fairly clear in their structure, they often had text that was very difficult to read, and I’m sure this will be a problem if they are printed in a final manuscript without changes. In many cases, duplicate axes and legends could be removed to increase space, but some figures may need more consideration as to how to become legible. The map figure (Fig 1) is also particularly lacking, especially relative to the otherwise high quality of this manuscript.

Technical comments

The method of writing d¹⁸O and Δ¹⁷O with parenthesis as d(¹⁸O) and Δ(¹⁷O) is unusual and not standard. This not only comes across as slightly odd, but in my opinion reduces readability by adding more “clutter” to the text. And overall, the sheer number of parentheses used throughout makes reading difficult. In many cases, they seem unnecessary. For example, at 332: Δ(¹⁷O) value ((39±2) ‰; ..citation) could be Δ¹⁷O value (39±2 ‰; …citation) which is more readable. Use of parenthesis like δ(¹⁸O, O₃^*) instead of the more standard d¹⁸O_O3* or d¹⁸O(O₃*) makes it more difficult to understand and bulkier to read.

At some times in the abstract and throughout, the term significant/significance is used to describe a result, but it isn’t clear whether this is referring to statistical significance or not. In some cases, perhaps consider rewording to remove any ambiguity.

The use of nitrate vs. NO₃⁻ is inconsistent throughout. It seems to shift from nitrate to NO₃⁻ in the methods, and then shift back to just nitrate.

14: First sentence is worded unwieldly with “by high population density, high emissions density and degraded air quality and acid rain”

18: “Oxygen isotope deltas” is odd phrasing. Perhaps just “oxygen isotopic ratios”? I did a search for this term and the only result on the internet that came back was for this preprint.

23: pNO₃?

72: Subject verb agreement

150: This is a long paragraph, and might benefit from being split.

153: Perhaps add the citation as a reference instead of a link here

193: Space missing I think here between O3 and O3*

212: The water isotope assumed to be -6, but this would vary seasonally. Between GNIP and USNIP, we have good records of the seasonal variability of water isotopes in precipitation. I’m not sure how much this would impact your modelling results, but if any substantial oxygen exchange is occurring between water and nitrogen oxides, it could explain some of the model discrepancy between observed values and the modelled values. For example, the d¹⁸O_NO3 values in winter are lower than predicted by the model, but this would be a time when d¹⁸O_precip values are often < –15 ‰ in New York, for example, and much lower than the –6 ‰ included in your model.

217: We have direct water vapor isotopic measurements from eastern N America (https://doi.org/10.1038/sdata.2018.302). Similar to the liquid water comment above, these also vary dramatically with seasons (usually with vapor varying even more than precipitation, since the dry winter air can be very isotopically light when there is no precipitation).

332: Notably? Instead of notable, perhaps

Figure 1. This map is extremely basic and lacks any contextual information that could help us understand the study region better. There is no scale, or geographic coordinates, or legend. The projections clearly differ between the two maps, but there’s no way to determine what matches what because there is no spatial referencing. Also, this means that the area covered in the box at left doesn’t match the extent covered in the inset (the box would need distorted and angled to accurately pair up with the inset). A map that includes features that directly impact the study would be immensely beneficial, such as one showing local urban areas, land use, transportation routes. And even though Canada is directly upwind of these sites, the country doesn’t exist on the inset map.

Fig 4. I like the data presentation here, but the text and labels are impossible to read without zooming in 300%. Many of the axes and labels are repeated across plots, so perhaps you could eliminate axes labels for many and use the saved space to increase label size.

Fig 6. Just for consideration, in many cases a bar plot can get across the point of a pie chart more clearly and more effectively. Humans are bad at judging relative angular sizes, but much better at comparing relative heights in a bar plot. It might help get the point here across better. But not a required revision from me.

Fig 7. Again, the small multiples approach is good, but there is a lot of individual text on them that is impossible to read and thus it is hard to understand what the overall story the reader is supposed to get from this plot. Eliminating axes and perhaps moving the regression information to a table would help.

GENERAL COMMENTS

The authors investigate the atmospheric nitrate formation pathways, along a highly populated urban corridor, using ∆¹⁷O and δ¹⁸O in weekly sampled nitric acid (HNO₃) and particulate (pNO₃) nitrates, collected by EPA from three CASTNET sites of Northeastern USA, from December 2016 to Dec 2018. They employ the GEOS-Chem model to verify the production pathways of atmospheric nitrate using their nitrate concentrations and ∆¹⁷O and δ¹⁸O results. They find that the model overestimates the concentrations by 2 or 3 times; and generate isotopic values closer to reality for warm months relative to cold months. They explain these discrepancies between modeling and observations by the model inflating the heterogeneous N₂O₅ hydrolysis production of HNO₃ and pNO₃.

In general, the article is well written, well organized, and scientifically sound, and undeniably deserves publication in ACP. The required changes for publication are of moderate level.

MAIN CONCERNS

In terms of structure and content, the article would be optimized if: a) the authors presented their objectives and working hypothesis at the end of the introduction (see below); and b) the section on results and discussion was better organized (see below). They could better articulate their main contribution n the basis of these clear objectives.

Regarding the science, some parts of the interpretation need to be expanded. A first aspect regards the mechanisms invoked to control the seasonal concentration and isotope patterns. These concentration and isotope changes with seasons are clear and likely combined, and their controlling factors should be discussed together while explaining both observations (see below). The performance of their model changes with seasons as well. Are all seasonal observations linked to the same mechanisms? This should be clearly discussed (better wrapped up). A second aspect is regarding the δ¹⁸O values of O₃ and O₂/RO₂/HO₂ that are obtained/suggested to optimize their model outputs (Table 2). The validity of such values for describing natural systems should be better supported.

SCIENCE

Lines 32-33 The authors should rephrase as there is no δ¹⁵N values presented in the manuscript. The abstract should summarize the content of the current article in terms of data.

Lines 146-147 – The authors should only present the significant digits of the deviations estimated for ∆¹⁷O values using USGS34 and USGS35, that at the unit, i.e., 1 and 2‰, respectively. The presentation of their results should conform to that deviation as the first digit after the dot does not mean anything (1.1 and 2.4‰).

Sub-section 2.3 The confidence interval of the estimated pNO₃ and HNO₃ concentrations should be provided so that the readers can judged by themselves if the departures between measured and modeled concentrations are significant or not.

Lines 253-255, 261-262 and Figure 3 (1) The reader can only disagree with the statement that the overestimation by model is for the entire year. In fact, the model does not overestimate the pNO₃ concentration of the warm months or the HNO₃ of the cold months, at all sites (Fig. 3). (2) What is the confidence interval on the modeled concentrations? It would be useful to indicate it on each graph.

Section 3.2 What are the uncertainties (or confidence intervals) on the isotopic outputs of the models?

Lines 312-313 This observation is true for the cold periods only. The ∆¹⁷O pNO3 minus ∆¹⁷O HNO₃ difference becomes practically nil or negative during the warm months (Fig. 4). This is combined with the fact that pNO₃ concentrations are low during warm months. The explanatory text (lines 315-322) does not present an interpretation for these seasonal observations.

Line 335 The two isotopic groups overlap noticeably, they have the same slope as mentioned and similar ranges, and they practically have similar intercepts (within error margin). Samples of the two matrices with upper right values contain more O₃ than the other samples, clearly. Is it rigorous to suggest that more O₃ is incorporated in pNO₃?

Line 349 In line with the statements, the reference to Figure 6 must be to 6a? The statement is true only for that panel of results.

Lines 352-355, and 360-362 Do the authors refer to the Base GEOS-Chem only or to the two versions of the model (base and optimized GEOS-Chem) ? Overall, the performance of the models (the fit with isotopic observations) is not uniform. Depicting it with the average residuals does not fully reflect the reality. In 50% of the reported cases, the quality of the fits varies seasonally. To explain in detail, at all sites, the model fits better during warm months than during cold ones for: the Base model ∆¹⁷O and δ¹⁸O outputs for HNO₃, and the two models δ¹⁸O outputs for pNO₃.

Lines 367-368 Indeed. As suggested above, what are the uncertainties on the isotopic outputs of the models?

Line 368 Please indicate which biases.

Lines 395-403 The text should be clarified and smoothed as there is no isotopic data on Figure 6. Instead, Figure 6 serves as basis for the interpretation of the previously presented seasonal changes in ∆¹⁷O and δ¹⁸O values in terms of pathways.

Line 419 Replace initial by well known.

Lines 419-422 Ok, So what? Please explain. How such a value (11‰) can exist?

Lines 430-435 As in the former question, how such a value (89.9‰) can exist? Lowering by 20‰ as calculated by Walter and Michalski (2016) does cover such a change as the one proposed here. Please explain how the value is credible.

Lines 456-457 The referred article is not yet published (but cited in the discussion, which is fine), and this is a conclusion which should directly derive from the data set presented in the manuscript. It is better advised to present conclusions based on the current set of data.

FORM

The last paragraph of the introduction (lines 93-99) presents the main findings of the study, is that a format encouraged by ACP? In a classical scientific manner, the readers would appreciate reading the objectives of the research and the working hypothesis advanced by the authors. It is suggested here that lines 93-99 be replaced by the objectives of the research, with possibly the hypothesis posed by the authors prior to conducting their research.

Lines 324-327 These two sentences should be merged as they are partly repetitive.

Section 3.3 For the reader, the text of this section is hard to follow as it jumps from Figure 6, to Figure 7 then back to 4, back to 7, then to 6. The issue does not simply relate to the references to figures, but to the way the train of thoughts is presented from examining the agreements between model and observation at a given site, then going to the spatial limitation of the modeling... The section needs reorganization: a simple way would be to first discuss Fig. 4, then 6 and then 7, highlighting the key observations and wrapping up with the integrated interpretation at the end.

Lines 330-351 For coherence, the observations based on the data of 6b and 6c should be presented before jumping to Figure 7.

Lines 445-446 What is the reference for the δ¹⁵N study? We understand that there is a companion article to be published in ACP that is different from the former study.

Line 467 Replace ‘better’ by ‘improved’.

OTHER Specific points

Lines 72-79 (and all text) - why carry parentheses when using the Delta notation? Most scientists using isotopes do not. Makes the notation heavy without justification or need.

Line 77 – remove Oxygen from parenthesis, as it is clear that the reference material is for O measurements.

Line 101 change police of 2. M

Line 102 write ‘Sample collection at CASTNET sites’

Line 114 write ‘analyses’ instead of analysis, because the term refers to different analyses

Line 141 replace is by was, for coherence with the rest of the sentence.

Line 149 add ‘modeling’ to this title

Line 151 replace ‘to’ by ‘and’ or ‘to model’ by ‘using’ (?); replace isotope by values.

Line 176 add ‘from model outputs’ to this title

Line 229 remove ‘s’ from discussion

Lines 285-286 rephrase (, ‘which were or are’ instead of ‘were’?); there is a word missing.

FIGURES

Figure 6 The three model outputs presented in (a) are for