General Comments

The goal of this paper is to use analysis of the relative abundance of stable isotopes of N and O to plumb the interactions coupled NOx and alpha pinene oxidation. It is an ambitious goal and a powerful tool, and the authors are able to derive some important and unique results. The authors use a sophisticated atmospheric chamber and isotopic measurement methods and protocols that have been developed, painstakingly, over many years. There can be a gap between the isotope and aerosol communities and one concern is that the results be presented in a way that allows both groups to understand the work and its implications. Here I am mainly thinking of researchers outside the isotope community. In addition, the style should be adjusted to present quantitative results in place of broad-brush qualitative descriptions. A final concern is that modeling is used to derive the results and additional work should be done to describe the impacts of the many necessary assumptions. This can be done by paying attention to error budgets and sensitivity analysis, and by validating the model through comparison to experimental and field results. Overall I like the paper very much and recommend publication after revision to address these points.

Specific Comments

The prose flows, there are many details, and it is entirely possible for the reader to get lost in the trees and fail to appreciate the landscape. I suggest being sure to add text to frame or give context, for example by adding transitions to introduce sections and show how they fit into the bigger picture. One example is that Section 3 dives straight into Section 3.1 and then into subsection 3.1.1 without a word of text, just section headings. 

There are many passages that make strong qualitative claims and I strongly advise to instead show the evidence, 'write it in numbers', and let the data speak for itself. Examples below.

 

The Abstract says that there are uncertainties regarding coupling between a-pinene and NOx in NOx loss, renoxification and oxidation chemistry, and says that the study 'provides insights into D17O transfer dynamics, nitrogen isotope fractionation, and the role of NOx-BVOC chemistry in air quality, highlighting the potential of D17O and d15N as tools for evaluating complex atmospheric processes.' Is it possible to convert some or all of these claims into quantitative statements? What specifically is the new insight into D17O transfer dynamics? Is the promise of D17O and d15N analysis realized? Has the new mechanism been able to explain something that could not otherwise be explained, or make predictions?

In the Introduction line 41, reading that the 'interplay bears significant consequences' is saying, 'take my word for it'. Please rewrite to give evidence. The reader is provided with eight references that cover 'air quality, climate, global reactive nitrogen budget and secondary organic aerosols'. The authors seem to be asking us to go figure it out. Instead I would suggest taking the time to identify a significant consequence of BVOC oxidation in the presence of NOx on a few of these areas and give specific examples. This paragraph has 27 references but the reader is left uncertain regarding why exactly 'Understanding the fates of organic nitrogen and the feedback in oxidation chemistry arising from BVOC/NOx interactions is critical for accurately assessing their roles in NOx loss and recycling, O3 formation, and SOA generation.'

Line 59, 'The natural variations..may be a promising tool to enhance our insight into the intricate connections..and their implications for atmospheric composition.' A promise is made to the reader here - be sure to revisit this point in the discussion at the end. Does the present work provide the evidence?

Line 61, 'Stable isotope approaches offer novel avenues to probe and refine our understanding..unravel the dynamics..of interactions and ultimately contribute to formulating informed air quality management strategies.' Also here - this sounds nice, but would be more valuable if it is connected with specific findings. What specific, informed air quality management strategies can be made based on the work described in this paper? 

How common are the conditions under which BVOC-NOx interactions will be important? Given the relatively short lifetimes of each, the overlap might be restricted to specific zones. However, the authors are claiming global impacts in addition to regional. Please walk the reader through how these larger phenomenon can arise.

There are many approximations in the model and even for experts it is difficult to disentangle the implications of the assumptions and uncertainties.

Some examples:

Line 33, 15alpha for NO2+OH is taken as 0.997. How well known is this value? What happens if the value is taken as 0.998, or 1.1?

Line 204 mass-dependent coefficient taken to be 0.52. What is the error, what are the implications of this choice?

Line 222, uncertainties were calculated to be less than 4.1, 1.4 and 0.9. Thank you, it is good, and please add just a bit to put the information in context: are these values significant?

Line 289 'This value was not measured but assumed..'

Line 297 15N/14N ratio taken as 0.003677 --  is there an error on this number?

Lines 295 to 305, a series of values are assumed. How sensitive is the result to these values?

Line 309, Wall loss is not considered in the model. How severe is this approximation, detail chamber volume, leak rate/lifetime of air in chamber, diffusion time to wall, etc to put in perspective.

Line 326, 'The δ18O of RO2/HO2 radicals has previously been suggested to be near δ18O(O2)' How near? Suggested? Are we on solid ground?

Line 327 'the derived d18O of 11.8 +/- 1.0 ‰ is near the atmospheric d18O(O2) value of 23.2 ‰' (Thank you that here, there is a space between number and unit). These two values are not within their mutual error ranges and one is twice that of the other, please help the reader understand how this is 'near'?

Please walk the reader through the inputs and outputs of the model, the assumptions and adjustable parameters. Conduct sensitivity analysis and validation. It would be helpful to provide an analysis of which parts of the model require additional research, to help guide future research/as a service to the community.

Line 310 'low relative humidity conditions', but how low, there must be a measurement?

The Conclusion section is powerful, thank you. It ties the paper together. It could be revisited during the rewrite - to bring focus, brevity, specific quantified results. These could include results from the sensitivity analysis and specific research needs.

Setting 'the weighted branching ratio of α-pinene+OH+NO leading to organic nitrate versus NO2 production' to 0.222 is a very specific number and deserves further comment. Do you have any thoughts how this value would change with atmospheric conditions like humidity, temperature, pressure, NO concentration? Is it as accurate as three digits or is it merely to within e.g. 10%?

Line 699, 'Our findings strongly suggest that pNO3 in these experiments originated exclusively from organic nitrate, a conclusion supported by online AMS data. Furthermore, the Δ17O and δ15N evidence demonstrated that organic nitrate hydrolysis was not a major source of HNO3 under the studied conditions, which predominantly involved low relative humidity.' I just want to say that these are excellent results, very interesting! Thank you.

Technical Corrections

Recommended practice by professional societies such as IUPAC and SI is that there should always be a space between a number and a unit. So for example 1.7 ‰ not 1.7‰. Check throughout, current usage is inconsistent.

Line 217 'corresponds to the fraction of NO3- that corresponds to the blank.' Please rewrite.

Line 260 change experiment to experimental

Figure 1 inset, y, p, r, x should be italicized. Also caption of Table 2, 'Robs' should be italicized e.g. '$R_{obs}$'. All variables should be italicized.

Table 2, what are the uncertainties on the values in the final three columns? Perhaps a blanket uncertainty could be used e.g. '+/- 5 %' or '10 % of the given value'.

Line 437 suggest rewriting this sentence for clarity, tone, grammar, break into two etc. 'The offline filter collection and extraction technique matches the trend in which more pNO3 hydrolyzed for the photochemical experiments compared to the nighttime; however, the filter technique would indicate a higher proportion of potential hydrolysable pNO3 from photochemical experiment than these previous estimates, though with a different timescale.'

Line 370 spelling 'masse'

Line 445, check word choice, consider replacing 'speciation' with 'interpretation' or 'assignment'?

Figure 3 caption, 'The observed pNO3 concentrations are faceted by the various experiments conducted'. Do I understand this correctly to mean, 'This figure shows how the variety of experiments performed impact the observed pNO3 concentrations'? I found it hard to interpret and suggest rewriting for simplicity, clarity.

Line 459, 'This comparison indicates that the developed mechanism well represents the oxidation of α-pinene and formation of oxidants under a wide range of experimental conditions. The simulations using the USC-API mechanism was a vast improvement' Please quantify; 'well represents', 'wide range' and 'vast improvement' are imprecise and will mean different things to different readers. Similar line 489, 'well-suited', line 497 'well-reproduced' and line 501, 'well-calibrated'.

Line 493 'leaded' to 'leading' (I think?) and this sentence should be rewritten to simplify, clarify: 'Oxygen isotope mass-balance indicates that the α-pinene-derived peroxy radicals + NO pathway would be the expected pathway leaded to a low Δ17 O(pNO3 ) value as only one oxygen atom in the nitro group of the generated RONO 2could derive from O3.'

526 suggest change 'enable' to 'allow'

552 'partially improve', how is this different from 'improve'? Suggest edit.

Figures 6, 7, 8, 9, 10 and 11 have largely identical captions, mit doesn't seem necessary that they all repeat the same details. They also all have the gramamtical error, 'with the black line span the collection time range'.

Table S1 and S2, suggest taking a moment to edit the superscripts and subscripts in chemical formulas (subscript numbers), term symbols (superscript numbers), etc.

Table S2, do you have the references for these rate coefficient values? Note that it is not a reaction rate but a rate coefficient. What is the difference? Consider A + B --> C with rate coefficient k. The rate of the process is r = k[A][B] = d[C]/dt. The value 'k' is sometimes called the rate constant, but it is not constant, it changes with temperature, etc.; it is the rate coefficient. It would be useful to indicate the units for these rate coefficients, 1/s, cm^3/s etc. I might guess the activation energies are given in units of Kelvin, is that correct? Add a footnote. R022 says to multiply by 'H2O', should this be '[H2O]'? R039 and R040 are not reaction rates r or rate coefficients k, they are equilibrium constants K.

This manuscript aims to modify the NOx-BVOC chemical mechanism in the INRACM model by analyzing stable nitrogen and oxygen isotopes (Δ17O and δ15N) of chamber experimental samples, particularly focusing on the interaction mechanism between nitrogen oxides and the oxidation of α-pinene. However, the description of the experimental sample collection in the chamber and the testing methods for stable nitrogen and oxygen isotopes using IRMS in the manuscript is somewhat thin and requires further elaboration of experimental details. Additionally, regarding the bacterial denitrification method for testing δ18O, Δ17O, and δ15N, the authors report high blanks (or low sample amounts) in the tests, which may not be convincing to the community developing low-sample-amount testing methods. The last concern is in the model section, where the authors use multiple assumptions in the parameter setting part and do not provide sufficient evidence to convince the community. Therefore, a comparison study with actual observations can make the results more solid. Overall, this is a work on modeling the mechanism of organic nitrate formation, and the mechanism proposed in this paper is expected to improve the simulation of organic nitrate concentration in box models or transport models. In all, I l recommend this manuscript to be published after revision of the following comments. 

Major comments:

1 . When gas-source IRMS is used for isotope testing, the isotope values of the corresponding gases will gradually increase and stabilize as the amount of prepared gas samples increases. Previous results on gas-source IRMS articles have shown that a sample amount of 10 nmol (0.2 nmol blank) is usually required to achieve the precision of effective testing within an error range of 0.4 per mil. The authors claim that the Monte Carlo method used in the article can achieve isotope testing of tiny amount of samples within an error of 1.1 per mil, but there is not enough solid evidence to convince the community.

Firstly, the concentration of the blank itself varies, and testing with low sample amounts using gas-source IRMS itself brings great uncertainty. The authors report that the isotope values of the three blanks are no meaning for further analysis. Because the 1 standard deviation of the three blanks is greater than 1 per mil, indicating that the difference between the blanks themselves is at least more than 2 per mil. The author cliamed that this 2 per mil (1SD) error could be combined with Monte Carlo testing and then used to reduce the overall error to <1 per mil. At least in the current evidence, the effectiveness of this method is in doubt.

Secondly, regarding the precision of the method reported by the authors, are the authors referring to the standard deviation of the mean obtained by multiple Monte Carlo tests on the same standard to characterize the overall standard deviation of the test? If this is the case, the isotope values reported by the authors may not be much convincing.

In addition, the blank concentration accounts for 30% of the total sample amount. If assuming the entire process blank as 0.2 nmol, some sample amounts are even less than 1 nmol. This extremely low sample amount may not provide precise enough data for the discussion of the α-pinene and NOx mechanisms in this article. It is recommended that the authors use higher sample amounts or lower blanks to retest the generated chamber samples.

The blank of isotope testing is the key factor limiting the sample amount. The authors should follow the practices of other laboratories in dealing with N pollution and strive to reduce the sample blank, instead of using this 30% blank to report the test results of the samples.

2 . Memory effect: The Δ17O results shown by the authors in Figure 1 are between 0 and 40 per mil. This magnitude of difference has a significant memory effect on the testing of small sample amounts, that is: the O2 split from part of the samples in the previous test will remain in the Pt/Au tube in the conflo-IRMS, contaminating the O2 split from the next sample test, thereby causing deviations in the isotope values. The authors need to carefully discuss the potential effects of these effect, and carefully revised their manuscript. 

Other comments:

Line 189-190: In citation part, Casciotti et al., 2002 and Sigman et al., 2001 is based on bacterial conversion of nitrate to N2O, while McIlvin and Altabet, 2005 and Walters and Hastings, 2023 using chemical reaction to convert nitrate to N2O. I don’t understand the meaning of those citations. Which method are you using? 

Line 195: “The pooled standard deviations of the standards were ±0.1‰ and ±0.6‰ for δ15N and δ18O of the NO3- standards (n = 78) and ±0.3‰ and ±0.3‰ for δ15N and δ18O of the NO2- reference materials (n = 15), respectively. The Δ17O had a pooled standard deviation of ±0.6 ‰ (n = 53) .”Can the author explain the sample size of the different standards tested here and the chamber experimental sample used in this work? Does they have the exactly the same molar amount, at the same level, or not comparable? 

Besides, the ±0.1‰ is the detection limite of d15N measurement or the 1 SD of your 78 times’ measurement?

Equation 1: usually we use R^{15}N, R^{18}O, and R^{17}O, not {15}RN, {18}RO, and {17}RO, so the xRsample should be changed to R^{x}_{sample}. 

Section 2.4: How about the error of this simulation? Does particle inorgnaic nitrate only pair with NH4+? 

Line 261: one right parenthesis of “(RACM” is missing; “Master Chemical Mechanism v3.3.1” should be “Master Chemical Mechanism v3.3.1 (MCMv3.3.1 )”

Line 267: The format of “3” in O3 and NO3 is different from others. Please check. 

Line 286: You write Δ17O(O3term) = 39±2‰ here, while you use Δ17O(O3term) = 39.3±2.0‰ in Lines 323, 346, etc. Should be consistence. 

Line 341: night time also have OH radicals which could form NO3 by the following equation: HNO3 + OH = H2O + NO3. It’s better to consider both NO3 from N2O5 as well as HNO3 or NO3- in the Δ17O calculation. 

Lines 366-367: “δ15N(NO2) that averaged -52.5 ±25.2‰ (n = 20), which were higher than δ15N(pNO3) that averaged -72.6±22.9‰ (n = 7)” However, -52.5 ±25.2‰ and -72.6±22.9‰ almost at the same level by considering the 25 per mil standard deviations. 

Lines 403-404: The author assumed that the NO3- extracted from the filter collection could represent the organic nitrate by using the d15N isotope value. What kind of d15N value should the organic nitrate should have? 

Table 2, why the Filter/AMS of experiment 2 is higher than 100%?

Besides, The calculated f(pNO3, Org) was higher than 1, does it mean this method has some problem?

If all pNO3- measured in this experiment all from organic nitrate, does it mean all pNO3- measured in field observation from organic nitrate?

Fig.8: For D17O(HNO3) value, the observation results shown different with the simulation results, why?

Fig.11: some experiments correlated with USC_API mechanism, experiment 5 correlated with USC_API_KIE mechanism. need explaination. 

General Comments

The goal of this manuscript is to investigate the interaction between nitrogen oxides (NOx) and α-pinene oxidation reactions by conducting chamber experiments and analyzing stable nitrogen (N) and oxygen (O) isotopes of nitrogen species, comparing the results with a model developed by the authors (using separate models for O and N). This research incorporates various innovative aspects, including the development of the model, methods for analyzing the isotopes of different nitrogen compounds, chamber experiments, and the analysis of organic nitrates. The originality of the authors' work is clearly reflected throughout the manuscript.

Given the importance and novelty of this research, I believe the manuscript should be considered for publication with revisions addressing the following comments.

1. Abstract and Introduction

The expressions such as "However, uncertainties remain regarding their coupling in NOx loss, renoxification, and oxidation chemistry" and "This study provides insights into Δ17O transfer dynamics, nitrogen isotope fractionation, and the role of NOx-BVOC chemistry in air quality, highlighting the potential of Δ17O and δ15N as tools for evaluating complex atmospheric processes" are quite general and lack specific details about the research. These phrases may be more appropriate for a broader overview, but for a scientific manuscript, I recommend specifying how the controlled laboratory experiments involving α-pinene, which are introduced for the first time, are crucial to understanding the issue. The introduction would benefit from a clearer statement about the significance of this understanding and how the absence of this knowledge has impacted the field. Specifically, I would like the authors to emphasize the necessity of considering organic nitrate in the context of previous observations of inorganic nitrate's Δ17O and δ15N, and how these experiments and models address gaps in previous work.

2. Organic Nitrate and p-NO3 Relationship

I understand that organic nitrate is collected after passing through a denuder system and hydrolyzed to nitrate for isotope analysis. However, is organic nitrate always expected to exist as a particle (nothing in gas-phase?)? For example, PAN is considered to exist in the gas phase. Thus, the equivalence of organic nitrate and p-NO3 is somewhat unclear. At the very least, I believe the authors should clarify why p-NO3 is considered to be organic nitrate and provide further discussion, potentially citing references, about the particle-phase composition of organic nitrate as they see it.

3. Isotopic Exchange Between HNO3 and p-NO3

It seems that the authors assume no isotopic exchange between HNO3 and p-NO3 after production in the chamber experiments. However, existing research suggests that HNO3 and p-NO3 should be in equilibrium, with HNO3 showing a lower δ15N and p-NO3 a higher δ15N (e.g., Geng et al., 2014 PNAS). The authors' atmospheric observations also reproduce this δ15N pattern between HNO3 and p-NO3 (Bekker et al., 2023, https://doi.org/10.5194/acp-23-4185-2023). The authors seem to suggest that no such isotopic exchange occurs in their experiments, but it would be helpful to introduce this existing pattern and explain why it does not occur in their experiments. Specifically, what conditions in their chamber experiments prevent isotopic exchange between HNO3 and p-NO3.

4. Presentation of δ15N

In Figures 2 and 9-11, it seems that δ15N is shown relative to atmospheric N2. Given that the initial δ15N of the N sources differs, the resulting δ15N values also vary. For clarity, I suggest normalizing the data by presenting δ15N vs initial NOy values, which would better illustrate the change relative to initial values. Or, it would also be helpful to specify on the y-axis of the figures not only the units in permil but also the reference point (e.g., vs. N2), and add d15N of initial precursor.

Specific Comments

• L146: It is stated that particles collected on a Teflon filter using FIGAERO are analyzed using HR-ToF-I-CIMS. However, it is unclear how the particles collected on the Teflon filter are introduced into HR-ToF-I-CIMS for analysis. Specifically, the process by which the filter particles are treated and converted into a measurable form for analysis is not described in detail. Could you please clarify this step?
• L152: Please provide more detail on "water-soluble aerosol components".
• L167: Why was a quartz filter used? It seems that Teflon might also have been considered, as noted in L146. Also, was it considered that organic nitrate primarily exists in the particle phase and may not have been captured in the HNO3 or NO2 collections? Did the authors explore the possibility of gas-phase organic nitrates, and if so, how did the filter pass through them?
• L206: The 'O' should not be italicized.
• L207: The term "mass-independent effect" is unclear. Does it refer to mass-independent isotope effects or mass-independent fractionation?
• L296: If discussing NOx oxidation, reactions such as NO2 photolysis are not included as an “oxidation process”. If needed, please rephrase this.
• L327: The difference between 11.8 ‰ and 23.2 ‰ is not a "slight difference". The authors suggest this difference arises due to kinetic isotope effects associated with RO2/HO2 reactions. Are there any relevant studies that predict such a difference between O2 and RO2/HO2, and is this comparison reasonable?
• L337: It is clear that a balance exists between NO branching ratios involving O3 and RO2/HO2. However, it would be helpful to add that O3 has a high Δ17O value and RO2/HO2 has a low Δ17O to clarify this point.
• L371: Could the authors explain why 1.040 was used for Fang et al., 2021?
• L377-379: I agree with predicting from isotopic data, but it would be helpful to discuss why condensation from HNO3 to p-NO3 or thermal equilibrium between HNO3 and p-NO3 does not occur in the chamber. The discussion should address this point as it is linked to Major Comment 2.
• 3: The y-axis is labeled "p-NO3", but I believe AMS is not directly measuring p-NO3. Other methods involve converting the particle form to NO3- before measurement. Could the authors clarify this discrepancy?
• L491: The relative production routes of organic nitrate (+OH/O2/NO vs +NO3) are unclear. I believe it would be useful to describe the relationship between Δ17O values and oxidants in this context.